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Frankiezafe (Talk | contribs) m (Frankiezafe moved page Notes:Math to Notes:Geometry without leaving a redirect) |
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| − | This page contains | + | This page contains snippets of useful math methods already turned into pseudo-code. |
== Geometry == | == Geometry == | ||
| − | === Segments' intersection <ref>Adapted from a stackoverflow post | + | === Segments' intersection <ref name="two-line-segments-are-crossing">Adapted from a stackoverflow post by ''ubuntu'' - [http://stackoverflow.com/questions/15297590/improve-in-coding-saving-how-to-check-if-two-line-segments-are-crossing-in-pytho stackoverflow.com]</ref> === |
| − | + | vec2f intersection( vec2f a1, vec2f a2, vec2f b1, vec2f b2 ) { | |
float a = a2.x - a1.x; | float a = a2.x - a1.x; | ||
float b = b1.x - b2.x; | float b = b1.x - b2.x; | ||
| Line 16: | Line 16: | ||
if ( abs( denom ) < 1e-5 ) { | if ( abs( denom ) < 1e-5 ) { | ||
// parrallel | // parrallel | ||
| − | return | + | return 0; |
} else { | } else { | ||
float t = (e*d - b*f)/denom; | float t = (e*d - b*f)/denom; | ||
| − | return new | + | 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 <ref name="two-line-segments-are-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 ); | ||
| + | } | ||
| + | } | ||
| + | |||
| + | |||
<references/> | <references/> | ||
| + | |||
| + | [[Category:math]] | ||
| + | [[Category:code snippet]] | ||
| + | [[Category:pseudocode]] | ||
This page contains snippets of useful math methods already turned into pseudo-code.
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 ) ) {
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 );
}
}
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