/// <summary>
/// Computes the extents of the path, if the path had been transformed with
/// the given transform.
/// </summary>
/// <param name="t"></param>
/// <returns></returns>
public Box2d GetTransformedExtents(Transform2d t)
{
Box2d res = new Box2d();
double penx = 0.0, peny = 0.0;
double x, y;
foreach (GFXPathMoveTo node in PathPoints)
{
if (node is GFXPathLineTo)
{
t.Apply(node.X, node.Y, out x, out y, true);
res.Append(x, y);
t.Apply(penx, peny, out x, out y, true);
res.Append(x, y);
}
else if (node is GFXPathArcTo)
{
res.Append(GeomUtil.GetTransformedArcExtents(penx, peny, node.X, node.Y, ((GFXPathArcTo)node).Bulge, t));
}
else if (node is GFXPathBezierTo)
{
GFXPathBezierTo bn = (GFXPathBezierTo)node;
res.Append(GeomUtil.GetTransformedBezierExtents(penx, peny, bn.XC1, bn.YC1, bn.XC2, bn.YC2, bn.X, bn.Y, t));
}
penx = node.X;
peny = node.Y;
}
return(res);
}
public static Box2d GetBezierExtents(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4)
{
//equations for differentiations of the bezier polynoimial in x and y:
double t2x = 9 * x2 - 9 * x3 + 3 * x4 - 3 * x1;
double t1x = 6 * x1 - 12 * x2 + 6 * x3;
double t0x = 3 * x2 - 3 * x1;
double t2y = 9 * y2 - 9 * y3 + 3 * y4 - 3 * y1;
double t1y = 6 * y1 - 12 * y2 + 6 * y3;
double t0y = 3 * y2 - 3 * y1;
double extrema1, extrema2, xp, yp;
Box2d res = new Box2d(x1, y1, x4, y4);
//solve x extremas
if (MathUtil.SolveQuadratic(t2x, t1x, t0x, out extrema1, out extrema2))
{
if (extrema1 > 0.0 && extrema1 < 1.0)
{
EvalBezier(x1, y1, x2, y2, x3, y3, x4, y4, extrema1, out xp, out yp);
res.Append(xp, yp);
}
if (extrema2 > 0.0 && extrema2 < 1.0)
{
EvalBezier(x1, y1, x2, y2, x3, y3, x4, y4, extrema2, out xp, out yp);
res.Append(xp, yp);
}
}
//solve y extremas
if (MathUtil.SolveQuadratic(t2y, t1y, t0y, out extrema1, out extrema2))
{
if (extrema1 > 0.0 && extrema1 < 1.0)
{
EvalBezier(x1, y1, x2, y2, x3, y3, x4, y4, extrema1, out xp, out yp);
res.Append(xp, yp);
}
if (extrema2 > 0.0 && extrema2 < 1.0)
{
EvalBezier(x1, y1, x2, y2, x3, y3, x4, y4, extrema2, out xp, out yp);
res.Append(xp, yp);
}
}
return(res);
}
public static Box2d GetArcExtents(double x1, double y1, double x2, double y2, double bulge)
{
double cx, cy, rad, side;
Box2d res = new Box2d(x1, y1, x2, y2);
//append quadrants if included
if (!GetArcCenterFromBulge(x1, y1, x2, y2, bulge, out cx, out cy))
{
return(res); //arc is a line
}
rad = GetArcRadiusFromBulge(x1, y1, x2, y2, bulge);
//include quadrant points of circle if on arc
side = SideOfPoint(x1, y1, x2, y2, cx + rad, cy);
if ((bulge < 0.0 && side >= 0.0) || (bulge > 0.0 && side <= 0.0))
{
res.Append(cx + rad, cy);
}
side = SideOfPoint(x1, y1, x2, y2, cx, cy + rad);
if ((bulge < 0.0 && side >= 0.0) || (bulge > 0.0 && side <= 0.0))
{
res.Append(cx, cy + rad);
}
side = SideOfPoint(x1, y1, x2, y2, cx - rad, cy);
if ((bulge < 0.0 && side >= 0.0) || (bulge > 0.0 && side <= 0.0))
{
res.Append(cx - rad, cy);
}
side = SideOfPoint(x1, y1, x2, y2, cx, cy - rad);
if ((bulge < 0.0 && side >= 0.0) || (bulge > 0.0 && side <= 0.0))
{
res.Append(cx, cy - rad);
}
return(res);
}
/// <summary>
/// Checks if this path, after a given transformation will have a bounding box smaller than a given size. THis can be done quickly since the
/// check can be terminated as soon as it finds a segment large enough.
/// </summary>
public bool IsTransformedSmallerThan(Transform2d tr, double maxwidth, double maxheight)
{
double penx = 0.0, peny = 0.0;
Box2d ext = new Box2d();
foreach (GFXPathMoveTo mt in PathPoints)
{
if (mt is GFXPathBezierTo)
{
var bez = mt as GFXPathBezierTo;
Box2d bext = GeomUtil.GetTransformedBezierExtents(penx, peny, bez.XC1, bez.YC1, bez.XC2, bez.YC2, bez.X, bez.Y, tr);
ext.Append(bext);
}
else if (mt is GFXPathArcTo)
{
var arc = mt as GFXPathArcTo;
Box2d aext = GeomUtil.GetTransformedArcExtents(penx, peny, arc.X, arc.Y, arc.Bulge, tr);
ext.Append(aext);
}
else if (mt is GFXPathLineTo)
{
double x1, y1, x2, y2;
tr.Apply(penx, peny, out x1, out y1, true);
tr.Apply(mt.X, mt.Y, out x2, out y2, true);
ext.Append(x1, y1, x2, y2);
}
// closepath and moveto needs no special handling...
if (!ext.Empty && (ext.Width > maxwidth || ext.Height > maxheight))
{
return(false);
}
penx = mt.X;
peny = mt.Y;
}
return(true);
}
private void AppendPathToExtents(bool uselinewidth, bool usetransform, GFXPath pth)
{
Box2d ext;
if (usetransform)
{
ext = pth.GetTransformedExtents(Transform);
}
else
{
ext = pth.Extents;
}
if (uselinewidth)
{
AppendWithLineWidth(pth.Extents);
}
else
{
RecordedExtents.Append(ext.XMin, ext.YMin, ext.XMax, ext.YMax);
}
}
public static Box2d GetEllipticExtents(double cx, double cy, double aradius, double bradius, double startangle, double sweepangle, double tilt)
{
Box2d extents = new Box2d();
double vmaxx, vmaxy;
if (MathUtil.IsZero(bradius)) //special case for zero bradius, assume maxima lies in tilt direction
{
vmaxy = tilt;
}
else
{
vmaxy = Math.Atan(bradius / (aradius * Math.Tan(tilt)));
}
if (MathUtil.IsZero(aradius)) //special case for zero bradius, assume maxima lies in tilt direction
{
vmaxx = tilt;
}
else
{
vmaxx = -Math.Atan((bradius * Math.Tan(tilt)) / aradius);
}
double startparam = EllipseAngleToParam(startangle, aradius, bradius);
double endparam = EllipseAngleToParam(startangle + sweepangle, aradius, bradius);
bool ccw = sweepangle >= 0.0;
if (Math.Abs(sweepangle) < MathUtil.Deg360)
{
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, startparam));
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, endparam));
if (MathUtil.IsAngleBetween(startparam, endparam, vmaxy, ccw))
{
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, vmaxy));
}
if (MathUtil.IsAngleBetween(startparam, endparam, vmaxy + MathUtil.Deg180, ccw))
{
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, vmaxy + MathUtil.Deg180));
}
if (MathUtil.IsAngleBetween(startparam, endparam, vmaxx, ccw))
{
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, vmaxx));
}
if (MathUtil.IsAngleBetween(startparam, endparam, vmaxx + MathUtil.Deg180, ccw))
{
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, vmaxx + MathUtil.Deg180));
}
}
else
{
//not an arc, all extreme ellipse points are included => a little faster
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, vmaxy));
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, vmaxy + MathUtil.Deg180));
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, vmaxx));
extents.Append(EvalEllipseParam(cx, cy, aradius, bradius, tilt, vmaxx + MathUtil.Deg180));
}
return(extents);
}
