private static void AddExtremeVertex(List <Double2> vertices, double halfWidth, Double2 x,
double entryAngle, double exitAngle, bool startVertex)
{
var offset = halfWidth * Double2.FromAngle((startVertex ? exitAngle : entryAngle) + Pi_2);
if (!startVertex)
{
offset = -offset;
}
// There are two cases to process on the start point:
// When the angles are equal, there is no need to generate the "gap" to be filled by the joint
if (RoughlyEquals(exitAngle, entryAngle))
{
vertices.Add(x + offset);
vertices.Add(x - offset);
}
// When the angles are different, we generate the perpendicular bisector
else
{
// The sign difference between the entry angle and the previous curve's exit angle will tell
// where the angle bisector will need to be put
var diff = (exitAngle - entryAngle).WrapAngle();
var bisectorOffset = halfWidth / Math.Cos(Math.Abs(diff) / 2) * Double2.FromAngle(entryAngle + diff / 2 + Pi_2);
if (!startVertex)
{
bisectorOffset = -bisectorOffset;
}
// If the difference is positive, the bisector is to the right (i.e. AFTER the first point)
if (startVertex == (diff > 0))
{
vertices.Add(x + bisectorOffset);
vertices.Add(x);
vertices.Add(x - offset);
}
// If it is negative, the bisector is to the left (i.e. BEFORE the point)
else
{
vertices.Add(x + offset);
vertices.Add(x);
vertices.Add(x - bisectorOffset);
}
}
}
private static void GenerateLineJoints(List <Triangle> triangles, List <CurveTriangle> curveTriangles,
Curve prevCurve, Curve nextCurve, double halfWidth, StrokeLineJoin lineJoin, double miterLimit)
{
// First, calculate the difference between the angles to check where the joint need to be formed
var exitAngle = prevCurve.ExitAngle;
var entryAngle = nextCurve.EntryAngle;
var diff = (exitAngle - entryAngle).WrapAngle();
var sd = Math.Sign(diff);
// Skip creating the joint if the diff is small enough
if (RoughlyZero(diff))
{
return;
}
// The common point and the offset vectors
var p = (prevCurve.At(1) + nextCurve.At(0)) / 2;
var entryOffset = sd * halfWidth * Double2.FromAngle(entryAngle + Pi_2);
var exitOffset = sd * halfWidth * Double2.FromAngle(exitAngle + Pi_2);
// Calculate the bisector and miter length
var miter = halfWidth / Math.Cos(Math.Abs(diff) / 2);
var bisectorOffset = sd * miter * Double2.FromAngle(entryAngle + diff / 2 + Pi_2);
// Utility function for miter and round
Double2[] GenerateClippedTriangle(bool forRound)
{
var miterWidth = halfWidth * (forRound ? 1f : miterLimit);
if (miter < miterWidth)
{
return new[] { Double2.Zero, entryOffset, bisectorOffset, exitOffset }
}
;
else
{
// Clip the miter
var p1 = entryOffset + miterWidth * (bisectorOffset - entryOffset) / miter;
var p2 = exitOffset + miterWidth * (bisectorOffset - exitOffset) / miter;
return(new[] { Double2.Zero, entryOffset, p1, p2, exitOffset });
}
}
// Now, create the next triangles if necessary
switch (lineJoin)
{
case StrokeLineJoin.Bevel:
// Create the bevel triangle
triangles.Add(new Triangle(p, p + entryOffset, p + exitOffset));
break;
case StrokeLineJoin.Miter:
case StrokeLineJoin.MiterClip:
{
// Check the conditions for the miter (only clip if miter-clip is explicity selected)
if (lineJoin == StrokeLineJoin.Miter && miter >= halfWidth * miterLimit)
{
break;
}
// Generate the miter
var polygon = GenerateClippedTriangle(false).Select(v => p + v).ToArray();
triangles.AddRange(Triangle.MakeTriangleFan(polygon));
break;
}
case StrokeLineJoin.Round:
{
// Generate the round triangle
var curvePolygon = GenerateClippedTriangle(true)
.Select(v => new CurveVertex(p + v, new Double4(v.X, v.Y, -v.Y, 1f))).ToArray();
curveTriangles.AddRange(CurveVertex.MakeTriangleFan(curvePolygon));
break;
}
case StrokeLineJoin.Arcs:
{
// Compute the curvatures of the curves
var exitKappa = prevCurve.ExitCurvature;
var entryKappa = nextCurve.EntryCurvature;
// If both of them are zero, fall back to miter
if (RoughlyZero(exitKappa) && RoughlyZero(entryKappa))
{
goto case StrokeLineJoin.MiterClip;
}
throw new NotImplementedException("Later i'll end it");
}
break;
default: break;
}
}
public static DoubleMatrix Rotate(double angle)
{
var rot = Double2.FromAngle(angle);
return(new DoubleMatrix(rot.X, rot.Y, -rot.Y, rot.X, 0, 0));
}