Three-dimensional graph

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Graph of the function f(x, y) = sin(x2)*cos(y2).

A three-dimensional graph is the graph of a function f(x, y) of two variables, or the graph of a relationship g(x, y, z) among three variables.

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.

Examples[edit]

The graph of the trigonometric function on the real line

f (x, y) = \sin{x^2}\cdot \cos{y^2}

is

\{(x, y, \sin{x^2}\cdot \cos{y^2}) : x,y \in \mathbb{R}\}.

If this set is plotted on a three dimensional Cartesian coordinate system, the result is a surface (see figure).

A two-dimensional perspective projection of a sphere

A three-dimensional graph of a sphere, with equation x^2+y^2+z^2=r^2 is shown at left.

Collapsing the information in a three-dimensional graph into a two-dimensional graph[edit]

The information in a three-dimensional graph is often collapsed into a two-dimensional graph with the use of contour lines. The x and y axes are retained, but instead of depicting a z axis as "coming out of the page (or screen)", all x, y combinations giving rise to the same z value are connected with a contour line; an arbitrary number of these may be shown for various values of z.

See also[edit]