## Geometry

### Segments' intersection [1]

```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 [1]

``` 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 );
}
}
```

1. Adapted from a stackoverflow post by ubuntu - stackoverflow.com

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