Пример #1
0
        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);
        }
Пример #2
0
        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);
        }