BLI_math: Add function to calculate circular cubic curve tangents

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

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;
+	}
+}