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Assets/Plugins/Poly2Tri/Triangulation/Util/TriangulationUtil.cs Normal file
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/* Poly2Tri
* Copyright (c) 2009-2010, Poly2Tri Contributors
* http://code.google.com/p/poly2tri/
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* * 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
* prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
using System;
using System.Collections.Generic;
using System.Text;
namespace 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;
}
}
}