Fix T87779: Asymmetric vertex positions in circles primitives

Add sin_cos_from_fraction which ensures each quadrant has matching
values when their sign is flipped.

2 files changed, 69 insertions, 0 deletions

diff --git a/source/blender/blenlib/BLI_math_rotation.h b/source/blender/blenlib/BLI_math_rotation.h
index 192ad482a69..fef51fa780e 100644
--- a/source/blender/blenlib/BLI_math_rotation.h
+++ b/source/blender/blenlib/BLI_math_rotation.h
@@ -176,6 +176,26 @@ void mat3_to_quat_is_ok(float q[4], const float mat[3][3]);
 
 /* Other. */
 
+/**
+ * Utility function that performs `sinf` & `cosf` where the quadrants of the circle
+ * will have exactly matching values when their sign is flipped.
+ * This works as long as the denominator can be divided by 2 or 4,
+ * otherwise `sinf` & `cosf` are used without any additional logic.
+ *
+ * Besides adjustments to precision, this function is the equivalent of:
+ * \code {.c}
+ * float phi = (2 * M_PI) * (float)i / (float)denominator;
+ * *r_sin = sinf(phi);
+ * *r_cos = cosf(phi);
+ * \endcode
+ *
+ * \param numerator: An integer factor in [0..denominator] (inclusive).
+ * \param denominator: The faction denominator (typically the number of segments of the circle).
+ * \param r_sin: The resulting sine.
+ * \param r_cos: The resulting cosine.
+ */
+void sin_cos_from_fraction(const int numerator, const int denominator, float *r_sin, float *r_cos);
+
 void print_qt(const char *str, const float q[4]);
 
 #define print_qt_id(q) print_qt(STRINGIFY(q), q)
diff --git a/source/blender/blenlib/intern/math_rotation.c b/source/blender/blenlib/intern/math_rotation.c
index 92223bdf1d5..f0bfc7c21e1 100644
--- a/source/blender/blenlib/intern/math_rotation.c
+++ b/source/blender/blenlib/intern/math_rotation.c
@@ -915,6 +915,55 @@ float tri_to_quat(float q[4], const float a[3], const float b[3], const float c[
   return len;
 }
 
+void sin_cos_from_fraction(const int numerator, const int denominator, float *r_sin, float *r_cos)
+{
+  BLI_assert((numerator <= denominator) && (denominator > 0));
+  if ((denominator & 3) == 0) {
+    const int denominator_4 = denominator / 4;
+    if (numerator <= denominator_4) {
+      /* Fall through. */
+    }
+    else {
+      if (numerator <= denominator_4 * 2) {
+        const float phi = (float)(2.0 * M_PI) *
+                          ((float)(numerator - denominator_4) / (float)denominator);
+        *r_sin = cosf(phi);
+        *r_cos = -sinf(phi);
+      }
+      else if (numerator <= denominator_4 * 3) {
+        const float phi = (float)(2.0 * M_PI) *
+                          ((float)(numerator - (denominator_4 * 2)) / (float)denominator);
+        *r_sin = -sinf(phi);
+        *r_cos = -cosf(phi);
+      }
+      else {
+        const float phi = (float)(2.0 * M_PI) *
+                          ((float)(numerator - (denominator_4 * 3)) / (float)denominator);
+        *r_cos = sinf(phi);
+        *r_sin = -cosf(phi);
+      }
+      return;
+    }
+  }
+  else if ((denominator & 1) == 0) {
+    const int denominator_2 = denominator / 2;
+    if (numerator <= denominator_2) {
+      /* Fall through. */
+    }
+    else {
+      const float phi = (float)(2.0 * M_PI) *
+                        ((float)(numerator - denominator_2) / (float)denominator);
+      *r_sin = -sinf(phi);
+      *r_cos = -cosf(phi);
+      return;
+    }
+  }
+
+  const float phi = (float)(2.0 * M_PI) * ((float)numerator / (float)denominator);
+  *r_sin = sinf(phi);
+  *r_cos = cosf(phi);
+}
+
 void print_qt(const char *str, const float q[4])
 {
   printf("%s: %.3f %.3f %.3f %.3f\n", str, q[0], q[1], q[2], q[3]);