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Ray casting is the methodological basis for 3-D CAD/CAM solid modeling and image rendering. It is essentially the same as ray tracing (graphics) for computer graphics where virtual light rays are "cast" or "traced" on their path from the focal point of a camera through each pixel in the camera sensor to determine what is visible along the ray in the 3-D scene. The term "Ray Casting" was introduced by Scott Roth while at the General Motors Research Labs from 1978-1980. His paper, "Ray Casting for Modeling Solids", describes modeled solid objects by combining primitive solids, such as blocks and cylinders, using the set operators union, intersection, and difference. This figure shows a universal joint modeled from cylinders and blocks using the set operators union (+), intersection (&), and difference (-) in a binary tree, circa 1979.
Before ray casting (and ray tracing), surfaces or edges (e.g., lines) were projected from the 3-D world to the image plane where visibility logic had to be applied. Ray casting greatly simplified image rendering of 3-D objects and scenes because a line transforms to a line under all perspective linear transformations. A perspective linear transformation is defined by a 4x4 matrix transformation with a division. So, instead of projecting an arbitrary curved surface to the image plane, lines (rays) are transformed into the local coordinate system of the surface where the line-surface intersection is simplest to compute. While simplifying the mathematics, the algorithm is very computer-processor intensive. Pixar has large render farms, buildings with 1000's of CPUs, to make their animations using ray casting [aka "ray tracing"] as a core technique.
From the abstract for the paper "Ray Casting for Modeling Solids": "To visualize and analyze the composite solids modeled, virtual light rays are cast as probes. By virtue of its simplicity, ray casting is reliable and extensible. The most difficult mathematical problem is finding line-surface intersection points. So, surfaces as planes, quadrics, tori, and probably even parametric surface patches may bound the primitive solids. The adequacy and efficiency of ray casting are issues addressed here. A fast picture generation capability for interactive modeling is the biggest challenge."
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xxx Ray casting is the most basic of many computer graphics rendering algorithms that use the geometric algorithm of ray tracing. Ray tracing-based rendering algorithms operate in image order to render three-dimensional scenes to two-dimensional images. Geometric rays are traced from the eye of the observer to sample the light (radiance) travelling toward the observer from the ray direction. The speed and simplicity of ray casting comes from computing the color of the light without recursively tracing additional rays that sample the radiance incident on the point that the ray hit. This eliminates the possibility of accurately rendering reflections, refractions, or the natural falloff of shadows; however all of these elements can be faked to a degree, by creative use of texture maps or other methods. The high speed of calculation made ray casting a handy rendering method in early real-time 3D video games.
In nature, a light source emits a ray of light that travels, eventually, to a surface that interrupts its progress. One can think of this "ray" as a stream of photons travelling along the same path. At this point, any combination of three things might happen with this light ray: absorption, reflection, and refraction. The surface may reflect all or part of the light ray, in one or more directions. It might also absorb part of the light ray, resulting in a loss of intensity of the reflected and/or refracted light. If the surface has any transparent or translucent properties, it refracts a portion of the light beam into itself in a different direction while absorbing some (or all) of the spectrum (and possibly altering the color). Between absorption, reflection, and refraction, all of the incoming light must be accounted for, and no more. A surface cannot, for instance, reflect 66% of an incoming light ray, and refract 50%, since the two would add up to be 116%. From here, the reflected and/or refracted rays may strike other surfaces, where their absorptive, refractive, and reflective properties are again calculated based on the incoming rays. Some of these rays travel in such a way that they hit our eye, causing us to see the scene and so contribute to the final rendered image. Attempting to simulate this real-world process of tracing light rays using a computer can be considered extremely wasteful, as only a minuscule fraction of the rays in a scene would actually reach the eye.
The first ray casting algorithm used for rendering was presented by Arthur Appel in 1968. The idea behind ray casting is to trace rays from the eye, one per pixel, and find the closest object blocking the path of that ray – think of an image as a screen-door, with each square in the screen being a pixel. This is then the object the eye sees through that pixel. Using the material properties and the effect of the lights in the scene, this algorithm can determine the shading of this object. The simplifying assumption is made that if a surface faces a light, the light will reach that surface and not be blocked or in shadow. The shading of the surface is computed using traditional 3D computer graphics shading models. One important advantage ray casting offered over older scanline algorithms was its ability to easily deal with non-planar surfaces and solids, such as cones and spheres. If a mathematical surface can be intersected by a ray, it can be rendered using ray casting. Elaborate objects can be created by using solid modelling techniques and easily rendered.
Ray casting in computer games
The world in the famous video game Wolfenstein 3D is built from a square based grid of uniform height walls meeting solid coloured floors and ceilings. In order to draw the world, a single ray is traced for every column of screen pixels and a vertical slice of wall texture is selected and scaled according to where in the world the ray hits a wall and how far it travels before doing so.
The purpose of the grid based levels is twofold – ray to wall collisions can be found more quickly since the potential hits become more predictable and memory overhead is reduced. However, encoding wide-open areas takes extra space.
The Voxel Space engine developed by NovaLogic for the Comanche games traces a ray through each column of screen pixels and tests each ray against points in a heightmap. Then it transforms each element of the heightmap into a column of pixels, determines which are visible (that is, have not been occluded by pixels that have been drawn in front), and draws them with the corresponding color from the texture map.
Computational geometry setting
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In computational geometry, the ray casting problem is also known as the ray shooting problem and may be stated as the following query problem: given a set of objects in d-dimensional space, preprocess them into a data structure so that for each query ray, the initial object hit by the ray can be found quickly. The problem has been investigated for various settings: space dimension, types of objects, restrictions on query rays, etc. One technique is to use a sparse voxel octree.
- Roth, Scott D. (February 1982), "Ray Casting for Modeling Solids", Computer Graphics and Image Processing, 18 (2): 109–144, doi:10.1016/0146-664X(82)90169-1
- "Ray-tracing and other Rendering Approaches" (PDF), lecture notes, MSc Computer Animation and Visual Effects, Jon Macey, University of Bournemouth
- Goldstein, Robert A.; Nagel, Roger (19 August 2016). "3-D Visual simulation". Simulation. 16 (1): 25–31. doi:10.1177/003754977101600104.
- Wolfenstein-style ray casting tutorial by F. Permadi
- Andre LaMothe. Black Art of 3D Game Programming. 1995, pp. 14, 398, 935-936, 941-943. ISBN 1-57169-004-2.
- "Ray shooting, depth orders and hidden surface removal", by Mark de Berg, Springer-Verlag, 1993, ISBN 3-540-57020-9, 201 pp.