public override void findBounds(ref double left, ref double bottom, ref double right, ref double top)
{
Vector2.pointBounds(_p0, ref left, ref bottom, ref right, ref top);
Vector2.pointBounds(_p3, ref left, ref bottom, ref right, ref top);
//
Vector2 a0 = _p1 - _p0;
Vector2 a1 = 2 * (_p2 - _p1 - a0);
Vector2 a2 = _p3 - 3 * _p2 + 3 * _p1 - _p0;
//
EqResult pars = new EqResult();
int solutions = EquationSolver.SolveQuadratic(ref pars, a2.x, a1.x, a0.x);
for (int i = 0; i < solutions; ++i)
{
double par = pars[i];
if (par > 0 && par < 1)
{
Vector2.pointBounds(point(par), ref left, ref bottom, ref right, ref top);
}
}
pars = new EqResult();
solutions = EquationSolver.SolveQuadratic(ref pars, a2.y, a1.y, a0.y);
for (int i = 0; i < solutions; ++i)
{
double par = pars[i];
if (par > 0 && par < 1)
{
Vector2.pointBounds(point(par), ref left, ref bottom, ref right, ref top);
}
}
}
public override SignedDistance signedDistance(Vector2 origin, out double param)
{
Vector2 qa = _p0 - origin;
Vector2 ab = _p1 - _p0;
Vector2 br = _p0 + _p2 - _p1 - _p1;//
double a = Vector2.dotProduct(br, br);
double b = 3 * Vector2.dotProduct(ab, br);
double c = 2 * Vector2.dotProduct(ab, ab) + Vector2.dotProduct(qa, br);
double d = Vector2.dotProduct(qa, ab);
EqResult t = new EqResult();
int solutions = EquationSolver.SolveCubic(ref t, a, b, c, d);
double minDistance = nonZeroSign(Vector2.crossProduct(ab, qa)) * qa.Length(); // distance from A
param = -Vector2.dotProduct(qa, ab) / Vector2.dotProduct(ab, ab);
{
double distance = nonZeroSign(
Vector2.crossProduct(_p2 - _p1, _p2 - origin)) * (_p2 - origin).Length(); // distance from B
if (Math.Abs(distance) < Math.Abs(minDistance))
{
minDistance = distance;
param = Vector2.dotProduct(origin - _p1, _p2 - _p1) / Vector2.dotProduct(_p2 - _p1, _p2 - _p1);
}
}
//possible solution -1,0,1,2
for (int i = 0; i < solutions; ++i)
{
double ti = t[i];
if (ti > 0 && ti < 1)
{
Vector2 endpoint = _p0 + 2 * ti * ab + ti * ti * br;
double distance = nonZeroSign(
Vector2.crossProduct(_p2 - _p0, endpoint - origin)) * (endpoint - origin).Length();
if (Math.Abs(distance) <= Math.Abs(minDistance))
{
minDistance = distance;
param = ti;
}
}
}
if (param >= 0 && param <= 1)
{
return(new SignedDistance(minDistance, 0));
}
if (param < .5)
{
return(new SignedDistance(minDistance, Math.Abs(Vector2.dotProduct(ab.normalize(), qa.normalize()))));
}
else
{
return(new SignedDistance(minDistance, Math.Abs(Vector2.dotProduct((_p2 - _p1).normalize(), (_p2 - origin).normalize()))));
}
}
public override SignedDistance signedDistance(Vector2 origin, out double param)
{
Vector2 qa = _p0 - origin;
Vector2 ab = _p1 - _p0;
Vector2 br = _p2 - _p1 - ab;
Vector2 as_ = (_p3 - _p2) - (_p2 - _p1) - br;
Vector2 epDir = direction(0);
double minDistance = nonZeroSign(Vector2.crossProduct(epDir, qa)) * qa.Length(); // distance from A
param = -Vector2.dotProduct(qa, epDir) / Vector2.dotProduct(epDir, epDir);
{
epDir = direction(1);
double distance = nonZeroSign(Vector2.crossProduct(epDir, _p3 - origin)) * (_p3 - origin).Length(); // distance from B
if (EquationSolver.fabs(distance) < EquationSolver.fabs(minDistance))
{
minDistance = distance;
param = Vector2.dotProduct(origin + epDir - _p3, epDir) / Vector2.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);
for (int step = 0; ; ++step)
{
Vector2 qpt = point(t) - origin;
double distance = nonZeroSign(Vector2.crossProduct(direction(t), qpt)) * qpt.Length();
if (EquationSolver.fabs(distance) < EquationSolver.fabs(minDistance))
{
minDistance = distance;
param = t;
}
if (step == MSDFGEN_CUBIC_SEARCH_STEPS)
{
break;
}
// Improve t
Vector2 d1 = 3 * as_ * t * t + 6 * br * t + 3 * ab;
Vector2 d2 = 6 * as_ * t + 6 * br;
t -= Vector2.dotProduct(qpt, d1) / (Vector2.dotProduct(d1, d1) + Vector2.dotProduct(qpt, d2));
if (t < 0 || t > 1)
{
break;
}
}
}
if (param >= 0 && param <= 1)
{
return(new SignedDistance(minDistance, 0));
}
if (param < .5)
{
return(new SignedDistance(minDistance,
EquationSolver.fabs(Vector2.dotProduct(direction(0), qa.normalize()))));
}
else
{
return(new SignedDistance(minDistance,
EquationSolver.fabs(Vector2.dotProduct(direction(1).normalize(), (_p3 - origin).normalize()))));
}
}