public static Intersection QuadraticBezierLineSegmentIntersection0(
double p1X, double p1Y,
double p2X, double p2Y,
double p3X, double p3Y,
double a1X, double a1Y,
double a2X, double a2Y,
double epsilon = Epsilon)
{
var min = MinPointTests.MinPoint(a1X, a1Y, a2X, a2Y);
var max = MaxPointTests.MaxPoint(a1X, a1Y, a2X, a2Y);
var result = new Intersection(IntersectionStates.NoIntersection);
var a = new Vector2D(p2X, p2Y) * (-2);
var c2 = new Vector2D(p1X, p1Y) + (a + new Vector2D(p3X, p3Y));
a = new Vector2D(p1X, p1Y) * (-2);
var b = new Vector2D(p2X, p2Y) * 2;
var c1 = a + b;
var c0 = new Point2D(p1X, p1Y);
var n = new Point2D(a1Y - a2Y, a2X - a1X);
var cl = (a1X * a2Y) - (a2X * a1Y);
var roots = QuadraticRootsTests.QuadraticRoots(
DotProduct2Vector2DTests.DotProduct2D(n.X, n.Y, c2.I, c2.J),
DotProduct2Vector2DTests.DotProduct2D(n.X, n.Y, c1.I, c1.J),
DotProduct2Vector2DTests.DotProduct2D(n.X, n.Y, c0.X + cl, c0.Y + cl),
epsilon);
for (var i = 0; i < roots.Count; i++)
{
var t = roots[i];
if (0 <= t && t <= 1)
{
var p4 = InterpolateLinear2DTests.LinearInterpolate2D(t, p1X, p1Y, p2X, p2Y);
var p5 = InterpolateLinear2DTests.LinearInterpolate2D(t, p2X, p2Y, p3X, p3Y);
var p6 = InterpolateLinear2DTests.LinearInterpolate2D(t, p4.X, p4.Y, p5.X, p5.Y);
if (a1X == a2X)
{
if (min.Y <= p6.Y && p6.Y <= max.Y)
{
result.State = IntersectionStates.Intersection;
result.AppendPoint(p6);
}
}
else if (a1Y == a2Y)
{
if (min.X <= p6.X && p6.X <= max.X)
{
result.State = IntersectionStates.Intersection;
result.AppendPoint(p6);
}
}
else if (GreaterThanOrEqualTests.GreaterThanOrEqual(p6.X, p6.Y, min.X, min.Y) && LessThanOrEqualTests.LessThanOrEqual(p6.X, p6.Y, max.X, max.Y))
{
result.State = IntersectionStates.Intersection;
result.AppendPoint(p6);
}
}
}
return(result);
}
public static Intersection CubicBezierLineIntersection0(
double p1X, double p1Y,
double p2X, double p2Y,
double p3X, double p3Y,
double p4X, double p4Y,
double a1X, double a1Y,
double a2X, double a2Y,
double epsilon = Epsilon)
{
Vector2D a, b, c, d;
Vector2D c3, c2, c1, c0;
double cl;
Vector2D n;
var min = MinPointTests.MinPoint(a1X, a1Y, a2X, a2Y);
var max = MaxPointTests.MaxPoint(a1X, a1Y, a2X, a2Y);
var result = new Intersection(IntersectionStates.NoIntersection);
a = new Vector2D(p1X, p1Y) * (-1);
b = new Vector2D(p2X, p2Y) * 3;
c = new Vector2D(p3X, p3Y) * (-3);
d = a + (b + (c + new Vector2D(p4X, p4Y)));
c3 = new Vector2D(d.I, d.J);
a = new Vector2D(p1X, p1Y) * 3;
b = new Vector2D(p2X, p2Y) * (-6);
c = new Vector2D(p3X, p3Y) * 3;
d = a + (b + c);
c2 = new Vector2D(d.I, d.J);
a = new Vector2D(p1X, p1Y) * (-3);
b = new Vector2D(p2X, p2Y) * 3;
c = a + b;
c1 = new Vector2D(c.I, c.J);
c0 = new Vector2D(p1X, p1Y);
n = new Vector2D(a1Y - a2Y, a2X - a1X);
cl = (a1X * a2Y) - (a2X * a1Y);
var roots = CubicRootsTests.CubicRoots(
DotProduct2Vector2DTests.DotProduct2D(n.I, n.J, c3.I, c3.J),
DotProduct2Vector2DTests.DotProduct2D(n.I, n.J, c2.I, c2.J),
DotProduct2Vector2DTests.DotProduct2D(n.I, n.J, c1.I, c1.J),
DotProduct2Vector2DTests.DotProduct2D(n.I, n.J, c0.I + cl, c0.J + cl),
epsilon);
for (var i = 0; i < roots.Count; i++)
{
var t = roots[i];
if (0 <= t && t <= 1)
{
var p5 = InterpolateLinear2DTests.LinearInterpolate2D(t, p1X, p1Y, p2X, p2Y);
var p6 = InterpolateLinear2DTests.LinearInterpolate2D(t, p2X, p2Y, p3X, p3Y);
var p7 = InterpolateLinear2DTests.LinearInterpolate2D(t, p3X, p3Y, p4X, p4Y);
var p8 = InterpolateLinear2DTests.LinearInterpolate2D(t, p5.X, p5.Y, p6.X, p6.Y);
var p9 = InterpolateLinear2DTests.LinearInterpolate2D(t, p6.X, p6.Y, p7.X, p7.Y);
var p10 = InterpolateLinear2DTests.LinearInterpolate2D(t, p8.X, p8.Y, p9.X, p9.Y);
if (a1X == a2X)
{
result.State = IntersectionStates.Intersection;
result.AppendPoint(p10);
}
else if (a1Y == a2Y)
{
result.State = IntersectionStates.Intersection;
result.AppendPoint(p10);
}
else if (GreaterThanOrEqualTests.GreaterThanOrEqual(p10.X, p10.Y, min.X, min.Y) && LessThanOrEqualTests.LessThanOrEqual(p10.X, p10.Y, max.X, max.Y))
{
result.State = IntersectionStates.Intersection;
result.AppendPoint(p10);
}
}
}
return(result);
}
