void DrawCubicBezierSpline(IApiDraw api, Vertex pt)
{
Point midp = (pt.p1+pt.p2) / 2;
// GDI equiv being curveto()
// draw fake cubic bezier curve lines (in two parts)
if (api!=null) api.curveTo(pt.p1,midp);
if (api!=null) api.curveTo(pt.p2,pt.p3);
}
static int SliceCubicBézierSegments( IApiDraw api, Vertex PT, double n1, double n2, Tuple<Point,LineObj> Tu1, Tuple<Point,LineObj> Tu2, int recursion )
{
// Tu1 may be null and cause Exception
// Tu2 may be null and cause Exception
// infinity recursion ?
if (recursion > MAX_RECURSION)
{
Point P = Tu2.Item1;
if (api!=null) api.lineTo(Tu2.Item1);
return 1;
}
// process segment
Point CP = Tu1.Item2.GetLineCross(Tu2.Item2);
// a controlpoint is considered misplaced if its distance
// from one of the anchor is greater than the distance
// between the two anchors.
Point PO = Tu1.Item1-Tu2.Item1; // point
double DN = PO.Pow(); // double
double D0 = Tu1.Item1.To(CP); // double
double D1 = Tu1.Item1.To(Tu2.Item1); // double
double D2 = Tu2.Item1.To(CP); // double
if ( CP == null || D1 > D0 || D2 > D0)
{
int total = 0; // total for this subsegment starts at 0
double umid = (n1 + n2) / 2D; // if misplaced control-point, slice segment more
Vertex PM = PT.CloneAt(Convert.ToInt64(umid));
Tuple<Point,LineObj> tumid = PM.CubicTangent();
// sub segment count
total += SliceCubicBézierSegments(api, PT, n1, umid, Tu1, tumid, recursion+1);
total += SliceCubicBézierSegments(api, PT, umid, n2, tumid, Tu2, recursion+1);
return total;
}
else
{
// draw curve
if (api!=null) api.curveTo(CP.X, CP.Y, Tu2.Item1.X, Tu2.Item1.Y);
return 1;
}
}
int DrawCubicBézier(IApiDraw api, Vertex pt)
{
Tuple<Point,LineObj> curt = null; // Tangent Object (LineObj)?
Tuple<Point,LineObj> next; // Tangent Object (LineObj)?
int total = 0; // int or long
int nSegment = numSegments < 2 ? 4 : this.numSegments;
double tstep = 1 / nSegment;
curt = new Tuple<Point,LineObj>(pt.p0,LineObj.GetLine(pt.p0,pt.p1));
if (api!=null) api.moveTo(pt.p0);
for (int i=1; i < nSegment; i++)
{
next = pt.CubicTangent(Convert.ToInt32(i * tstep)); // next tangent
total += SliceCubicBézierSegments( api, pt, (i - 1) * tstep, i * tstep, curt, next, 0); // current segment
if (total > numSegments) {} curt = next;
}
return total;
}
void DrawCubicBézier2(IApiDraw api, Vertex pt)
{
// base-points
Point PA = pt.p0.GetPointOnSegment(pt.p1, 3/4);
Point PB = pt.p3.GetPointOnSegment(pt.p2, 3/4);
Point d = (pt.p3 - pt.p0) / 16;
Point Pc_1 = pt.p0.GetPointOnSegment(pt.p1, 3/8);
Point Pc_2 = PA.GetPointOnSegment(PB, 3/8) - d;
Point Pc_3 = PB.GetPointOnSegment(PA, 3/8) + d;
Point Pc_4 = pt.p3.GetPointOnSegment(pt.p2, 3/8) + d;
// three anchor points
Point Pa_1 = Pc_1.GetMiddle(Pc_2);
Point Pa_2 = PA.GetMiddle(PB);
Point Pa_3 = Pc_3.GetMiddle(Pc_4);
// draw four quadratic segments
if (api!=null) api.curveTo(Pc_1, Pa_1);
if (api!=null) api.curveTo(Pc_2, Pa_2);
if (api!=null) api.curveTo(Pc_3, Pa_3);
if (api!=null) api.curveTo(Pc_4, pt.p3);
}