public static bool CatmullRomSegmentToCurve4(this PathWriter _writer,
double x0, double y0, //p0 //explicit x0 y0
double x1, double y1, //p1
double x2, double y2, //p2
double x3, double y3) //p3
{
//just experiment only,
//not correct now
//https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline
//https://stackoverflow.com/questions/30748316/catmull-rom-interpolation-on-svg-paths
double t0 = 0.0f,
t1 = CatmullRomGetT(t0, x0, y0, x1, y1),
t2 = CatmullRomGetT(t1, x1, y1, x2, y2),
t3 = CatmullRomGetT(t2, x2, y2, x3, y3);
if ((t0 == t1) || (t1 == t2) || (t2 == t3))
{
//invalid
_writer.LineTo(x1, y1);
_writer.LineTo(x2, y2);
return(false);
}
double c1 = (t2 - t1) / (t2 - t0),
c2 = (t1 - t0) / (t2 - t0),
d1 = (t3 - t2) / (t3 - t1),
d2 = (t2 - t1) / (t3 - t1);
double m1x = (t2 - t1) * (c1 * (x1 - x0) / (t1 - t0) + c2 * (x2 - x1) / (t2 - t1));
double m2x = (t2 - t1) * (d1 * (x2 - x1) / (t2 - t1) + d2 * (x3 - x2) / (t3 - t2));
double m1y = (t2 - t1) * (c1 * (y1 - y0) / (t1 - t0) + c2 * (y2 - y1) / (t2 - t1));
double m2y = (t2 - t1) * (d1 * (y2 - y1) / (t2 - t1) + d2 * (y3 - y2) / (t3 - t2));
//Q0 = P1
//Q1 = P1 + M1 / 3
//Q2 = P2 - M2 / 3
//Q3 = P2
_writer.LineTo(x1, y1);
_writer.Curve4(x1 + m1x / 3, y1 + m1y / 3, x2 - m2x / 3, y2 - m2y / 3, x2, y2);
return(true);
}
public static void Hermite(this PathWriter pw, double[] xyCoords)
{
Curve4Points curve4_points = pw._c4_points;
pw.MoveTo(xyCoords[0], xyCoords[1]);
for (int i = 0; i < xyCoords.Length - (4 * 2);)
{
Curves.HermiteToBezier(
xyCoords[i], xyCoords[i + 1],
xyCoords[i + 2], xyCoords[i + 3],
xyCoords[i + 4], xyCoords[i + 5],
xyCoords[i + 6], xyCoords[i + 7],
curve4_points
);
pw.Curve4(curve4_points.x1, curve4_points.y1,
curve4_points.x2, curve4_points.y2,
curve4_points.x3, curve4_points.y3
);
i += 2;
}
}
public static void CatmulRom(this PathWriter pw, double[] xyCoords)
{
Curve4Points curve4_points = pw._c4_points;
pw.MoveTo(xyCoords[2], xyCoords[3]);//***
for (int i = 0; i < xyCoords.Length - (4 * 2);)
{
Curves.CatromToBezier(
xyCoords[i], xyCoords[i + 1],
xyCoords[i + 2], xyCoords[i + 3],
xyCoords[i + 4], xyCoords[i + 5],
xyCoords[i + 6], xyCoords[i + 7],
pw._c4_points
);
pw.Curve4(curve4_points.x1, curve4_points.y1,
curve4_points.x2, curve4_points.y2,
curve4_points.x3, curve4_points.y3
);
i += 2;
}
}