axiosengine/axios/Common/Decomposition/CDT/TriangulationUtil.cs

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2012-03-19 23:57:59 +00:00
/* 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 FarseerPhysics.Common.Decomposition.CDT;
namespace Poly2Tri.Triangulation
{
/**
* @author Thomas Åhlén, thahlen@gmail.com
*/
public class TriangulationUtil
{
public static double EPSILON = 1e-12;
/// <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(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc,
TriangulationPoint 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(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc,
TriangulationPoint 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(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint 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 > -EPSILON && val < EPSILON)
{
return Orientation.Collinear;
}
else if (val > 0)
{
return Orientation.CCW;
}
return Orientation.CW;
}
}
}