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util/geometry: small ellipse collision optimizations

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Andrei Alexeyev 2023-09-23 13:35:42 +02:00
parent 4f6384b257
commit b02d831e41
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GPG key ID: 72D26128040B9690
1 changed files with 24 additions and 21 deletions
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45
src/util/geometry.c
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@ -12,7 +12,7 @@
#include "miscmath.h"
Rect ellipse_bbox(Ellipse e) {
double largest_radius = fmax(re(e.axes), im(e.axes)) * 0.5;
double largest_radius = max(re(e.axes), im(e.axes)) * 0.5;
cmplx d = CMPLX(largest_radius, largest_radius);
return (Rect) {
.top_left = e.origin - d,
@ -21,24 +21,27 @@ Rect ellipse_bbox(Ellipse e) {
}
bool point_in_ellipse(cmplx p, Ellipse e) {
double Xp = re(p);
double Yp = im(p);
double Xe = re(e.origin);
double Ye = im(e.origin);
double a = e.angle;
Rect e_bbox = ellipse_bbox(e);
return point_in_rect(p, e_bbox) && (
pow(cos(a) * (Xp - Xe) + sin(a) * (Yp - Ye), 2) / pow(re(e.axes)/2, 2) +
pow(sin(a) * (Xp - Xe) - cos(a) * (Yp - Ye), 2) / pow(im(e.axes)/2, 2)
) <= 1;
if(!point_in_rect(p, e_bbox)) {
return false;
}
p -= e.origin;
cmplx dir = cdir(e.angle);
cmplx dotcross = CMPLX(cdot(p, dir), ccross(p, dir));
cmplx dotcross2 = cwmul(dotcross, dotcross);
cmplx terms = cwdiv(dotcross2, cwmul(e.axes, e.axes));
return re(terms) + im(terms) <= 0.25;
}
Rect lineseg_bbox(LineSegment seg) {
cmplx rmm = csort(CMPLX(re(seg.a), re(seg.b)));
cmplx imm = csort(CMPLX(im(seg.a), im(seg.b)));
return (Rect) {
.top_left = fmin(re(seg.a), re(seg.b)) + I * fmin(im(seg.a), im(seg.b)),
.bottom_right = fmax(re(seg.a), re(seg.b)) + I * fmax(im(seg.a), im(seg.b))
.top_left = CMPLX(re(rmm), re(imm)),
.bottom_right = CMPLX(im(rmm), im(imm))
};
}
@ -61,8 +64,8 @@ static double lineseg_closest_factor_impl(cmplx m, cmplx v) {
return 0;
}
double f = -re(v * conj(m)) / lm2; // project v onto the line
f = clamp(f, 0, 1); // restrict it to segment
double f = -re(cmul_finite(v, conj(m))) / lm2; // project v onto the line
f = clamp(f, 0, 1); // restrict it to segment
return f;
}
@ -106,13 +109,13 @@ bool lineseg_ellipse_intersect(LineSegment seg, Ellipse e) {
seg.b -= e.origin;
double ratio = re(e.axes) / im(e.axes);
cmplx rotation = cexp(I * -e.angle);
seg.a *= rotation;
seg.b *= rotation;
seg.a = re(seg.a) + I * ratio * im(seg.a);
seg.b = re(seg.b) + I * ratio * im(seg.b);
cmplx rotation = cdir(-e.angle);
seg.a = cmul_finite(seg.a, rotation);
seg.b = cmul_finite(seg.b, rotation);
im(seg.a) *= ratio;
im(seg.b) *= ratio;
Circle c = { .radius = re(e.axes) / 2 };
Circle c = { .radius = re(e.axes) * 0.5 };
return lineseg_circle_intersect_fallback(seg, c) >= 0;
}