偶遇需要拆解凹多邊形
using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; using System.Windows; using System.Windows.Media;namespace DrawPolygon {public static class Settings{public const float Epsilon = 1.192092896e-07f;/// <summary>/// The maximum number of vertices on a convex polygon./// </summary>public static int MaxPolygonVertices = 7;}public class Vertices : List<Point>{public Vertices(){}public Vertices(int capacity){Capacity = capacity;}public Vertices(Point[] Point){for (int i = 0; i < Point.Length; i++){Add(Point[i]);}}public Vertices(IList<Point> vertices){for (int i = 0; i < vertices.Count; i++){Add(vertices[i]);}}public int NextIndex(int index){if (index == Count - 1){return 0;}return index + 1;}public Point NextVertex(int index){return this[NextIndex(index)];}public int PreviousIndex(int index){if (index == 0){return Count - 1;}return index - 1;}public Point PreviousVertex(int index){return this[PreviousIndex(index)];}public float GetSignedArea(){int i;float area = 0;for (i = 0; i < Count; i++){int j = (i + 1) % Count;area += (float)(this[i].X * this[j].Y);area -= (float)(this[i].Y * this[j].X);}area /= 2.0f;return area;}public const float Pi = 3.14159f;public bool IsCounterClockWise(){return Count < 3 ? true : (GetSignedArea() > 0.0f);}public void ForceCounterClockWise(){if (!IsCounterClockWise()){Reverse();}}public override string ToString(){StringBuilder builder = new StringBuilder();for (int i = 0; i < Count; i++){builder.Append(this[i].ToString());if (i < Count - 1){builder.Append(" ");}}return builder.ToString();}}public static class BayazitDecomposer{private static int num = 1;private static int stop = 20;private static int stopTemp = 12;public static List<Vertices> GetConvexPartition(PointCollection points){return GetConvexPartition(new Vertices(points));}public static List<Vertices> GetConvexPartition(Vertices vertices){stop = 50;stopTemp = 20;return ConvexPartition(vertices, 1);}private static List<Vertices> ConvexPartition(Vertices vertices, int verticesTemp){stopTemp++;num = verticesTemp;//verticesTemp為1時正常分解，為2時代表遇到不能分解的輪廓，這時返回null，并放棄這個輪廓的更新if (stop == 1){stop = vertices.Count;}if (stopTemp >= stop){num = 2;}if (num == 1){if (vertices == null)return null;vertices.ForceCounterClockWise();List<Vertices> list = new List<Vertices>();float d, lowerDist, upperDist;Point p;Point lowerInt = new Point();Point upperInt = new Point();int lowerIndex = 0, upperIndex = 0;Vertices lowerPoly, upperPoly;for (int i = 0; i < vertices.Count; ++i){try { Reflex(i, vertices); }catch{num = 2;return null;}if (Reflex(i, vertices)){lowerDist = upperDist = float.MaxValue;for (int j = 0; j < vertices.Count; ++j){// if line intersects with an edgeif (Left(At(i - 1, vertices), At(i, vertices), At(j, vertices)) && RightOn(At(i - 1, vertices), At(i, vertices), At(j - 1, vertices))){// find the point of intersectionp = LineTools.LineIntersect(At(i - 1, vertices), At(i, vertices), At(j, vertices), At(j - 1, vertices));if (Right(At(i + 1, vertices), At(i, vertices), p)){// make sure it's inside the polyd = SquareDist(At(i, vertices), p);if (d < lowerDist){// keep only the closest intersectionlowerDist = d;lowerInt = p;lowerIndex = j;}}}if (Left(At(i + 1, vertices), At(i, vertices), At(j + 1, vertices)) && RightOn(At(i + 1, vertices), At(i, vertices), At(j, vertices))){p = LineTools.LineIntersect(At(i + 1, vertices), At(i, vertices), At(j, vertices), At(j + 1, vertices));if (Left(At(i - 1, vertices), At(i, vertices), p)){d = SquareDist(At(i, vertices), p);if (d < upperDist){upperDist = d;upperIndex = j;upperInt = p;}}}}// if there are no vertices to connect to, choose a point in the middleif (lowerIndex == (upperIndex + 1) % vertices.Count){Point sp = new Point((lowerInt.X + upperInt.X) / 2, (lowerInt.Y + upperInt.Y) / 2);lowerPoly = Copy(i, upperIndex, vertices);lowerPoly.Add(sp);upperPoly = Copy(lowerIndex, i, vertices);upperPoly.Add(sp);}else{double highestScore = 0, bestIndex = lowerIndex;while (upperIndex < lowerIndex) upperIndex += vertices.Count;for (int j = lowerIndex; j <= upperIndex; ++j){if (CanSee(i, j, vertices)){double score = 1 / (SquareDist(At(i, vertices), At(j, vertices)) + 1);if (Reflex(j, vertices)){if (RightOn(At(j - 1, vertices), At(j, vertices), At(i, vertices)) && LeftOn(At(j + 1, vertices), At(j, vertices), At(i, vertices))){score += 3;}else{score += 2;}}else{score += 1;}if (score > highestScore){bestIndex = j;highestScore = score;}}}lowerPoly = Copy(i, (int)bestIndex, vertices);upperPoly = Copy((int)bestIndex, i, vertices);}//在每次遞歸時都進行檢測，遇到不能分解的就開始跳出循環var lslowerPoly = ConvexPartition(lowerPoly, num);var lsupperPoly = ConvexPartition(upperPoly, num);if (lslowerPoly == null || lsupperPoly == null){return null;}list.AddRange(lslowerPoly);list.AddRange(lsupperPoly);return list;}}// polygon is already convexif (vertices.Count > Settings.MaxPolygonVertices){lowerPoly = Copy(0, vertices.Count / 2, vertices);upperPoly = Copy(vertices.Count / 2, 0, vertices);//當輪廓的點數目大于Settings.MaxPolygonVertices時分解輪廓的帶你數目var lslowerPoly = ConvexPartition(lowerPoly, num);var lsupperPoly = ConvexPartition(upperPoly, num);if (lslowerPoly == null || lsupperPoly == null){return null;}list.AddRange(lslowerPoly);list.AddRange(lsupperPoly);}else{list.Add(vertices);}//The polygons are not guaranteed to be without collinear points. We remove them to be sure.for (int i = 0; i < list.Count; i++){list[i] = SimplifyTools.CollinearSimplify(list[i], 0);}//Remove empty vertice collectionsfor (int i = list.Count - 1; i >= 0; i--){if (list[i].Count == 0){list.RemoveAt(i);}}return list;}return null;}private static bool Reflex(int i, Vertices vertices){return Right(i, vertices);}private static bool Right(int i, Vertices vertices){return Right(At(i - 1, vertices), At(i, vertices), At(i + 1, vertices));}private static bool Left(Point a, Point b, Point c){return MathUtils.Area(ref a, ref b, ref c) > 0;}private static bool LeftOn(Point a, Point b, Point c){return MathUtils.Area(ref a, ref b, ref c) >= 0;}private static bool Right(Point a, Point b, Point c){return MathUtils.Area(ref a, ref b, ref c) < 0;}private static bool RightOn(Point a, Point b, Point c){return MathUtils.Area(ref a, ref b, ref c) <= 0;}private static float SquareDist(Point a, Point b){float dx = (float)(b.X - a.X);float dy = (float)(b.Y - a.Y);return dx * dx + dy * dy;}private static Point At(int i, Vertices vertices){int s = vertices.Count;return vertices[i < 0 ? s - (-i % s) : i % s];}private static Vertices Copy(int i, int j, Vertices vertices){Vertices p = new Vertices();while (j < i) j += vertices.Count;for (; i <= j; ++i){p.Add(At(i, vertices));}return p;}private static bool CanSee(int i, int j, Vertices vertices){if (Reflex(i, vertices)){if (LeftOn(At(i, vertices), At(i - 1, vertices), At(j, vertices)) &&RightOn(At(i, vertices), At(i + 1, vertices), At(j, vertices))) return false;}else{if (RightOn(At(i, vertices), At(i + 1, vertices), At(j, vertices)) ||LeftOn(At(i, vertices), At(i - 1, vertices), At(j, vertices))) return false;}if (Reflex(j, vertices)){if (LeftOn(At(j, vertices), At(j - 1, vertices), At(i, vertices)) &&RightOn(At(j, vertices), At(j + 1, vertices), At(i, vertices))) return false;}else{if (RightOn(At(j, vertices), At(j + 1, vertices), At(i, vertices)) ||LeftOn(At(j, vertices), At(j - 1, vertices), At(i, vertices))) return false;}for (int k = 0; k < vertices.Count; ++k){if ((k + 1) % vertices.Count == i || k == i || (k + 1) % vertices.Count == j || k == j){continue;}Point intersectionPoint;if (LineTools.LineIntersect(At(i, vertices), At(j, vertices), At(k, vertices), At(k + 1, vertices), out intersectionPoint)){return false;}}return true;}}public static class MathUtils{public static bool IsValid(double x){return double.IsNaN(x) ? false : !double.IsInfinity(x);}public static void Cross(ref Point a, ref Point b, out float c){c = (float)(a.X * b.Y - a.Y * b.X);}public static float Area(ref Point a, ref Point b, ref Point c){return (float)(a.X * (b.Y - c.Y) + b.X * (c.Y - a.Y) + c.X * (a.Y - b.Y));}public static bool Collinear(ref Point a, ref Point b, ref Point c, float tolerance){return FloatInRange(Area(ref a, ref b, ref c), -tolerance, tolerance);}public static bool FloatEquals(float value1, float value2){return Math.Abs(value1 - value2) <= Settings.Epsilon;}public static bool FloatInRange(float value, float min, float max){return (value >= min && value <= max);}}public static class SimplifyTools{public static Vertices CollinearSimplify(Vertices vertices, float collinearityTolerance){if (vertices.Count < 3)return vertices;Vertices simplified = new Vertices();for (int i = 0; i < vertices.Count; i++){int prevId = vertices.PreviousIndex(i);int nextId = vertices.NextIndex(i);Point prev = vertices[prevId];Point current = vertices[i];Point next = vertices[nextId];if (MathUtils.Collinear(ref prev, ref current, ref next, collinearityTolerance))continue;simplified.Add(current);}return simplified;}}public static class LineTools{public static Point LineIntersect(Point p1, Point p2, Point q1, Point q2){Point i = new Point(0, 0);float a1 = (float)(p2.Y - p1.Y);float b1 = (float)(p1.X - p2.X);float c1 = (float)(a1 * p1.X + b1 * p1.Y);float a2 = (float)(q2.Y - q1.Y);float b2 = (float)(q1.X - q2.X);float c2 = (float)(a2 * q1.X + b2 * q1.Y);float det = a1 * b2 - a2 * b1;if (!MathUtils.FloatEquals(det, 0)){i.X = (b2 * c1 - b1 * c2) / det;i.Y = (a1 * c2 - a2 * c1) / det;}return i;}public static bool LineIntersect(ref Point point1, ref Point point2, ref Point point3, ref Point point4, bool firstIsSegment, bool secondIsSegment, out Point point){point = new Point();float a = (float)(point4.Y - point3.Y);float b = (float)(point2.X - point1.X);float c = (float)(point4.X - point3.X);float d = (float)(point2.Y - point1.Y);float denom = (a * b) - (c * d);if (!(denom >= -Settings.Epsilon && denom <= Settings.Epsilon)){float e = (float)(point1.Y - point3.Y);float f = (float)(point1.X - point3.X);float oneOverDenom = 1.0f / denom;float ua = (c * e) - (a * f);ua *= oneOverDenom;if (!firstIsSegment || ua >= 0.0f && ua <= 1.0f){float ub = (b * e) - (d * f);ub *= oneOverDenom;if (!secondIsSegment || ub >= 0.0f && ub <= 1.0f){if (ua != 0f || ub != 0f){point.X = point1.X + ua * b;point.Y = point1.Y + ua * d;return true;}}}}return false;}public static bool LineIntersect(Point point1, Point point2, Point point3, Point point4, out Point intersectionPoint){return LineIntersect(ref point1, ref point2, ref point3, ref point4, true, true, out intersectionPoint);}} }
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