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Java implementation of BSP based CSG (Constructive Solid Geometry)
/**
* TriangulationUtil.java
*
* Copyright 2014-2014 Michael Hoffer . All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification, are
* permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this list of
* conditions and the following disclaimer.
*
* 2. 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.
*
* THIS SOFTWARE IS PROVIDED BY Michael Hoffer "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 Michael Hoffer 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.
*
* The views and conclusions contained in the software and documentation are those of the
* authors and should not be interpreted as representing official policies, either expressed
* or implied, of Michael Hoffer .
*/
package eu.mihosoft.vrl.v3d.ext.org.poly2tri;
/**
* @author Thomas ???, [email protected]
*/
class TriangulationUtil
{
public final static double EPSILON = 1e-12;
// Returns triangle circumcircle point and radius
// public static Tuple2 circumCircle( TPoint a, TPoint b, TPoint c )
// {
// double A = det( a, b, c );
// double C = detC( a, b, c );
//
// double sa = a.getX() * a.getX() + a.getY() * a.getY();
// double sb = b.getX() * b.getX() + b.getY() * b.getY();
// double sc = c.getX() * c.getX() + c.getY() * c.getY();
//
// TPoint bx1 = new TPoint( sa, a.getY() );
// TPoint bx2 = new TPoint( sb, b.getY() );
// TPoint bx3 = new TPoint( sc, c.getY() );
// double bx = det( bx1, bx2, bx3 );
//
// TPoint by1 = new TPoint( sa, a.getX() );
// TPoint by2 = new TPoint( sb, b.getX() );
// TPoint by3 = new TPoint( sc, c.getX() );
// double by = det( by1, by2, by3 );
//
// double x = bx / ( 2 * A );
// double y = by / ( 2 * A );
//
// TPoint center = new TPoint( x, y );
// double radius = Math.sqrt( bx * bx + by * by - 4 * A * C ) / ( 2 * Math.abs( A ) );
//
// return new Tuple2( center, radius );
// }
/**
* Requirement:
* 1. a,b and c form a triangle.
* 2. a and d is know to be on opposite side of bc
*
* a
* +
* / \
* / \
* b/ \c
* +-------+
* / B \
* / \
*
* Fact: 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
* @param a - triangle point, opposite d
* @param b - triangle point
* @param c - triangle point
* @param d - point opposite a
* @return true if d is inside circle, false if on circle edge
*/
public static boolean smartIncircle( final TriangulationPoint pa,
final TriangulationPoint pb,
final TriangulationPoint pc,
final TriangulationPoint pd )
{
final double pdx = pd.getX();
final double pdy = pd.getY();
final double adx = pa.getX() - pdx;
final double ady = pa.getY() - pdy;
final double bdx = pb.getX() - pdx;
final double bdy = pb.getY() - pdy;
final double adxbdy = adx * bdy;
final double bdxady = bdx * ady;
final double oabd = adxbdy - bdxady;
// oabd = orient2d(pa,pb,pd);
if( oabd <= 0 )
{
return false;
}
final double cdx = pc.getX() - pdx;
final double cdy = pc.getY() - pdy;
final double cdxady = cdx * ady;
final double adxcdy = adx * cdy;
final double ocad = cdxady - adxcdy;
// ocad = orient2d(pc,pa,pd);
if( ocad <= 0 )
{
return false;
}
final double bdxcdy = bdx * cdy;
final double cdxbdy = cdx * bdy;
final double alift = adx * adx + ady * ady;
final double blift = bdx * bdx + bdy * bdy;
final double clift = cdx * cdx + cdy * cdy;
final double det = alift * ( bdxcdy - cdxbdy ) + blift * ocad + clift * oabd;
return det > 0;
}
/**
* @see smartIncircle
* @param pa
* @param pb
* @param pc
* @param pd
* @return
*/
public static boolean inScanArea( final TriangulationPoint pa,
final TriangulationPoint pb,
final TriangulationPoint pc,
final TriangulationPoint pd )
{
final double pdx = pd.getX();
final double pdy = pd.getY();
final double adx = pa.getX() - pdx;
final double ady = pa.getY() - pdy;
final double bdx = pb.getX() - pdx;
final double bdy = pb.getY() - pdy;
final double adxbdy = adx * bdy;
final double bdxady = bdx * ady;
final double oabd = adxbdy - bdxady;
// oabd = orient2d(pa,pb,pd);
if( oabd <= 0 )
{
return false;
}
final double cdx = pc.getX() - pdx;
final double cdy = pc.getY() - pdy;
final double cdxady = cdx * ady;
final double adxcdy = adx * cdy;
final 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.getX() - pc.getX() ) * ( pb.getY() - pc.getY() );
double detright = ( pa.getY() - pc.getY() ) * ( pb.getX() - pc.getX() );
double val = detleft - detright;
if( val > -EPSILON && val < EPSILON )
{
return Orientation.Collinear;
}
else if( val > 0 )
{
return Orientation.CCW;
}
return Orientation.CW;
}
public enum Orientation
{
CW,CCW,Collinear;
}
}