BSNS102 Study Guide - Final Guide: Cross Product, Glossary Of Computer Graphics, Pythagorean Theorem
28 Jan 2021
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If the lines are parallel (or coincident), then the cross product of d1 and d2 is the zero vector, and the denominator of both equations is zero. If the lines are skew, then p1(t1) and p2(t2) are the points of closest approach. To distinguish between skew and intersecting lines, we examine the distance between p1(t1) and p2(t2). Of course, in practice, an exact intersection rarely occurs due to float- ing-point imprecision, and a tolerance must be used. The above discussion assumes that the range of the parameters t1 and t2 is not restricted. If the rays have finite length (or only extend in one direction), then the appropriate boundary tests would be applied after computing t1 and t2. A ray intersects a plane in 3d at a point. The plane will be defined in the standard manner, by all points p such that:
