//-----------------------------------------------------ubspline_to_bezier
public static void UbSplineToBezier(double x1, double y1,
double x2, double y2,
double x3, double y3,
double x4, double y4,
Curve4Points output)
{
// Trans. matrix Uniform BSpline to Bezier
//
// 1/6 4/6 1/6 0
// 0 4/6 2/6 0
// 0 2/6 4/6 0
// 0 1/6 4/6 1/6
//
output.Set(
(x1 + 4 * x2 + x3) / 6,
(y1 + 4 * y2 + y3) / 6,
(4 * x2 + 2 * x3) / 6,
(4 * y2 + 2 * y3) / 6,
(2 * x2 + 4 * x3) / 6,
(2 * y2 + 4 * y3) / 6,
(x2 + 4 * x3 + x4) / 6,
(y2 + 4 * y3 + y4) / 6);
}
//------------------------------------------------------hermite_to_bezier
public static void HermiteToBezier(double x1, double y1,
double x2, double y2,
double x3, double y3,
double x4, double y4,
Curve4Points output)
{
// Trans. matrix Hermite to Bezier
//
// 1 0 0 0
// 1 0 1/3 0
// 0 1 0 -1/3
// 0 1 0 0
//
output.Set(
x1,
y1,
(3 * x1 + x3) / 3,
(3 * y1 + y3) / 3,
(3 * x2 - x4) / 3,
(3 * y2 - y4) / 3,
x2,
y2);
}
//-------------------------------------------------------catrom_to_bezier
public static void CatromToBezier(double x1, double y1,
double x2, double y2,
double x3, double y3,
double x4, double y4,
Curve4Points output)
{
// Trans. matrix Catmull-Rom to Bezier
//
// 0 1 0 0
// -1/6 1 1/6 0
// 0 1/6 1 -1/6
// 0 0 1 0
//
output.Set(
x2,
y2,
(-x1 + 6 * x2 + x3) / 6,
(-y1 + 6 * y2 + y3) / 6,
(x2 + 6 * x3 - x4) / 6,
(y2 + 6 * y3 - y4) / 6,
x3,
y3);
}