DCDC24-EmissionVision/Assets/WorldPoliticalMapGlobeEdition/Scripts/PolyTri/Triangulation/Util/TriangulationUtil.cs

/* Poly2Tri
 * Copyright (c) 2009-2010, Poly2Tri Contributors
 * http://code.google.com/p/poly2tri/
 *
 * All rights reserved.
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 *   this list of conditions and the following disclaimer in the documentation
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 * * Neither the name of Poly2Tri nor the names of its contributors may be
 *   used to endorse or promote products derived from this software without specific
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 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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using System;
using System.Collections.Generic;
using System.Text;

namespace WPM.Poly2Tri {
	/**
     * @author Thomas Åhlén, thahlen@gmail.com
     */
	public class TriangulationUtil {
		/// <summary>
		///   Requirements:
		/// 1. a,b and c form a triangle.
		/// 2. a and d is know to be on opposite side of bc
		/// <code>
		///                a
		///                +
		///               / \
		///              /   \
		///            b/     \c
		///            +-------+ 
		///           /    B    \  
		///          /           \ 
		/// </code>
		///    Facts:
		///  d has to be in area B to have a chance to be inside the circle formed by a,b and c
		///  d is outside B if orient2d(a,b,d) or orient2d(c,a,d) is CW
		///  This preknowledge gives us a way to optimize the incircle test
		/// </summary>
		/// <param name="pa">triangle point, opposite d</param>
		/// <param name="pb">triangle point</param>
		/// <param name="pc">triangle point</param>
		/// <param name="pd">point opposite a</param>
		/// <returns>true if d is inside circle, false if on circle edge</returns>
		public static bool SmartIncircle (Point2D pa, Point2D pb, Point2D pc, Point2D pd) {
			double pdx = pd.X;
			double pdy = pd.Y;
			double adx = pa.X - pdx;
			double ady = pa.Y - pdy;
			double bdx = pb.X - pdx;
			double bdy = pb.Y - pdy;

			double adxbdy = adx * bdy;
			double bdxady = bdx * ady;
			double oabd = adxbdy - bdxady;
			//        oabd = orient2d(pa,pb,pd);
			if (oabd <= 0) {
				return false;
			}

			double cdx = pc.X - pdx;
			double cdy = pc.Y - pdy;

			double cdxady = cdx * ady;
			double adxcdy = adx * cdy;
			double ocad = cdxady - adxcdy;
			//      ocad = orient2d(pc,pa,pd);
			if (ocad <= 0) {
				return false;
			}

			double bdxcdy = bdx * cdy;
			double cdxbdy = cdx * bdy;

			double alift = adx * adx + ady * ady;
			double blift = bdx * bdx + bdy * bdy;
			double clift = cdx * cdx + cdy * cdy;

			double det = alift * (bdxcdy - cdxbdy) + blift * ocad + clift * oabd;

			return det > 0;
		}

		public static bool InScanArea (Point2D pa, Point2D pb, Point2D pc, Point2D pd) {
			double pdx = pd.X;
			double pdy = pd.Y;
			double adx = pa.X - pdx;
			double ady = pa.Y - pdy;
			double bdx = pb.X - pdx;
			double bdy = pb.Y - pdy;

			double adxbdy = adx * bdy;
			double bdxady = bdx * ady;
			double oabd = adxbdy - bdxady;
			//        oabd = orient2d(pa,pb,pd);
			if (oabd <= 0) {
				return false;
			}

			double cdx = pc.X - pdx;
			double cdy = pc.Y - pdy;

			double cdxady = cdx * ady;
			double adxcdy = adx * cdy;
			double ocad = cdxady - adxcdy;
			//      ocad = orient2d(pc,pa,pd);
			if (ocad <= 0) {
				return false;
			}
			return true;
		}


		/// Forumla to calculate signed area
		/// Positive if CCW
		/// Negative if CW
		/// 0 if collinear
		/// A[P1,P2,P3]  =  (x1*y2 - y1*x2) + (x2*y3 - y2*x3) + (x3*y1 - y3*x1)
		///              =  (x1-x3)*(y2-y3) - (y1-y3)*(x2-x3)
		public static Orientation Orient2d (Point2D pa, Point2D pb, Point2D pc) {
			double detleft = (pa.X - pc.X) * (pb.Y - pc.Y);
			double detright = (pa.Y - pc.Y) * (pb.X - pc.X);
			double val = detleft - detright;
			if (val > -MathUtil.EPSILON && val < MathUtil.EPSILON) {
				return Orientation.Collinear;
			} else if (val > 0) {
				return Orientation.CCW;
			}
			return Orientation.CW;
		}


		///////////////////////////////////////////////////////////////////////////////
		// PointRelativeToLine2D
		//
		// Returns -1 if point is on left of line, 0 if point is on line, and 1 if 
		// the point is to the right of the line. This assumes a coordinate system
		// whereby the y axis goes upward when the x axis goes rightward. This is how
		// 3D systems (both right and left-handed) and PostScript works, but is not 
		// how the Win32 GUI works. If you are using a 'y goes downward' coordinate 
		// system, simply negate the return value from this function.
		//
		// Given a point (a,b) and a line from (x1,y1) to (x2,y2), we calculate the 
		// following equation:
		//    (y2-y1)*(a-x1)-(x2-x1)*(b-y1)                        (left)
		// If the result is > 0, the point is on             1 --------------> 2
		// the right, else left.                                   (right)
		//
		// For example, with a point at (1,1) and a 
		// line going from (0,0) to (2,0), we get:
		//    (0-0)*(1-0)-(2-0)*(1-0)
		// which equals:
		//    -2
		// Which indicates the point is (correctly)
		// on the left of the directed line.
		//
		// This function has been checked to a good degree.
		// 
		/////////////////////////////////////////////////////////////////////////////
		//public static double PointRelativeToLine2D(Point2D ptPoint, Point2D ptLineBegin, Point2D ptLineEnd)
		//{
		//    return (ptLineEnd.Y - ptLineBegin.Y) * (ptPoint.X - ptLineBegin.X) - (ptLineEnd.X - ptLineBegin.X) * (ptPoint.Y - ptLineBegin.Y);
		//}


		///////////////////////////////////////////////////////////////////////////
		// PointInBoundingBox - checks if a point is completely inside an 
		// axis-aligned bounding box defined by xmin, xmax, ymin, and ymax.
		// Note that the point must be fully inside for this method to return
		// true - it cannot lie on the border of the bounding box.
		///////////////////////////////////////////////////////////////////////////
		public static bool PointInBoundingBox (double xmin, double xmax, double ymin, double ymax, Point2D p) {
			return (p.X > xmin && p.X < xmax && p.Y > ymin && p.Y < ymax);
		}

		public static bool PointOnLineSegment2D (Point2D lineStart, Point2D lineEnd, Point2D p, double epsilon) {
			return TriangulationUtil.PointOnLineSegment2D (lineStart.X, lineStart.Y, lineEnd.X, lineEnd.Y, p.X, p.Y, epsilon);
		}

		public static bool PointOnLineSegment2D (double x1, double y1, double x2, double y2, double x, double y, double epsilon) {
			// First checking if (x, z) is in the range of the line segment's end points.
			if (MathUtil.IsValueBetween (x, x1, x2, epsilon) && MathUtil.IsValueBetween (y, y1, y2, epsilon)) {
				if (MathUtil.AreValuesEqual (x2 - x1, 0.0f, epsilon)) {
					// Vertical line.
					return true;
				}

				double slope = (y2 - y1) / (x2 - x1);
				double yIntercept = -(slope * x1) + y1;

				// Checking if (x, y) is on the line passing through the end points.
				double t = y - ((slope * x) + yIntercept);

				return MathUtil.AreValuesEqual (t, 0.0f, epsilon);
			}

			return false;
		}
        
		public static bool RectsIntersect (Rect2D r1, Rect2D r2) {
			return  (r1.Right > r2.Left) &&
				(r1.Left < r2.Right) &&
				(r1.Bottom > r2.Top) &&
				(r1.Top < r2.Bottom);
		}


		/// <summary>
		/// This method detects if two line segments (or lines) intersect,
		/// and, if so, the point of intersection. Use the <paramref name="firstIsSegment"/> and
		/// <paramref name="secondIsSegment"/> parameters to set whether the intersection point
		/// must be on the first and second line segments. Setting these
		/// both to true means you are doing a line-segment to line-segment
		/// intersection. Setting one of them to true means you are doing a
		/// line to line-segment intersection test, and so on.
		/// Note: If two line segments are coincident, then 
		/// no intersection is detected (there are actually
		/// infinite intersection points).
		/// </summary>
		/// <param name="ptStart0">The first point of the first line segment.</param>
		/// <param name="ptEnd0">The second point of the first line segment.</param>
		/// <param name="ptStart1">The first point of the second line segment.</param>
		/// <param name="ptEnd1">The second point of the second line segment.</param>
		/// <param name="firstIsSegment">Set this to true to require that the 
		/// intersection point be on the first line segment.</param>
		/// <param name="secondIsSegment">Set this to true to require that the
		/// intersection point be on the second line segment.</param>
		/// <param name="coincidentEndPointCollisions">Set this to true to enable collisions if the line segments share
		/// an endpoint</param>
		/// <param name="pIntersectionPt">This is set to the intersection
		/// point if an intersection is detected.</param>
		/// <returns>True if an intersection is detected, false otherwise.</returns>
		public static bool LinesIntersect2D (Point2D ptStart0, Point2D ptEnd0,
                                                Point2D ptStart1, Point2D ptEnd1,
                                                bool firstIsSegment, bool secondIsSegment, bool coincidentEndPointCollisions,
                                                ref Point2D pIntersectionPt,
                                                double epsilon) {
			double d = (ptEnd0.X - ptStart0.X) * (ptStart1.Y - ptEnd1.Y) - (ptStart1.X - ptEnd1.X) * (ptEnd0.Y - ptStart0.Y);
			if (Math.Abs (d) < epsilon) {
				//The lines are parallel.
				return false;
			}

			double d0 = (ptStart1.X - ptStart0.X) * (ptStart1.Y - ptEnd1.Y) - (ptStart1.X - ptEnd1.X) * (ptStart1.Y - ptStart0.Y);
			double d1 = (ptEnd0.X - ptStart0.X) * (ptStart1.Y - ptStart0.Y) - (ptStart1.X - ptStart0.X) * (ptEnd0.Y - ptStart0.Y);
			double kOneOverD = 1 / d;
			double t0 = d0 * kOneOverD;
			double t1 = d1 * kOneOverD;

			if ((!firstIsSegment || ((t0 >= 0.0) && (t0 <= 1.0))) &&
				(!secondIsSegment || ((t1 >= 0.0) && (t1 <= 1.0))) &&
				(coincidentEndPointCollisions || (!MathUtil.AreValuesEqual (0.0, t0, epsilon) && !MathUtil.AreValuesEqual (0.0, t1, epsilon)))) {
				if (pIntersectionPt != null) {
					pIntersectionPt.X = ptStart0.X + t0 * (ptEnd0.X - ptStart0.X);
					pIntersectionPt.Y = ptStart0.Y + t0 * (ptEnd0.Y - ptStart0.Y);
				}

				return true;
			}

			return false;
		}

		public static bool LinesIntersect2D (Point2D ptStart0, Point2D ptEnd0,
                                                Point2D ptStart1, Point2D ptEnd1,
                                                ref Point2D pIntersectionPt,
                                                double epsilon) {
			return TriangulationUtil.LinesIntersect2D (ptStart0, ptEnd0, ptStart1, ptEnd1, true, true, false, ref pIntersectionPt, epsilon);
		}

        
		///////////////////////////////////////////////////////////////////////////
		// RaysIntersect2D
		//
		// Given two lines defined by (sorry about the lame notation):
		//    x0 = x00 + vector_x0*s;
		//    y0 = y00 + vector_y0*s;
		//
		//    x1 = x10 + vector_x1*t;
		//    y1 = y10 + vector_y1*t;
		//
		// This function determines the intersection between them, if there is any.
		//
		// This function assumes the lines to have no endpoints and will intersect
		// them anywhere in 2D space.
		//
		// This algorithm taken from "Realtime-Rendering" section 10.12.
		// 
		// This function has been checked to a good degree.
		// 
		///////////////////////////////////////////////////////////////////////////
		public static double LI2DDotProduct (Point2D v0, Point2D v1) {
			return ((v0.X * v1.X) + (v0.Y * v1.Y));
		}

		public static bool RaysIntersect2D (Point2D ptRayOrigin0, Point2D ptRayVector0,
                                            Point2D ptRayOrigin1, Point2D ptRayVector1,
                                            ref Point2D ptIntersection) {
			double kEpsilon = 0.01;

			if (ptIntersection != null) {
				//If the user wants an actual intersection result...

				//This is a vector from pLineOrigin0 to ptLineOrigin1.
				Point2D ptTemp1 = new Point2D (ptRayOrigin1.X - ptRayOrigin0.X, ptRayOrigin1.Y - ptRayOrigin0.Y);

				//This is a vector perpendicular to ptVector1.
				Point2D ptTemp2 = new Point2D (-ptRayVector1.Y, ptRayVector1.X);

				double fDot1 = TriangulationUtil.LI2DDotProduct (ptRayVector0, ptTemp2);

				if (Math.Abs (fDot1) < kEpsilon) {
					return false; //The lines are essentially parallel.
				}

				double fDot2 = TriangulationUtil.LI2DDotProduct (ptTemp1, ptTemp2);
				double s = fDot2 / fDot1;
				ptIntersection.X = ptRayOrigin0.X + ptRayVector0.X * s;
				ptIntersection.Y = ptRayOrigin0.Y + ptRayVector0.Y * s;
				return true;
			}

			//Else the user just wants to know if there is an intersection...
			//In this case we need only compare the slopes of the lines.
			double delta = ptRayVector1.X - ptRayVector0.X;
			if (Math.Abs (delta) > kEpsilon) {
				delta = ptRayVector1.Y - ptRayVector0.Y;
				if (Math.Abs (delta) > kEpsilon) {
					return true; //The lines are not parallel.
				}
			}

			return false;
		}

	}


}