** Overview**

A plane in three-dimensional space is the locus of points that are
perpendicular to a vector
(commonly called the normal vector)
and that pass through a point .
They form the fundamental geometric structure for many operations in
computer graphics (* e.g.*, clipping) and geometric modeling (* e.g.*, tangent
planes to surfaces). Two equivalent definitions of a plane are
used and we present both in these notes.

For a pdf version of these notes look here.

** Specifying a Point and a Vector**

A plane in three-dimensional space is the locus of points that are perpendicular to a vector and that pass through a point . The point and the vector uniquely define the plane. Let be the plane defined by and . Then for any point on the plane, we must have that

** A Plane Equation**

Suppose we are given a plane defined by a point and a vector . If we write the vector as , the point as , and an arbitrary point on the plane as , then from the above we have that

0 | ||

and so we can write,

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**This document maintained by Ken
Joy**

All contents copyright (c) 1996, 1997, 1998,
1999

Computer Science Department

University of California, Davis

All rights reserved.

1999-12-06