View source for Rendering (computer graphics)

{{Short description|Process of generating an image from a model}}
{{Redirect-distinguish-for|Image synthesis|Text-to-image model|4=Computer graphics#Image types}}
{{About||3-dimensional rendering|3D rendering|rendering of HTML|browser engine}}
{{More citations needed|date=May 2020}}
[[File:Render Types.png|thumb|A variety of rendering techniques applied to a single 3D scene]]
[[Image:Glasses 800 edit.png|thumb|An image created by using [[POV-Ray]] 3.6]]
<!-- Deleted image removed: [[Image:CNC Rotary Table edit.png|thumb|UCAM CNC Rotary Table rendered image created by using [[Solidworks]] 2012]] -->
'''Rendering''' or '''image synthesis''' is the process of generating a [[physically-based rendering|photorealistic]] or [[Non-photorealistic rendering|non-photorealistic]] image from a [[2D model|2D]] or [[3D model]] by means of a [[computer program]].{{Citation needed|date=March 2023}}  The resulting image is referred to as a '''rendering'''.  Multiple models can be defined in a ''scene file'' containing objects in a strictly defined language or [[data structure]].  The scene file contains geometry, viewpoint, [[Texture mapping|textures]], [[computer graphics lighting|lighting]], and [[shading]] information describing the virtual scene. The data contained in the scene file is then passed to a rendering program to be processed and output to a [[digital image]] or [[raster graphics]] image file. The term "rendering" is analogous to the concept of an [[artist's impression]] of a scene.  The term "rendering" is also used to describe the process of calculating effects in a video editing program to produce the final video output.

A [[application software|software application]] or [[component-based software engineering|component]] that performs rendering is called a '''rendering [[software engine|engine]]''',<ref>{{cite web | url=https://arvisual.eu/dictionary/rendering-engine/#:~:text=Definition,with%20a%20given%203D%20software. | title=What is a Rendering Engine? &#124; Dictionary | access-date=2024-02-21 | archive-date=2024-02-21 | archive-url=https://web.archive.org/web/20240221024025/https://arvisual.eu/dictionary/rendering-engine/#:~:text=Definition,with%20a%20given%203D%20software. | url-status=live }}</ref> '''render engine''', '''[[:Category: Rendering systems|rendering system]]''', '''graphics engine''', or simply a '''renderer'''.

Rendering is one of the major sub-topics of [[3D computer graphics]], and in practice it is always connected to the others. It is the last major step in the [[graphics pipeline]], giving models and animation their final appearance. With the increasing sophistication of computer graphics since the 1970s, it has become a more distinct subject.

Rendering has uses in [[Architectural rendering|architecture]], [[video game]]s, [[simulation|simulators]], movie and TV [[visual effects]], and design visualization, each employing a different balance of features and techniques. A wide variety of renderers are available for use. Some are integrated into larger modeling and animation packages, some are stand-alone, and some are free open-source projects. On the inside, a renderer is a carefully engineered program based on multiple disciplines, including [[optics|light physics]], [[visual system|visual perception]], [[mathematics]], and [[software engineering|software development]].

Though the technical details of rendering methods vary, the general challenges to overcome in producing a 2D image on a screen from a 3D representation stored in a scene file are handled by the [[graphics pipeline]] in a rendering device such as a [[Graphics processing unit|GPU]]. A GPU is a purpose-built device that assists a [[Central processing unit|CPU]] in performing complex rendering calculations. If a scene is to look relatively realistic and predictable under virtual lighting, the rendering software must solve the [[rendering equation]]. The rendering equation does not account for all lighting phenomena, but instead acts as a general lighting model for computer-generated imagery.

In the case of 3D graphics, scenes can be [[pre-rendered]] or generated in realtime.  Pre-rendering is a slow, computationally intensive process that is typically used for movie creation, where scenes can be generated ahead of time, while [[Real-time computer graphics|real-time]] rendering is often done for 3D video games and other applications that must dynamically create scenes.  3D [[hardware accelerators]] can improve realtime rendering performance.

== Features ==
A rendered image can be understood in terms of a number of visible features. Rendering [[research and development]] has been largely motivated by finding ways to simulate these efficiently. Some relate directly to particular algorithms and techniques, while others are produced together.

* [[Shading]]{{snd}} how the color and brightness of a surface varies with lighting
* [[Texture mapping|Texture-mapping]]{{snd}} a method of applying detail to surfaces
* [[Bump mapping|Bump-mapping]]{{snd}} a method of simulating small-scale bumpiness on surfaces
* [[Distance fog|Fogging/participating medium]]{{snd}} how light dims when passing through non-clear atmosphere or air
* [[Shadow]]s{{snd}} the effect of obstructing light
* [[Soft shadows]]{{snd}} varying darkness caused by partially obscured light sources
* [[Reflection (computer graphics)|Reflection]]{{snd}} mirror-like or highly glossy reflection
* [[Transparency (optics)]], [[transparency (graphic)]] or [[Opacity (optics)|opacity]]{{snd}} sharp transmission of light through solid objects
* [[Translucency]]{{snd}} highly scattered transmission of light through solid objects
* [[Refraction]]{{snd}} bending of light associated with transparency
* [[Diffraction]]{{snd}} bending, spreading, and interference of light passing by an object or aperture that disrupts the ray
* [[Global illumination|Indirect illumination]]{{snd}} surfaces illuminated by light reflected off other surfaces, rather than directly from a light source (also known as global illumination)
* [[Caustic (optics)|Caustics]] (a form of indirect illumination){{snd}} reflection of light off a shiny object, or focusing of light through a transparent object, to produce bright highlights on another object
* [[Depth of field]]{{snd}} objects appear blurry or out of focus when too far in front of or behind the object in focus
* [[Motion blur]]{{snd}} objects appear blurry due to high-speed motion, or the motion of the camera
* [[Non-photorealistic rendering]]{{snd}} rendering of scenes in an artistic style, intended to look like a painting or drawing

== Inputs ==
Before a 3D scene or 2D image can be rendered, it must be described in a way that the rendering software can understand. Historically, inputs for both 2D and 3D rendering were usually [[text file]]s, which are easier than binary files for humans to edit and debug. For 3D graphics, text formats have largely been supplanted by more efficient [[binary file|binary formats]], and by [[API]]s which allow interactive applications to communicate directly with a rendering component without generating a file on disk (although a scene description is usually still created in memory prior to rendering).{{r|n=Raghavachary2005|loc=1.2, 3.2.6, 3.3.1, 3.3.7}}

Traditional rendering algorithms use geometric descriptions of 3D scenes or 2D images. Applications and algorithms that render [[Visualization (graphics)|visualizations]] of data scanned from the real world, or scientific [[Computer simulation|simulations]], may require different types of input data.

The [[PostScript]] format (which is often credited with the rise of [[desktop publishing]]) provides a standardized, interoperable way to describe 2D graphics and [[page layout]]. The [[SVG|Scalable Vector Graphics (SVG)]] format is also text-based, and the [[PDF]] format uses the PostScript language internally. In contrast, although many 3D graphics file formats have been standardized (including text-based formats such as [[VRML]] and [[X3D]]), different rendering applications typically use formats tailored to their needs, and this has led to a proliferation of proprietary and open formats, with binary files being more common.{{r|n=Raghavachary2005|loc=3.2.3, 3.2.5, 3.3.7}}{{r|n=PSRef|p=vii}}{{r|n=MDN_SVG}}{{r|n=Hughes2014|loc=16.5.2.}}{{r|n=BlenderImportExport}}

=== 2D vector graphics ===
A [[vector graphics]] image description may include:{{r|n=PSRef}}{{r|n=MDN_SVG}}
* [[Cartesian coordinate system|Coordinates]] and [[curvature]] information for [[line segments]], [[Circular arc|arcs]], and [[Bézier curve]]s (which may be used as boundaries of filled shapes)
* Center coordinates, width, and height (or [[Minimum bounding rectangle|bounding rectangle]] coordinates) of [[geometric primitive|basic]] shapes such as [[rectangle]]s, [[circle]]s and [[ellipse]]s
* Color, width and pattern (such as dashed or dotted) for rendering lines
* Colors, patterns, and [[Color gradient|gradients]] for filling shapes
* [[Bitmap]] image data (either embedded or in an external file) along with scale and position information
* [[Font rasterization|Text to be rendered]] (along with size, position, orientation, color, and font)
* [[Clipping (computer graphics)|Clipping]] information, if only part of a shape or bitmap image should be rendered
* Transparency and [[compositing]] information for rendering overlapping shapes
* [[Color space]] information, allowing the image to be rendered consistently on different displays and printers

=== 3D geometry ===
A geometric scene description may include:{{r|n=Raghavachary2005|loc=Ch. 4-7, 8.7}}{{r|n=pbrt4FF}}
* Size, position, and orientation of [[geometric primitive]]s such as spheres and cones (which may be [[Constructive solid geometry|combined in various ways]] to create more complex objects)
* [[Vertex (geometry)|Vertex]] [[Cartesian coordinate system|coordinates]] and [[Normal (geometry)|surface normal]] [[Euclidean vector|vectors]] for [[Polygon mesh|meshes]] of triangles or polygons (often rendered as smooth surfaces by [[Subdivision surface|subdividing]] the mesh)
* [[Geometric transformation|Transformations]] for positioning, rotating, and scaling objects within a scene (allowing parts of the scene to use different local coordinate systems).
* "Camera" information describing how the scene is being viewed (position, direction, [[focal length]], and [[field of view]])
* Light information (location, type, brightness, and color)
* Optical properties of surfaces, such as [[albedo]], [[reflectance]], and [[refractive index]],
* Optical properties of media through which light passes (transparent solids, liquids, clouds, smoke), e.g. [[Absorption cross section|absorption]] and [[Cross_section_(physics)#Scattering_of_light|scattering]] cross sections
* [[Bitmap]] image data used as [[Texture mapping|texture maps]] for surfaces
* Small scripts or programs for generating complex 3D shapes or scenes [[Procedural generation|procedurally]]
* Description of how object and camera locations and other information change over time, for rendering an animation

Many file formats exist for storing individual 3D objects or "[[3D modeling|models]]". These can be imported into a larger scene, or loaded on-demand by rendering software or games. A realistic scene may require hundreds of items like household objects, vehicles, and trees, and [[Environment artist|3D artists]] often utilize large libraries of models. In game production, these models (along with other data such as textures, audio files, and animations) are referred to as "[[Digital asset|assets]]".{{r|n=BlenderImportExport}}{{r|n=Dunlop2014|loc=Ch. 4}}

=== Volumetric data ===
Scientific and engineering [[Visualization (graphics)|visualization]] often requires rendering [[voxel|volumetric data]] generated by 3D scans or [[Computer simulation|simulations]]. Perhaps the most common source of such data is medical [[CT scan|CT]] and [[Magnetic resonance imaging|MRI]] scans, which need to be rendered for diagnosis. Volumetric data can be extremely large, and requires [[OpenVDB|specialized data formats]] to store it efficiently, particularly if the volume is ''[[Sparse matrix|sparse]]'' (with empty regions that do not contain data).{{r|n=AkenineMöller2018|loc=14.3.1}}{{r|n=OpenVDBAbout}}{{r|n=Museth2013}}

Before rendering, [[level set]]s for volumetric data can be extracted and converted into a mesh of triangles, e.g. by using the [[marching cubes]] algorithm. Algorithms have also been developed that work directly with volumetric data, for example to render realistic depictions of the way light is scattered and absorbed by clouds and smoke, and this type of volumetric rendering is used extensively in visual effects for movies. When rendering lower-resolution volumetric data without interpolation, the individual cubes or "[[voxel]]s" may be visible, an effect sometimes used deliberately for game graphics.{{r|n=Bridson2015|loc=4.6}}{{r|n=AkenineMöller2018|loc=13.10, Ch. 14, 16.1}}

=== Photogrammetry and scanning ===
Photographs of real world objects can be incorporated into a rendered scene by using them as [[Texture mapping|textures]] for 3D objects. Photos of a scene can also be stitched together to create [[panorama|panoramic images]] or [[Reflection mapping|environment maps]], which allow the scene to be rendered very efficiently but only from a single viewpoint. Scanning of real objects and scenes using [[Structured-light 3D scanner|structured light]] or [[lidar]] produces [[point cloud]]s consisting of the coordinates of millions of individual points in space, sometimes along with color information. These point clouds may either be rendered directly or [[Point_cloud#Conversion_to_3D_surfaces|converted into meshes]] before rendering. (Note: "point cloud" sometimes also refers to a minimalist rendering style that can be used for any 3D geometry, similar to wireframe rendering.){{r|n=AkenineMöller2018|loc=13.3, 13.9}}{{r|n=Raghavachary2005|loc=1.3}}

=== Neural approximations and light fields ===
A more recent, experimental approach is description of scenes using [[neural radiance field|radiance fields]] which define the color, intensity, and direction of incoming light at each point in space. (This is conceptually similar to, but not identical to, the [[light field]] recorded by a [[Holography|hologram]].) For any useful resolution, the amount of data in a radiance field is so large that it is impractical to represent it directly as volumetric data, and an [[approximation]] function must be found. [[Deep learning|Neural networks]] are typically used to generate and evaluate these approximations, sometimes using video frames, or a collection of photographs of a scene taken at different angles, as "[[Training,_validation,_and_test_data_sets#Training_data_set|training data]]".{{r|n=Schmid2023}}{{r|n=Mildenhall2020}}

Algorithms related to neural networks have recently been used to find approximations of a scene as [[Gaussian splatting|3D Gaussians]]. The resulting representation is similar to a [[point cloud]], except that it uses fuzzy, partially-transparent blobs of varying dimensions and orientations instead of points. As with [[neural radiance field]]s, these approximations are often generated from photographs or video frames.{{r|n=Kerbl2023}}

== Outputs ==
The output of rendering may be displayed immediately on the screen (many times a second, in the case of real-time rendering such as games) or saved in a [[raster graphics]] file format such as [[JPEG]] or [[PNG]]. High-end rendering applications commonly use the [[OpenEXR]] file format, which can represent finer gradations of colors and [[high dynamic range]] lighting, allowing [[tone mapping]] or other adjustments to be applied afterwards without loss of quality.{{r|n=pbrt4UG}}{{r|n=Brinkmann2008|loc=Ch. 14, Ap. B}}

Quickly rendered animations can be saved directly as video files, but for high-quality rendering, individual frames (which may be rendered by different computers in a [[Computer cluster|cluster]] or ''[[render farm]]'' and may take hours or even days to render) are output as separate files and combined later into a video clip.{{r|n=BlenderRenderingAnimations}}{{r|n=Dunlop2014|loc=1.5, 3.11, 8.11}}

The output of a renderer sometimes includes more than just [[RGB_color_model#Numeric_representations|RGB color values]]. For example, the spectrum can be sampled using multiple wavelengths of light, or additional information such as depth (distance from camera) or the material of each point in the image can be included (this data can be used during compositing or when generating [[Texture mapping|texture maps]] for real-time rendering, or used to assist in [[Noise_reduction#In_images|removing noise]] from a path-traced image). Transparency information can be included, allowing rendered foreground objects to be composited with photographs or video. It is also sometimes useful to store the contributions of different lights, or of specular and diffuse lighting, as separate channels, so lighting can be adjusted after rendering. The [[OpenEXR]] format allows storing many channels of data in a single file.{{r|n=pbrt4UG}}{{r|n=Brinkmann2008|loc=Ch. 14, Ap. B}}

== Techniques ==
Choosing how to render a 3D scene usually involves trade-offs between speed, memory usage, and realism (although realism is not always desired). The '''{{visible anchor|algorithms}}''' developed over the years follow a loose progression, with more advanced methods becoming practical as computing power and memory capacity increased. Multiple techniques may be used for a single final image.

An important distinction is between [[Image and object order rendering|image order]] algorithms, which iterate over pixels of the image plane, and [[Image and object order rendering|object order]] algorithms, which iterate over objects in the scene. For simple scenes, object order is usually more efficient, as there are fewer objects than pixels.{{r|n=Marschner2022|loc=Ch. 4}}

; [[vector graphics|2D vector graphics]]
: The [[vector monitor|vector displays]] of the 1960s-1970s used deflection of an [[Cathode ray|electron beam]] to draw [[line segment]]s directly on the screen. Nowadays, [[vector graphics]] are rendered by [[rasterization]] algorithms that also support filled shapes. In principle, any 2D vector graphics renderer can be used to render 3D objects by first projecting them onto a 2D image plane. {{r|n=Foley82|p=93, 431, 505, 553}}
; [[Rasterisation#3D_images|3D rasterization]]
: Adapts 2D rasterization algorithms so they can be used more efficiently for 3D rendering, handling [[Hidden-surface determination|hidden surface removal]] via [[scanline rendering|scanline]] or [[Z-buffering|z-buffer]] techniques. Different realistic or stylized effects can be obtained by coloring the pixels covered by the objects in different ways. [[Computer representation of surfaces|Surfaces]] are typically divided into [[Polygon mesh|meshes]] of triangles before being rasterized. Rasterization is usually synonymous with "object order" rendering (as described above).{{r|n=Foley82|p=560-561, 575-590}}{{r|n=Raghavachary2005|loc=8.5}}{{r|n=Marschner2022|loc=Ch. 9}}
; [[Ray casting]]
: Uses geometric formulas to compute the first object that a [[Line (geometry)#Ray|ray]] intersects.{{r|n=RayTracingGems_1|p=8}} It can be used to implement "image order" rendering by casting a ray for each pixel, and finding a corresponding point in the scene. Ray casting is a fundamental operation used for both graphical and non-graphical purposes,{{r|n=RealTimeRayTracing|p=6}} e.g. determining whether a point is in shadow, or checking what an enemy can see in a [[Artificial intelligence in video games|game]].
; [[Ray tracing (graphics)|Ray tracing]]
: Simulates the bouncing paths of light caused by [[specular reflection]] and [[refraction]], requiring a varying number of ray casting operations for each path. Advanced forms use [[Monte Carlo method|Monte Carlo techniques]] to render effects such as area lights, [[depth of field]], blurry reflections, and [[Umbra, penumbra and antumbra|soft shadows]], but computing [[global illumination]] is usually in the domain of path tracing.{{r|n=RayTracingGems_1|p=9-13}}{{r|IntroToRTCh5}}
; [[Radiosity (computer graphics)|Radiosity]]
: A [[Finite_element_method|finite element analysis]] approach that breaks surfaces in the scene into pieces, and estimates the amount of light that each piece receives from light sources, or indirectly from other surfaces. Once the [[irradiance]] of each surface is known, the scene can be rendered using rasterization or ray tracing.{{r|Glassner95|p=888-890, 1044-1045}}
; [[Path tracing]]
: Uses [[Monte Carlo method|Monte Carlo integration]] with a simplified form of ray tracing, computing the average brightness of a [[Sampling (statistics)|sample]] of the possible paths that a photon could take when traveling from a light source to the camera (for some images, thousands of paths need to be sampled per pixel{{r|n=RealTimeRayTracing|p=8}}). It was introduced as a [[Unbiased rendering|statistically unbiased]] way to solve the [[rendering equation]], giving ray tracing a rigorous mathematical foundation.{{r|Kajiya1986}}{{r|n=RayTracingGems_1|p=11-13}}

Each of the above approaches has many variations, and there is some overlap. Path tracing may be considered either a distinct technique or a particular type of ray tracing.{{r|Glassner95|p=846, 1021}} Note that the [[usage (language)|usage]] of terminology related to ray tracing and path tracing has changed significantly over time.{{r|n=RayTracingGems_1|p=7}}

[[File:Real-time_Raymarched_Terrain.png|thumb|Rendering of a fractal terrain by [[ray marching]]]]
[[Ray marching]] is a family of algorithms, used by ray casting, for finding intersections between a ray and a complex object, such as a [[Volume_ray_casting|volumetric dataset]] or a surface defined by a [[signed distance function]]. It is not, by itself, a rendering method, but it can be incorporated into ray tracing and path tracing, and is used by rasterization to implement screen-space reflection and other effects.{{r|n=RayTracingGems_1|p=13}}

A technique called [[photon mapping]] traces paths of photons from a light source to an object, accumulating data about [[irradiance]] which is then used during conventional ray tracing or path tracing.{{r|Glassner95|p=1037-1039}} Rendering a scene using only rays traced from the light source to the camera is impractical, even though it corresponds more closely to reality, because a huge number of photons would need to be simulated, only a tiny fraction of which actually hit the camera.{{r|IntroToRTCh1|p=7-9}}{{r|n=Foley82|p=587}}

Some authors call conventional ray tracing "backward" ray tracing because it traces the paths of photons backwards from the camera to the light source, and call following paths from the light source (as in photon mapping) "forward" ray tracing.{{r|IntroToRTCh1|p=7-9}} However sometimes the meaning of these terms is reversed.{{r|Arvo1986}} Tracing rays starting at the light source can also be called ''particle tracing'' or ''light tracing'', which avoids this ambiguity.{{r|Veach1997|p=92}}{{r|Dutré2015|loc=4.5.4}}

Real-time rendering, including video game graphics, typically uses rasterization, but increasingly combines it with ray tracing and path tracing.{{r|RealTimeRayTracing|page=2}} To enable realistic [[global illumination]], real-time rendering often relies on pre-rendered ("baked") lighting for stationary objects. For moving objects, it may use a technique called ''light probes'', in which lighting is recorded by rendering omnidirectional views of the scene at chosen points in space (often points on a grid to allow easier [[interpolation]]). These are similar to [[reflection mapping|environment maps]], but typically use a very low resolution or an approximation such as [[spherical harmonics]].{{r|UnityLightProbes}} (Note: [[Blender (software)|Blender]] uses the term 'light probes' for a more general class of pre-recorded lighting data, including reflection maps.{{r|BlenderSettingsLightProbes}})

{{Gallery
| title = Examples comparing different rendering techniques
| mode = nolines
| File:Rendering techniques example, rasterization, low quality, Blender EEVEE.png
    | A low quality rasterized image, rendered by [[Blender (software)|Blender]]'s EEVEE renderer with low [[shadow mapping|shadow map]] resolution and a low-resolution mesh| alt1 = 3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The shadows of the cows are blocky (like blurry pixels) due to low quality settings in the renderer.
| File:Rendering techniques example, path tracing, low quality, Blender Cycles.png
    | A low quality path traced image, rendered by Blender's Cycles renderer with only 16 sampled paths per pixel and a low-resolution mesh| alt2 = 3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The image is speckled with many white dots, especially in the shadowed areas, due to low quality settings in the renderer. The reflection, transparency, and lighting are realistic, but the speckles distract from this.
| File:Rendering techniques example, ray tracing, low quality, POV-Ray.png
    | A ray traced image, using the [[POV-Ray]] program (using only its ray tracing features) with a low-resolution mesh| alt3 = 3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The outlines are angular and there are some defects (due to the low-resolution mesh of the models), and the transparent cow has no shadow.
| File:Rendering techniques example, rasterization, high quality, Blender EEVEE.png
    | A higher quality rasterized image, using [[Blender (software)|Blender]]'s EEVEE renderer with light probes| alt4 = 3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The outlines of the cows and the shadows are smooth with no blockiness or angular defects, and the reflection looks quite realistic, but the transparency does not look convincing, and the lighting in the shadowed areas of the cows is not quite realistic.
| File:Rendering techniques example, path tracing, high quality, Blender Cycles.png
    | A higher quality path traced image, using [[Blender (software)|Blender]]'s Cycles renderer with 2000 sampled paths per pixel  | alt5 = 3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The outlines of the cows and the shadows are smooth with no blockiness or angular defects. There are a few speckles of white pixels, but far fewer than in the low-quality image. The reflection, transparency, and lighting look realistic.
| File:Rendering techniques example, ray tracing, radiosity, photon mapping, POV-Ray.png
    | An image rendered using [[POV-Ray]]'s [[ray tracing (graphics)|ray tracing]], [[radiosity (computer graphics)|radiosity]] and [[photon mapping]] features| alt6 = 3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The outlines of the cows and the shadows are smooth with no blockiness or angular defects. The lighting is realistic, including in the shadowed areas. The base surface is illuminated by bright spots and lines ("caustics") caused by light being focused by the reflective and transparent cows.
| File:Rendering techniques example, path tracing, realistic, Blender Cycles.jpg
    | A more realistic path traced image, using [[Blender (software)|Blender]]'s Cycles renderer with [[image-based lighting]]| alt7 = 3D rendered image showing three copies of a cartoon cow. The one on the left has a metalic surface, and the one on the right uses a transparent glass material. The cow in the center appears made of glazed porcelain. The cows are standing on a wooden table. Lights and other background details from a cafe environment are reflected in the slightly glossy table and the cows.
| File:Rendering techniques example, spectral, photon mapping, POV-Ray.png
    | A [[spectral rendering|spectral rendered]] image, using [[POV-Ray]]'s [[ray tracing (graphics)|ray tracing]], [[radiosity (computer graphics)|radiosity]] and [[photon mapping]] features| alt8 = 3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The base surface is illuminated by finely detailed bright spots and lines ("caustics") caused by light being focused by the reflective and transparent cows. The caustics are colorful in some places, due to chromatic dispersion.
}}

===Rasterization<span class="anchor" id="Rasterization"></span><span class="anchor" id="Scanline rendering and rasterization"></span>===
{{main|Rasterization}}
[[File:Latest Rendering of the E-ELT.jpg|thumb|Rendering of the [[Extremely Large Telescope]]]]

The term ''rasterization'' (in a broad sense) encompasses many techniques used for 2D rendering and [[Real-time computer graphics|real-time]] 3D rendering. 3D [[Computer animation|animated films]] were rendered by rasterization before [[Ray tracing (graphics)|ray tracing]] and [[path tracing]] became practical.

A renderer combines rasterization with ''geometry processing'' (which is not specific to rasterization) and ''pixel processing'' which computes the [[RGB color model|RGB color values]] to be placed in the ''[[framebuffer]]'' for display.{{r|AkenineMöller2018|loc=2.1}}{{r|Marschner2022|loc=9}}

The main tasks of rasterization (including pixel processing) are:{{r|AkenineMöller2018|loc=2, 3.8, 23.1.1}}
* Determining which pixels are covered by each geometric shape in the 3D scene or 2D image (this is the actual rasterization step, in the strictest sense)
* Blending between colors and depths defined at the [[Vertex (computer graphics)|vertices]] of shapes, e.g. using [[Barycentric coordinate system|barycentric coordinates]] (''interpolation'')
* Determining if parts of shapes are hidden by other shapes, due to 2D layering or 3D depth (''[[Hidden-surface determination|hidden surface removal]]'')
* Evaluating a function for each pixel covered by a shape (''[[shading]]'')
* Smoothing edges of shapes so pixels are less visible (''[[Spatial anti-aliasing|anti-aliasing]]'')
* Blending overlapping transparent shapes (''[[compositing]]'')

3D rasterization is typically part of a ''[[graphics pipeline]]'' in which an application provides [[Triangle mesh|lists of triangles]] to be rendered, and the rendering system transforms and [[3D projection|projects]] their coordinates, determines which triangles are potentially visible in the ''[[viewport]]'', and performs the above rasterization and pixel processing tasks before displaying the final result on the screen.{{r|AkenineMöller2018|loc=2.1}}{{r|Marschner2022|loc=9}}

Historically, 3D rasterization used algorithms like the ''[[Warnock algorithm]]'' and ''[[scanline rendering]]'' (also called "scan-conversion"), which can handle arbitrary polygons and can rasterize many shapes simultaneously. Although such algorithms are still important for 2D rendering, 3D rendering now usually divides shapes into triangles and rasterizes them individually using simpler methods.{{r|Warnock1969}}{{r|Bouknight1970}}{{r|Foley82|pp=456, 561-569}}

[[Digital differential analyzer (graphics algorithm)|High-performance algorithms]] exist for rasterizing [[Bresenham's line algorithm|2D lines]], including [[Xiaolin Wu's line algorithm|anti-aliased lines]], as well as [[Midpoint circle algorithm|ellipses]] and filled triangles. An important special case of 2D rasterization is [[Font rasterization|text rendering]], which requires careful anti-aliasing and rounding of coordinates to avoid distorting the [[letterform]]s and preserve spacing, density, and sharpness.{{r|Marschner2022|loc=9.1.1}}{{r|RasterTragedy}}

After 3D coordinates have been [[3D projection|projected]] onto the [[image plane]], rasterization is primarily a 2D problem, but the 3rd dimension necessitates ''[[Hidden-surface determination|hidden surface removal]]''. Early computer graphics used [[Computational geometry|geometric algorithms]] or ray casting to remove the hidden portions of shapes, or used the ''[[painter's algorithm]]'', which sorts shapes by depth (distance from camera) and renders them from back to front. Depth sorting was later avoided by incorporating depth comparison into the [[scanline rendering]] algorithm. The ''[[Z-buffering|z-buffer ]]'' algorithm performs the comparisons indirectly by including a depth or "z" value in the [[framebuffer]]. A pixel is only covered by a shape if that shape's z value is lower (indicating closer to the camera) than the z value currently in the buffer. The z-buffer requires additional memory (an expensive resource at the time it was invented) but simplifies the rasterization code and permits multiple passes. Memory is now faster and more plentiful, and a z-buffer is almost always used for real-time rendering.{{r|Watkins1970}}{{r|Catmull1974}}{{r|Foley82|pp=553-570}}{{r|AkenineMöller2018|loc=2.5.2}}

A drawback of the basic [[Z-buffering|z-buffer algorithm]] is that each pixel ends up either entirely covered by a single object or filled with the background color, causing jagged edges in the final image. Early ''[[Spatial anti-aliasing|anti-aliasing]]'' approaches addressed this by detecting when a pixel is partially covered by a shape, and calculating the covered area. The [[A-buffer]] (and other [[Subpixel rendering|sub-pixel]] and [[Multisample anti-aliasing|multi-sampling]] techniques) solve the problem less precisely but with higher performance. For real-time 3D graphics, it has become common to use [[Fast approximate anti-aliasing|complicated heuristics]] (and even [[Deep learning anti-aliasing| neural-networks]]) to perform anti-aliasing.{{r|Catmull1974}}{{r|Carpenter1984}}{{r|Marschner2022|loc=9.3}}{{r|AkenineMöller2018|loc=5.4.2}}

In 3D rasterization, color is usually determined by a ''[[Shader#Pixel_shaders|pixel shader]]'' or ''fragment shader'', a small program that is run for each pixel. The shader does not (or cannot) directly access 3D data for the entire scene (this would be very slow, and would result in an algorithm similar to ray tracing) and a variety of techniques have been developed to render effects like [[Shadow mapping|shadows]] and [[Reflection (computer graphics)|reflections]] using only [[texture mapping]] and multiple passes.{{r|Marschner2022|loc=17.8}}

Older and more basic 3D rasterization implementations did not support shaders, and used simple shading techniques such as ''[[Shading#Flat_shading|flat shading]]'' (lighting is computed once for each triangle, which is then rendered entirely in one color), ''[[Gouraud shading]]'' (lighting is computed using [[Normal (geometry)|normal vectors]] defined at vertices and then colors are interpolated across each triangle), or ''[[Phong shading]]'' (normal vectors are interpolated across each triangle and lighting is computed for each pixel).{{r|Marschner2022|loc=9.2}}

Until relatively recently, [[Pixar]] used rasterization for rendering its [[Computer animation|animated films]]. Unlike the renderers commonly used for real-time graphics, the [[Reyes rendering|Reyes rendering system]] in Pixar's [[Pixar RenderMan|RenderMan]] software was optimized for rendering very small (pixel-sized) polygons, and incorporated [[stochastic]] sampling techniques more typically associated with [[Ray tracing (graphics)|ray tracing]].{{r|Raghavachary2005|loc=2, 6.3}}{{r|Cook1987}}

=== Ray casting ===
{{Main|Ray casting}}

One of the simplest ways to render a 3D scene is to test if a [[Line_(geometry)#Ray|ray]] starting at the viewpoint (the "eye" or "camera") intersects any of the geometric shapes in the scene, repeating this test using a different ray direction for each pixel. This method, called ''ray casting'', was important in early computer graphics, and is a fundamental building block for more advanced algorithms. Ray casting can be used to render shapes defined by ''[[constructive solid geometry]]'' (CSG) operations.{{r|RayTracingGems_1|p=8-9}}{{r|IntroToRTCh6|pp=246-249}}

Early ray casting experiments include the work of Arthur Appel in the 1960s. Appel rendered shadows by casting an additional ray from each visible surface point towards a light source. He also tried rendering the density of illumination by casting random rays from the light source towards the object and [[Plotter|plotting]] the intersection points (similar to the later technique called ''[[photon mapping]]'').{{r|Appel1968}}

[[File:Mandelbulb_p8a.jpg|thumb|[[Ray marching]] can be used to find the first intersection of a ray with an intricate shape such as this [[Mandelbulb]] fractal.]]
When rendering scenes containing many objects, testing the intersection of a ray with every object becomes very expensive. Special [[data structure]]s are used to speed up this process by allowing large numbers of objects to be excluded quickly (such as objects behind the camera). These structures are analogous to [[database index]]es for finding the relevant objects. The most common are the ''[[bounding volume hierarchy]]'' (BVH), which stores a pre-computed [[bounding volume|bounding box or sphere]] for each branch of a [[Tree (data structure)|tree]] of objects, and the ''[[k-d tree]]'' which [[Recursion_(computer_science)|recursively]] divides space into two parts. Recent [[GPU]]s include hardware acceleration for BVH intersection tests. K-d trees are a special case of ''[[binary space partitioning]]'', which was frequently used in early computer graphics (it can also generate a rasterization order for the [[painter's algorithm]]). ''[[Octree]]s'', another historically popular technique, are still often used for volumetric data.{{r|RealTimeRayTracing|pp=16-17}}{{r|RayTracingGems_Forword_Stich}}{{r|IntroToRTCh6}}{{r|Hughes2014|loc=36.2}}

Geometric formulas are sufficient for finding the intersection of a ray with shapes like [[sphere]]s, [[polygon]]s, and [[polyhedron|polyhedra]], but for most curved surfaces there is no [[Closed-form_expression#Analytic_expression|analytic solution]], or the intersection is difficult to compute accurately using limited precision [[Floating-point arithmetic|floating point numbers]]. [[Root-finding algorithm]]s such as [[Newton's method]] can sometimes be used. To avoid these complications, curved surfaces are often approximated as [[Triangle mesh|meshes of triangles]]. [[Volume rendering]] (e.g. rendering clouds and smoke), and some surfaces such as [[fractal]]s, may require [[ray marching]] instead of basic ray casting.{{r|IntroToRTCh2}}{{r|RayTracingGems_1|p=13}}{{r|AkenineMöller2018|loc=14, 17.3}}

=== Ray tracing ===
[[Image:SpiralSphereAndJuliaDetail1.jpg|thumb|250px|''Spiral Sphere and Julia, Detail'', a computer-generated image created by visual artist Robert W. McGregor using only [[POV-Ray]] 3.6 and its built-in scene description language]]
{{Main|Ray tracing (graphics)}}

Ray casting can be used to render an image by tracing [[Ray (optics)|light rays]] backwards from a simulated camera. After finding a point on a surface where a ray originated, another ray is traced towards the light source to determine if anything is casting a shadow on that point. If not, a ''[[Bidirectional reflectance distribution function|reflectance model]]'' (such as [[Lambertian reflectance]] for [[Paint sheen|matte]] surfaces, or the [[Phong reflection model]] for glossy surfaces) is used to compute the probability that a [[photon]] arriving from the light would be reflected towards the camera, and this is multiplied by the brightness of the light to determine the pixel brightness. If there are multiple light sources, brightness contributions of the lights are added together. For color images, calculations are repeated for multiple [[Visible spectrum|wavelengths]] of light (e.g. red, green, and blue).{{r|AkenineMöller2018|loc=11.2.2}}{{r|RayTracingGems_1|p=8}}

''Classical ray tracing'' (also called ''Whitted-style'' or ''recursive'' ray tracing) extends this method so it can render mirrors and transparent objects. If a ray traced backwards from the camera originates at a point on a mirror, the [[Specular reflection|reflection formula]] from [[geometric optics]] is used to calculate the direction the reflected ray came from, and another ray is cast backwards in that direction. If a ray originates at a transparent surface, rays are cast backwards for both [[Specular reflection|reflected]] and [[Refraction|refracted]] rays (using [[Snell's law]] to compute the refracted direction), and so ray tracing needs to support a branching "tree" of rays. In simple implementations, a [[Recursion (computer science)|recursive function]] is called to trace each ray.{{r|AkenineMöller2018|loc=11.2.2}}{{r|RayTracingGems_1|p=9}}

Ray tracing usually performs [[Spatial anti-aliasing|anti-aliasing]] by taking the average of multiple [[Sampling (statistics)|samples]] for each pixel. It may also use multiple samples for effects like [[depth of field]] and [[motion blur]]. If evenly-spaced ray directions or times are used for each of these features, many rays are required, and some aliasing will remain. ''Cook-style'', ''stochastic'', or ''Monte Carlo ray tracing'' avoids this problem by using [[Monte Carlo method|random sampling]] instead of evenly-spaced samples. This type of ray tracing is commonly called [[distributed ray tracing|''distributed ray tracing'', or ''distribution ray tracing'']] because it samples rays from [[probability distribution]]s. Distribution ray tracing can also render realistic "soft" shadows from large lights by using a random sample of points on the light when testing for shadowing, and it can simulate [[chromatic aberration]] by sampling multiple wavelengths from the [[Visible spectrum|spectrum of light]].{{r|RayTracingGems_1|p=10}}{{r|IntroToRTCh1|p=25}}

Real surface materials reflect small amounts of light in almost every direction because they have small (or microscopic) bumps and grooves. A distribution ray tracer can simulate this by sampling possible ray directions, which allows rendering blurry reflections from glossy and metallic surfaces. However if this procedure is repeated [[Recursion|recursively]] to simulate realistic indirect lighting, and if more than one sample is taken at each surface point, the tree of rays quickly becomes huge. Another kind of ray tracing, called ''path tracing'', handles indirect light more efficiently, avoiding branching, and ensures that the distribution of all possible paths from a light source to the camera is sampled in an [[Unbiased rendering|unbiased]] way.{{r|IntroToRTCh1|pp=25-27}}{{r|Kajiya1986}}

Ray tracing was often used for rendering reflections in animated films, until path tracing became standard for film rendering. Films such as [[Shrek 2]] and [[Monsters University]] also used distribution ray tracing or path tracing to precompute indirect illumination for a scene or frame prior to rendering it using rasterization.{{r|Christensen2016|pp=118-121}}

Advances in GPU technology have made real-time ray tracing possible in games, although it is currently almost always used in combination with rasterization.{{r|RealTimeRayTracing|page=2}} This enables visual effects that are difficult with only rasterization, including reflection from curved surfaces and interreflective objects,{{r|RayTracingGems_19|page=305}} and shadows that are accurate over a wide range of distances and surface orientations.{{r|n=RayTracingGems_13|p=159-160}} Ray tracing support is included in recent versions of the graphics APIs used by games, such as [[DirectX Raytracing|DirectX]], [[Metal (API)|Metal]], and [[Vulkan]].{{r|KhronosRTInVukan}}

Ray tracing has been used to render simulated [[black hole]]s, and the appearance of objects moving at close to the speed of light, by taking [[curved spacetime|spacetime curvature]] and [[Special relativity|relativistic effects]] into account during light ray simulation.{{r|Riazuelo2019}}{{r|Howard1995}}

=== Radiosity ===
{{Main|Radiosity (computer graphics)}}

[[File:Classical radiosity example, simple scene, no interpolation, direct only and full.png|thumb|Classical radiosity demonstration. Surfaces are divided into 16x16 or 16x32 meshes. Top: direct light only. Bottom: radiosity solution (for [[albedo]] 0.85).]]
[[File:Classical radiosity comparison with path tracing, simple scene, interpolated.png|thumb|Top: the same scene with a finer radiosity mesh, smoothing the patches during final rendering using [[bilinear interpolation]]. Bottom: the scene rendered with path tracing (using the PBRT renderer).]]
Radiosity (named after the [[Radiosity (radiometry)|radiometric quantity of the same name]]) is a method for rendering objects illuminated by light [[Diffuse reflection|bouncing off rough or matte surfaces]]. This type of illumination is called ''indirect light'', ''environment lighting'', or ''diffuse lighting'', and the problem of rendering it realistically is called ''global illumination''. Rasterization and basic forms of ray tracing (other than distribution ray tracing and path tracing) can only roughly approximate indirect light, e.g. by adding a uniform "ambient" lighting amount chosen by the artist. Radiosity techniques are also suited to rendering scenes with ''area lights'' such as rectangular fluorescent lighting panels, which are difficult for rasterization and traditional ray tracing. Radiosity is considered a [[Physically based rendering|physically-based method]], meaning that it aims to simulate the flow of light in an environment using equations and experimental data from physics, however it often assumes that all surfaces are opaque and perfectly [[Lambertian reflectance|Lambertian]], which reduces realism and limits its applicability.{{r|AkenineMöller2018|loc=10, 11.2.1}}{{r|Glassner95|p=888, 893}}{{r|Goral1984}}

In the original radiosity method (first proposed in 1984) now called ''classical radiosity'', surfaces and lights in the scene are split into pieces called ''patches'', a process called ''[[Mesh generation|meshing]]'' (this step makes it a [[finite element method]]). The rendering code must then determine what fraction of the light being emitted or [[Diffuse reflection|diffusely reflected]] (scattered) by each patch is received by each other patch. These fractions are called ''form factors'' or ''[[view factor]]s'' (first used in engineering to model [[Thermal radiation|radiative heat transfer]]). The form factors are multiplied by the [[albedo]] of the receiving surface and put in a [[Matrix (mathematics)|matrix]]. The lighting in the scene can then be expressed as a matrix equation (or equivalently a [[system of linear equations]]) that can be solved by methods from [[linear algebra]].{{r|Goral1984}}{{r|Dutré2003|p=46}}{{r|Glassner95|p=888, 896}}

Solving the radiosity equation gives the total amount of light emitted and reflected by each patch, which is divided by area to get a value called ''[[Radiosity (radiometry)|radiosity]]'' that can be used when rasterizing or ray tracing to determine the color of pixels corresponding to visible parts of the patch. For real-time rendering, this value (or more commonly the [[irradiance]], which does not depend on local surface albedo) can be pre-computed and stored in a texture (called an ''irradiance map'') or stored as vertex data for 3D models. This feature was used in architectural visualization software to allow real-time walk-throughs of a building interior after computing the lighting.{{r|Glassner95|p=890}}{{r|AkenineMöller2018|loc=11.5.1}}{{r|Cohen1993|p=332}}

The large size of the matrices used in classical radiosity (the square of the number of patches) causes problems for realistic scenes. Practical implementations may use [[Jacobi method|Jacobi]] or [[Gauss–Seidel method|Gauss-Seidel]] iterations, which is equivalent (at least in the Jacobi case) to simulating the propagation of light one bounce at a time until the amount of light remaining (not yet absorbed by surfaces) is insignificant. The number of iterations (bounces) required is dependent on the scene, not the number of patches, so the total work is proportional to the square of the number of patches (in contrast, solving the matrix equation using [[Gaussian elimination]] requires work proportional to the cube of the number of patches). Form factors may be recomputed when they are needed, to avoid storing a complete matrix in memory.{{r|Glassner95|pp=901, 907}}

The quality of rendering is often determined by the size of the patches, e.g. very fine meshes are needed to depict the edges of shadows accurately. An important improvement is ''hierarchical radiosity'', which uses a coarser mesh (larger patches) for simulating the transfer of light between surfaces that are far away from one another, and adaptively sub-divides the patches as needed. This allows radiosity to be used for much larger and more complex scenes.{{r|Glassner95|pp=975, 939}}

Alternative and extended versions of the radiosity method support non-Lambertian surfaces, such as glossy surfaces and mirrors, and sometimes use volumes or "clusters" of objects as well as surface patches. Stochastic or [[Monte Carlo method|Monte Carlo]] radiosity uses [[Sampling (statistics)|random sampling]] in various ways, e.g. taking samples of incident light instead of integrating over all patches, which can improve performance but adds noise (this noise can be reduced by using deterministic iterations as a final step, unlike path tracing noise). Simplified and partially precomputed versions of radiosity are widely used for real-time rendering, combined with techniques such as ''[[octree]] radiosity'' that store approximations of the [[light field]].{{r|Glassner95|pp=979, 982}}{{r|Dutré2003|p=49}}{{r|Bekaert1999}}{{r|AkenineMöller2018|loc=11.5}}

=== Path tracing ===
{{Main|Path tracing}}
As part of the approach known as ''[[physically based rendering]]'', '''[[path tracing]]''' has become the dominant technique for rendering realistic scenes, including effects for movies.{{r|Pharr2023_1_6}} For example, the popular open source 3D software [[Blender (software)|Blender]] uses path tracing in its Cycles renderer.{{r|BlenderCyclesIntro}} Images produced using path tracing for [[global illumination]] are generally noisier than when using [[Radiosity (computer graphics)|radiosity]] (the main competing algorithm for realistic lighting), but radiosity can be difficult to apply to complex scenes and is prone to artifacts that arise from using a [[Tessellation (computer graphics)|tessellated]] representation of [[irradiance]].{{r|Pharr2023_1_6}}{{r|Glassner95|p=975-976, 1045}}

Like ''[[distributed ray tracing]]'', path tracing is a kind of ''[[stochastic]]'' or ''[[Randomized algorithm|randomized]]'' [[Ray tracing (graphics)|ray tracing]] that uses [[Monte Carlo integration|Monte Carlo]] or [[Quasi-Monte Carlo method|Quasi-Monte Carlo]] integration. It was proposed and named in 1986 by [[Jim Kajiya]] in the same paper as the [[rendering equation]]. Kajiya observed that much of the complexity of [[distributed ray tracing]] could be avoided by only tracing a single path from the camera at a time (in Kajiya's implementation, this "no branching" rule was broken by tracing additional rays from each surface intersection point to randomly chosen points on each light source). Kajiya suggested reducing the noise present in the output images by using ''[[stratified sampling]]'' and ''[[importance sampling]]'' for making random decisions such as choosing which ray to follow at each step of a path. Even with these techniques, path tracing would not have been practical for film rendering, using computers available at the time, because the computational cost of generating enough samples to reduce [[variance]] to an acceptable level was too high. [[Monster_House_(film)|Monster House]], the first feature film rendered entirely using path tracing, was not released until 20 years later.{{r|Kajiya1986}}{{r|Pharr2023_1_6}}{{r|Kulla2017}}

In its basic form, path tracing is inefficient (requiring too many samples) for rendering [[Caustic (optics)|caustics]] and scenes where light enters indirectly through narrow spaces. Attempts were made to address these weaknesses in the 1990s. ''[[Path tracing#Bidirectional_path_tracing|Bidirectional path tracing]]'' has similarities to [[photon mapping]], tracing rays from the light source and the camera separately, and then finding ways to connect these paths (but unlike photon mapping it usually samples new light paths for each pixel rather than using the same cached data for all pixels). ''[[Metropolis light transport]]'' samples paths by modifying paths that were previously traced, spending more time exploring paths that are similar to other "bright" paths, which increases the chance of discovering even brighter paths. ''Multiple importance sampling'' provides a way to reduce [[variance]] when combining samples from more than one sampling method, particularly when some samples are much noisier than the others.{{r|Pharr2023_1_6}}{{r|Veach1997}}

This later work was summarized and expanded upon in [[Eric Veach]]'s 1997 PhD thesis, which helped raise interest in path tracing in the computer graphics community. The [[Autodesk Arnold|Arnold renderer]], first released in 1998, proved that path tracing was practical for rendering frames for films, and that there was a demand for [[Unbiased rendering|unbiased]] and [[Physically based rendering|physically based]] rendering in the film industry; other commercial and open source path tracing renderers began appearing. Computational cost was addressed by rapid advances in [[CPU]] and [[Computer cluster|cluster]] performance.{{r|Pharr2023_1_6}}

Path tracing's relative simplicity and its nature as a [[Monte Carlo method]] (sampling hundreds or thousands of paths per pixel) have made it attractive to implement on a [[Graphics processing unit|GPU]], especially on recent GPUs that support ray tracing acceleration technology such as Nvidia's [[Nvidia RTX|RTX]] and [[OptiX]].{{r|Pharr2023_15}} However bidirectional path tracing and Metropolis light transport are more difficult to implement efficiently on a GPU.{{r|Otte2015}}{{r|Schmidt2016}}

Research into improving path tracing continues. Recent ''path guiding'' approaches construct approximations of the [[light field]] probability distribution in each volume of space, so paths can be sampled more effectively.{{r|Pharr2023_13fr}} Many techniques have been developed to [[Noise reduction|denoise]] the output of path tracing, reducing the number of paths required to achieve acceptable quality, at the risk of losing some detail or introducing small-scale artifacts that are more objectionable than noise;{{r|Pharr2023_5fr}}{{r|BlenderCyclesReducingNoise}} [[Artificial neural network|neural networks]] are now widely used for this purpose.{{r|BlenderSettingsDenoising}}{{r|OpenImageDenoise}}{{r|NvidiaOptiXDenoiser}}

=== Neural rendering ===
'''Neural rendering''' is a rendering method using [[artificial neural network]]s.<ref name="Tewari">{{Cite journal|url=https://onlinelibrary.wiley.com/doi/am-pdf/10.1111/cgf.14022|doi=10.1111/cgf.14022|title=State of the Art on Neural Rendering|year=2020|last1=Tewari|first1=A.|last2=Fried|first2=O.|last3=Thies|first3=J.|last4=Sitzmann|first4=V.|last5=Lombardi|first5=S.|last6=Sunkavalli|first6=K.|last7=Martin-Brualla|first7=R.|last8=Simon|first8=T.|last9=Saragih|first9=J.|last10=Nießner|first10=M.|last11=Pandey|first11=R.|last12=Fanello|first12=S.|last13=Wetzstein|first13=G.|last14=Zhu|first14=J.-Y.|last15=Theobalt|first15=C.|last16=Agrawala|first16=M.|last17=Shechtman|first17=E.|last18=Goldman|first18=D. B.|last19=Zollhöfer|first19=M.|journal=Computer Graphics Forum|volume=39|issue=2|pages=701–727|arxiv=2004.03805|s2cid=215416317}}</ref><ref>{{Cite magazine|last=Knight|first=Will|title=A New Trick Lets Artificial Intelligence See in 3D|language=en-US|magazine=Wired|url=https://www.wired.com/story/new-way-ai-see-3d/|access-date=2022-02-08|issn=1059-1028|archive-date=2022-02-07|archive-url=https://web.archive.org/web/20220207230740/https://www.wired.com/story/new-way-ai-see-3d/|url-status=live}}</ref> Neural rendering includes [[image-based rendering]] methods that are used to [[3D reconstruction|reconstruct 3D models]] from 2-dimensional images.<ref name="Tewari"/>One of these methods are [[photogrammetry]], which is a method in which a collection of images from multiple angles of an object are turned into a 3D model. There have also been recent developments in generating and rendering 3D models from text and coarse paintings by notably [[Nvidia]], [[Google]] and various other companies.

{{Expand section|date=February 2022}}

== Scientific and mathematical basis ==
{{Main|Unbiased rendering}}

The implementation of a realistic renderer always has some basic element of physical simulation or emulation{{snd}} some computation which resembles or abstracts a real physical process.

The term "''[[physically based rendering|physically based]]''" indicates the use of physical models and approximations that are more general and widely accepted outside rendering. A particular set of related techniques have gradually become established in the rendering community.

The basic concepts are moderately straightforward, but intractable to calculate; and a single elegant algorithm or approach has been elusive for more general purpose renderers. In order to meet demands of robustness, accuracy and practicality, an implementation will be a complex combination of different techniques.

Rendering research is concerned with both the adaptation of scientific models and their efficient application.

Mathematics used in rendering includes: [[linear algebra]], [[calculus]], [[numerical analysis|numerical mathematics]], [[digital signal processing|signal processing]], and [[Monte Carlo methods]].

=== The rendering equation ===
{{Main|Rendering equation}}

This is the key academic/theoretical concept in rendering. It serves as the most abstract formal expression of the non-perceptual aspect of rendering. All more complete algorithms can be seen as solutions to particular formulations of this equation.

: <math>L_o(x, \omega) = L_e(x, \omega) + \int_\Omega L_i(x, \omega') f_r(x, \omega', \omega)  (\omega' \cdot n) \, \mathrm d \omega'</math>
Meaning: at a particular position and direction, the outgoing light (L<sub>o</sub>) is the sum of the emitted light (L<sub>e</sub>) and the reflected light. The reflected light being the sum of the incoming light (L<sub>i</sub>) from all directions, multiplied by the surface reflection and incoming angle. By connecting outward light to inward light, via an interaction point, this equation stands for the whole 'light transport'{{snd}} all the movement of light{{snd}} in a scene.

=== The bidirectional reflectance distribution function ===
The '''[[bidirectional reflectance distribution function]]''' (BRDF) expresses a simple model of light interaction with a surface as follows:

: <math>f_r(x, \omega', \omega) = \frac{\mathrm d L_r(x, \omega)}{L_i(x, \omega')(\omega' \cdot \vec n) \mathrm d \omega'}</math>

Light interaction is often approximated by the even simpler models: diffuse reflection and specular reflection, although both can ALSO be BRDFs.

=== Geometric optics ===
Rendering is practically exclusively concerned with the particle aspect of light physics{{snd}} known as [[geometrical optics]]. Treating light, at its basic level, as particles bouncing around is a simplification, but appropriate: the wave aspects of light are negligible in most scenes, and are significantly more difficult to simulate. Notable wave aspect phenomena include diffraction (as seen in the colours of [[Compact disc|CDs]] and [[DVD]]s) and polarisation (as seen in [[Liquid-crystal display|LCDs]]). Both types of effect, if needed, are made by appearance-oriented adjustment of the reflection model.

=== Visual perception ===
Though it receives less attention, an understanding of [[human visual perception]] is valuable to rendering. This is mainly because image displays and human perception have restricted ranges. A renderer can simulate a wide range of light brightness and color, but current displays{{snd}} movie screen, computer monitor, etc.{{snd}} cannot handle so much, and something must be discarded or compressed. Human perception also has limits, and so does not need to be given large-range images to create realism. This can help solve the problem of fitting images into displays, and, furthermore, suggest what short-cuts could be used in the rendering simulation, since certain subtleties will not be noticeable. This related subject is [[tone mapping]].

=== Sampling and filtering ===
One problem that any rendering system must deal with, no matter which approach it takes, is the '''sampling problem'''.  Essentially, the rendering process tries to depict a [[continuous function]] from image space to colors by using a finite number of pixels.  As a consequence of the [[Nyquist–Shannon sampling theorem]] (or Kotelnikov theorem), any spatial waveform that can be displayed must consist of at least two pixels, which is proportional to [[image resolution]].  In simpler terms, this expresses the idea that an image cannot display details, peaks or troughs in color or intensity, that are smaller than one pixel.

If a naive rendering algorithm is used without any filtering, high frequencies in the image function will cause ugly [[aliasing]] to be present in the final image.  Aliasing typically manifests itself as [[jaggies]], or jagged edges on objects where the pixel grid is visible.  In order to remove aliasing, all rendering algorithms (if they are to produce good-looking images) must use some kind of [[low-pass filter]] on the image function to remove high frequencies, a process called [[Spatial anti-aliasing|antialiasing]].

== Hardware ==
Rendering is usually limited by available computing power and memory [[Bandwidth (computing)|bandwidth]], and so specialized [[Computer hardware|hardware]] has been developed to speed it up ("accelerate" it), particularly for [[Real-time computer graphics|real-time rendering]]. Hardware features such as a [[framebuffer]] for raster graphics are required to display the output of rendering smoothly in real time.

=== History ===
In the era of [[vector monitor]]s (also called ''calligraphic displays''), a display processing unit (DPU) was a dedicated [[Central processing unit|CPU]] or [[coprocessor]] that maintained a list of visual elements and redrew them continuously on the screen by controlling an [[Cathode ray|electron beam]]. Advanced DPUs such as [[Evans & Sutherland]]'s [[Line Drawing System-1]] (and later models produced into the 1980s) incorporated 3D coordinate transformation features to accelerate rendering of [[Wire-frame model|wire-frame images]].{{r|n=Foley82|pp=93-94, 404-421}}{{r|EandS1979}} Evans & Sutherland also made the [[Digistar]] [[planetarium]] projection system, which was a vector display that could render both stars and wire-frame graphics (the vector-based Digistar and Digistar II were used in many planetariums, and a few may still be in operation).{{r|NagoyaCityScienceMuseum}}{{r|WorldwidePlanetariumsDatabase1}}{{r|WorldwidePlanetariumsDatabase2}} A Digistar prototype was used for rendering 3D star fields for the film [[Star Trek II: The Wrath of Khan]] &ndash; some of the first 3D computer graphics sequences ever seen in a feature film.{{r|Smith1982}}

Shaded 3D graphics rendering in the 1970s and early 1980s was usually implemented on general-purpose computers, such as the [[PDP-10]] used by researchers at the University of Utah{{r|Phong1973}}{{r|Catmull1974}}. It was difficult to speed up using specialized hardware because it involves a [[Graphics pipeline|pipeline]] of complex steps, requiring data addressing, decision-making, and computation capabilities typically only provided by CPUs (although dedicated circuits for speeding up particular operations were proposed {{r|Phong1973}}). [[Supercomputer]]s or specially designed multi-CPU computers or [[computer cluster|clusters]] were sometimes used for ray tracing.{{r|n=IntroToRTCh6}} In 1981, [[James H. Clark]] and [[Marc Hannah]] designed the Geometry Engine, a [[Very-large-scale integration|VLSI]] chip for performing some of the steps of the 3D rasterization pipeline, and started the company [[Silicon Graphics]] (SGI) to commercialize this technology.{{r|Peddie2020}}{{r|Clark1980}}

[[Home computer]]s and [[Video game console|game consoles]] in the 1980s contained graphics [[coprocessor]]s that were capable of scrolling and filling areas of the display, and drawing [[Sprite (computer graphics)|sprites]] and lines, though they were not useful for rendering realistic images.{{r|Fox2024}}{{r|NESDevPPU}} Towards the end of the 1980s [[Graphics card|PC graphics cards]] and [[Arcade video game|arcade games]] with 3D rendering acceleration began to appear, and in the 1990s such technology became commonplace. Today, even low-power [[mobile processor]]s typically incorporate 3D graphics acceleration features.{{r|Peddie2020}}{{r|PowerVRAt25}}

=== GPUs ===
{{main|Graphics processing unit}}
The [[Graphics card|3D graphics accelerators]] of the 1990s evolved into modern GPUs. GPUs are general-purpose processors, like [[Central processing unit|CPUs]], but they are designed for tasks that can be broken into many small, similar, mostly independent sub-tasks (such as rendering individual pixels) and performed in [[Parallel computing|parallel]]. This means that a GPU can speed up any rendering algorithm that can be split into subtasks in this way, in contrast to 1990s 3D accelerators which were only designed to speed up specific rasterization algorithms and simple shading and lighting effects (although [[Kludge#Computer_science|tricks]] could be used to perform more general computations).{{r|n=AkenineMöller2018|loc=ch3}}{{r|Peercy2000}}

Due to their origins, GPUs typically still provide specialized hardware acceleration for some steps of a traditional 3D rasterization [[Graphics pipeline|pipeline]], including hidden surface removal using a [[Z-buffering|z-buffer]], and [[texture mapping]] with [[mipmap]]s, but these features are no longer always used.{{r|n=AkenineMöller2018|loc=ch3}} Recent GPUs have features to accelerate finding the intersections of rays with a [[bounding volume hierarchy]], to help speed up all variants of [[Ray tracing (graphics)|ray tracing]] and [[path tracing]],{{r|n=RayTracingGems_Forword_Stich}} as well as [[Neural network (machine learning)|neural network]] acceleration features sometimes useful for rendering.{{r|NvidiaDLSS}}

GPUs are usually integrated with [[GDDR SDRAM|high-bandwidth memory systems]] to support the read and write [[memory bandwidth|bandwidth]] requirements of high-resolution, real-time rendering, particularly when multiple passes are required to render a frame, however memory [[memory latency|latency]] may be higher than on a CPU, which can be a problem if the [[Analysis of parallel algorithms#Critical path|critical path]] in an algorithm involves many memory accesses. GPU design accepts high latency as inevitable (in part because a large number of [[Thread (computing)|threads]] are sharing the [[Bus_(computing)#Memory_bus|memory bus]]) and attempts to "hide" it by efficiently switching between threads, so a different thread can be performing computations while the first thread is waiting for a read or write to complete.{{r|n=AkenineMöller2018|loc=ch3}}{{r|Lam2021}}{{r|Gong2019}}

Rendering algorithms will run efficiently on a GPU only if they can be implemented using small groups of threads that perform mostly the same operations. As an example of code that meets this requirement: when rendering a small square of pixels in a simple [[Ray tracing (graphics)|ray-traced]] image, all threads will likely be intersecting rays with the same object and performing the same lighting computations. For performance and architectural reasons, GPUs run groups of around 16-64 threads called ''warps'' or ''wavefronts'' in [[Single instruction, multiple threads|lock-step]] (all threads in the group are executing the same instructions at the same time). If not all threads in the group need to run particular blocks of code (due to conditions) then some threads will be idle, or the results of their computations will be discarded, causing degraded performance.{{r|n=AkenineMöller2018|loc=ch3}}{{r|Gong2019}}

== Chronology of algorithms and techniques<span class="anchor" id="Chronology of concepts"></span> ==
The following is a rough timeline of frequently mentioned rendering techniques, including areas of current research. Note that even in cases where an idea was named in a specific paper, there were almost always multiple researchers or teams working in the same area (including earlier related work). When a method is first proposed it is often very inefficient, and it takes additional research and practical efforts to turn it into a useful technique.{{r|Glassner95|p=887}}

The list focuses on academic research and does not include hardware. (For more history see [[#External links]], as well as [[Computer graphics#History]] and [[Golden_age_of_arcade_video_games#Technology]].)

{{Div col|colwidth=20em}}
* 1760 - [[Lambertian reflectance|Lambertian reflectance model]]{{r|n=AkenineMöller2018|loc=5.2}}
* 1968 - [[Ray casting]]{{r|Appel1968}}
* 1968 - [[Warnock algorithm|Warnock hidden surface removal]]{{r|Warnock1968}}{{r|Warnock1969}}
* 1970 - [[Scanline rendering]]{{r|Bouknight1970}}{{r|Watkins1970}}
* 1971 - [[Gouraud shading]]<ref>{{Cite journal |last=Gouraud |first=H. |author-link=Henri Gouraud (computer scientist) |year=1971 |title=Continuous shading of curved surfaces |url=http://www.cs.uiowa.edu/~cwyman/classes/spring05-22C251/papers/ContinuousShadingOfCurvedSurfaces.pdf |url-status=dead |journal=IEEE Transactions on Computers |volume=20 |issue=6 |pages=623–629 |doi=10.1109/t-c.1971.223313 |s2cid=123827991 |archive-url=https://web.archive.org/web/20100702012343/http://www.cs.uiowa.edu/~cwyman/classes/spring05-22C251/papers/ContinuousShadingOfCurvedSurfaces.pdf |archive-date=2010-07-02}}</ref>
* 1973 - [[Phong shading]]<ref name="phong">{{Cite web |title=History &#124; School of Computing |url=https://www.cs.utah.edu/about/history/ |url-status=live |archive-url=https://web.archive.org/web/20131203035242/http://www.cs.utah.edu/dept/history/ |archive-date=2013-12-03 |access-date=2021-11-22 |language=en-US}}</ref><ref name=phong1975>{{Cite journal |last=Phong |first=B-T |author-link=Bui Tuong Phong |year=1975 |title=Illumination for computer generated pictures |url=http://jesper.kalliope.org/blog/library/p311-phong.pdf |url-status=dead |journal=Communications of the ACM |volume=18 |issue=6 |pages=311–316 |citeseerx=10.1.1.330.4718 |doi=10.1145/360825.360839 |s2cid=1439868 |archive-url=https://web.archive.org/web/20120327165141/http://jesper.kalliope.org/blog/library/p311-phong.pdf |archive-date=2012-03-27}}</ref>
* 1973 - [[Phong reflection model|Phong reflectance model]]<ref name=phong/><ref name=phong1975/>
* 1974 - [[Texture mapping]]{{r|Catmull1974}}
* 1974 - [[Z-buffering]]{{r|Catmull1974}}
* 1976 - [[Environment mapping]]<ref>{{Cite journal |last1=Blinn |first1=J.F. |author-link=James F. Blinn |last2=Newell |first2=M.E. |author-link2=M. E. Newell |year=1976 |title=Texture and reflection in computer generated images |journal=Communications of the ACM |volume=19 |issue=10 |pages=542–546 |citeseerx=10.1.1.87.8903 |doi=10.1145/360349.360353 |s2cid=408793}}</ref>
* 1977 - [[Blinn-Phong shading model|Blinn-Phong reflectance model]]<ref>{{Cite journal |last=Blinn |first=James F. |date=20 July 1977 |title=Models of light reflection for computer synthesized pictures |journal=ACM SIGGRAPH Computer Graphics |volume=11 |issue=2 |pages=192–198 |doi=10.1145/965141.563893 |via=dl.acm.org |doi-access=free}}</ref>
* 1977 - [[Shadow volume]]s<ref>{{Cite conference |last=Crow |first=F.C. |author-link=Franklin C. Crow |year=1977 |title=Shadow algorithms for computer graphics |url=http://design.osu.edu/carlson/history/PDFs/crow-shadows.pdf |volume=11 |issue=2 |pages=242–248 |archive-url=https://web.archive.org/web/20120113074712/https://design.osu.edu/carlson/history/PDFs/crow-shadows.pdf |archive-date=2012-01-13 |access-date=2011-07-15 |book-title=Computer Graphics (Proceedings of SIGGRAPH 1977) |url-status=dead}}</ref>
* 1978 - [[Shadow mapping]]<ref>{{Cite conference |last=Williams |first=L. |author-link=Lance Williams (graphics researcher) |year=1978 |title=Casting curved shadows on curved surfaces |volume=12 |issue=3 |pages=270–274 |citeseerx=10.1.1.134.8225 |book-title=Computer Graphics (Proceedings of SIGGRAPH 1978)}}</ref>
* 1978 - [[Bump mapping]]<ref>{{Cite conference |last=Blinn |first=J.F. |author-link=James F. Blinn |year=1978 |title=Simulation of wrinkled surfaces |url=http://research.microsoft.com/pubs/73939/p286-blinn.pdf |conference=Computer Graphics (Proceedings of SIGGRAPH 1978) |volume=12 |issue=3 |pages=286–292 |archive-url=https://web.archive.org/web/20120121143525/http://research.microsoft.com/pubs/73939/p286-blinn.pdf |archive-date=2012-01-21 |url-status=live}}</ref>
* 1980 - [[BSP trees]]<ref>{{Cite conference |last1=Fuchs |first1=H. |author-link=Henry Fuchs |last2=Kedem |first2=Z.M. |author-link2=Zvi M. Kedem |last3=Naylor |first3=B.F. |author-link3=Bruce F. Naylor |year=1980 |title=On visible surface generation by a priori tree structures |conference=Computer Graphics (Proceedings of SIGGRAPH 1980) |volume=14 |issue=3 |pages=124–133 |citeseerx=10.1.1.112.4406}}</ref>
* 1980 - [[Ray tracing (graphics)|Ray tracing]]<ref>{{Cite journal |last=Whitted |first=T. |author-link=Turner Whitted |year=1980 |title=An improved illumination model for shaded display |journal=Communications of the ACM |volume=23 |issue=6 |pages=343–349 |citeseerx=10.1.1.114.7629 |doi=10.1145/358876.358882 |s2cid=9524504}}</ref>
* 1981 - [[Specular_highlight#Cook–Torrance_model|Cook-Torrance reflectance model]]<ref>{{Cite conference |last1=Cook |first1=R.L. |author-link=Robert L. Cook |last2=Torrance |first2=K.E. |author-link2=Kenneth E. Torrance |year=1981 |title=A reflectance model for computer graphics |conference=Computer Graphics (Proceedings of SIGGRAPH 1981) |volume=15 |issue=3 |pages=307–316 |citeseerx=10.1.1.88.7796}}</ref>
* 1983 - [[Mipmap|MIP maps]]<ref>{{Cite conference |last=Williams |first=L. |author-link=Lance Williams (graphics researcher) |year=1983 |title=Pyramidal parametrics |conference=Computer Graphics (Proceedings of SIGGRAPH 1983) |volume=17 |issue=3 |pages=1–11 |citeseerx=10.1.1.163.6298}}</ref>
* 1984 - [[Octree]] ray tracing<ref>{{Cite journal |last=Glassner |first=A.S. |author-link=Andrew Glassner |year=1984 |title=Space subdivision for fast ray tracing |journal=IEEE Computer Graphics & Applications |volume=4 |issue=10 |pages=15–22 |doi=10.1109/mcg.1984.6429331 |s2cid=16965964}}</ref>
* 1984 - [[Alpha compositing]]<ref>{{Cite conference |last1=Porter |first1=T. |last2=Duff |first2=T. |author-link2=Tom Duff |year=1984 |title=Compositing digital images |url=http://keithp.com/~keithp/porterduff/p253-porter.pdf |conference=Computer Graphics (Proceedings of SIGGRAPH 1984) |volume=18 |issue=3 |pages=253–259 |archive-url=https://web.archive.org/web/20150216062332/http://keithp.com/~keithp/porterduff/p253-porter.pdf |archive-date=2015-02-16 |url-status=live}}</ref>
* 1984 - [[Distributed ray tracing]]<ref>{{Cite conference |last1=Cook |first1=R.L. |author-link=Robert L. Cook |last2=Porter |first2=T. |last3=Carpenter |first3=L. |author-link3=Loren Carpenter |year=1984 |title=Distributed ray tracing |url=http://www.cs.rutgers.edu/~nealen/teaching/cs428_fall09/readings/cook84.pdf |conference=Computer Graphics (Proceedings of SIGGRAPH 1984) |volume=18 |issue=3 |pages=137–145}}{{dead link|date=April 2018 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>
* 1984 - [[Radiosity (computer graphics)|Radiosity]]<ref>{{Cite conference |last1=Goral |first1=C. |author-link=Cindy M. Goral |last2=Torrance |first2=K.E. |author-link2=Kenneth E. Torrance |last3=Greenberg |first3=D.P. |author-link3=Donald P. Greenberg |last4=Battaile |first4=B. |author-link4=Bennett Battaile |year=1984 |title=Modeling the interaction of light between diffuse surfaces |conference=Computer Graphics (Proceedings of SIGGRAPH 1984) |volume=18 |issue=3 |pages=213–222 |citeseerx=10.1.1.112.356}}</ref>
* 1984 - [[A-buffer]]{{r|Carpenter1984}}
* 1985 - [[Hemicube (computer graphics)|Hemicube]] radiosity<ref>{{Cite conference |last1=Cohen |first1=M.F. |author-link=Michael F. Cohen |last2=Greenberg |first2=D.P. |author-link2=Donald P. Greenberg |year=1985 |title=The hemi-cube: a radiosity solution for complex environments |url=http://www.arnetminer.org/dev.do?m=downloadpdf&url=http://arnetminer.org/pdf/PDFFiles2/--g---g-Index1255026826706/The%20hemi-cube%20%20a%20radiosity%20solution%20for%20complex%20environments1255058011060.pdf |conference=Computer Graphics (Proceedings of SIGGRAPH 1985) |volume=19 |issue=3 |pages=31–40 |doi=10.1145/325165.325171 |archive-url=https://web.archive.org/web/20140424063155/http://arnetminer.org/dev.do?m=downloadpdf&url=http%3A%2F%2Farnetminer.org%2Fpdf%2FPDFFiles2%2F--g---g-Index1255026826706%2FThe%2520hemi-cube%2520%2520a%2520radiosity%2520solution%2520for%2520complex%2520environments1255058011060.pdf |archive-date=2014-04-24 |access-date=2020-03-25 |url-status=dead}}</ref>
* 1986 - Light source tracing<ref>{{Cite conference |last=Arvo |first=J. |author-link=James Arvo |year=1986 |title=Backward ray tracing |conference=SIGGRAPH 1986 Developments in Ray Tracing course notes |citeseerx=10.1.1.31.581}}</ref>
* 1986 - [[Rendering equation]]{{r|n=Kajiya1986}}
* 1986 - [[Path tracing]]{{r|n=Kajiya1986}}
* 1987 - [[Reyes rendering]]{{r|Cook1987}}
* 1991 - [[Xiaolin Wu's line algorithm|Xiaolin Wu line anti-aliasing]]<ref>{{Cite book |last=Wu, Xiaolin |title=An efficient antialiasing technique |journal=ACM SIGGRAPH Computer Graphics |date=July 1991  |url=http://portal.acm.org/citation.cfm?id=122734 |volume=25 |issue=4 |pages=143–152 |doi=10.1145/127719.122734 |isbn=978-0-89791-436-9}}</ref><ref>{{Cite book |last=Wu, Xiaolin |title=Graphics Gems II |publisher=Morgan Kaufmann |year=1991 |isbn=978-0-12-064480-3 |editor-last=James Arvo |location=San Francisco |pages=446–450 |chapter=Fast Anti-Aliased Circle Generation}}</ref>
* 1991 - Hierarchical radiosity<ref>{{Cite conference |last1=Hanrahan |first1=P. |author-link=Pat Hanrahan |last2=Salzman |first2=D. |author-link2=David Salzman |last3=Aupperle |first3=L. |author-link3=Larry Aupperle |year=1991 |title=A rapid hierarchical radiosity algorithm |conference=Computer Graphics (Proceedings of SIGGRAPH 1991) |volume=25 |issue=4 |pages=197–206 |citeseerx=10.1.1.93.5694}}</ref>
* 1993 - [[Oren–Nayar reflectance model|Oren–Nayar reflectance model]]<ref name="oren-nayar">M. Oren and S.K. Nayar, "[http://www1.cs.columbia.edu/CAVE/publications/pdfs/Oren_SIGGRAPH94.pdf Generalization of Lambert's Reflectance Model] {{webarchive|url=https://web.archive.org/web/20100215153120/http://www1.cs.columbia.edu/CAVE/publications/pdfs/Oren_SIGGRAPH94.pdf |date=2010-02-15 }}". SIGGRAPH. pp.239-246, Jul, 1994</ref>
* 1993 - [[Tone mapping]]<ref>{{Cite journal |last1=Tumblin |first1=J. |author-link=Jack Tumblin |last2=Rushmeier |first2=H.E. |author-link2=Holly Rushmeier |year=1993 |title=Tone reproduction for realistic computer generated images |url=http://smartech.gatech.edu/bitstream/handle/1853/3686/92-31.pdf?sequence=1 |url-status=live |journal=IEEE Computer Graphics & Applications |volume=13 |issue=6 |pages=42–48 |doi=10.1109/38.252554 |s2cid=6459836 |archive-url=https://web.archive.org/web/20111208231341/http://smartech.gatech.edu/bitstream/handle/1853/3686/92-31.pdf?sequence=1 |archive-date=2011-12-08}}</ref>
* 1993 - [[Subsurface scattering]]<ref>{{Cite conference |last1=Hanrahan |first1=P. |author-link=Pat Hanrahan |last2=Krueger |first2=W. |author-link2=Wolfgang Krueger |year=1993 |title=Reflection from layered surfaces due to subsurface scattering |conference=Computer Graphics (Proceedings of SIGGRAPH 1993) |volume=27 |pages=165–174 |citeseerx=10.1.1.57.9761}}</ref>
* 1993 - [[Path_tracing#Bidirectional_path_tracing|Bidirectional path tracing]] (Lafortune & Willems formulation)<ref>{{Cite conference |last1=Lafortune |first1=Eric |last2=Willems |first2=Yves |date=December 1993 |title=Bi-directional path tracing |url=https://www.cs.princeton.edu/courses/archive/fall03/cs526/papers/lafortune93.pdf |pages=145–153 |access-date=2 September 2024 |book-title=Proceedings of Third International Conference on Computational Graphics and Visualization Techniques (CompuGraphics) |archive-date=21 May 2022 |archive-url=https://web.archive.org/web/20220521174659/https://www.cs.princeton.edu/courses/archive/fall03/cs526/papers/lafortune93.pdf |url-status=live }}</ref>
* 1994 - [[Ambient occlusion]]<ref>{{Cite book |last=Miller |first=Gavin |title=Proceedings of the 21st annual conference on Computer graphics and interactive techniques - SIGGRAPH '94 |date=24 July 1994 |publisher=ACM |isbn=978-0897916677 |pages=319–326 |chapter=Efficient algorithms for local and global accessibility shading |doi=10.1145/192161.192244 |access-date=7 May 2018 |chapter-url=http://dl.acm.org/citation.cfm?id=192161.192244 |archive-url=https://web.archive.org/web/20211122155805/https://dl.acm.org/doi/10.1145/192161.192244 |archive-date=22 November 2021 |url-status=live |via=dl.acm.org |s2cid=15271113}}</ref>
* 1995 - [[Photon mapping]]<ref>{{Cite journal |last1=Jensen |first1=H.W. |author-link=Henrik Wann Jensen |last2=Christensen |first2=N.J. |author-link2=Niels Jørgen Christensen |year=1995 |title=Photon maps in bidirectional monte carlo ray tracing of complex objects |journal=Computers & Graphics |volume=19 |issue=2 |pages=215–224 |citeseerx=10.1.1.97.2724 |doi=10.1016/0097-8493(94)00145-o}}</ref>
* 1995 - Multiple importance sampling<ref>{{Cite conference |last1=Veach |first1=Eric |last2=Guibas |first2=Leonidas J. |date=15 September 1995 |title=Optimally combining sampling techniques for Monte Carlo rendering |url=https://dl.acm.org/doi/10.1145/218380.218498 |pages=419–428 |doi=10.1145/218380.218498 |access-date=2 September 2024 |book-title=SIGGRAPH95: 22nd International ACM Conference on Computer Graphics and Interactive Techniques |archive-date=26 July 2024 |archive-url=https://web.archive.org/web/20240726032649/https://dl.acm.org/doi/10.1145/218380.218498 |url-status=live }}</ref>
* 1997 - [[Path_tracing#Bidirectional_path_tracing|Bidirectional path tracing]] (Veach & Guibas formulation)<ref>{{Cite conference |last1=Veach |first1=E. |author-link=Eric Veach |last2=Guibas |first2=L. |author-link2=Leonidas J. Guibas |year=1997 |title=Metropolis light transport |conference=Computer Graphics (Proceedings of SIGGRAPH 1997) |volume=16 |pages=65–76 |citeseerx=10.1.1.88.944}}</ref>
* 1997 - [[Metropolis light transport]]<ref>{{Cite conference |last1=Veach |first1=E. |author-link=Eric Veach |last2=Guibas |first2=L. |author-link2=Leonidas J. Guibas |year=1997 |title=Metropolis light transport |conference=Computer Graphics (Proceedings of SIGGRAPH 1997) |volume=16 |pages=65–76 |citeseerx=10.1.1.88.944}}</ref>
* 1997 - Instant Radiosity<ref>{{Cite conference |last=Keller |first=A. |author-link=Alex Keller |year=1997 |title=Instant Radiosity |conference=Computer Graphics (Proceedings of SIGGRAPH 1997) |volume=24 |pages=49–56 |citeseerx=10.1.1.15.240}}</ref>
* 2002 - [[Precomputed Radiance Transfer]]<ref>{{Cite conference |last1=Sloan |first1=P. |author-link=Peter Pike Sloan |last2=Kautz |first2=J. |author-link2=Jan Kautz |last3=Snyder |first3=J. |author-link3=John Snyder (computer scientist) |year=2002 |title=Precomputed Radiance Transfer for Real-Time Rendering in Dynamic, Low Frequency Lighting Environments |url=http://www.mpi-inf.mpg.de/~jnkautz/projects/prt/prtSIG02.pdf |conference=Computer Graphics (Proceedings of SIGGRAPH 2002) |volume=29 |pages=527–536 |archive-url=https://web.archive.org/web/20110724151631/http://www.mpi-inf.mpg.de/~jnkautz/projects/prt/prtSIG02.pdf |archive-date=2011-07-24 |url-status=dead}}</ref>
* 2003 - [[Mitsubishi Electric Research Laboratories|MERL]] [[Bidirectional reflectance distribution function|BRDF]] database<ref>{{Cite journal |last1=Matusik |first1=W. |last2=Pfister |first2=H. |last3=Brand |first3=M. |last4=McMillan |first4=L. |date=July 2003 |title=A Data-Driven Reflectance Model |journal=ACM Transactions on Graphics (TOG)|volume=22 |issue=3 |pages=759–769 |doi=10.1145/882262.882343|url=https://www.merl.com/publications/TR2003-83 |access-date=23 November 2024}}</ref>
* 2014 - [[Michael J. Black#Differentiable_rendering|Differentiable rendering]]<ref>{{Cite conference |last1=Loper |first1=Matthew M |last2=Black |first2=Michael J |date=6 September 2014 |title=OpenDR: An approximate differentiable renderer |url=http://files.is.tue.mpg.de/black/papers/OpenDR.pdf |location=Zurich, Switzerland |publisher=Springer International Publishing |volume=8695 |pages=154–169 |doi=10.1007/978-3-319-10584-0_11 |access-date=2 September 2024 |book-title=Computer Vision - ECCV 2014 |archive-date=24 June 2024 |archive-url=https://web.archive.org/web/20240624151721/https://files.is.tue.mpg.de/black/papers/OpenDR.pdf |url-status=live }}</ref>
* 2017 - Path guiding (using adaptive SD-tree)<ref name="Mueller2017">{{cite journal | title=Practical Path Guiding for Efficient Light-Transport Simulation | last1=Müller | first1=Thomas | last2=Gross | first2=Markus | last3=Novák | first3=Jan | journal=Computer Graphics Forum (Proceedings of EGSR) | volume=36 | issue=4 | date=June 2017 | pages=91–100 | publisher=The Eurographs Association & John Wiley & Sons, Ltd. | doi=10.1111/cgf.13227 | url=https://jannovak.info/publications/PathGuide/index.html | access-date=4 September 2024}}</ref>
* 2020 - Spatiotemporal [[Reservoir sampling|reservoir]] resampling (ReSTIR)<ref>{{Cite journal |last1=Bitterli |first1=Benedikt |last2=Wyman |first2=Chris |last3=Pharr |first3=Matt |last4=Shirley |first4=Peter |last5=Lefohn |first5=Aaron |last6=Jarosz |first6=Wojciech |date=July 2020 |title=Spatiotemporal reservoir resampling for real-time ray tracing with dynamic direct lighting |url=https://cs.dartmouth.edu/~wjarosz/publications/bitterli20spatiotemporal.html |journal= ACM Transactions on Graphics|volume=39 |issue=4 |doi=10.1145/3386569.3392481 |access-date=2 September 2024 |archive-date=1 March 2024 |archive-url=https://web.archive.org/web/20240301064934/https://cs.dartmouth.edu/~wjarosz/publications/bitterli20spatiotemporal.html |url-status=live }}</ref>
* 2020 - [[Neural radiance field]]s{{r|n=Mildenhall2020}}
* 2023 - 3D [[Gaussian splatting]]{{r|n=Kerbl2023}}
{{Div col end}}

== See also ==
{{Div col}}
* {{annotated link|2D computer graphics}}
* {{annotated link|3D computer graphics}}
* {{annotated link|3D rendering}}
* {{annotated link|Artistic rendering}}
* {{annotated link|Architectural rendering}}
* {{annotated link|Chromatic aberration}}
* {{annotated link|Displacement mapping}}
* {{annotated link|Font rasterization}}
* {{annotated link|Global illumination}}
* {{annotated link|Graphics pipeline}}
* {{annotated link|Heightmap}}
* {{annotated link|High-dynamic-range rendering}}
* {{annotated link|Image-based modeling and rendering}}
* {{annotated link|List of 3D rendering software}}
* {{annotated link|Motion blur}}
* {{annotated link|Non-photorealistic rendering}}
* {{annotated link|Normal mapping}}
* {{annotated link|Painter's algorithm}}
* [[Per-pixel lighting]]
* {{annotated link|Physically based rendering}}
* {{annotated link|Pre-rendering}}
* {{annotated link|Raster image processor}}
* {{annotated link|Radiosity (computer graphics)|Radiosity}}
* {{annotated link|Ray tracing (graphics)|Ray tracing}}
* {{annotated link|Real-time computer graphics}}
* {{annotated link|Reyes rendering|Reyes}}
* {{annotated link|Scanline rendering|Scanline rendering/Scanline algorithm}}
* {{annotated link|Software rendering}}
* {{annotated link|Sprite (computer graphics)}}
* {{annotated link|Unbiased rendering}}
* {{annotated link|Vector graphics}}
* {{annotated link|VirtualGL}}
* {{annotated link|Virtual model}}
* {{annotated link|Virtual studio}}
* {{annotated link|Volume rendering}}
* {{annotated link|Z-buffering|Z-buffer algorithms}}
{{Div col end}}

== References ==
{{Reflist|30em|refs=

<ref name="AkenineMöller2018">{{cite book
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}}</ref>

<ref name=Appel1968>{{Cite conference
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}}</ref>

<ref name=Arvo1986>{{Cite conference
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}}</ref>

<ref name = "Bekaert1999">{{cite thesis
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<ref name="BlenderCyclesIntro">{{cite web
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<ref name="BlenderCyclesReducingNoise">{{cite web
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<ref name="BlenderSettingsDenoising">{{cite web
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<ref name="BlenderSettingsLightProbes">{{cite web
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<ref name=Bouknight1970>{{Cite journal
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<ref name="Bridson2015">{{cite book
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<ref name="Brinkmann2008">{{cite book
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<ref name=Carpenter1984>{{cite journal
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<ref name=Catmull1974>{{Cite thesis
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<ref name="Cohen1993">{{cite book
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<ref name=Cook1987>{{cite journal
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    | access-date=19 September 2024
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    | archive-date=2011-07-15
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<ref name="Dunlop2014">{{cite book
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<ref name="Dutré2003">{{Citation
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<ref name="Dutré2015">{{cite book
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<ref name=EandS1979>{{Citation
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<ref name="Fox2024">{{cite book
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<ref name="Glassner95">{{cite book
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<ref name=Gong2019>{{cite journal
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<ref name=Goral1984>{{cite book
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<ref name=Howard1995>{{citation
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<ref name="Hughes2014">{{cite book
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<ref name="IntroToRTCh1">{{cite book
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    | url = https://www.realtimerendering.com/raytracing/An-Introduction-to-Ray-Tracing-The-Morgan-Kaufmann-Series-in-Computer-Graphics-.pdf
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    | url-status = live
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<ref name="IntroToRTCh2">{{cite book
    | last1 = Hanrahan
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    | editor-last = Glassner
    | editor-first = Andrew S.
    | editor-link = Andrew Glassner
    | date = April 11, 2019
    | orig-date = 1989
    | title = An Introduction to Ray Tracing
    | publisher = ACADEMIC PRESS
    | isbn = 978-0-12-286160-4
    | url = https://www.realtimerendering.com/raytracing/An-Introduction-to-Ray-Tracing-The-Morgan-Kaufmann-Series-in-Computer-Graphics-.pdf
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<ref name="IntroToRTCh5">{{cite book
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    | title = An Introduction to Ray Tracing
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<ref name="IntroToRTCh6">{{cite book
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<ref name="Kajiya1986">{{cite journal
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    | title = The rendering equation
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    | access-date = 27 January 2024
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<ref name="Kerbl2023">{{cite journal
 |title        = 3D Gaussian Splatting for Real-Time Radiance Field Rendering
 |last1        = Kerbl
 |first1       = Bernhard
 |last2        = Kopanas
 |first2       = Georgios
 |last3        = Leimkühler
 |first3       = Thomas
 |last4        = Drettakis
 |first4       = George
 |journal      = ACM Transactions on Graphics
 |volume       = 42
 |issue        = 4
 |date         = July 2023
 |pages        = 1–14
 |doi          = 10.1145/3592433
 |url          = https://repo-sam.inria.fr/fungraph/3d-gaussian-splatting/
 |access-date  = 31 August 2024
 |archive-date = 22 August 2024
 |archive-url  = https://web.archive.org/web/20240822130514/https://repo-sam.inria.fr/fungraph/3d-gaussian-splatting/
 |url-status   = live
|arxiv= 2308.04079
 }}</ref>

<ref name="KhronosRTInVukan">{{cite web 
    | url=https://www.khronos.org/blog/ray-tracing-in-vulkan
    | title= Khronos Blog: Ray Tracing In Vulkan
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    | website = www.khronos.org
    | access-date = 27 January 2024
}}</ref>

<ref name="Kulla2017">{{Citation
    | last = Kulla
    | first = Christopher
    | title = Arnold at Sony Pictures Imageworks: From Monster House to Smurfs: The Lost Village (course slides)
    | series = SIGGRAPH
    | place = Los Angeles
    | date = 30 July 2017
    | url = https://jo.dreggn.org/path-tracing-in-production/2017/arnold-sony-pictures.pdf
}}</ref>

<ref name="Lam2021">{{cite web
    | last=Lam
    | first=Chester
    | url=https://chipsandcheese.com/2021/04/16/measuring-gpu-memory-latency/
    | title=Measuring GPU Memory Latency
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<ref name="Marschner2022">{{cite book
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	| title = Fundamentals of Computer Graphics
    | edition = 5th
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}}</ref>

<ref name="MDN_SVG">{{cite web
    | url = https://developer.mozilla.org/en-US/docs/Web/SVG
    | title = SVG: Scalable Vector Graphics
    | date = 7 August 2024
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<ref name="Mildenhall2020">{{cite web 
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<ref name="Museth2013">{{cite journal
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    | url = https://www.museth.org/Ken/Publications_files/Museth_TOG13.pdf
    | access-date = 31 August 2024
    | archive-date = 15 April 2024
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<ref name="NagoyaCityScienceMuseum">{{cite web
    | url=http://www.ncsm.city.nagoya.jp/cgi-bin/en/exhibition_guide/exhibit.cgi?id=A536
    | title=Nagoya City Science Museum - Exhibition Guide - Digistar II
    | publisher=Nagoya City Science Museum
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<ref name="NESDevPPU">{{cite web
    | url=https://www.nesdev.org/wiki/PPU
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    }}</ref>

<ref name="NvidiaDLSS">{{cite web
    | url=https://www.nvidia.com/en-us/geforce/technologies/dlss/
    | title=NVIDIA DLSS 3
    | publisher=NVIDIA Corporation
    | website=nvidia.com
    | access-date= 13 September 2024
    }}</ref>

<ref name="NvidiaOptiXDenoiser">{{cite web
    | url= https://developer.nvidia.com/optix-denoiser
    | title= NVIDIA OptiX™ AI-Accelerated Denoiser
    | publisher= NVIDIA Corporation
    | website= developer.nvidia.com
    | access-date= 27 January 2024
    | archive-date= 18 January 2024
    | archive-url= https://web.archive.org/web/20240118071717/https://developer.nvidia.com/optix-denoiser
    | url-status= live
    }}</ref>

<ref name="OpenImageDenoise">{{cite web
    | url= https://www.openimagedenoise.org/
    | title= Intel® Open Image Denoise: High-Performance Denoising Library for Ray Tracing
    | publisher= Intel Corporation
    | website= www.openimagedenoise.org
    | access-date= 27 January 2024
    | archive-date= 6 January 2024
    | archive-url= https://web.archive.org/web/20240106131722/https://www.openimagedenoise.org/
    | url-status= live
    }}</ref>

<ref name="OpenVDBAbout">{{cite web
    | url = https://www.openvdb.org/about/
    | title = About OpenVDB
    | publisher = Academy Software Foundation
    | website = www.openvdb.org
    | access-date = 31 August 2024
    | archive-date = 3 September 2024
    | archive-url = https://web.archive.org/web/20240903072553/https://www.openvdb.org/about/
    | url-status = live
    }}</ref>

<ref name = "Otte2015">{{cite thesis
    | last = Otte
    | first = Vilém
    | title = Bi-directional Path Tracing on GPU
    | year = 2015
    | degree = Master
    | publisher = Masaryk University, Brno
    | url = https://is.muni.cz/th/yidjt/bidirectional_path_tracing_on_gpu_thesis.pdf
    }}</ref>

<ref name="pbrt4FF">{{cite web 
	| last1 = Pharr
	| first1 = Matt
	| last2 = Jakob
	| first2 = Wenzel
	| last3 = Humphreys
	| first3 = Greg
	| year = 2023
    | url = https://pbrt.org/fileformat-v4
    | title = pbrt-v4 Input File Format
    | access-date = 31 August 2024
}}</ref>

<ref name="pbrt4UG">{{cite web
	| last1 = Pharr
	| first1 = Matt
	| last2 = Jakob
	| first2 = Wenzel
	| last3 = Humphreys
	| first3 = Greg
	| year = 2023
	| url = https://pbrt.org/users-guide-v4
	| title = pbrt-v4 User's Guide
	| access-date = 31 August 2024
	| archive-date = 3 September 2024
	| archive-url = https://web.archive.org/web/20240903072555/https://pbrt.org/users-guide-v4
	| url-status = live
	}}</ref>

<ref name="Peddie2020">{{cite web
    | last=Peddie
    | first=Jon
    | date=24 September 2020
    | url=https://www.computer.org/publications/tech-news/chasing-pixels/geometry-engine
    | title=Famous Graphics Chips: Geometry Engine
    | website=www.computer.org
    | publisher=Institute of Electrical and Electronics Engineers (IEEE)
    | access-date= 13 September 2024
    }}</ref>
    
<ref name=Peercy2000>{{cite book
    | last1=Peercy   | first1=Mark S.
    | last2=Olano    | first2=Marc
    | last3=Airey    | first3=John
    | last4=Ungar    | first4=P. Jeffrey
    | title=Proceedings of the 27th annual conference on Computer graphics and interactive techniques - SIGGRAPH '00
 | chapter=Interactive multi-pass programmable shading
 | year=2000
    | page=425-432
    | chapter-url=https://cseweb.ucsd.edu/~ravir/6160-fall04/papers/p425-peercy.pdf
    | access-date= 13 September 2024
    | doi=10.1145/344779.344976
    | isbn=1-58113-208-5
 }}</ref>
    
<ref name="Pharr2023_1_6">{{cite book
	| last1 = Pharr
	| first1 = Matt
	| last2 = Jakob
	| first2 = Wenzel
	| last3 = Humphreys
	| first3 = Greg
	| author-link1 = Matt Pharr
	| date = March 28, 2023
	| title = Physically Based Rendering: From Theory to Implementation
	| url = https://pbr-book.org/4ed/contents
	| location = Cambridge, Massachusetts
	| publisher = The MIT Press
	| isbn = 978-0262048026
	| edition = 4th
	| section = 1.6
	| section-url = https://pbr-book.org/4ed/Introduction/A_Brief_History_of_Physically_Based_Rendering
	| access-date = January 27, 2024
	| archive-date = January 27, 2024
	| archive-url = https://web.archive.org/web/20240127220804/https://pbr-book.org/4ed/contents
	| url-status = live
	}}</ref>
 
<ref name="Pharr2023_5fr">{{cite book
	| last1 = Pharr
	| first1 = Matt
	| last2 = Jakob
	| first2 = Wenzel
	| last3 = Humphreys
	| first3 = Greg
	| author-link1 = Matt Pharr
	| date = March 28, 2023
	| title = Physically Based Rendering: From Theory to Implementation
	| url = https://pbr-book.org/4ed/contents
	| location = Cambridge, Massachusetts
	| publisher = The MIT Press
	| isbn = 978-0262048026
	| edition = 4th
	| section = 5. Further Reading: Denoising
	| section-url = https://pbr-book.org/4ed/Cameras_and_Film/Further_Reading#x7-Denoising
	| access-date = January 27, 2024
	| archive-date = January 27, 2024
	| archive-url = https://web.archive.org/web/20240127220804/https://pbr-book.org/4ed/contents
	| url-status = live
	}}</ref>
 
<ref name="Pharr2023_13fr">{{cite book
	| last1 = Pharr
	| first1 = Matt
	| last2 = Jakob
	| first2 = Wenzel
	| last3 = Humphreys
	| first3 = Greg
	| author-link1 = Matt Pharr
	| date = March 28, 2023
	| title = Physically Based Rendering: From Theory to Implementation
	| url = https://pbr-book.org/4ed/contents
	| location = Cambridge, Massachusetts
	| publisher = The MIT Press
	| isbn = 978-0262048026
	| edition = 4th
	| section = 13. Further Reading: Path Guiding
	| section-url = https://www.pbr-book.org/4ed/Light_Transport_I_Surface_Reflection/Further_Reading#x1-PathGuiding
	| access-date = 8 September 2024
	}}</ref>
    
<ref name="Pharr2023_15">{{cite book
	| last1 = Pharr
	| first1 = Matt
	| last2 = Jakob
	| first2 = Wenzel
	| last3 = Humphreys
	| first3 = Greg
	| author-link1 = Matt Pharr
	| date = March 28, 2023
	| title = Physically Based Rendering: From Theory to Implementation
	| url = https://pbr-book.org/4ed/contents
	| location = Cambridge, Massachusetts
	| publisher = The MIT Press
	| isbn = 978-0262048026
	| edition = 4th
	| chapter = 15. Wavefront Rendering on GPUs
	| section-url = https://pbr-book.org/4ed/Wavefront_Rendering_on_GPUs
	| access-date = January 27, 2024
	| archive-date = January 27, 2024
	| archive-url = https://web.archive.org/web/20240127220804/https://pbr-book.org/4ed/contents
	| url-status = live
	}}</ref>

<ref name="Phong1973">{{cite thesis
    | last = Bùi
    | first = Tường-Phong
    | title = Illumination for Computer-Generated Images
    | year = 1973
    | degree = PhD
    | publisher = University of Utah
    | url = https://apps.dtic.mil/sti/tr/pdf/ADA008786.pdf
    }}</ref>
    
<ref name="PowerVRAt25">{{cite web
    | last=Harold
    | first=David
    | date=11 August 2017
    | url=https://blog.imaginationtech.com/powervr-at-25-the-story-of-a-graphics-revolution/
    | title=PowerVR at 25: The story of a graphics revolution
    | publisher=Imagination Technologies Limited
    | website=blog.imaginationtech.com
    | access-date= 13 September 2024
    }}</ref>
  
<ref name="PSRef">{{cite book
	| author = Adobe Systems Incorporated
    | year = 1990
	| title = PostScript Language Reference Manual
    | edition = 2nd
	| publisher = Addison-Wesley Publishing Company
	| isbn = 0-201-18127-4
}}</ref>

<ref name="Raghavachary2005">{{cite book
	| last = Raghavachary
	| first = Saty
    | date = 2005
	| title = Rendering for Beginners
	| publisher = Focal Press
	| isbn = 0-240-51935-3
}}</ref>

<ref name="RasterTragedy">{{cite web
    | last = Stamm
    | first = Beat
    | url = http://rastertragedy.com/
    | title = The Raster Tragedy at Low-Resolution Revisited: Opportunities and Challenges beyond "Delta-Hinting"
    | website = rastertragedy.com
    | date = 21 June 2018
    | access-date = 19 September 2024
    }}</ref>

<ref name="RayTracingGems_Forword_Stich">{{cite book
	| last1 = Stich
	| first1 = Martin
	| editor-first1 = Eric
	| editor-first2 = Tomas
	| editor-last1 = Haines
	| editor-last2 = Akenine-Möller
	| date = February 25, 2019
	| title = Ray Tracing Gems: High-Quality and Real-Time Rendering with DXR and Other APIs
	| publisher = Apress
	| location = Berkeley, CA
	| isbn = 978-1-4842-4427-2
	| chapter = Foreword
	| doi = 10.1007/978-1-4842-4427-2
	| s2cid = 71144394
	| url = https://link.springer.com/book/10.1007/978-1-4842-4427-2
	| access-date = 13 September 2024
	}}</ref>
    
<ref name="RayTracingGems_1">{{cite book
	| last1 = Haines
	| first1 = Eric
	| last2 = Shirley
	| first2 = Peter
	| date = February 25, 2019
	| title = Ray Tracing Gems: High-Quality and Real-Time Rendering with DXR and Other APIs
	| publisher = Apress
	| location = Berkeley, CA
	| isbn = 978-1-4842-4427-2
	| chapter = 1. Ray Tracing Terminology
	| doi = 10.1007/978-1-4842-4427-2
	| s2cid = 71144394
	| url = https://link.springer.com/book/10.1007/978-1-4842-4427-2
	| access-date = January 27, 2024
	| archive-date = January 27, 2024
	| archive-url = https://web.archive.org/web/20240127220804/https://link.springer.com/book/10.1007/978-1-4842-4427-2
	| url-status = live
	}}</ref>

<ref name="RayTracingGems_13">{{cite book
	| last1 = Boksansky
	| first1 = Jakub
	| last2 = Wimmer
	| first2 = Michael
	| last3 = Bittner
	| first3 = Jiri
	| date = February 25, 2019
	| title = Ray Tracing Gems: High-Quality and Real-Time Rendering with DXR and Other APIs
	| publisher = Apress
	| location = Berkeley, CA
	| isbn = 978-1-4842-4427-2
	| chapter = 13. Ray Traced Shadows: Maintaining Real-Time Frame Rates
	| doi = 10.1007/978-1-4842-4427-2
	| s2cid = 71144394
	| url = https://link.springer.com/book/10.1007/978-1-4842-4427-2
	| access-date = January 27, 2024
	| archive-date = January 27, 2024
	| archive-url = https://web.archive.org/web/20240127220804/https://link.springer.com/book/10.1007/978-1-4842-4427-2
	| url-status = live
	}}</ref>

<ref name="RayTracingGems_19">{{cite book
	| last1 = Liu
	| first1 = Edward
	| last2 = Llamas
	| first2 = Ignacio
	| last3 = Cañada
	| first3 = Juan
	| last4 = Kelly
	| first4 = Patrick
	| date = February 25, 2019
	| title = Ray Tracing Gems: High-Quality and Real-Time Rendering with DXR and Other APIs
	| publisher = Apress
	| location = Berkeley, CA
	| isbn = 978-1-4842-4427-2
	| chapter = 19: Cinematic Rendering in UE4 with Real-Time Ray Tracing and Denoising
	| doi = 10.1007/978-1-4842-4427-2
	| s2cid = 71144394
	| url = https://link.springer.com/book/10.1007/978-1-4842-4427-2
	| access-date = January 27, 2024
	| archive-date = January 27, 2024
	| archive-url = https://web.archive.org/web/20240127220804/https://link.springer.com/book/10.1007/978-1-4842-4427-2
	| url-status = live
	}}</ref>

<ref name="RealTimeRayTracing">{{cite book
	| last1 = Akenine-Möller
	| first1 = Tomas
	| last2 = Haines
	| first2 = Eric
	| last3 = Hoffman
	| first3 = Naty
	| last4 = Pesce
	| first4 = Angelo
	| last5 = Iwanicki
	| first5 = Michał
	| last6 = Hillaire
	| first6 = Sébastien
	| date = August 6, 2018
	| title = Real-Time Rendering
	| location = Boca Raton, FL
	| publisher = A K Peters/CRC Press
	| isbn = 978-1138627000
	| edition = 4th
	| chapter = Online chapter 26. Real-Time Ray Tracing
	| section-url = https://www.realtimerendering.com/Real-Time_Rendering_4th-Real-Time_Ray_Tracing.pdf
	| access-date = January 27, 2024
	| archive-date = January 27, 2024
	| archive-url = https://web.archive.org/web/20240127220835/https://www.realtimerendering.com/Real-Time_Rendering_4th-Real-Time_Ray_Tracing.pdf
	| url-status = live
	}}</ref>

<ref name=Riazuelo2019>{{cite journal
    | last=Alain
    | first=Riazuelo
    | title=Seeing relativity-I: Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars
    | journal=International Journal of Modern Physics D
    | date=March 2019
    | volume=28
    | issue=2
    | doi=10.1142/S0218271819500421
    | arxiv=1511.06025
    | bibcode=2019IJMPD..2850042R
 }}</ref>

<ref name="Schmid2023">{{cite web
    | url = https://radiancefields.com/history-of-neural-radiance-fields
    | title = A short 170 year history of Neural Radiance Fields (NeRF), Holograms, and Light Fields
    | last = Schmid
    | first = Katrin
    | date = March 2, 2023
    | website = radiancefields.com
    | access-date = 31 August 2024
    | archive-date = 31 August 2024
    | archive-url = https://web.archive.org/web/20240831194910/https://radiancefields.com/history-of-neural-radiance-fields
    | url-status = live
    }}</ref>

<ref name = "Schmidt2016">{{cite journal
    | last1 = Schmidt
    | first1 = Martin
    | last2 = Lobachev
    | first2 = Oleg
    | last3 = Guthe
    | first3 = Michael
    | title = Coherent Metropolis Light Transport on the GPU using Speculative Mutations
    | year = 2016
    | journal = Journal of WSCG
    | volume = 24
    | issue = 1
    | pages = 1–8
    | issn = 1213-6972
    | url = https://www.mathematik.uni-marburg.de/~lobachev/papers/schmidt-2016-metropolis.pdf
    }}</ref>

<ref name=Smith1982>{{cite journal
    | last=Smith
    | first=Alvy Ray
    | date=October 1982
    | title=Special Effects for Star Trek II: The Genesis Demo
    | journal=American Cinematographer
    | page=1038
    | url=https://ohiostate.pressbooks.pub/app/uploads/sites/45/2020/01/StarTrekII_GenesisDemo.pdf
    | access-date= 13 September 2024
    }}</ref>
    
<ref name="UnityLightProbes">{{cite web
    | url = https://docs.unity3d.com/540/Documentation/Manual/LightProbes.html
    | title = Unity Manual:Light Probes: Introduction
    | website = docs.unity3d.com
    | access-date = 27 January 2024
    | archive-date = 3 September 2024
    | archive-url = https://web.archive.org/web/20240903072556/https://docs.unity3d.com/540/Documentation/Manual/LightProbes.html
    | url-status = live
    }}</ref>

<ref name="Veach1997">{{cite thesis
    | last = Veach
    | first = Eric
    | title = Robust Monte Carlo methods for light transport simulation
    | year = 1997
    | degree = PhD
    | publisher = Stanford University
    | url = https://graphics.stanford.edu/papers/veach_thesis/thesis.pdf
    }}</ref>

<ref name="Warnock1968">{{Citation
    | title=A Hidden Line Algorithm For Halftone Picture Representation
    | last=Warnock
    | first=John
    | author-link=John Warnock
    | publisher=University of Utah
    | date=20 May 1968
    | id=TR 4-5
    | url=https://core.ac.uk/download/pdf/276286863.pdf
    | access-date=19 September 2024
    }}</ref>

<ref name="Warnock1969">{{Citation
    | title=A hidden surface algorithm for computer generated halftone pictures
    | last=Warnock
    | first=John
    | author-link=John Warnock
    | url=https://archive.org/details/DTIC_AD0753671
    | publisher=University of Utah
    | date=June 1969
    | id=TR 69-249
    | access-date=19 September 2024
    }}</ref>

<ref name=Watkins1970>{{Citation
    | last=Watkins
    | first=Gary Scott
    | title=A Real Time Visible Surface Algorithm
    | publisher=University of Utah 
    | url=https://archive.org/details/utech-csc-70-101_watkins_dissertation_jun70
    | date=June 1970
    | access-date=19 September 2024
    }}</ref>

<ref name="WorldwidePlanetariumsDatabase1">{{cite web
    | url= https://planetariums-database.org/sheet_projector.php?menu=sheet_projector&brand=Evans_and_Sutherland&model=Digistar-II
    | title= Evans_and_Sutherland Digistar-II
    | publisher=Worldwide Planetariums Database
    | website=planetariums-database.org
    | access-date=13 September 2024
    }}</ref>
    
<ref name="WorldwidePlanetariumsDatabase2">{{cite web
    | url=https://planetariums-database.org/list_projectors.php?menu=list_projectors&brand=Evans_and_Sutherland&model=Digistar-II
    | title= Listing of Planetariums using a Evans_and_Sutherland Digistar-II
    | publisher=Worldwide Planetariums Database
    | website=planetariums-database.org
    | access-date=13 September 2024
    }}</ref>
    
}}

== Further reading ==
{{div col|colwidth=30em}}
* {{cite book |last1=Akenine-Möller |first1=Tomas |title=Real-time rendering |year=2018 |publisher=AK Peters |location=Boca Raton, FL, USA. |isbn=978-1-13862-700-0 |edition=4 |first2=Eric |last3=Hoffman |first3=Naty |last4=Pesce |first4=Angelo |last5=Iwanicki |first5=Micał |last6=Hillaire |first6=Sébastien |last2=Haines |url=https://www.realtimerendering.com/}}
* {{cite book |last=Blinn |first=Jim |author-link=Jim Blinn |title=Jim Blinn's corner : a trip down the graphics pipeline |year=1996 |publisher=Morgan Kaufmann Publishers |location=San Francisco, Calif. |isbn=978-1-55860-387-5}}
* {{cite book |last1=Cohen |first1=Michael F. |title=Radiosity and realistic image synthesis |year=1998 |publisher=Academic Press Professional |location=Boston, Mass. [u.a.] |isbn=978-0-12-178270-2 |edition=3 |first2=John R. |last2=Wallace}}
* {{cite book |author1=Philip Dutré |title=Advanced global illumination |year=2003 |publisher=A K Peters |location=Natick, Mass. |isbn=978-1-56881-177-2 |edition=[Online-Ausg.] |first2=Philippe |last2=Bekaert |first3=Kavita |last3=Bala}}
* {{cite book |last=Foley |first=James D. |title=Computer graphics : principles and practice |year=1990 |publisher=Addison-Wesley |location=Reading, Mass. |isbn=978-0-201-12110-0 |edition=2 |author2=Van Dam |author3=Feiner |author4=Hughes |author-link=James D. Foley |url=https://archive.org/details/computergraphics00fole}}
* {{cite book |title=An introduction to ray tracing |year=1989 |publisher=Acad. Press |location=London [u.a.] |isbn=978-0-12-286160-4 |edition=3 |editor=Andrew S. Glassner}}
* {{cite book |last=Glassner |first=Andrew S. |title=Principles of digital image synthesis |year=2004 |publisher=Kaufmann |location=San Francisco, Calif. |isbn=978-1-55860-276-2 |edition=2 |author-link=Andrew Glassner}}
* {{cite book |last1=Gooch |first1=Bruce |title=Non-photorealistic rendering |year=2001 |publisher=A K Peters |location=Natick, Mass. |isbn=978-1-56881-133-8 |first2=Amy |last2=Gooch |author2-link=Amy Ashurst Gooch}}
* {{cite book |last=Jensen |first=Henrik Wann |title=Realistic image synthesis using photon mapping |year=2001 |publisher=AK Peters |location=Natick, Mass. |isbn=978-1-56881-147-5 |edition=[Nachdr.]}}
* {{cite book |last1=Pharr |first1=Matt |title=Physically based rendering from theory to implementation |year=2004 |publisher=Elsevier/Morgan Kaufmann |location=Amsterdam |isbn=978-0-12-553180-1 |first2=Greg |last2=Humphreys}}
* {{cite book |last1=Shirley |first1=Peter |title=Realistic ray tracing |year=2003 |publisher=AK Peters |location=Natick, Mass. |isbn=978-1-56881-198-7 |edition=2 |first2=R. Keith |last2=Morley |author1-link=Peter Shirley}}
* {{cite book |last1=Strothotte |first1=Thomas |title=Non-photorealistic computer graphics modeling, rendering, and animation |year=2002 |publisher=Morgan Kaufmann |location=San Francisco, CA |isbn=978-1-55860-787-3 |edition=2 |first2=Stefan |last2=Schlechtweg}}
* {{cite book |chapter-url=http://radsite.lbl.gov/radiance/papers/sg94.1/ |last=Ward |first=Gregory J. |title=Proceedings of the 21st annual conference on Computer graphics and interactive techniques - SIGGRAPH '94 |chapter=The RADIANCE lighting simulation and rendering system |date=July 1994 |pages=459–72 |doi=10.1145/192161.192286 |isbn=0897916670 |s2cid=2487835}}
{{div col end}}

== External links ==
{{Wiktionary|renderer}}
{{commons cat}}
* [https://web.archive.org/web/19961221040900/http://siggraph.org/ SIGGRAPH]{{snd}} the ACMs special interest group in graphics{{snd}} the largest academic and professional association and conference
* [https://vintage3d.org/history.php vintage3d.org "The way to home 3d"]{{snd}} Extensive history of computer graphics hardware, including research, commercialization, and video games and consoles
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{{DEFAULTSORT:Rendering (Computer Graphics)}}
[[Category:3D rendering]]