private static FloatRgb Mix(FloatRgb a, FloatRgb b, double weight)
{
var output = new FloatRgb
{
R = Arithmetic.Mix(a.R, b.R, weight),
G = Arithmetic.Mix(a.G, b.G, weight),
B = Arithmetic.Mix(a.B, b.B, weight)
};
return(output);
}
public override unsafe SignedDistance SignedDistance(Vector2 origin, ref double param)
{
var qa = _p[0] - origin;
var ab = _p[1] - _p[0];
var br = _p[0] + _p[2] - _p[1] - _p[1];
var coefficient = stackalloc[]
{
Vector2.Dot(br, br),
3 * Vector2.Dot(ab, br),
2 * Vector2.Dot(ab, ab) + Vector2.Dot(qa, br),
Vector2.Dot(qa, ab)
};
var t = stackalloc double[3];
var solutions = Equations.SolveCubic(t, coefficient);
var minDistance = Arithmetic.NonZeroSign(Vector2.Cross(ab, qa)) * qa.Length(); // distance from A
param = -Vector2.Dot(qa, ab) / Vector2.Dot(ab, ab);
{
var distance = Arithmetic.NonZeroSign(Vector2.Cross(_p[2] - _p[1], _p[2] - origin)) *
(_p[2] - origin).Length(); // distance from B
if (Math.Abs(distance) < Math.Abs(minDistance))
{
minDistance = distance;
param = Vector2.Dot(origin - _p[1], _p[2] - _p[1]) /
Vector2.Dot(_p[2] - _p[1], _p[2] - _p[1]);
}
}
for (var i = 0; i < solutions; ++i)
{
if (t[i] > 0 && t[i] < 1)
{
var endpoint = _p[0] + 2 * t[i] * ab + t[i] * t[i] * br;
var distance = Arithmetic.NonZeroSign(Vector2.Cross(_p[2] - _p[0], endpoint - origin)) *
(endpoint - origin).Length();
if (Math.Abs(distance) <= Math.Abs(minDistance))
{
minDistance = distance;
param = t[i];
}
}
}
if (param >= 0 && param <= 1)
{
return(new SignedDistance(minDistance, 0));
}
if (param < .5)
{
return(new SignedDistance(minDistance, Math.Abs(Vector2.Dot(ab.Normalize(), qa.Normalize()))));
}
return(new SignedDistance(minDistance,
Math.Abs(Vector2.Dot((_p[2] - _p[1]).Normalize(), (_p[2] - origin).Normalize()))));
}
public static void RenderSdf(Bitmap <float> output, Bitmap <FloatRgb> sdf, double pxRange)
{
int w = output.Width, h = output.Height;
pxRange *= (double)(w + h) / (sdf.Width + sdf.Height);
for (var y = 0; y < h; ++y)
{
for (var x = 0; x < w; ++x)
{
var s = Sample(sdf, new Vector2((x + .5) / w, (y + .5) / h));
output[x, y] = DistVal(Arithmetic.Median(s.R, s.G, s.B), pxRange);
}
}
}
private static float Sample(Bitmap <float> bitmap, Vector2 pos)
{
int w = bitmap.Width, h = bitmap.Height;
var x = pos.X * w - .5;
var y = pos.Y * h - .5;
var l = (int)Math.Floor(x);
var b = (int)Math.Floor(y);
var r = l + 1;
var t = b + 1;
var lr = x - l;
var bt = y - b;
l = Math.Clamp(l, 0, w - 1);
r = Math.Clamp(r, 0, w - 1);
b = Math.Clamp(b, 0, h - 1);
t = Math.Clamp(t, 0, h - 1);
return(Arithmetic.Mix(Arithmetic.Mix(bitmap[l, b], bitmap[r, b], lr),
Arithmetic.Mix(bitmap[l, t], bitmap[r, t], lr), bt));
}
public override Vector2 Direction(double param)
{
var tangent = Arithmetic.Mix(Arithmetic.Mix(_p[1] - _p[0], _p[2] - _p[1], param),
Arithmetic.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);
}
public override SignedDistance SignedDistance(Vector2 origin, ref double param)
{
var aq = origin - _p[0];
var ab = _p[1] - _p[0];
param = Vector2.Dot(aq, ab) / Vector2.Dot(ab, ab);
var eq = _p[param > 0.5 ? 1 : 0] - origin;
var endpointDistance = eq.Length();
if (param > 0 && param < 1)
{
var orthoDistance = Vector2.Dot(ab.GetOrthonormal(), aq);
if (Math.Abs(orthoDistance) < endpointDistance)
{
return(new SignedDistance(orthoDistance, 0));
}
}
return(new SignedDistance(Arithmetic.NonZeroSign(Vector2.Cross(aq, ab)) * endpointDistance,
Math.Abs(Vector2.Dot(ab.Normalize(), eq.Normalize()))));
}
public override void SplitInThirds(out EdgeSegment part1, out EdgeSegment part2, out EdgeSegment part3)
{
part1 = new CubicSegment(Color, _p[0], _p[0] == _p[1] ? _p[0] : Arithmetic.Mix(_p[0], _p[1], 1.0 / 3.0),
Arithmetic.Mix(Arithmetic.Mix(_p[0], _p[1], 1.0 / 3.0), Arithmetic.Mix(_p[1], _p[2], 1.0 / 3.0),
1.0 / 3.0), Point(1.0 / 3.0));
part2 = new CubicSegment(Color, Point(1.0 / 3.0),
Arithmetic.Mix(
Arithmetic.Mix(Arithmetic.Mix(_p[0], _p[1], 1.0 / 3.0), Arithmetic.Mix(_p[1], _p[2], 1.0 / 3.0),
1.0 / 3.0),
Arithmetic.Mix(Arithmetic.Mix(_p[1], _p[2], 1.0 / 3.0), Arithmetic.Mix(_p[2], _p[3], 1.0 / 3.0),
1.0 / 3.0), 2.0 / 3.0),
Arithmetic.Mix(
Arithmetic.Mix(Arithmetic.Mix(_p[0], _p[1], 2.0 / 3.0), Arithmetic.Mix(_p[1], _p[2], 2.0 / 3.0),
2.0 / 3.0),
Arithmetic.Mix(Arithmetic.Mix(_p[1], _p[2], 2.0 / 3.0), Arithmetic.Mix(_p[2], _p[3], 2.0 / 3.0),
2.0 / 3.0), 1.0 / 3.0),
Point(2.0 / 3.0));
part3 = new CubicSegment(Color, Point(2.0 / 3.0),
Arithmetic.Mix(Arithmetic.Mix(_p[1], _p[2], 2.0 / 3.0), Arithmetic.Mix(_p[2], _p[3], 2.0 / 3.0),
2.0 / 3.0),
_p[2] == _p[3] ? _p[3] : Arithmetic.Mix(_p[2], _p[3], 2.0 / 3.0), _p[3]);
}
public override SignedDistance SignedDistance(Vector2 origin, ref double param)
{
var qa = _p[0] - origin;
var ab = _p[1] - _p[0];
var br = _p[2] - _p[1] - ab;
var as_ = _p[3] - _p[2] - (_p[2] - _p[1]) - br;
var epDir = Direction(0);
var minDistance = Arithmetic.NonZeroSign(Vector2.Cross(epDir, qa)) * qa.Length(); // distance from A
param = -Vector2.Dot(qa, epDir) / Vector2.Dot(epDir, epDir);
{
epDir = Direction(1);
var distance =
Arithmetic.NonZeroSign(Vector2.Cross(epDir, _p[3] - origin)) *
(_p[3] - origin).Length(); // distance from B
if (Math.Abs(distance) < Math.Abs(minDistance))
{
minDistance = distance;
param = Vector2.Dot(origin + epDir - _p[3], epDir) / Vector2.Dot(epDir, epDir);
}
}
// Iterative minimum distance search
for (var i = 0; i <= MsdfgenCubicSearchStarts; ++i)
{
var t = (double)i / MsdfgenCubicSearchStarts;
for (var step = 0;; ++step)
{
var qpt = Point(t) - origin;
var distance = Arithmetic.NonZeroSign(Vector2.Cross(Direction(t), qpt)) * qpt.Length();
if (Math.Abs(distance) < Math.Abs(minDistance))
{
minDistance = distance;
param = t;
}
if (step == MsdfgenCubicSearchSteps)
{
break;
}
// Improve t
var d1 = 3 * as_ * t * t + 6 * br * t + 3 * ab;
var d2 = 6 * as_ * t + 6 * br;
t -= Vector2.Dot(qpt, d1) / (Vector2.Dot(d1, d1) + Vector2.Dot(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, Math.Abs(Vector2.Dot(Direction(0).Normalize(), qa.Normalize()))));
}
return(new SignedDistance(minDistance,
Math.Abs(Vector2.Dot(Direction(1).Normalize(), (_p[3] - origin).Normalize()))));
}
public override void SplitInThirds(out EdgeSegment part1, out EdgeSegment part2, out EdgeSegment part3)
{
part1 = new QuadraticSegment(Color, _p[0], Arithmetic.Mix(_p[0], _p[1], 1.0 / 3.0), Point(1.0 / 3.0));
part2 = new QuadraticSegment(Color, Point(1.0 / 3.0),
Arithmetic.Mix(Arithmetic.Mix(_p[0], _p[1], 5.0 / 9.0), Arithmetic.Mix(_p[1], _p[2], 4.0 / 9.0), 0.5),
Point(2 / 3.0));
part3 = new QuadraticSegment(Color, Point(2.0 / 3.0), Arithmetic.Mix(_p[1], _p[2], 2.0 / 3.0), _p[2]);
}
public override Vector2 Direction(double param)
{
return(Arithmetic.Mix(_p[1] - _p[0], _p[2] - _p[1], param));
}
public override Vector2 Point(double param)
{
return(Arithmetic.Mix(Arithmetic.Mix(_p[0], _p[1], param), Arithmetic.Mix(_p[1], _p[2], param), param));
}