Notes:Geometry

This page contains snippets of useful math methods already turned into pseudo-code.

Geometry

Segments' intersection

vec2f intersection( vec2f a1, vec2f a2, vec2f b1, vec2f b2 ) {
   float a = a2.x - a1.x;
   float b = b1.x - b2.x;
   float c = a2.y - a1.y;
   float d = b1.y - b2.y;
   float e = b1.x - a1.x;
   float f = b1.y - a1.y;
   float denom = a * d - b * c;
   if ( abs( denom ) < 1e-5 ) {
     // parrallel
     return 0;
   } else {
     float t = (e*d - b*f)/denom;
     float s = (a*f - e*c)/denom;
     if ( t >= 0 && t <= 1 && s >= 0 && s<=1 ) {
       return new vec2f( a1.x + t * ( a2.x - a1.x ), a1.y + t * ( a2.y - a1.y ) );
     }
     return 0;
   }
 }

To transform this method into a line intersection detection, just comment the test on t and s. The smarter thing to do is to make this test optional:

vec2f intersection( vec2f a1, vec2f a2, vec2f b1, vec2f b2, bool keep_in_segment = true ) {
...
     if ( ( keep_in_segment && t >= 0 && t <= 1 && s >= 0 && s<=1 ) || ( !keep_in_segment ) ) {

Segments' crossing

 boolean crosses( vec2f a1, vec2f a2, vec2f b1, vec2f b2 ) {
   float a = a2.x - a1.x;
   float b = b1.x - b2.x;
   float c = a2.y - a1.y;
   float d = b1.y - b2.y;
   float e = b1.x - a1.x;
   float f = b1.y - a1.y;
   float denom = a * d - b * c;
   if ( abs( denom ) < 1e-5 ) {
     // parrallel
     return false;
   } else {
     float t = (e*d - b*f)/denom;
     float s = (a*f - e*c)/denom;
     return ( t >= 0 && t <= 1 && s >= 0 && s<=1 );
   }
 }