[gtk/path-ops: 7/23] curve: Move some curve apis to gskcurve.c

[Matthias Clasen <matthiasc src gnome org>]

commit cf2070ad3dbee4fc287cdc1a97ebeefe9a41327d
Author: Matthias Clasen <mclasen redhat com>
Date:   Sun Mar 20 23:08:47 2022 -0400

    curve: Move some curve apis to gskcurve.c
    
    Some of this will be reused elsewhere, so move
    it out of gskpathstroke.c.

 gsk/gskcurve.c        | 144 +++++++++++++++++++++++++++++++++++++++++++++++++
 gsk/gskcurveprivate.h |   6 +++
 gsk/gskpathstroke.c   | 145 +-------------------------------------------------
 3 files changed, 152 insertions(+), 143 deletions(-)
---
diff --git a/gsk/gskcurve.c b/gsk/gskcurve.c
index 2f1894f297..1a38a6425e 100644
--- a/gsk/gskcurve.c
+++ b/gsk/gskcurve.c
@@ -1802,3 +1802,147 @@ gsk_curve_get_curvature (const GskCurve   *curve,
 
   return k;
 }
+
+static void
+align_points (const graphene_point_t *p,
+              const graphene_point_t *a,
+              const graphene_point_t *b,
+              graphene_point_t       *q,
+              int                     n)
+{
+  graphene_vec2_t n1;
+  float angle;
+  float s, c;
+
+  get_tangent (a, b, &n1);
+  angle = - atan2 (graphene_vec2_get_y (&n1), graphene_vec2_get_x (&n1));
+  sincosf (angle, &s, &c);
+
+  for (int i = 0; i < n; i++)
+    {
+      q[i].x = (p[i].x - a->x) * c - (p[i].y - a->y) * s;
+      q[i].y = (p[i].x - a->x) * s + (p[i].y - a->y) * c;
+    }
+}
+
+/* find solutions for at^2 + bt + c = 0 */
+static int
+solve_quadratic (float a, float b, float c, float t[2])
+{
+  float d;
+  int n = 0;
+
+  if (fabs (a) > 0.0001)
+    {
+      if (b*b > 4*a*c)
+        {
+          d = sqrt (b*b - 4*a*c);
+          t[n++] = (-b + d)/(2*a);
+          t[n++] = (-b - d)/(2*a);
+        }
+      else
+        {
+          t[n++] = -b / (2*a);
+        }
+    }
+  else if (fabs (b) > 0.0001)
+    {
+      t[n++] = -c / b;
+    }
+
+  return n;
+}
+
+static int
+filter_allowable (float t[3],
+                  int   n)
+{
+  float g[3];
+  int j = 0;
+
+  for (int i = 0; i < n; i++)
+    if (0 < t[i] && t[i] < 1)
+      g[j++] = t[i];
+  for (int i = 0; i < j; i++)
+    t[i] = g[i];
+  return j;
+}
+
+/* Get the points where the curvature of curve is
+ * zero, or a maximum or minimum, inside the open
+ * interval from 0 to 1.
+ */
+int
+gsk_curve_get_curvature_points (const GskCurve *curve,
+                                float           t[3])
+{
+  const graphene_point_t *pts = curve->curve.points;
+  graphene_point_t p[4];
+  float a, b, c, d;
+  float x, y, z;
+  int n;
+
+  align_points (pts, &pts[0], &pts[3], p, 4);
+
+  a = p[2].x * p[1].y;
+  b = p[3].x * p[1].y;
+  c = p[1].x * p[2].y;
+  d = p[3].x * p[2].y;
+
+  x = - 3*a + 2*b + 3*c - d;
+  y = 3*a - b - 3*c;
+  z = c - a;
+
+  n = solve_quadratic (x, y, z, t);
+  return filter_allowable (t, n);
+}
+
+/* Find cusps inside the open interval from 0 to 1. According
+ * to Stone & deRose, A Geometric Characterization of Parametric
+ * Cubic curves, a necessary and sufficient condition is that
+ * the first derivative vanishes.
+ */
+int
+gsk_curve_get_cusps (const GskCurve *curve,
+                     float           t[2])
+{
+  const graphene_point_t *pts = curve->curve.points;
+  graphene_point_t p[3];
+  float ax, bx, cx;
+  float ay, by, cy;
+  float tx[3];
+  int nx;
+  int n = 0;
+
+  if (curve->op != GSK_PATH_CURVE)
+    return 0;
+
+  p[0].x = 3 * (pts[1].x - pts[0].x);
+  p[0].y = 3 * (pts[1].y - pts[0].y);
+  p[1].x = 3 * (pts[2].x - pts[1].x);
+  p[1].y = 3 * (pts[2].y - pts[1].y);
+  p[2].x = 3 * (pts[3].x - pts[2].x);
+  p[2].y = 3 * (pts[3].y - pts[2].y);
+
+  ax = p[0].x - 2 * p[1].x + p[2].x;
+  bx = - 2 * p[0].x + 2 * p[1].x;
+  cx = p[0].x;
+
+  nx = solve_quadratic (ax, bx, cx, tx);
+  nx = filter_allowable (tx, nx);
+
+  ay = p[0].y - 2 * p[1].y + p[2].y;
+  by = - 2 * p[0].y + 2 * p[1].y;
+  cy = p[0].y;
+
+  for (int i = 0; i < nx; i++)
+    {
+      float ti = tx[i];
+
+      if (0 < ti && ti < 1 &&
+          fabs (ay * ti * ti + by * ti + cy) < 0.001)
+        t[n++] = ti;
+    }
+
+  return n;
+}
diff --git a/gsk/gskcurveprivate.h b/gsk/gskcurveprivate.h
index 5af65f6fa9..cacc5eb06a 100644
--- a/gsk/gskcurveprivate.h
+++ b/gsk/gskcurveprivate.h
@@ -149,6 +149,12 @@ float                   gsk_curve_get_curvature                 (const GskCurve
                                                                  float                   t,
                                                                  graphene_point_t       *center);
 
+int                     gsk_curve_get_curvature_points          (const GskCurve         *curve,
+                                                                 float                   t[3]);
+
+int                     gsk_curve_get_cusps                     (const GskCurve         *curve,
+                                                                 float                   t[2]);
+
 G_END_DECLS
 
 #endif /* __GSK_CURVE_PRIVATE_H__ */
diff --git a/gsk/gskpathstroke.c b/gsk/gskpathstroke.c
index e5ad1cc41e..08ec5cd451 100644
--- a/gsk/gskpathstroke.c
+++ b/gsk/gskpathstroke.c
@@ -573,147 +573,6 @@ conic_is_degenerate (const GskCurve *curve)
   return FALSE;
 }
 
-static void
-align_points (const graphene_point_t *p,
-              const graphene_point_t *a,
-              const graphene_point_t *b,
-              graphene_point_t       *q,
-              int                     n)
-{
-  graphene_vec2_t n1;
-  float angle;
-  float s, c;
-
-  get_tangent (a, b, &n1);
-  angle = - atan2 (graphene_vec2_get_y (&n1), graphene_vec2_get_x (&n1));
-  sincosf (angle, &s, &c);
-
-  for (int i = 0; i < n; i++)
-    {
-      q[i].x = (p[i].x - a->x) * c - (p[i].y - a->y) * s;
-      q[i].y = (p[i].x - a->x) * s + (p[i].y - a->y) * c;
-    }
-}
-
-/* find solutions for at^2 + bt + c = 0 */
-static int
-solve_quadratic (float a, float b, float c, float t[2])
-{
-  float d;
-  int n = 0;
-
-  if (fabs (a) > 0.0001)
-    {
-      if (b*b > 4*a*c)
-        {
-          d = sqrt (b*b - 4*a*c);
-          t[n++] = (-b + d)/(2*a);
-          t[n++] = (-b - d)/(2*a);
-        }
-      else
-        {
-          t[n++] = -b / (2*a);
-        }
-    }
-  else if (fabs (b) > 0.0001)
-    {
-      t[n++] = -c / b;
-    }
-
-  return n;
-}
-
-static int
-filter_allowable (float t[3],
-                  int   n)
-{
-  float g[3];
-  int j = 0;
-
-  for (int i = 0; i < n; i++)
-    if (0 < t[i] && t[i] < 1)
-      g[j++] = t[i];
-  for (int i = 0; i < j; i++)
-    t[i] = g[i];
-  return j;
-}
-
-/* Get the points where the curvature of curve is
- * zero, or a maximum or minimum, inside the open
- * interval from 0 to 1.
- */
-static int
-cubic_curvature_points (const GskCurve *curve,
-                        float           t[3])
-{
-  const graphene_point_t *pts = curve->curve.points;
-  graphene_point_t p[4];
-  float a, b, c, d;
-  float x, y, z;
-  int n;
-
-  align_points (pts, &pts[0], &pts[3], p, 4);
-
-  a = p[2].x * p[1].y;
-  b = p[3].x * p[1].y;
-  c = p[1].x * p[2].y;
-  d = p[3].x * p[2].y;
-
-  x = - 3*a + 2*b + 3*c - d;
-  y = 3*a - b - 3*c;
-  z = c - a;
-
-  n = solve_quadratic (x, y, z, t);
-  return filter_allowable (t, n);
-}
-
-/* Find cusps inside the open interval from 0 to 1. According
- * to Stone & deRose, A Geometric Characterization of Parametric
- * Cubic curves, a necessary and sufficient condition is that
- * the first derivative vanishes.
- */
-static int
-find_cusps (const GskCurve *curve,
-            float           t[2])
-{
-  const graphene_point_t *pts = curve->curve.points;
-  graphene_point_t p[3];
-  float ax, bx, cx;
-  float ay, by, cy;
-  float tx[3];
-  int nx;
-  int n = 0;
-
-  p[0].x = 3 * (pts[1].x - pts[0].x);
-  p[0].y = 3 * (pts[1].y - pts[0].y);
-  p[1].x = 3 * (pts[2].x - pts[1].x);
-  p[1].y = 3 * (pts[2].y - pts[1].y);
-  p[2].x = 3 * (pts[3].x - pts[2].x);
-  p[2].y = 3 * (pts[3].y - pts[2].y);
-
-  ax = p[0].x - 2 * p[1].x + p[2].x;
-  bx = - 2 * p[0].x + 2 * p[1].x;
-  cx = p[0].x;
-
-  nx = solve_quadratic (ax, bx, cx, tx);
-  nx = filter_allowable (tx, nx);
-
-  ay = p[0].y - 2 * p[1].y + p[2].y;
-  by = - 2 * p[0].y + 2 * p[1].y;
-  cy = p[0].y;
-
-  for (int i = 0; i < nx; i++)
-    {
-      float ti = tx[i];
-
-      if (0 < ti && ti < 1 &&
-          fabs (ay * ti * ti + by * ti + cy) < 0.001)
-        t[n++] = ti;
-    }
-
-  return n;
-}
-
 /* }}} */
 /* {{{ Stroke helpers */
 
@@ -1760,7 +1619,7 @@ subdivide_and_add_curve (const GskCurve *curve,
     add_curve_cb (curve, force_round_join, data);
   else if (level < MAX_SUBDIVISION && cubic_is_simple (curve))
     add_curve_cb (curve, force_round_join, data);
-  else if (level == MAX_SUBDIVISION && (n = find_cusps (curve, t)) > 0)
+  else if (level == MAX_SUBDIVISION && (n = gsk_curve_get_cusps (curve, t)) > 0)
     {
       t[n++] = 0;
       t[n++] = 1;
@@ -1782,7 +1641,7 @@ subdivide_and_add_curve (const GskCurve *curve,
 
       if (level == MAX_SUBDIVISION)
         {
-          n += cubic_curvature_points (curve, &t[n]);
+          n += gsk_curve_get_curvature_points (curve, &t[n]);
           qsort (t, n, sizeof (float), cmpfloat);
         }