Commit: bc0ce658dd7808f894bef0842b2501abca9c84ed
Author: Campbell Barton
Date: Mon May 23 21:31:22 2016 +1000
Branches: compositor-2016
https://developer.blender.org/rBbc0ce658dd7808f894bef0842b2501abca9c84ed
BLI_math: Add function to calculate circular cubic curve tangents
===================================================================
M source/blender/blenlib/BLI_math_geom.h
M source/blender/blenlib/intern/math_geom.c
===================================================================
diff --git a/source/blender/blenlib/BLI_math_geom.h
b/source/blender/blenlib/BLI_math_geom.h
index 45edaca..54b824c9 100644
--- a/source/blender/blenlib/BLI_math_geom.h
+++ b/source/blender/blenlib/BLI_math_geom.h
@@ -470,6 +470,10 @@ MINLINE float shell_v2v2_normalized_to_dist(const float
a[2], const float b[2]);
MINLINE float shell_v3v3_mid_normalized_to_dist(const float a[3], const float
b[3]);
MINLINE float shell_v2v2_mid_normalized_to_dist(const float a[2], const float
b[2]);
+/********************************* Cubic (Bezier)
*******************************/
+
+float cubic_tangent_factor_circle_v3(const float tan_l[3], const float
tan_r[3]);
+
/**************************** Inline Definitions
******************************/
#if BLI_MATH_DO_INLINE
diff --git a/source/blender/blenlib/intern/math_geom.c
b/source/blender/blenlib/intern/math_geom.c
index f80099b..370e8bb 100644
--- a/source/blender/blenlib/intern/math_geom.c
+++ b/source/blender/blenlib/intern/math_geom.c
@@ -4988,3 +4988,37 @@ int is_quad_flip_v3(const float v1[3], const float
v2[3], const float v3[3], con
return ret;
}
+
+/**
+ * Return the value which the distance between points will need to be scaled
by,
+ * to define a handle, given both points are on a perfect circle.
+ *
+ * Use when we want a bezier curve to match a circle as closely as possible.
+ *
+ * \note the return value will need to be divided by 0.75 for correct results.
+ */
+float cubic_tangent_factor_circle_v3(const float tan_l[3], const float
tan_r[3])
+{
+ BLI_ASSERT_UNIT_V3(tan_l);
+ BLI_ASSERT_UNIT_V3(tan_r);
+
+ const float eps = 1e-7f;
+ const float tan_dot = dot_v3v3(tan_l, tan_r);
+ if (tan_dot > 1.0f - eps) {
+ /* no angle difference (use fallback, length wont make any
difference) */
+ return (1.0f / 3.0f) * 0.75f;
+ }
+ else if (tan_dot < -1.0f + eps) {
+ /* parallele tangents (half-circle) */
+ return (1.0f / 2.0f);
+ }
+ else {
+ /* non-aligned tangents, calculate handle length */
+ const float angle = acosf(tan_dot) / 2.0f;
+
+ /* could also use 'angle_sin = len_vnvn(tan_l, tan_r, dims) /
2.0' */
+ const float angle_sin = sinf(angle);
+ const float angle_cos = cosf(angle);
+ return ((1.0f - angle_cos) / (angle_sin * 2.0f)) / angle_sin;
+ }
+}
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