public static Intersection CubicBezierLineSegmentIntersection1(
double p0x, double p0y,
double p1x, double p1y,
double p2x, double p2y,
double p3x, double p3y,
double l0x, double l0y,
double l1x, double l1y,
double epsilon = Epsilon)
{
_ = epsilon;
// ToDo: Figure out why this can't handle intersection with horizontal lines.
var I = new Intersection(IntersectionStates.NoIntersection);
var A = l1y - l0y; //A=y2-y1
var B = l0x - l1x; //B=x1-x2
var C = (l0x * (l0y - l1y)) + (l0y * (l1x - l0x)); //C=x1*(y1-y2)+y1*(x2-x1)
var xCoeff = CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(p0x, p1x, p2x, p3x);
var yCoeff = CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(p0y, p1y, p2y, p3y);
var r = CubicRootsTests.CubicRoots(
/* t^3 */ (A * xCoeff.D) + (B * yCoeff.D),
/* t^2 */ (A * xCoeff.C) + (B * yCoeff.C),
/* t^1 */ (A * xCoeff.B) + (B * yCoeff.B),
/* 1 */ (A * xCoeff.A) + (B * yCoeff.A) + C
);
/*verify the roots are in bounds of the linear segment*/
for (var i = 0; i < 3; i++)
{
var t = r[i];
var x = (xCoeff.D * t * t * t) + (xCoeff.C * t * t) + (xCoeff.B * t) + xCoeff.A;
var y = (yCoeff.D * t * t * t) + (yCoeff.C * t * t) + (yCoeff.B * t) + yCoeff.A;
/*above is intersection point assuming infinitely long line segment,
* make sure we are also in bounds of the line*/
double m;
m = (l1x - l0x) != 0 ? (x - l0x) / (l1x - l0x) : (y - l0y) / (l1y - l0y);
/*in bounds?*/
if (t < 0 || t > 1d || m < 0 || m > 1d)
{
x = 0; // -100; /*move off screen*/
y = 0; // -100;
}
else
{
/*intersection point*/
I.AppendPoint(new Point2D(x, y));
I.State = IntersectionStates.Intersection;
}
}
return(I);
}
public static (double X, double Y)? CubicBezierSelfIntersection1(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)
{
var(xCurveA, xCurveB, xCurveC, xCurveD) = CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(x0, x1, x2, x3);
(var a, var b) = (xCurveD == 0d) ? (xCurveC, xCurveB) : (xCurveC / xCurveD, xCurveB / xCurveD);
var(yCurveA, yCurveB, yCurveC, yCurveD) = CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(y0, y1, y2, y3);
(var p, var q) = (yCurveD == 0d) ? (yCurveC, yCurveB) : (yCurveC / yCurveD, yCurveB / yCurveD);
if (a == p || q == b)
{
return(null);
}
var k = (q - b) / (a - p);
var poly = new double[]
{
(-k * k * k) - (a * k * k) - (b * k),
(3 * k * k) + (2 * k * a) + (2 * b),
-3 * k,
2
};
var roots = CubicRootsTests.CubicRoots(poly[3], poly[2], poly[1], poly[0])
.OrderByDescending(c => c).ToArray();
if (roots.Length != 3)
{
return(null);
}
if (roots[0] >= 0d && roots[0] <= 1d && roots[2] >= 0d && roots[2] <= 1d)
{
return(InterpolateCubic2DTests.CubicInterpolate2D(roots[0], x0, y0, x1, y1, x2, y2, x3, y3));
}
return(null);
}
public static Intersection CubicBezierSegmentOrthogonalEllipseIntersection(double b1X, double b1Y, double b2X, double b2Y, double b3X, double b3Y, double b4X, double b4Y, double h, double k, double a, double b, double epsilon = double.Epsilon) => BernsteinCubicBezierSegmentOrthogonalEllipseIntersectionTests.CubicBezierSegmentOrthogonalEllipseIntersection(CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(b1X, b2X, b3X, b4X), CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(b1Y, b2Y, b3Y, b4Y), h, k, a, b, epsilon);
public static (double X, double Y)? CubicBezierSelfIntersectionX(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)
{
return(CubicBezierSelfIntersectionX(
CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(x0, x1, x2, x3),
CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(y0, y1, y2, y3)));
}
public static (double A, double B, double C, double D, double E) QuarticBezierCoefficientsRecursive(double a, double b, double c, double d, double e)
{
var polynomial = (Polynomial.OneMinusT * CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(a, b, c, d)) + (Polynomial.T * CubicBezierBernsteinBasisTests.CubicBezierBernsteinBasis(b, c, d, e));
return(polynomial[PolynomialTerm.a], polynomial[PolynomialTerm.b], polynomial[PolynomialTerm.c], polynomial[PolynomialTerm.d], polynomial[PolynomialTerm.e]);
}