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Provided that x, y, and z or f(x, y) are real numbers, the graph can be represented as a planar or curved surface in a three-dimensional Cartesian coordinate system. A three-dimensional graph is typically drawn on a two-dimensional page or screen using perspective methods, so that one of the dimensions appears to be coming out of the page.
If this set is plotted on a three dimensional Cartesian coordinate system, the result is a surface (see above figure).
A three-dimensional graph of a sphere, with equation is shown at left.
Collapsing the information in a three-dimensional graph into a two-dimensional graph
The information in a three-dimensional graph is often collapsed into a two-dimensional graph with the use of contour lines, as illustrated at right. The x and y axes are retained, but instead of depicting a z or f(x, y) axis as "coming out of the page (or screen)", all x, y combinations giving rise to the same z or f(x, y) value are connected with a contour line; an arbitrary number of these may be shown for various values of z or f(x, y).
- Graph (disambiguation)
- Analytic geometry
- Cartesian coordinate system
- Euclidean space
- Coordinate system
- List of surfaces
- List of polygons, polyhedra and polytopes
- List of regular polytopes
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