Vec2 ScallopedSector::sample(RNG &rng)
{
float angle = calcAngleForArea(area*rng.getFloatL(), rng);
float d1 = distToCurve(angle, 0);
float d2 = distToCurve(angle, 1);
float d = sqrt(d1*d1 + (d2*d2 - d1*d1)*rng.getFloat());
return Vec2(P.x + cos(angle)*d, P.y + sin(angle)*d);
}
static double totalMeanError(const vector<Vector2f> &dataPoints, const vector<Vector2f> &curve)
{
double distance = 0.0;
for(int i = 1; i < dataPoints.size()-1; ++i)
distance += distToCurve(dataPoints[i], curve);
distance /= (dataPoints.size()-2);
return distance;
}
void ScallopedSector::subtractDisk(Vec2 &C, float r, std::vector<ScallopedSector> *regions)
{
std::vector<float> angles;
Vec2 v(C.x - P.x, C.y-P.y);
float d = sqrt(v.x*v.x + v.y*v.y);
if (r<d) {
float theta = atan2(v.y, v.x);
float x = sqrt(d*d-r*r);
float angle, alpha = asin(r/d);
angle = canonizeAngle(theta+alpha);
if (a1<angle && angle<a2) {
if (distToCurve(angle,0)<x && x<distToCurve(angle,1))
angles.push_back(angle);
}
angle = canonizeAngle(theta-alpha);
if (a1<angle && angle<a2) {
if (distToCurve(angle,0)<x && x<distToCurve(angle,1))
angles.push_back(angle);
}
}
for (int arcIndex=0; arcIndex<2; arcIndex++) {
Vec2 &C2 = arcs[arcIndex].P;
float R = arcs[arcIndex].r;
Vec2 v(C.x - C2.x, C.y - C2.y);
float d = sqrt(v.x*v.x + v.y*v.y);
if (d>FLT_EPSILON) {
float invD = 1.0f/d;
float x = (d*d - r*r + R*R)*invD*.5f;
float k = R*R - x*x;
if (k>0) {
float y = sqrt(k);
float vx = v.x*invD;
float vy = v.y*invD;
float vx_x = vx*x, vy_x = vy*x;
float vx_y = vx*y, vy_y = vy*y;
float angle;
angle = canonizeAngle(atan2(C2.y + vy_x + vx_y - P.y,
C2.x + vx_x - vy_y - P.x));
if (a1<angle && angle<a2) angles.push_back(angle);
angle = canonizeAngle(atan2(C2.y + vy_x - vx_y - P.y,
C2.x + vx_x + vy_y - P.x));
if (a1<angle && angle<a2) angles.push_back(angle);
}
}
}
sort(angles.begin(), angles.end());
angles.insert(angles.begin(), a1);
angles.push_back(a2);
for (unsigned int i=1; i<angles.size(); i++) {
float a1 = angles[i-1], a2 = angles[i];
float midA = (a1+a2)*.5f;
float inner = distToCurve(midA,0);
float outer = distToCurve(midA,1);
float d1, d2;
distToCircle(midA, C, r, &d1, &d2); // d1<=d2
if (d2<inner || d1>outer) {
regions->push_back(ScallopedSector(P, a1, a2, arcs[0].P, arcs[0].r, arcs[0].sign, arcs[1].P, arcs[1].r, arcs[1].sign));
} else {
if (inner<d1) {
regions->push_back(ScallopedSector(P, a1, a2, arcs[0].P, arcs[0].r, arcs[0].sign, C, r, -1));
}
if (d2<outer) {
regions->push_back(ScallopedSector(P, a1, a2, C, r, 1, arcs[1].P, arcs[1].r, arcs[1].sign));
}
}
}
}
