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
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