Fix T44604 bad quality of rake with bezier curves.

We can calculate tangents analytically for bezier curves, so just make
them awesome. New code uses forward differencing calculation for
efficiency just like curve calculation.

Picture before/after:

http://www.pasteall.org/pic/87843

1 files changed, 24 insertions, 0 deletions

diff --git a/source/blender/blenkernel/intern/curve.c b/source/blender/blenkernel/intern/curve.c
index 30ceaea89b8..c27460b81c0 100644
--- a/source/blender/blenkernel/intern/curve.c
+++ b/source/blender/blenkernel/intern/curve.c
@@ -1384,6 +1384,30 @@ void BKE_curve_forward_diff_bezier(float q0, float q1, float q2, float q3, float
 	}
 }
 
+/* forward differencing method for first derivative of cubic bezier curve */
+void BKE_curve_forward_diff_tangent_bezier(float q0, float q1, float q2, float q3, float *p, int it, int stride)
+{
+	float rt0, rt1, rt2, f;
+	int a;
+
+	f = 1.0f / (float)it;
+
+	rt0 = 3.0f * (q1 - q0);
+	rt1 = f * (3.0f * (q3 - q0) + 9.0f * (q1 - q2));
+	rt2 = 6.0f * (q0 + q2)- 12.0f * q1;
+
+	q0 = rt0;
+	q1 = f * (rt1 + rt2);
+	q2 = 2.0f * f * rt1;
+
+	for (a = 0; a <= it; a++) {
+		*p = q0;
+		p = (float *)(((char *)p) + stride);
+		q0 += q1;
+		q1 += q2;
+	}
+}
+
 static void forward_diff_bezier_cotangent(const float p0[3], const float p1[3], const float p2[3], const float p3[3],
                                           float p[3], int it, int stride)
 {