/// <summary>
/// Creates a bounding parallelogram on a curve segment
/// We suppose here that the segment is convex or concave from start to end,
/// that is the region bounded by the straight segment seg[start], seg[end] and the curve seg is convex
/// </summary>
internal static bool CreateParallelogramOnSubSeg(double start, double end, ICurve seg, ref Parallelogram box,
Point startPoint, Point endPoint)
{
if (seg is CubicBezierSegment)
{
return(CreateParallelogramOnSubSegOnBezierSeg(start, end, seg, ref box));
}
Point tan1 = seg.Derivative(start);
Point tan2 = seg.Derivative(end);
Point tan2Perp = Point.P(-tan2.Y, tan2.X);
Point p = endPoint - startPoint;
double numerator = p * tan2Perp;
double denumerator = (tan1 * tan2Perp);
double x;// = (p * tan2Perp) / (tan1 * tan2Perp);
if (Math.Abs(numerator) < ApproximateComparer.DistanceEpsilon)
{
x = 0;
}
else if (Math.Abs(denumerator) < ApproximateComparer.DistanceEpsilon)
{
//it is degenerated; adjacent sides are parallel, but
//since p * tan2Perp is big it does not contain e
return(false);
}
else
{
x = numerator / denumerator;
}
tan1 *= x;
box = new Parallelogram(startPoint, tan1, endPoint - startPoint - tan1);
#if DEBUGCURVES
if (!box.Contains(seg[end]))
{
throw new InvalidOperationException();//"the box does not contain the end of the segment");
}
#endif
double delta = (end - start) / 64;
for (int i = 1; i < 64; i++)
{
if (!box.Contains(seg[start + delta * i]))
{
return(false);
}
}
return(true);
}
internal static bool CreateParallelogramOnSubSegOnBezierSeg(double start, double end, ICurve seg, ref Parallelogram box)
{
CubicBezierSegment trimSeg = seg.Trim(start, end) as CubicBezierSegment;
B b = trimSeg.B;
Point a = b(1) - b(0);
box = new Parallelogram(b(0), a, b(3) - b(0));
if (box.Contains(b(2)))
{
return(true);
}
box = new Parallelogram(b(3), b(2) - b(3), b(0) - b(3));
if (box.Contains(b(1)))
{
return(true);
}
return(false);
}
internal static bool CreateParallelogramOnSubSegOnBezierSeg(double start, double end, ICurve seg, ref Parallelogram box) {
CubicBezierSegment trimSeg = seg.Trim(start, end) as CubicBezierSegment;
B b = trimSeg.B;
Point a = b(1) - b(0);
box = new Parallelogram(b(0), a, b(3) - b(0));
if (box.Contains(b(2)))
return true;
box = new Parallelogram(b(3), b(2) - b(3), b(0) - b(3));
if (box.Contains(b(1)))
return true;
return false;
}
/// <summary>
/// Creates a bounding parallelogram on a curve segment
/// We suppose here that the segment is convex or concave from start to end,
/// that is the region bounded by the straight segment seg[start], seg[end] and the curve seg is convex
/// </summary>
internal static bool CreateParallelogramOnSubSeg(double start, double end, ICurve seg, ref Parallelogram box,
Point startPoint, Point endPoint) {
if (seg is CubicBezierSegment)
return CreateParallelogramOnSubSegOnBezierSeg(start, end, seg, ref box);
Point tan1 = seg.Derivative(start);
Point tan2 = seg.Derivative(end);
Point tan2Perp = Point.P(-tan2.Y, tan2.X);
Point p = endPoint - startPoint;
double numerator = p * tan2Perp;
double denumerator = (tan1 * tan2Perp);
double x;// = (p * tan2Perp) / (tan1 * tan2Perp);
if (Math.Abs(numerator) < ApproximateComparer.DistanceEpsilon)
x = 0;
else if (Math.Abs(denumerator) < ApproximateComparer.DistanceEpsilon) {
//it is degenerated; adjacent sides are parallel, but
//since p * tan2Perp is big it does not contain e
return false;
} else x = numerator / denumerator;
tan1 *= x;
box = new Parallelogram(startPoint, tan1, endPoint - startPoint - tan1);
#if DEBUGCURVES
if (!box.Contains(seg[end]))
{
throw new InvalidOperationException();//"the box does not contain the end of the segment");
}
#endif
double delta = (end - start) / 64;
for (int i = 1; i < 64; i++) {
if (!box.Contains(seg[start + delta * i]))
return false;
}
return true;
}