3D Math - Support Functions

This algorithms described in this document rely on a set of simple geometry routines and structures:

Data types

 struct Point    { float x, y, z ; } ;
 typedef Point Vector ;
 struct Sphere   { float radius ; Point center ; } ;
 struct Triangle { Point a, b, c ; } ;
 struct Plane    { float A, B, C, D ; } ;
 struct AxialBox { Point min, max ; } ;
 struct Line     { Point start ; Vector vec ; } ;
 struct LineSeg  { Point start ; Point  end ; } ;

Normalize a vector

 float Normalize ( Vector *dst, Vector *src )
 {
   float leng = sqrt ( Square ( src->x ) +
                       Square ( src->y ) +
                       Square ( src->z ) ) ;
   if ( leng <= 0.0f )
   {
     dst->x = 0.0 ;
     dst->y = 0.0 ;
     dst->z = 1.0 ;
     return 0.0 ;
   }
   float recip = 1.0f / leng ;
   dst->x = src->x * recip ;
   dst->y = src->y * recip ;
   dst->z = src->z * recip ;
   return leng ;  /* Sometimes it's handy to know this value. */
 }

Cross Product (aka Vector Product)

 void CrossProduct ( Vector *dst, Vector *v1, Vector *v2 )
 {
   dst->x = v1->y * v2->z - v1->z * v2->y ;
   dst->y = v1->z * v2->x - v1->x * v2->z ;
   dst->z = v1->x * v2->y - v1->y * v2->x ;
 }

Dot Product (aka Scalar Product)

 float DotProduct ( Point *p1, Point *p2 )
 {
   return p1->x * p2->x + p1->y * p2->y + p1->z * p2->z ;
 }

Square a number

 float Square ( float x ) { return x * x ; } ;

The square of the distance between two points

 float SqrDistancePt3 ( Point *p1, Point *p2 )
 {
   return Square ( p1->x - p2->x ) +
          Square ( p1->y - p2->y ) +
          Square ( p1->z - p2->z ) ;
 }