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Analytic length of quadratic segment

This commit is contained in:
Viktor Chlumský 2020-10-30 10:02:40 +01:00
parent 9d22335ea0
commit 9af250c7d6
2 changed files with 22 additions and 0 deletions
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20
core/edge-segments.cpp
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@ -113,6 +113,26 @@ Vector2 CubicSegment::directionChange(double param) const {
return mix((p[2]-p[1])-(p[1]-p[0]), (p[3]-p[2])-(p[2]-p[1]), param);
}
double LinearSegment::length() const {
return (p[1]-p[0]).length();
}
double QuadraticSegment::length() const {
Vector2 ab = p[1]-p[0];
Vector2 br = p[2]-p[1]-ab;
float abab = dotProduct(ab, ab);
float abbr = dotProduct(ab, br);
float brbr = dotProduct(br, br);
float abLen = sqrt(abab);
float brLen = sqrt(brbr);
float crs = crossProduct(ab, br);
float h = sqrt(abab+abbr+abbr+brbr);
return (
brLen*((abbr+brbr)*h-abbr*abLen)+
crs*crs*log((brLen*h+abbr+brbr)/(brLen*abLen+abbr))
)/(brbr*brLen);
}
SignedDistance LinearSegment::signedDistance(Point2 origin, double &param) const {
Vector2 aq = origin-p[0];
Vector2 ab = p[1]-p[0];

2
core/edge-segments.h
View File

@ -58,6 +58,7 @@ public:
Point2 point(double param) const;
Vector2 direction(double param) const;
Vector2 directionChange(double param) const;
double length() const;
SignedDistance signedDistance(Point2 origin, double &param) const;
int scanlineIntersections(double x[3], int dy[3], double y) const;
void bound(double &l, double &b, double &r, double &t) const;
@ -80,6 +81,7 @@ public:
Point2 point(double param) const;
Vector2 direction(double param) const;
Vector2 directionChange(double param) const;
double length() const;
SignedDistance signedDistance(Point2 origin, double &param) const;
int scanlineIntersections(double x[3], int dy[3], double y) const;
void bound(double &l, double &b, double &r, double &t) const;