private static void GenerateCurveTriangles(List <CurveTriangle> curveTriangles, Curve curve,
double halfWidth, double prevAngle, double nextAngle)
{
// First, to generate the curve, pick the polygons
var poly = curve.CurveVertices;
// Fall back to line triangles
if (poly.Length < 3)
{
return;
}
// Pick three vertices
Double2 a = poly[0].Position, b = poly[1].Position, c = poly[2].Position;
Double4 ta = poly[0].CurveCoords, tb = poly[1].CurveCoords, tc = poly[2].CurveCoords;
var k = (b - a).Cross(c - a);
// Generate extrusion
CurveVertex Extrapolate(Double2 x)
{
var u = (x - a).Cross(c - a) / k;
var v = -(x - a).Cross(b - a) / k;
return(new CurveVertex(x, ta + u * (tb - ta) + v * (tc - ta)));
}
// The curve's entry angle and exit angle
var entryAngle = curve.EntryAngle;
var exitAngle = curve.ExitAngle;
// Generate the polygon list
var list = new List <Double2>(poly.Length + 4);
// Add the vertex extremes
AddExtremeVertex(list, halfWidth, poly[0].Position, prevAngle, entryAngle, true);
// The order of the points is different for whether the curve is convex or not
// Concave is: start - end - controls (reversed)
// Convex is: start - controls - end
if (!curve.IsConvex)
{
AddExtremeVertex(list, halfWidth, poly[poly.Length - 1].Position, exitAngle, nextAngle, false);
Array.Reverse(poly);
}
// Extrapolate each vertex
for (int i = 1; i < poly.Length - 1; i++)
{
var dv1 = (poly[i - 1].Position - poly[i].Position).Normalized;
var dv2 = (poly[i + 1].Position - poly[i].Position).Normalized;
// Use the half-arc sine rule here to calcualte the tangent vector
var sec = 1 / Math.Sqrt(0.5 - 0.5 * dv1.Dot(dv2));
if (true)
{
list.Add(poly[i].Position + halfWidth * dv1.Rotate(Pi_2));
list.Add(poly[i].Position - halfWidth * dv2.Rotate(Pi_2));
}
else
{
list.Add(poly[i].Position - halfWidth * sec * (dv1 + dv2).Normalized);
}
}
if (curve.IsConvex)
{
AddExtremeVertex(list, halfWidth, poly[poly.Length - 1].Position, exitAngle, nextAngle, false);
}
// Triangulate the extrapolated list
curveTriangles.AddRange(CurveVertex.MakeTriangleFan(list.Select(Extrapolate).ToArray()));
}
public double DistanceSquaredTo(Double4 o) => (o - this).LengthSquared;
public double DistanceTo(Double4 o) => (o - this).Length;
public double Dot(Double4 o) => X * o.X + Y * o.Y + Z * o.Z + W * o.W;
