74 lines
2.0 KiB
C#
74 lines
2.0 KiB
C#
using System;
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using System.Collections.Generic;
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using System.Linq;
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using System.Text;
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using System.Windows;
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using System.Windows.Media.Media3D;
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namespace Microsoft.Research.DynamicDataDisplay.Common.Auxiliary
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{
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public static class TriangleMath
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{
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public static bool TriangleContains(Point a, Point b, Point c, Point m)
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{
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double a0 = a.X - c.X;
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double a1 = b.X - c.X;
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double a2 = a.Y - c.Y;
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double a3 = b.Y - c.Y;
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if (AreClose(a0 * a3, a1 * a2))
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{
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// determinant is too close to zero => apexes are on one line
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Vector ab = a - b;
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Vector ac = a - c;
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Vector bc = b - c;
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Vector ax = a - m;
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Vector bx = b - m;
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bool res = AreClose(ab.X * ax.Y, ab.Y * ax.X) && !AreClose(ab.LengthSquared, 0) ||
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AreClose(ac.X * ax.Y, ac.Y * ax.X) && !AreClose(ac.LengthSquared, 0) ||
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AreClose(bc.X * bx.Y, bc.Y * bx.X) && !AreClose(bc.LengthSquared, 0);
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return res;
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}
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else
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{
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double b1 = m.X - c.X;
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double b2 = m.Y - c.Y;
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// alpha, beta and gamma - are baricentric coordinates of v
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// in triangle with apexes a, b and c
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double beta = (b2 / a2 * a0 - b1) / (a3 / a2 * a0 - a1);
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double alpha = (b1 - a1 * beta) / a0;
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double gamma = 1 - beta - alpha;
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return alpha >= 0 && beta >= 0 && gamma >= 0;
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}
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}
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private const double eps = 0.00001;
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private static bool AreClose(double x, double y)
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{
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return Math.Abs(x - y) < eps;
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}
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public static Vector3D GetBaricentricCoordinates(Point a, Point b, Point c, Point m)
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{
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double Sac = GetSquare(a, c, m);
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double Sbc = GetSquare(b, c, m);
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double Sab = GetSquare(a, b, m);
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double sum = (Sab + Sac + Sbc) / 3;
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return new Vector3D(Sbc / sum, Sac / sum, Sab / sum);
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}
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public static double GetSquare(Point a, Point b, Point c)
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{
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double ab = (a - b).Length;
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double ac = (a - c).Length;
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double bc = (b - c).Length;
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double p = 0.5 * (ab + ac + bc); // half of perimeter
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return Math.Sqrt(p * (p - ab) * (p - ac) * (p - bc));
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}
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}
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}
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