Background Information and Techniques - Computer Animation: Algorithms and Techniques - page 419

where y is the angle from A to B ,0< y < 180

jA Bj¼ 0 if and only if A and B are colinear ; (B.29)

i.e., sin y ¼ sin 0 ¼ 0, or A ¼ 0or B ¼ 0.

B.2.5 Vector and matrix routines
Simple vector and matrix routines are given here ( Figure B.12 ). These are used in some of the routines
presented elsewhere in this appendix.

Vector routines
Some vector routines can be implemented just as easily as in-line code using C's #define construction.

B.2.6 Closest point between two lines in three-space
The intersection of two lines in three-space often needs to be calculated. Because of numerical impre-
cision, the lines rarely, if ever, actually intersect in three-space. As a result, the computation that needs
to be performed is to find the two points, one from each line, at which the lines are closest to each other.

FIGURE B.12
Vector routines.