[Bf-blender-cvs] [3a3f90cef1b] temp-gpencil-bezier-stroke-type: GPencil: Add find_cubic_bezier_stationary_points

[Falk David]

Commit: 3a3f90cef1b11ce977d1e3b919a1f0dc9232ffd9
Author: Falk David
Date:   Sat Apr 24 18:55:03 2021 +0200
Branches: temp-gpencil-bezier-stroke-type
https://developer.blender.org/rB3a3f90cef1b11ce977d1e3b919a1f0dc9232ffd9

GPencil: Add find_cubic_bezier_stationary_points

This function calculates the stationary points of a bezier curve.

The new fitting implementation will use this function to determin where
to place control points so that attributes, like the thickness, can be
fitted to the curve. Since we do not have handles to control the falloff
of attributes, we have to find points of interest where our
interpolation between two points gives good results.

===================================================================

M	source/blender/blenkernel/intern/gpencil_curve.c

===================================================================

diff --git a/source/blender/blenkernel/intern/gpencil_curve.c b/source/blender/blenkernel/intern/gpencil_curve.c
index 053cf6cc1a0..feae52b6e78 100644
--- a/source/blender/blenkernel/intern/gpencil_curve.c
+++ b/source/blender/blenkernel/intern/gpencil_curve.c
@@ -599,6 +599,55 @@ typedef struct tGPCurveSegment {
 
 } tGPCurveSegment;
 
+/**
+ * Find the stationary points of a cubic bezier curve.
+ * Calcualtes the t-values (factor along curve) of the stationary points of a cubic bezier curve by
+ * finding the roots of the first derivative. If no roots where found the function returns false.
+ * Otherwise if one of the roots was found, one of r_t1 or r_t2 will be NaN and the other will
+ * contain the t-value of the root found. If both roots were found, both r_t1 and r_t2 will contain
+ * a value.
+ * \param p1, p2, p3, p4: Points of the cubic bezier curve.
+ * \param r_t1, r_t2: Return t-values (factor along curve).
+ */
+static bool find_cubic_bezier_stationary_points(
+    const float p1, const float p2, const float p3, const float p4, float *r_t1, float *r_t2)
+{
+  float a = 6.0f * (-p1 + 3.0f * p2 - 3.0f * p3 + p4);
+  if (IS_EQF(a, 0.0f)) {
+    /* Special edge-case that we have to handle seperately.*/
+    if ((p1 == p4) && (p2 == p3)) {
+      if (p1 == p2) {
+        *r_t1 = NAN;
+        *r_t2 = NAN;
+        return false;
+      }
+      *r_t1 = 0.5f;
+      *r_t2 = NAN;
+      return true;
+    }
+    /* Denominator is zero. No roots. */
+    return false;
+  }
+
+  float x = p4 * (p1 - p2) - p3 * (p1 + p2) + p2 * p2 + p3 * p3;
+  if (x < 0.0f) {
+    /* Negative number under square root. No real roots. */
+    return false;
+  }
+
+  float s = 6.0f * sqrtf(x);
+  float b = 6.0f * (p1 - 2.0f * p2 + p3);
+
+  float t1 = (s - b) / a;
+  float t2 = -(s + b) / a;
+
+  /* Discard root outside of limits. */
+  *r_t1 = IN_RANGE_INCL(t1, 0.0f, 1.0f) ? t1 : NAN;
+  *r_t2 = IN_RANGE_INCL(t2, 0.0f, 1.0f) ? t2 : NAN;
+
+  return !(*r_t1 == NAN) || !(*r_t2 == NAN);
+}
+
 static void gpencil_free_curve_segment(tGPCurveSegment *tcs)
 {
   if (tcs == NULL) {