/// <summary>
/// Forumla to calculate signed area
/// <list type="bullet">
/// <item>Positive if CCW</item>
/// <item>Negative if CW</item>
/// <item>0 if collinear</item>
/// </list>
/// <code>
/// A[P1,P2,P3] = (x1*y2 - y1*x2) + (x2*y3 - y2*x3) + (x3*y1 - y3*x1)
/// = (x1-x3)*(y2-y3) - (y1-y3)*(x2-x3)
/// </code>
/// </summary>
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);
}
// Returns triangle circumcircle point and radius
// public static Tuple2<TPoint, Double> 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<TPoint, Double>( center, radius );
// }
/// <summary>
/// smartIncircle
/// Requirement:
/// <list type="number">
/// <item>a,b and c form a triangle.</item>
/// <item>a and d is know to be on opposite side of bc</item>
/// </list>
/// <code>
/// a
/// +
/// / \
/// / \
/// b/ \c
/// +-------+
/// / B \
/// / \
/// </code>
/// <b>Fact</b>: d has to be in area B to have a chance to be inside the circle formed by
/// a,b and c<br>
/// d is outside B if orient2d(a,b,d) or orient2d(c,a,d) is CW<br>
/// This preknowledge gives us a way to optimize the incircle test
/// </summary>
/// <param name="a">triangle point, opposite d</param>
/// <param name="b">triangle point</param>
/// <param name="c">triangle point</param>
/// <param name="d">point opposite a</param>
/// <return>true if d is inside circle, false if on circle edge</return>
///
public static bool smartIncircle(TriangulationPoint pa,
TriangulationPoint pb,
TriangulationPoint pc,
TriangulationPoint pd)
{
double pdx = pd.getX();
double pdy = pd.getY();
double adx = pa.getX() - pdx;
double ady = pa.getY() - pdy;
double bdx = pb.getX() - pdx;
double bdy = pb.getY() - 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.getX() - pdx;
double cdy = pc.getY() - 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);
}
/// <summary>
/// inScanArea
/// </summary>
/// <see cref="smartIncircle"/>
///
public static bool inScanArea(TriangulationPoint pa,
TriangulationPoint pb,
TriangulationPoint pc,
TriangulationPoint pd)
{
double pdx = pd.getX();
double pdy = pd.getY();
double adx = pa.getX() - pdx;
double ady = pa.getY() - pdy;
double bdx = pb.getX() - pdx;
double bdy = pb.getY() - 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.getX() - pdx;
double cdy = pc.getY() - 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);
}
