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godot/thirdparty/msdfgen/core/edge-segments.cpp
bruvzg 0d02568ff8
Update ICU and msdfgen.
2024-03-13 09:12:50 +02:00

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#include "edge-segments.h"
#include "arithmetics.hpp"
#include "equation-solver.h"
namespace msdfgen {
void EdgeSegment::distanceToPseudoDistance(SignedDistance &distance, Point2 origin, double param) const {
if (param < 0) {
Vector2 dir = direction(0).normalize();
Vector2 aq = origin-point(0);
double ts = dotProduct(aq, dir);
if (ts < 0) {
double pseudoDistance = crossProduct(aq, dir);
if (fabs(pseudoDistance) <= fabs(distance.distance)) {
distance.distance = pseudoDistance;
distance.dot = 0;
}
}
} else if (param > 1) {
Vector2 dir = direction(1).normalize();
Vector2 bq = origin-point(1);
double ts = dotProduct(bq, dir);
if (ts > 0) {
double pseudoDistance = crossProduct(bq, dir);
if (fabs(pseudoDistance) <= fabs(distance.distance)) {
distance.distance = pseudoDistance;
distance.dot = 0;
}
}
}
}
LinearSegment::LinearSegment(Point2 p0, Point2 p1, EdgeColor edgeColor) : EdgeSegment(edgeColor) {
p[0] = p0;
p[1] = p1;
}
QuadraticSegment::QuadraticSegment(Point2 p0, Point2 p1, Point2 p2, EdgeColor edgeColor) : EdgeSegment(edgeColor) {
if (p1 == p0 || p1 == p2)
p1 = 0.5*(p0+p2);
p[0] = p0;
p[1] = p1;
p[2] = p2;
}
CubicSegment::CubicSegment(Point2 p0, Point2 p1, Point2 p2, Point2 p3, EdgeColor edgeColor) : EdgeSegment(edgeColor) {
if ((p1 == p0 || p1 == p3) && (p2 == p0 || p2 == p3)) {
p1 = mix(p0, p3, 1/3.);
p2 = mix(p0, p3, 2/3.);
}
p[0] = p0;
p[1] = p1;
p[2] = p2;
p[3] = p3;
}
LinearSegment *LinearSegment::clone() const {
return new LinearSegment(p[0], p[1], color);
}
QuadraticSegment *QuadraticSegment::clone() const {
return new QuadraticSegment(p[0], p[1], p[2], color);
}
CubicSegment *CubicSegment::clone() const {
return new CubicSegment(p[0], p[1], p[2], p[3], color);
}
int LinearSegment::type() const {
return (int) EDGE_TYPE;
}
int QuadraticSegment::type() const {
return (int) EDGE_TYPE;
}
int CubicSegment::type() const {
return (int) EDGE_TYPE;
}
const Point2 *LinearSegment::controlPoints() const {
return p;
}
const Point2 *QuadraticSegment::controlPoints() const {
return p;
}
const Point2 *CubicSegment::controlPoints() const {
return p;
}
Point2 LinearSegment::point(double param) const {
return mix(p[0], p[1], param);
}
Point2 QuadraticSegment::point(double param) const {
return mix(mix(p[0], p[1], param), mix(p[1], p[2], param), param);
}
Point2 CubicSegment::point(double param) const {
Vector2 p12 = mix(p[1], p[2], param);
return mix(mix(mix(p[0], p[1], param), p12, param), mix(p12, mix(p[2], p[3], param), param), param);
}
Vector2 LinearSegment::direction(double param) const {
return p[1]-p[0];
}
Vector2 QuadraticSegment::direction(double param) const {
Vector2 tangent = mix(p[1]-p[0], p[2]-p[1], param);
if (!tangent)
return p[2]-p[0];
return tangent;
}
Vector2 CubicSegment::direction(double param) const {
Vector2 tangent = mix(mix(p[1]-p[0], p[2]-p[1], param), mix(p[2]-p[1], p[3]-p[2], param), param);
if (!tangent) {
if (param == 0) return p[2]-p[0];
if (param == 1) return p[3]-p[1];
}
return tangent;
}
Vector2 LinearSegment::directionChange(double param) const {
return Vector2();
}
Vector2 QuadraticSegment::directionChange(double param) const {
return (p[2]-p[1])-(p[1]-p[0]);
}
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;
double abab = dotProduct(ab, ab);
double abbr = dotProduct(ab, br);
double brbr = dotProduct(br, br);
double abLen = sqrt(abab);
double brLen = sqrt(brbr);
double crs = crossProduct(ab, br);
double 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];
param = dotProduct(aq, ab)/dotProduct(ab, ab);
Vector2 eq = p[param > .5]-origin;
double endpointDistance = eq.length();
if (param > 0 && param < 1) {
double orthoDistance = dotProduct(ab.getOrthonormal(false), aq);
if (fabs(orthoDistance) < endpointDistance)
return SignedDistance(orthoDistance, 0);
}
return SignedDistance(nonZeroSign(crossProduct(aq, ab))*endpointDistance, fabs(dotProduct(ab.normalize(), eq.normalize())));
}
SignedDistance QuadraticSegment::signedDistance(Point2 origin, double &param) const {
Vector2 qa = p[0]-origin;
Vector2 ab = p[1]-p[0];
Vector2 br = p[2]-p[1]-ab;
double a = dotProduct(br, br);
double b = 3*dotProduct(ab, br);
double c = 2*dotProduct(ab, ab)+dotProduct(qa, br);
double d = dotProduct(qa, ab);
double t[3];
int solutions = solveCubic(t, a, b, c, d);
Vector2 epDir = direction(0);
double minDistance = nonZeroSign(crossProduct(epDir, qa))*qa.length(); // distance from A
param = -dotProduct(qa, epDir)/dotProduct(epDir, epDir);
{
epDir = direction(1);
double distance = (p[2]-origin).length(); // distance from B
if (distance < fabs(minDistance)) {
minDistance = nonZeroSign(crossProduct(epDir, p[2]-origin))*distance;
param = dotProduct(origin-p[1], epDir)/dotProduct(epDir, epDir);
}
}
for (int i = 0; i < solutions; ++i) {
if (t[i] > 0 && t[i] < 1) {
Point2 qe = qa+2*t[i]*ab+t[i]*t[i]*br;
double distance = qe.length();
if (distance <= fabs(minDistance)) {
minDistance = nonZeroSign(crossProduct(ab+t[i]*br, qe))*distance;
param = t[i];
}
}
}
if (param >= 0 && param <= 1)
return SignedDistance(minDistance, 0);
if (param < .5)
return SignedDistance(minDistance, fabs(dotProduct(direction(0).normalize(), qa.normalize())));
else
return SignedDistance(minDistance, fabs(dotProduct(direction(1).normalize(), (p[2]-origin).normalize())));
}
SignedDistance CubicSegment::signedDistance(Point2 origin, double &param) const {
Vector2 qa = p[0]-origin;
Vector2 ab = p[1]-p[0];
Vector2 br = p[2]-p[1]-ab;
Vector2 as = (p[3]-p[2])-(p[2]-p[1])-br;
Vector2 epDir = direction(0);
double minDistance = nonZeroSign(crossProduct(epDir, qa))*qa.length(); // distance from A
param = -dotProduct(qa, epDir)/dotProduct(epDir, epDir);
{
epDir = direction(1);
double distance = (p[3]-origin).length(); // distance from B
if (distance < fabs(minDistance)) {
minDistance = nonZeroSign(crossProduct(epDir, p[3]-origin))*distance;
param = dotProduct(epDir-(p[3]-origin), epDir)/dotProduct(epDir, epDir);
}
}
// Iterative minimum distance search
for (int i = 0; i <= MSDFGEN_CUBIC_SEARCH_STARTS; ++i) {
double t = (double) i/MSDFGEN_CUBIC_SEARCH_STARTS;
Vector2 qe = qa+3*t*ab+3*t*t*br+t*t*t*as;
for (int step = 0; step < MSDFGEN_CUBIC_SEARCH_STEPS; ++step) {
// Improve t
Vector2 d1 = 3*ab+6*t*br+3*t*t*as;
Vector2 d2 = 6*br+6*t*as;
t -= dotProduct(qe, d1)/(dotProduct(d1, d1)+dotProduct(qe, d2));
if (t <= 0 || t >= 1)
break;
qe = qa+3*t*ab+3*t*t*br+t*t*t*as;
double distance = qe.length();
if (distance < fabs(minDistance)) {
minDistance = nonZeroSign(crossProduct(d1, qe))*distance;
param = t;
}
}
}
if (param >= 0 && param <= 1)
return SignedDistance(minDistance, 0);
if (param < .5)
return SignedDistance(minDistance, fabs(dotProduct(direction(0).normalize(), qa.normalize())));
else
return SignedDistance(minDistance, fabs(dotProduct(direction(1).normalize(), (p[3]-origin).normalize())));
}
int LinearSegment::scanlineIntersections(double x[3], int dy[3], double y) const {
if ((y >= p[0].y && y < p[1].y) || (y >= p[1].y && y < p[0].y)) {
double param = (y-p[0].y)/(p[1].y-p[0].y);
x[0] = mix(p[0].x, p[1].x, param);
dy[0] = sign(p[1].y-p[0].y);
return 1;
}
return 0;
}
int QuadraticSegment::scanlineIntersections(double x[3], int dy[3], double y) const {
int total = 0;
int nextDY = y > p[0].y ? 1 : -1;
x[total] = p[0].x;
if (p[0].y == y) {
if (p[0].y < p[1].y || (p[0].y == p[1].y && p[0].y < p[2].y))
dy[total++] = 1;
else
nextDY = 1;
}
{
Vector2 ab = p[1]-p[0];
Vector2 br = p[2]-p[1]-ab;
double t[2];
int solutions = solveQuadratic(t, br.y, 2*ab.y, p[0].y-y);
// Sort solutions
double tmp;
if (solutions >= 2 && t[0] > t[1])
tmp = t[0], t[0] = t[1], t[1] = tmp;
for (int i = 0; i < solutions && total < 2; ++i) {
if (t[i] >= 0 && t[i] <= 1) {
x[total] = p[0].x+2*t[i]*ab.x+t[i]*t[i]*br.x;
if (nextDY*(ab.y+t[i]*br.y) >= 0) {
dy[total++] = nextDY;
nextDY = -nextDY;
}
}
}
}
if (p[2].y == y) {
if (nextDY > 0 && total > 0) {
--total;
nextDY = -1;
}
if ((p[2].y < p[1].y || (p[2].y == p[1].y && p[2].y < p[0].y)) && total < 2) {
x[total] = p[2].x;
if (nextDY < 0) {
dy[total++] = -1;
nextDY = 1;
}
}
}
if (nextDY != (y >= p[2].y ? 1 : -1)) {
if (total > 0)
--total;
else {
if (fabs(p[2].y-y) < fabs(p[0].y-y))
x[total] = p[2].x;
dy[total++] = nextDY;
}
}
return total;
}
int CubicSegment::scanlineIntersections(double x[3], int dy[3], double y) const {
int total = 0;
int nextDY = y > p[0].y ? 1 : -1;
x[total] = p[0].x;
if (p[0].y == y) {
if (p[0].y < p[1].y || (p[0].y == p[1].y && (p[0].y < p[2].y || (p[0].y == p[2].y && p[0].y < p[3].y))))
dy[total++] = 1;
else
nextDY = 1;
}
{
Vector2 ab = p[1]-p[0];
Vector2 br = p[2]-p[1]-ab;
Vector2 as = (p[3]-p[2])-(p[2]-p[1])-br;
double t[3];
int solutions = solveCubic(t, as.y, 3*br.y, 3*ab.y, p[0].y-y);
// Sort solutions
double tmp;
if (solutions >= 2) {
if (t[0] > t[1])
tmp = t[0], t[0] = t[1], t[1] = tmp;
if (solutions >= 3 && t[1] > t[2]) {
tmp = t[1], t[1] = t[2], t[2] = tmp;
if (t[0] > t[1])
tmp = t[0], t[0] = t[1], t[1] = tmp;
}
}
for (int i = 0; i < solutions && total < 3; ++i) {
if (t[i] >= 0 && t[i] <= 1) {
x[total] = p[0].x+3*t[i]*ab.x+3*t[i]*t[i]*br.x+t[i]*t[i]*t[i]*as.x;
if (nextDY*(ab.y+2*t[i]*br.y+t[i]*t[i]*as.y) >= 0) {
dy[total++] = nextDY;
nextDY = -nextDY;
}
}
}
}
if (p[3].y == y) {
if (nextDY > 0 && total > 0) {
--total;
nextDY = -1;
}
if ((p[3].y < p[2].y || (p[3].y == p[2].y && (p[3].y < p[1].y || (p[3].y == p[1].y && p[3].y < p[0].y)))) && total < 3) {
x[total] = p[3].x;
if (nextDY < 0) {
dy[total++] = -1;
nextDY = 1;
}
}
}
if (nextDY != (y >= p[3].y ? 1 : -1)) {
if (total > 0)
--total;
else {
if (fabs(p[3].y-y) < fabs(p[0].y-y))
x[total] = p[3].x;
dy[total++] = nextDY;
}
}
return total;
}
static void pointBounds(Point2 p, double &l, double &b, double &r, double &t) {
if (p.x < l) l = p.x;
if (p.y < b) b = p.y;
if (p.x > r) r = p.x;
if (p.y > t) t = p.y;
}
void LinearSegment::bound(double &l, double &b, double &r, double &t) const {
pointBounds(p[0], l, b, r, t);
pointBounds(p[1], l, b, r, t);
}
void QuadraticSegment::bound(double &l, double &b, double &r, double &t) const {
pointBounds(p[0], l, b, r, t);
pointBounds(p[2], l, b, r, t);
Vector2 bot = (p[1]-p[0])-(p[2]-p[1]);
if (bot.x) {
double param = (p[1].x-p[0].x)/bot.x;
if (param > 0 && param < 1)
pointBounds(point(param), l, b, r, t);
}
if (bot.y) {
double param = (p[1].y-p[0].y)/bot.y;
if (param > 0 && param < 1)
pointBounds(point(param), l, b, r, t);
}
}
void CubicSegment::bound(double &l, double &b, double &r, double &t) const {
pointBounds(p[0], l, b, r, t);
pointBounds(p[3], l, b, r, t);
Vector2 a0 = p[1]-p[0];
Vector2 a1 = 2*(p[2]-p[1]-a0);
Vector2 a2 = p[3]-3*p[2]+3*p[1]-p[0];
double params[2];
int solutions;
solutions = solveQuadratic(params, a2.x, a1.x, a0.x);
for (int i = 0; i < solutions; ++i)
if (params[i] > 0 && params[i] < 1)
pointBounds(point(params[i]), l, b, r, t);
solutions = solveQuadratic(params, a2.y, a1.y, a0.y);
for (int i = 0; i < solutions; ++i)
if (params[i] > 0 && params[i] < 1)
pointBounds(point(params[i]), l, b, r, t);
}
void LinearSegment::reverse() {
Point2 tmp = p[0];
p[0] = p[1];
p[1] = tmp;
}
void QuadraticSegment::reverse() {
Point2 tmp = p[0];
p[0] = p[2];
p[2] = tmp;
}
void CubicSegment::reverse() {
Point2 tmp = p[0];
p[0] = p[3];
p[3] = tmp;
tmp = p[1];
p[1] = p[2];
p[2] = tmp;
}
void LinearSegment::moveStartPoint(Point2 to) {
p[0] = to;
}
void QuadraticSegment::moveStartPoint(Point2 to) {
Vector2 origSDir = p[0]-p[1];
Point2 origP1 = p[1];
p[1] += crossProduct(p[0]-p[1], to-p[0])/crossProduct(p[0]-p[1], p[2]-p[1])*(p[2]-p[1]);
p[0] = to;
if (dotProduct(origSDir, p[0]-p[1]) < 0)
p[1] = origP1;
}
void CubicSegment::moveStartPoint(Point2 to) {
p[1] += to-p[0];
p[0] = to;
}
void LinearSegment::moveEndPoint(Point2 to) {
p[1] = to;
}
void QuadraticSegment::moveEndPoint(Point2 to) {
Vector2 origEDir = p[2]-p[1];
Point2 origP1 = p[1];
p[1] += crossProduct(p[2]-p[1], to-p[2])/crossProduct(p[2]-p[1], p[0]-p[1])*(p[0]-p[1]);
p[2] = to;
if (dotProduct(origEDir, p[2]-p[1]) < 0)
p[1] = origP1;
}
void CubicSegment::moveEndPoint(Point2 to) {
p[2] += to-p[3];
p[3] = to;
}
void LinearSegment::splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeSegment *&part3) const {
part1 = new LinearSegment(p[0], point(1/3.), color);
part2 = new LinearSegment(point(1/3.), point(2/3.), color);
part3 = new LinearSegment(point(2/3.), p[1], color);
}
void QuadraticSegment::splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeSegment *&part3) const {
part1 = new QuadraticSegment(p[0], mix(p[0], p[1], 1/3.), point(1/3.), color);
part2 = new QuadraticSegment(point(1/3.), mix(mix(p[0], p[1], 5/9.), mix(p[1], p[2], 4/9.), .5), point(2/3.), color);
part3 = new QuadraticSegment(point(2/3.), mix(p[1], p[2], 2/3.), p[2], color);
}
void CubicSegment::splitInThirds(EdgeSegment *&part1, EdgeSegment *&part2, EdgeSegment *&part3) const {
part1 = new CubicSegment(p[0], p[0] == p[1] ? p[0] : mix(p[0], p[1], 1/3.), mix(mix(p[0], p[1], 1/3.), mix(p[1], p[2], 1/3.), 1/3.), point(1/3.), color);
part2 = new CubicSegment(point(1/3.),
mix(mix(mix(p[0], p[1], 1/3.), mix(p[1], p[2], 1/3.), 1/3.), mix(mix(p[1], p[2], 1/3.), mix(p[2], p[3], 1/3.), 1/3.), 2/3.),
mix(mix(mix(p[0], p[1], 2/3.), mix(p[1], p[2], 2/3.), 2/3.), mix(mix(p[1], p[2], 2/3.), mix(p[2], p[3], 2/3.), 2/3.), 1/3.),
point(2/3.), color);
part3 = new CubicSegment(point(2/3.), mix(mix(p[1], p[2], 2/3.), mix(p[2], p[3], 2/3.), 2/3.), p[2] == p[3] ? p[3] : mix(p[2], p[3], 2/3.), p[3], color);
}
EdgeSegment *QuadraticSegment::convertToCubic() const {
return new CubicSegment(p[0], mix(p[0], p[1], 2/3.), mix(p[1], p[2], 1/3.), p[2], color);
}
void CubicSegment::deconverge(int param, double amount) {
Vector2 dir = direction(param);
Vector2 normal = dir.getOrthonormal();
double h = dotProduct(directionChange(param)-dir, normal);
switch (param) {
case 0:
p[1] += amount*(dir+sign(h)*sqrt(fabs(h))*normal);
break;
case 1:
p[2] -= amount*(dir-sign(h)*sqrt(fabs(h))*normal);
break;
}
}
}
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