path: Add GskCurve

GskCurve is an abstraction for path operations. It's essentially a
collection of vfuncs per GskPathOperation.

GskStandardContour has been ported to use it where appropriate.

9 files changed, 901 insertions, 638 deletions

diff --git a/gsk/gskcontour.c b/gsk/gskcontour.c
index 359356d838..528540d2ad 100644
--- a/gsk/gskcontour.c
+++ b/gsk/gskcontour.c
@@ -21,6 +21,7 @@
 
 #include "gskcontourprivate.h"
 
+#include "gskcurveprivate.h"
 #include "gskpathbuilder.h"
 #include "gskpathprivate.h"
 #include "gsksplineprivate.h"
@@ -1047,7 +1048,7 @@ typedef struct
   GskStandardContourMeasure measure;
 } LengthDecompose;
 
-static void
+static gboolean
 gsk_standard_contour_measure_add_point (const graphene_point_t *from,
                                         const graphene_point_t *to,
                                         float                   from_progress,
@@ -1058,6 +1059,9 @@ gsk_standard_contour_measure_add_point (const graphene_point_t *from,
   float seg_length;
 
   seg_length = graphene_point_distance (from, to, NULL, NULL);
+  if (seg_length == 0)
+    return TRUE;
+
   decomp->measure.end += seg_length;
   decomp->measure.start_progress = from_progress;
   decomp->measure.end_progress = to_progress;
@@ -1066,6 +1070,8 @@ gsk_standard_contour_measure_add_point (const graphene_point_t *from,
   g_array_append_val (decomp->array, decomp->measure);
 
   decomp->measure.start += seg_length;
+
+  return TRUE;
 }
 
 static gpointer
@@ -1075,7 +1081,7 @@ gsk_standard_contour_init_measure (const GskContour *contour,
 {
   const GskStandardContour *self = (const GskStandardContour *) contour;
   gsize i;
-  float length, seg_length;
+  float length;
   GArray *array;
 
   array = g_array_new (FALSE, FALSE, sizeof (GskStandardContourMeasure));
@@ -1083,50 +1089,12 @@ gsk_standard_contour_init_measure (const GskContour *contour,
 
   for (i = 1; i < self->n_ops; i ++)
     {
-      const graphene_point_t *pt = gsk_pathop_points (self->ops[i]);
-
-      switch (gsk_pathop_op (self->ops[i]))
-      {
-        case GSK_PATH_MOVE:
-          break;
+      GskCurve curve;
+      LengthDecompose decomp = { array, { length, length, 0, 0, { }, i } };
 
-        case GSK_PATH_CLOSE:
-        case GSK_PATH_LINE:
-          seg_length = graphene_point_distance (&pt[0], &pt[1], NULL, NULL);
-          if (seg_length > 0)
-            {
-              g_array_append_vals (array,
-                                   &(GskStandardContourMeasure) {
-                                     length, 
-                                     length + seg_length,
-                                     0, 1,
-                                     pt[1],
-                                     i,
-                                   }, 1);
-              length += seg_length;
-            }
-          break;
-
-        case GSK_PATH_CURVE:
-          {
-            LengthDecompose decomp = { array, { length, length, 0, 0, pt[0], i } };
-            gsk_spline_decompose_cubic (pt, tolerance, gsk_standard_contour_measure_add_point, &decomp);
-            length = decomp.measure.start;
-          }
-          break;
-
-        case GSK_PATH_CONIC:
-          {
-            LengthDecompose decomp = { array, { length, length, 0, 0, pt[0], i } };
-            gsk_spline_decompose_conic (pt, tolerance, gsk_standard_contour_measure_add_point, &decomp);
-            length = decomp.measure.start;
-          }
-          break;
-
-        default:
-          g_assert_not_reached();
-          return NULL;
-      }
+      gsk_curve_init (&curve, self->ops[i]);
+      gsk_curve_decompose (&curve, tolerance, gsk_standard_contour_measure_add_point, &decomp);
+      length = decomp.measure.start;
     }
 
   *out_length = length;
@@ -1163,35 +1131,11 @@ gsk_standard_contour_measure_get_point (GskStandardContour        *self,
                                         graphene_point_t          *pos,
                                         graphene_vec2_t           *tangent)
 {
-  const graphene_point_t *pts;
+  GskCurve curve;
 
-  pts = gsk_pathop_points (self->ops[op]);
-  switch (gsk_pathop_op (self->ops[op]))
-    {
-      case GSK_PATH_LINE:
-      case GSK_PATH_CLOSE:
-        if (pos)
-          graphene_point_interpolate (&pts[0], &pts[1], progress, pos);
-        if (tangent)
-          {
-            graphene_vec2_init (tangent, pts[1].x - pts[0].x, pts[1].y - pts[0].y);
-            graphene_vec2_normalize (tangent, tangent);
-          }
-        break;
-
-      case GSK_PATH_CURVE:
-        gsk_spline_get_point_cubic (pts, progress, pos, tangent);
-        break;
-
-      case GSK_PATH_CONIC:
-        gsk_spline_get_point_conic (pts, progress, pos, tangent);
-        break;
-
-      case GSK_PATH_MOVE:
-      default:
-        g_assert_not_reached ();
-        return;
-    }
+  gsk_curve_init (&curve, self->ops[op]);
+
+  gsk_curve_eval (&curve, progress, pos, tangent);
 }
 
 static void
@@ -1382,144 +1326,52 @@ gsk_standard_contour_add_segment (const GskContour *contour,
    * taking care that first and last operation might be identical */
   if (start_measure)
     {
-      switch (gsk_pathop_op (self->ops[start_measure->op]))
-      {
-        case GSK_PATH_CLOSE:
-        case GSK_PATH_LINE:
-          {
-            const graphene_point_t *pts = gsk_pathop_points (self->ops[start_measure->op]);
-            graphene_point_t point;
-
-            graphene_point_interpolate (&pts[0], &pts[1], start_progress, &point);
-            gsk_path_builder_move_to (builder, point.x, point.y);
-            if (end_measure && end_measure->op == start_measure->op)
-              {
-                graphene_point_interpolate (&pts[0], &pts[1], end_progress, &point);
-                gsk_path_builder_line_to (builder, point.x, point.y);
-                return;
-              }
-            gsk_path_builder_line_to (builder, pts[1].x, pts[1].y);
-          }
-          break;
+      GskCurve curve, cut;
+      const graphene_point_t *start_point;
 
-        case GSK_PATH_CURVE:
-          {
-            const graphene_point_t *pts = gsk_pathop_points (self->ops[start_measure->op]);
-            graphene_point_t curve[4], discard[4];
-
-            gsk_spline_split_cubic (pts, discard, curve, start_progress);
-            if (end_measure && end_measure->op == start_measure->op)
-              {
-                graphene_point_t tiny[4];
-                gsk_spline_split_cubic (curve, tiny, discard, (end_progress - start_progress) / (1 - start_progress));
-                gsk_path_builder_move_to (builder, tiny[0].x, tiny[0].y);
-                gsk_path_builder_curve_to (builder, tiny[1].x, tiny[1].y, tiny[2].x, tiny[2].y, tiny[3].x, tiny[3].y);
-                return;
-              }
-            gsk_path_builder_move_to (builder, curve[0].x, curve[0].y);
-            gsk_path_builder_curve_to (builder, curve[1].x, curve[1].y, curve[2].x, curve[2].y, curve[3].x, curve[3].y);
-          }
-          break;
+      gsk_curve_init (&curve, self->ops[start_measure->op]);
 
-        case GSK_PATH_CONIC:
-          {
-            const graphene_point_t *pts = gsk_pathop_points (self->ops[start_measure->op]);
-            graphene_point_t curve[4], discard[4];
-
-            gsk_spline_split_conic (pts, discard, curve, start_progress);
-            if (end_measure && end_measure->op == start_measure->op)
-              {
-                graphene_point_t tiny[4];
-                gsk_spline_split_conic (curve, tiny, discard, (end_progress - start_progress) / (1 - start_progress));
-                gsk_path_builder_move_to (builder, tiny[0].x, tiny[0].y);
-                gsk_path_builder_conic_to (builder, tiny[1].x, tiny[1].y, tiny[3].x, tiny[3].y, tiny[2].x);
-                return;
-              }
-            gsk_path_builder_move_to (builder, curve[0].x, curve[0].y);
-            gsk_path_builder_conic_to (builder, curve[1].x, curve[1].y, curve[3].x, curve[3].y, curve[2].x);
-          }
-          break;
+      gsk_curve_split (&curve, start_progress, NULL, &cut);
+      start_point = gsk_curve_get_start_point (&cut);
+      gsk_path_builder_move_to (builder, start_point->x, start_point->y);
 
-        case GSK_PATH_MOVE:
-        default:
-          g_assert_not_reached();
+      if (end_measure && end_measure->op == start_measure->op)
+        {
+          GskCurve cut2;
+      
+          gsk_curve_split (&cut, (end_progress - start_progress) / (1 - start_progress), &cut2, NULL);
+          gsk_curve_builder_to (&cut2, builder);
           return;
-      }
+        }
+
+      gsk_curve_builder_to (&cut, builder);
       i = start_measure->op + 1;
     }
   else
     i = 0;
 
-  for (; i < (end_measure ? end_measure->op : self->n_ops); i++)
+  for (; i < (end_measure ? end_measure->op : self->n_ops - 1); i++)
     {
-      const graphene_point_t *pt = gsk_pathop_points (self->ops[i]);
-
-      switch (gsk_pathop_op (self->ops[i]))
-      {
-        case GSK_PATH_MOVE:
-          gsk_path_builder_move_to (builder, pt[0].x, pt[0].y);
-          break;
-
-        case GSK_PATH_LINE:
-        case GSK_PATH_CLOSE:
-          gsk_path_builder_line_to (builder, pt[1].x, pt[1].y);
-          break;
-
-        case GSK_PATH_CURVE:
-          gsk_path_builder_curve_to (builder, pt[1].x, pt[1].y, pt[2].x, pt[2].y, pt[3].x, pt[3].y);
-          break;
-
-        case GSK_PATH_CONIC:
-          gsk_path_builder_conic_to (builder, pt[1].x, pt[1].y, pt[3].x, pt[3].y, pt[2].x);
-          break;
-
-        default:
-          g_assert_not_reached();
-          return;
-      }
+      gsk_path_builder_pathop_to (builder, self->ops[i]);
     }
 
   /* Add the last partial operation */
   if (end_measure)
     {
-      switch (gsk_pathop_op (self->ops[end_measure->op]))
-      {
-        case GSK_PATH_CLOSE:
-        case GSK_PATH_LINE:
-          {
-            const graphene_point_t *pts = gsk_pathop_points (self->ops[end_measure->op]);
-            graphene_point_t point;
-
-            graphene_point_interpolate (&pts[0], &pts[1], end_progress, &point);
-            gsk_path_builder_line_to (builder, point.x, point.y);
-          }
-          break;
+      GskCurve curve, cut;
 
-        case GSK_PATH_CURVE:
-          {
-            const graphene_point_t *pts = gsk_pathop_points (self->ops[end_measure->op]);
-            graphene_point_t curve[4], discard[4];
-
-            gsk_spline_split_cubic (pts, curve, discard, end_progress);
-            gsk_path_builder_curve_to (builder, curve[1].x, curve[1].y, curve[2].x, curve[2].y, curve[3].x, curve[3].y);
-          }
-          break;
-
-        case GSK_PATH_CONIC:
-          {
-            const graphene_point_t *pts = gsk_pathop_points (self->ops[end_measure->op]);
-            graphene_point_t curve[4], discard[4];
+      gsk_curve_init (&curve, self->ops[end_measure->op]);
 
-            gsk_spline_split_conic (pts, curve, discard, end_progress);
-            gsk_path_builder_conic_to (builder, curve[1].x, curve[1].y, curve[3].x, curve[3].y, curve[2].x);
-          }
-          break;
-
-        case GSK_PATH_MOVE:
-        default:
-          g_assert_not_reached();
-          return;
-      }
+      gsk_curve_split (&curve, end_progress, &cut, NULL);
+      gsk_curve_builder_to (&cut, builder);
+    }
+  else if (i == self->n_ops - 1)
+    {
+      gskpathop op = self->ops[i];
+      if (gsk_pathop_op (op) == GSK_PATH_CLOSE)
+        gsk_path_builder_pathop_to (builder, gsk_pathop_encode (GSK_PATH_LINE, gsk_pathop_points (op)));
+      else
+        gsk_path_builder_pathop_to (builder, op);
     }
 }
 
diff --git a/gsk/gskcurve.c b/gsk/gskcurve.c
new file mode 100644
index 0000000000..2ecd3be146
--- /dev/null
+++ b/gsk/gskcurve.c
@@ -0,0 +1,705 @@
+/*
+ * Copyright © 2020 Benjamin Otte
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library. If not, see <http://www.gnu.org/licenses/>.
+ *
+ * Authors: Benjamin Otte <otte@gnome.org>
+ */
+
+#include "config.h"
+
+#include "gskcurveprivate.h"
+
+#define MIN_PROGRESS (1/1024.f)
+
+typedef struct _GskCurveClass GskCurveClass;
+
+struct _GskCurveClass
+{
+  void                          (* init)                (GskCurve               *curve,
+                                                         gskpathop               op);
+  void                          (* eval)                (const GskCurve         *curve,
+                                                         float                   progress,
+                                                         graphene_point_t       *pos,
+                                                         graphene_vec2_t        *tangent);
+  void                          (* split)               (const GskCurve         *curve,
+                                                         float                   progress,
+                                                         GskCurve               *result1,
+                                                         GskCurve               *result2);
+  gboolean                      (* decompose)           (const GskCurve         *curve,
+                                                         float                   tolerance,
+                                                         GskCurveAddLineFunc     add_line_func,
+                                                         gpointer                user_data);
+  gskpathop                     (* pathop)              (const GskCurve         *curve);
+  const graphene_point_t *      (* get_start_point)     (const GskCurve         *curve);
+  const graphene_point_t *      (* get_end_point)       (const GskCurve         *curve);
+};
+
+/** LINE **/
+
+static void
+gsk_line_curve_init_from_points (GskLineCurve           *self,
+                                 GskPathOperation        op,
+                                 const graphene_point_t *start,
+                                 const graphene_point_t *end)
+{
+  self->op = op;
+  self->points[0] = *start;
+  self->points[1] = *end;
+}
+
+static void
+gsk_line_curve_init (GskCurve  *curve,
+                     gskpathop  op)
+{
+  GskLineCurve *self = &curve->line;
+  const graphene_point_t *pts = gsk_pathop_points (op);
+
+  gsk_line_curve_init_from_points (self, gsk_pathop_op (op), &pts[0], &pts[1]);
+}
+
+static void
+gsk_line_curve_eval (const GskCurve   *curve,
+                     float             progress,
+                     graphene_point_t *pos,
+                     graphene_vec2_t  *tangent)
+{
+  const GskLineCurve *self = &curve->line;
+
+  if (pos)
+    graphene_point_interpolate (&self->points[0], &self->points[1], progress, pos);
+
+  if (tangent)
+    {
+      graphene_vec2_init (tangent, self->points[1].x - self->points[0].x, self->points[1].y - self->points[0].y);
+      graphene_vec2_normalize (tangent, tangent);
+    }
+}
+
+static void
+gsk_line_curve_split (const GskCurve   *curve,
+                      float             progress,
+                      GskCurve         *start,
+                      GskCurve         *end)
+{
+  const GskLineCurve *self = &curve->line;
+  graphene_point_t point;
+
+  graphene_point_interpolate (&self->points[0], &self->points[1], progress, &point);
+
+  if (start)
+    gsk_line_curve_init_from_points (&start->line, GSK_PATH_LINE, &self->points[0], &point);
+  if (end)
+    gsk_line_curve_init_from_points (&end->line, GSK_PATH_LINE, &point, &self->points[1]);
+}
+
+static gboolean
+gsk_line_curve_decompose (const GskCurve      *curve,
+                          float                tolerance,
+                          GskCurveAddLineFunc  add_line_func,
+                          gpointer             user_data)
+{
+  const GskLineCurve *self = &curve->line;
+
+  return add_line_func (&self->points[0], &self->points[1], 0.0f, 1.0f, user_data);
+}
+
+static gskpathop
+gsk_line_curve_pathop (const GskCurve *curve)
+{
+  const GskLineCurve *self = &curve->line;
+
+  return gsk_pathop_encode (self->op, self->points);
+}
+
+static const graphene_point_t *
+gsk_line_curve_get_start_point (const GskCurve *curve)
+{
+  const GskLineCurve *self = &curve->line;
+
+  return &self->points[0];
+}
+
+static const graphene_point_t *
+gsk_line_curve_get_end_point (const GskCurve *curve)
+{
+  const GskLineCurve *self = &curve->line;
+
+  return &self->points[1];
+}
+
+static const GskCurveClass GSK_LINE_CURVE_CLASS = {
+  gsk_line_curve_init,
+  gsk_line_curve_eval,
+  gsk_line_curve_split,
+  gsk_line_curve_decompose,
+  gsk_line_curve_pathop,
+  gsk_line_curve_get_start_point,
+  gsk_line_curve_get_end_point,
+};
+
+/** CURVE **/
+
+static void
+gsk_curve_curve_init_from_points (GskCurveCurve          *self,
+                                  const graphene_point_t  pts[4])
+{
+  self->op = GSK_PATH_CURVE;
+  self->has_coefficients = FALSE;
+  memcpy (self->points, pts, sizeof (graphene_point_t) * 4);
+}
+                                  
+static void
+gsk_curve_curve_init (GskCurve  *curve,
+                      gskpathop  op)
+{
+  GskCurveCurve *self = &curve->curve;
+
+  gsk_curve_curve_init_from_points (self, gsk_pathop_points (op));
+}
+
+static void
+gsk_curve_curve_ensure_coefficients (const GskCurveCurve *curve)
+{
+  GskCurveCurve *self = (GskCurveCurve *) curve;
+  const graphene_point_t *pts = &self->points[0];
+
+  if (self->has_coefficients)
+    return;
+
+  self->coeffs[0] = GRAPHENE_POINT_INIT (pts[3].x - 3.0f * pts[2].x + 3.0f * pts[1].x - pts[0].x,
+                                         pts[3].y - 3.0f * pts[2].y + 3.0f * pts[1].y - pts[0].y);
+  self->coeffs[1] = GRAPHENE_POINT_INIT (3.0f * pts[2].x - 6.0f * pts[1].x + 3.0f * pts[0].x,
+                                         3.0f * pts[2].y - 6.0f * pts[1].y + 3.0f * pts[0].y);
+  self->coeffs[2] = GRAPHENE_POINT_INIT (3.0f * pts[1].x - 3.0f * pts[0].x,
+                                         3.0f * pts[1].y - 3.0f * pts[0].y);
+  self->coeffs[3] = pts[0];
+
+  self->has_coefficients = TRUE;
+}
+
+static void
+gsk_curve_curve_eval (const GskCurve   *curve,
+                      float             progress,
+                      graphene_point_t *pos,
+                      graphene_vec2_t  *tangent)
+{
+  const GskCurveCurve *self = &curve->curve;
+  const graphene_point_t *c = self->coeffs;
+
+  gsk_curve_curve_ensure_coefficients (self);
+
+  if (pos)
+    *pos = GRAPHENE_POINT_INIT (((c[0].x * progress + c[1].x) * progress +c[2].x) * progress + c[3].x,
+                                ((c[0].y * progress + c[1].y) * progress +c[2].y) * progress + c[3].y);
+  if (tangent)
+    {
+      graphene_vec2_init (tangent,
+                          (3.0f * c[0].x * progress + 2.0f * c[1].x) * progress + c[2].x,
+                          (3.0f * c[0].y * progress + 2.0f * c[1].y) * progress + c[2].y);
+      graphene_vec2_normalize (tangent, tangent);
+    }
+}
+
+static void
+gsk_curve_curve_split (const GskCurve   *curve,
+                       float             progress,
+                       GskCurve         *start,
+                       GskCurve         *end)
+{
+  const GskCurveCurve *self = &curve->curve;
+  const graphene_point_t *pts = self->points;
+  graphene_point_t ab, bc, cd;
+  graphene_point_t abbc, bccd;
+  graphene_point_t final;
+
+  graphene_point_interpolate (&pts[0], &pts[1], progress, &ab);
+  graphene_point_interpolate (&pts[1], &pts[2], progress, &bc);
+  graphene_point_interpolate (&pts[2], &pts[3], progress, &cd);
+  graphene_point_interpolate (&ab, &bc, progress, &abbc);
+  graphene_point_interpolate (&bc, &cd, progress, &bccd);
+  graphene_point_interpolate (&abbc, &bccd, progress, &final);
+
+  if (start)
+    gsk_curve_curve_init_from_points (&start->curve, (graphene_point_t[4]) { pts[0], ab, abbc, final });
+  if (end)
+    gsk_curve_curve_init_from_points (&end->curve, (graphene_point_t[4]) { final, bccd, cd, pts[3] });
+}
+
+/* taken from Skia, including the very descriptive name */
+static gboolean
+gsk_curve_curve_too_curvy (const GskCurveCurve *self,
+                           float                tolerance)
+{
+  const graphene_point_t *pts = self->points;
+  graphene_point_t p;
+
+  graphene_point_interpolate (&pts[0], &pts[3], 1.0f / 3, &p);
+  if (ABS (p.x - pts[1].x) + ABS (p.y - pts[1].y)  > tolerance)
+    return TRUE;
+
+  graphene_point_interpolate (&pts[0], &pts[3], 2.0f / 3, &p);
+  if (ABS (p.x - pts[2].x) + ABS (p.y - pts[2].y)  > tolerance)
+    return TRUE;
+
+  return FALSE;
+}
+
+static gboolean
+gsk_curce_curve_decompose_step (const GskCurve      *curve,
+                                float                start_progress,
+                                float                end_progress,
+                                float                tolerance,
+                                GskCurveAddLineFunc  add_line_func,
+                                gpointer             user_data)
+{
+  const GskCurveCurve *self = &curve->curve;
+  GskCurve left, right;
+  float mid_progress;
+
+  if (!gsk_curve_curve_too_curvy (self, tolerance) || end_progress - start_progress <= MIN_PROGRESS)
+    return add_line_func (&self->points[0], &self->points[3], start_progress, end_progress, user_data);
+
+  gsk_curve_curve_split ((const GskCurve *) self, 0.5, &left, &right);
+  mid_progress = (start_progress + end_progress) / 2;
+
+  return gsk_curce_curve_decompose_step (&left, start_progress, mid_progress, tolerance, add_line_func, user_data)
+      && gsk_curce_curve_decompose_step (&right, mid_progress, end_progress, tolerance, add_line_func, user_data);
+}
+
+static gboolean
+gsk_curve_curve_decompose (const GskCurve      *curve,
+                           float                tolerance,
+                           GskCurveAddLineFunc  add_line_func,
+                           gpointer             user_data)
+{
+  return gsk_curce_curve_decompose_step (curve, 0.0, 1.0, tolerance, add_line_func, user_data);
+}
+
+static gskpathop
+gsk_curve_curve_pathop (const GskCurve *curve)
+{
+  const GskCurveCurve *self = &curve->curve;
+
+  return gsk_pathop_encode (self->op, self->points);
+}
+
+static const graphene_point_t *
+gsk_curve_curve_get_start_point (const GskCurve *curve)
+{
+  const GskCurveCurve *self = &curve->curve;
+
+  return &self->points[0];
+}
+
+static const graphene_point_t *
+gsk_curve_curve_get_end_point (const GskCurve *curve)
+{
+  const GskCurveCurve *self = &curve->curve;
+
+  return &self->points[3];
+}
+
+static const GskCurveClass GSK_CURVE_CURVE_CLASS = {
+  gsk_curve_curve_init,
+  gsk_curve_curve_eval,
+  gsk_curve_curve_split,
+  gsk_curve_curve_decompose,
+  gsk_curve_curve_pathop,
+  gsk_curve_curve_get_start_point,
+  gsk_curve_curve_get_end_point,
+};
+
+/** CONIC **/
+
+static void
+gsk_conic_curve_init_from_points (GskConicCurve          *self,
+                                  const graphene_point_t  pts[4])
+{
+  self->op = GSK_PATH_CONIC;
+  self->has_coefficients = FALSE;
+
+  memcpy (self->points, pts, sizeof (graphene_point_t) * 4);
+}
+                                  
+static void
+gsk_conic_curve_init (GskCurve  *curve,
+                      gskpathop  op)
+{
+  GskConicCurve *self = &curve->conic;
+
+  gsk_conic_curve_init_from_points (self, gsk_pathop_points (op));
+}
+
+static inline float
+gsk_conic_curve_get_weight (const GskConicCurve *self)
+{
+  return self->points[2].x;
+}
+
+static void
+gsk_conic_curve_ensure_coefficents (const GskConicCurve *curve)
+{
+  GskConicCurve *self = (GskConicCurve *) curve;
+  float w = gsk_conic_curve_get_weight (self);
+  const graphene_point_t *pts = self->points;
+  graphene_point_t pw = GRAPHENE_POINT_INIT (w * pts[1].x, w * pts[1].y);
+
+  if (self->has_coefficients)
+    return;
+
+  self->num[2] = pts[0];
+  self->num[1] = GRAPHENE_POINT_INIT (2 * (pw.x - pts[0].x),
+                                      2 * (pw.y - pts[0].y));
+  self->num[0] = GRAPHENE_POINT_INIT (pts[3].x - 2 * pw.x + pts[0].x,
+                                      pts[3].y - 2 * pw.y + pts[0].y);
+
+  self->denom[2] = GRAPHENE_POINT_INIT (1, 1);
+  self->denom[1] = GRAPHENE_POINT_INIT (2 * (w - 1), 2 * (w - 1));
+  self->denom[0] = GRAPHENE_POINT_INIT (-self->denom[1].x, -self->denom[1].y);
+
+  self->has_coefficients = TRUE;
+}
+
+static inline void
+gsk_curve_eval_quad (const graphene_point_t quad[3],
+                     float                  progress,
+                     graphene_point_t      *result)
+{
+  *result = GRAPHENE_POINT_INIT ((quad[0].x * progress + quad[1].x) * progress + quad[2].x,
+                                 (quad[0].y * progress + quad[1].y) * progress + quad[2].y);
+}
+
+static inline void
+gsk_conic_curve_eval_point (const GskConicCurve *self,
+                            float                progress,
+                            graphene_point_t    *point)
+{
+  graphene_point_t num, denom;
+
+  gsk_curve_eval_quad (self->num, progress, &num);
+  gsk_curve_eval_quad (self->denom, progress, &denom);
+
+  *point = GRAPHENE_POINT_INIT (num.x / denom.x, num.y / denom.y);
+}
+                       
+static void
+gsk_conic_curve_eval (const GskCurve   *curve,
+                      float             progress,
+                      graphene_point_t *pos,
+                      graphene_vec2_t  *tangent)
+{
+  const GskConicCurve *self = &curve->conic;
+
+  gsk_conic_curve_ensure_coefficents (self);
+
+  if (pos)
+    gsk_conic_curve_eval_point (self, progress, pos);
+
+  if (tangent)
+    {
+      graphene_point_t tmp;
+      float w = gsk_conic_curve_get_weight (self);
+      const graphene_point_t *pts = self->points;
+
+      /* The tangent will be 0 in these corner cases, just
+       * treat it like a line here. */
+      if ((progress <= 0.f && graphene_point_equal (&pts[0], &pts[1])) ||
+          (progress >= 1.f && graphene_point_equal (&pts[1], &pts[3])))
+        {
+          graphene_vec2_init (tangent, pts[3].x - pts[0].x, pts[3].y - pts[0].y);
+          return;
+        }
+
+      gsk_curve_eval_quad ((graphene_point_t[3]) {
+                             GRAPHENE_POINT_INIT ((w - 1) * (pts[3].x - pts[0].x),
+                                                  (w - 1) * (pts[3].y - pts[0].y)),
+                             GRAPHENE_POINT_INIT (pts[3].x - pts[0].x - 2 * w * (pts[1].x - pts[0].x),
+                                                  pts[3].y - pts[0].y - 2 * w * (pts[1].y - pts[0].y)),
+                             GRAPHENE_POINT_INIT (w * (pts[1].x - pts[0].x),
+                                                  w * (pts[1].y - pts[0].y))
+                           },
+                           progress,
+                           &tmp);
+      graphene_vec2_init (tangent, tmp.x, tmp.y);
+      graphene_vec2_normalize (tangent, tangent);
+    }
+}
+
+static void
+split_bezier3d_recurse (const graphene_point3d_t *p,
+                        int                       l,
+                        float                     t,
+                        graphene_point3d_t       *left,
+                        graphene_point3d_t       *right,
+                        int                      *lpos,
+                        int                      *rpos)
+{
+  if (l == 1)
+    {
+      left[*lpos] = p[0];
+      right[*rpos] = p[0];
+    }
+  else
+    {
+      graphene_point3d_t *np;
+      int i;
+
+      np = g_alloca (sizeof (graphene_point3d_t) * (l - 1));
+      for (i = 0; i < l - 1; i++)
+        {
+          if (i == 0)
+            {
+              left[*lpos] = p[i];
+              (*lpos)++;
+            }
+          if (i + 1 == l - 1)
+            {
+              right[*rpos] = p[i + 1];
+              (*rpos)--;
+            }
+          graphene_point3d_interpolate (&p[i], &p[i + 1], t, &np[i]);
+        }
+      split_bezier3d_recurse (np, l - 1, t, left, right, lpos, rpos);
+    }
+}
+
+static void
+split_bezier3d (const graphene_point3d_t *p,
+                int                       l,
+                float                     t,
+                graphene_point3d_t       *left,
+                graphene_point3d_t       *right)
+{
+  int lpos = 0;
+  int rpos = l - 1;
+  split_bezier3d_recurse (p, l, t, left, right, &lpos, &rpos);
+}
+
+static void
+gsk_conic_curve_split (const GskCurve   *curve,
+                       float             progress,
+                       GskCurve         *start,
+                       GskCurve         *end)
+{
+  const GskConicCurve *self = &curve->conic;
+  graphene_point3d_t p[3];
+  graphene_point3d_t l[3], r[3];
+  graphene_point_t left[4], right[4];
+  float w;
+
+  /* do de Casteljau in homogeneous coordinates... */
+  w = self->points[2].x;
+  p[0] = GRAPHENE_POINT3D_INIT (self->points[0].x, self->points[0].y, 1);
+  p[1] = GRAPHENE_POINT3D_INIT (self->points[1].x * w, self->points[1].y * w, w);
+  p[2] = GRAPHENE_POINT3D_INIT (self->points[3].x, self->points[3].y, 1);
+
+  split_bezier3d (p, 3, progress, l, r);
+
+  /* then project the control points down */
+  left[0] = GRAPHENE_POINT_INIT (l[0].x / l[0].z, l[0].y / l[0].z);
+  left[1] = GRAPHENE_POINT_INIT (l[1].x / l[1].z, l[1].y / l[1].z);
+  left[3] = GRAPHENE_POINT_INIT (l[2].x / l[2].z, l[2].y / l[2].z);
+
+  right[0] = GRAPHENE_POINT_INIT (r[0].x / r[0].z, r[0].y / r[0].z);
+  right[1] = GRAPHENE_POINT_INIT (r[1].x / r[1].z, r[1].y / r[1].z);
+  right[3] = GRAPHENE_POINT_INIT (r[2].x / r[2].z, r[2].y / r[2].z);
+
+  /* normalize the outer weights to be 1 by using
+   * the fact that weights w_i and c*w_i are equivalent
+   * for any nonzero constant c
+   */
+  for (int i = 0; i < 3; i++)
+    {
+      l[i].z /= l[0].z;
+      r[i].z /= r[2].z;
+    }
+
+  /* normalize the inner weight to be 1 by using
+   * the fact that w_0*w_2/w_1^2 is a constant for
+   * all equivalent weights.
+   */
+  left[2] = GRAPHENE_POINT_INIT (l[1].z / sqrt (l[2].z), 0);
+  right[2] = GRAPHENE_POINT_INIT (r[1].z / sqrt (r[0].z), 0);
+
+  if (start)
+    gsk_curve_init (start, gsk_pathop_encode (GSK_PATH_CONIC, left));
+  if (end)
+    gsk_curve_init (end, gsk_pathop_encode (GSK_PATH_CONIC, right));
+}
+
+/* taken from Skia, including the very descriptive name */
+static gboolean
+gsk_conic_curve_too_curvy (const graphene_point_t *start,
+                           const graphene_point_t *mid,
+                           const graphene_point_t *end,
+                           float                  tolerance)
+{
+  return fabs ((start->x + end->x) * 0.5 - mid->x) > tolerance
+      || fabs ((start->y + end->y) * 0.5 - mid->y) > tolerance;
+}
+
+static gboolean
+gsk_conic_curve_decompose_subdivide (const GskConicCurve    *self,
+                                     float                   tolerance,
+                                     const graphene_point_t *start,
+                                     float                   start_progress,
+                                     const graphene_point_t *end,
+                                     float                   end_progress,
+                                     GskCurveAddLineFunc     add_line_func,
+                                     gpointer                user_data)
+{
+  graphene_point_t mid;
+  float mid_progress;
+
+  mid_progress = (start_progress + end_progress) / 2;
+  gsk_conic_curve_eval_point (self, mid_progress, &mid);
+
+  if (end_progress - start_progress <= MIN_PROGRESS ||
+      !gsk_conic_curve_too_curvy (start, &mid, end, tolerance))
+    {
+      return add_line_func (start, end, start_progress, end_progress, user_data);
+    }
+
+  return gsk_conic_curve_decompose_subdivide (self, tolerance,
+                                              start, start_progress, &mid, mid_progress,
+                                              add_line_func, user_data)
+      && gsk_conic_curve_decompose_subdivide (self, tolerance, 
+                                              &mid, mid_progress, end, end_progress,
+                                              add_line_func, user_data);
+}
+
+static gboolean
+gsk_conic_curve_decompose (const GskCurve      *curve,
+                           float                tolerance,
+                           GskCurveAddLineFunc  add_line_func,
+                           gpointer             user_data)
+{
+  const GskConicCurve *self = &curve->conic;
+
+  gsk_conic_curve_ensure_coefficents (self);
+
+  return gsk_conic_curve_decompose_subdivide (self,
+                                              tolerance,
+                                              &self->points[0],
+                                              0.0f,
+                                              &self->points[3],
+                                              1.0f,
+                                              add_line_func,
+                                              user_data);
+}
+
+static gskpathop
+gsk_conic_curve_pathop (const GskCurve *curve)
+{
+  const GskConicCurve *self = &curve->conic;
+
+  return gsk_pathop_encode (self->op, self->points);
+}
+
+static const graphene_point_t *
+gsk_conic_curve_get_start_point (const GskCurve *curve)
+{
+  const GskConicCurve *self = &curve->conic;
+
+  return &self->points[0];
+}
+
+static const graphene_point_t *
+gsk_conic_curve_get_end_point (const GskCurve *curve)
+{
+  const GskConicCurve *self = &curve->conic;
+
+  return &self->points[3];
+}
+
+static const GskCurveClass GSK_CONIC_CURVE_CLASS = {
+  gsk_conic_curve_init,
+  gsk_conic_curve_eval,
+  gsk_conic_curve_split,
+  gsk_conic_curve_decompose,
+  gsk_conic_curve_pathop,
+  gsk_conic_curve_get_start_point,
+  gsk_conic_curve_get_end_point,
+};
+
+/** API **/
+
+static const GskCurveClass *
+get_class (GskPathOperation op)
+{
+  const GskCurveClass *klasses[] = {
+    [GSK_PATH_CLOSE] = &GSK_LINE_CURVE_CLASS,
+    [GSK_PATH_LINE] = &GSK_LINE_CURVE_CLASS,
+    [GSK_PATH_CURVE] = &GSK_CURVE_CURVE_CLASS,
+    [GSK_PATH_CONIC] = &GSK_CONIC_CURVE_CLASS,
+  };
+
+  g_assert (op < G_N_ELEMENTS (klasses) && klasses[op] != NULL);
+
+  return klasses[op];
+}
+
+void
+gsk_curve_init (GskCurve  *curve,
+                gskpathop  op)
+{
+  get_class (gsk_pathop_op (op))->init (curve, op);
+}
+
+void
+gsk_curve_eval (const GskCurve   *curve,
+                float             progress,
+                graphene_point_t *pos,
+                graphene_vec2_t  *tangent)
+{
+  get_class (curve->op)->eval (curve, progress, pos, tangent);
+}
+
+void
+gsk_curve_split (const GskCurve *curve,
+                 float           progress,
+                 GskCurve       *start,
+                 GskCurve       *end)
+{
+  get_class (curve->op)->split (curve, progress, start, end);
+}
+
+gboolean
+gsk_curve_decompose (const GskCurve      *curve,
+                     float                tolerance,
+                     GskCurveAddLineFunc  add_line_func,
+                     gpointer             user_data)
+{
+  return get_class (curve->op)->decompose (curve, tolerance, add_line_func, user_data);
+}
+
+gskpathop
+gsk_curve_pathop (const GskCurve *curve)
+{
+  return get_class (curve->op)->pathop (curve);
+}
+
+const graphene_point_t *
+gsk_curve_get_start_point (const GskCurve *curve)
+{
+  return get_class (curve->op)->get_start_point (curve);
+}
+
+const graphene_point_t *
+gsk_curve_get_end_point (const GskCurve *curve)
+{
+  return get_class (curve->op)->get_end_point (curve);
+}
+
diff --git a/gsk/gskcurveprivate.h b/gsk/gskcurveprivate.h
new file mode 100644
index 0000000000..720ee71f1c
--- /dev/null
+++ b/gsk/gskcurveprivate.h
@@ -0,0 +1,108 @@
+/*
+ * Copyright © 2020 Benjamin Otte
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library. If not, see <http://www.gnu.org/licenses/>.
+ *
+ * Authors: Benjamin Otte <otte@gnome.org>
+ */
+
+
+#ifndef __GSK_CURVE_PRIVATE_H__
+#define __GSK_CURVE_PRIVATE_H__
+
+#include "gskpathopprivate.h"
+
+G_BEGIN_DECLS
+
+typedef gpointer gskpathop;
+
+typedef union _GskCurve GskCurve;
+
+typedef struct _GskLineCurve GskLineCurve;
+typedef struct _GskCurveCurve GskCurveCurve;
+typedef struct _GskConicCurve GskConicCurve;
+
+struct _GskLineCurve
+{
+  GskPathOperation op;
+
+  gboolean padding;
+
+  graphene_point_t points[2];
+};
+
+struct _GskCurveCurve
+{
+  GskPathOperation op;
+
+  gboolean has_coefficients;
+
+  graphene_point_t points[4];
+
+  graphene_point_t coeffs[4];
+};
+
+struct _GskConicCurve
+{
+  GskPathOperation op;
+
+  gboolean has_coefficients;
+
+  graphene_point_t points[4];
+
+  graphene_point_t num[3];
+  graphene_point_t denom[3];
+};
+
+union _GskCurve
+{
+  GskPathOperation op;
+  GskLineCurve line;
+  GskCurveCurve curve;
+  GskConicCurve conic;
+};
+
+typedef gboolean (* GskCurveAddLineFunc) (const graphene_point_t *from,
+                                          const graphene_point_t *to,
+                                          float                   from_progress,
+                                          float                   to_progress,
+                                          gpointer                user_data);
+
+void                    gsk_curve_init                          (GskCurve               *curve,
+                                                                 gskpathop               op);
+
+void                    gsk_curve_eval                          (const GskCurve         *curve,
+                                                                 float                   progress,
+                                                                 graphene_point_t       *pos,
+                                                                 graphene_vec2_t        *tangent);
+void                    gsk_curve_split                         (const GskCurve         *curve,
+                                                                 float                   progress,
+                                                                 GskCurve               *start,
+                                                                 GskCurve               *end);
+gboolean                gsk_curve_decompose                     (const GskCurve         *curve,
+                                                                 float                   tolerance,
+                                                                 GskCurveAddLineFunc     add_line_func,
+                                                                 gpointer                user_data);
+gskpathop               gsk_curve_pathop                        (const GskCurve         *curve);
+#define gsk_curve_builder_to(curve, builder) gsk_path_builder_pathop_to ((builder), gsk_curve_pathop (curve))
+const graphene_point_t *gsk_curve_get_start_point               (const GskCurve         *curve);
+const graphene_point_t *gsk_curve_get_end_point                 (const GskCurve         *curve);
+
+
+
+
+G_END_DECLS
+
+#endif /* __GSK_CURVE_PRIVATE_H__ */
+
diff --git a/gsk/gskpath.c b/gsk/gskpath.c
index 1642481ab8..034107ac35 100644
--- a/gsk/gskpath.c
+++ b/gsk/gskpath.c
@@ -21,8 +21,8 @@
 
 #include "gskpathprivate.h"
 
+#include "gskcurveprivate.h"
 #include "gskpathbuilder.h"
-#include "gsksplineprivate.h"
 
 /**
  * SECTION:gskpath
@@ -445,26 +445,22 @@ struct _GskPathForeachTrampoline
   double tolerance;
   GskPathForeachFunc func;
   gpointer user_data;
-  gboolean retval;
 };
 
-static void 
-gsk_path_foreach_trampoline_add_point (const graphene_point_t *from,
-                                       const graphene_point_t *to,
-                                       float                   from_progress,
-                                       float                   to_progress,
-                                       gpointer                data)
+static gboolean
+gsk_path_foreach_trampoline_add_line (const graphene_point_t *from,
+                                      const graphene_point_t *to,
+                                      float                   from_progress,
+                                      float                   to_progress,
+                                      gpointer                data)
 {
   GskPathForeachTrampoline *trampoline = data;
 
-  if (!trampoline->retval)
-    return;
-
-  trampoline->retval = trampoline->func (GSK_PATH_LINE,
-                                         (graphene_point_t[2]) { *from, *to },
-                                         2,
-                                         0.0f,
-                                         trampoline->user_data);
+  return trampoline->func (GSK_PATH_LINE,
+                           (graphene_point_t[2]) { *from, *to },
+                           2,
+                           0.0f,
+                           trampoline->user_data);
 }
 
 static gboolean
@@ -484,25 +480,34 @@ gsk_path_foreach_trampoline (GskPathOperation        op,
       return trampoline->func (op, pts, n_pts, weight, trampoline->user_data);
 
     case GSK_PATH_CURVE:
-      if (trampoline->flags & GSK_PATH_FOREACH_ALLOW_CURVE)
-        return trampoline->func (op, pts, n_pts, weight, trampoline->user_data);
-      
-      gsk_spline_decompose_cubic (pts,
-                                  trampoline->tolerance,
-                                  gsk_path_foreach_trampoline_add_point,
-                                  trampoline);
-      return trampoline->retval;
+      {
+        GskCurve curve;
+
+        if (trampoline->flags & GSK_PATH_FOREACH_ALLOW_CURVE)
+          return trampoline->func (op, pts, n_pts, weight, trampoline->user_data);
+        
+        gsk_curve_init (&curve, gsk_pathop_encode (GSK_PATH_CURVE, pts));
+        return gsk_curve_decompose (&curve, 
+                                    trampoline->tolerance,
+                                    gsk_path_foreach_trampoline_add_line,
+                                    trampoline);
+      }
 
     case GSK_PATH_CONIC:
-      if (trampoline->flags & GSK_PATH_FOREACH_ALLOW_CONIC)
-        return trampoline->func (op, pts, n_pts, weight, trampoline->user_data);
+      {
+        GskCurve curve;
+
+        if (trampoline->flags & GSK_PATH_FOREACH_ALLOW_CONIC)
+          return trampoline->func (op, pts, n_pts, weight, trampoline->user_data);
+
+        /* XXX: decompose into curves if allowed */
+        gsk_curve_init (&curve, gsk_pathop_encode (GSK_PATH_CONIC, (graphene_point_t[4]) { pts[0], pts[1], { weight, }, pts[2] } ));
+        return gsk_curve_decompose (&curve, 
+                                    trampoline->tolerance,
+                                    gsk_path_foreach_trampoline_add_line,
+                                    trampoline);
+      }
 
-      /* XXX: decompose into curves if allowed */
-      gsk_spline_decompose_conic ((graphene_point_t[4]) { pts[0], pts[1], { weight, }, pts[2] },
-                                  trampoline->tolerance,
-                                  gsk_path_foreach_trampoline_add_point,
-                                  trampoline);
-      return trampoline->retval;
 
     default:
       g_assert_not_reached ();
@@ -523,7 +528,7 @@ gsk_path_foreach_with_tolerance (GskPath             *self,
   /* If we need to massage the data, set up a trampoline here */
   if (flags != (GSK_PATH_FOREACH_ALLOW_CURVE | GSK_PATH_FOREACH_ALLOW_CONIC))
     {
-      trampoline = (GskPathForeachTrampoline) { flags, tolerance, func, user_data, TRUE };
+      trampoline = (GskPathForeachTrampoline) { flags, tolerance, func, user_data };
       func = gsk_path_foreach_trampoline;
       user_data = &trampoline;
     }
diff --git a/gsk/gskpathopprivate.h b/gsk/gskpathopprivate.h
index 864e97e2ea..da1c3e63e4 100644
--- a/gsk/gskpathopprivate.h
+++ b/gsk/gskpathopprivate.h
@@ -58,6 +58,7 @@ gsk_pathop_encode (GskPathOperation        op,
                    const graphene_point_t *pts)
 {
   /* g_assert (op & GSK_PATHOP_OPERATION_MASK == op); */
+  g_assert ((GPOINTER_TO_SIZE (pts) & GSK_PATHOP_OPERATION_MASK) == 0);
 
   return GSIZE_TO_POINTER (GPOINTER_TO_SIZE (pts) | op);
 }
diff --git a/gsk/gskpathprivate.h b/gsk/gskpathprivate.h
index e9d9c386d9..4b403acbd6 100644
--- a/gsk/gskpathprivate.h
+++ b/gsk/gskpathprivate.h
@@ -24,6 +24,7 @@
 #include "gskpath.h"
 
 #include "gskcontourprivate.h"
+#include "gskpathopprivate.h"
 
 G_BEGIN_DECLS
 
diff --git a/gsk/gskspline.c b/gsk/gskspline.c
index 711226229c..5590c7f7e0 100644
--- a/gsk/gskspline.c
+++ b/gsk/gskspline.c
@@ -25,384 +25,6 @@
 
 #include <math.h>
 
-#define MIN_PROGRESS (1/1024.f)
-
-typedef struct
-{
-  graphene_point_t last_point;
-  float last_progress;
-  GskSplineAddPointFunc func;
-  gpointer user_data;
-} GskSplineDecompose;
-
-static void
-gsk_spline_decompose_add_point (GskSplineDecompose     *decomp,
-                                const graphene_point_t *pt,
-                                float                   progress)
-{
-  if (graphene_point_equal (&decomp->last_point, pt))
-    return;
-
-  decomp->func (&decomp->last_point, pt, decomp->last_progress, decomp->last_progress + progress, decomp->user_data);
-  decomp->last_point = *pt;
-  decomp->last_progress += progress;
-}
-
-static void
-gsk_spline_decompose_finish (GskSplineDecompose     *decomp,
-                             const graphene_point_t *end_point)
-{
-  g_assert (graphene_point_equal (&decomp->last_point, end_point));
-  g_assert (decomp->last_progress == 1.0f || decomp->last_progress == 0.0f);
-}
-
-typedef struct
-{
-  GskSplineDecompose decomp;
-  float tolerance;
-} GskCubicDecomposition;
-
-static void
-gsk_spline_cubic_get_coefficients (graphene_point_t       coeffs[4],
-                                   const graphene_point_t pts[4])
-{
-  coeffs[0] = GRAPHENE_POINT_INIT (pts[3].x - 3.0f * pts[2].x + 3.0f * pts[1].x - pts[0].x,
-                                   pts[3].y - 3.0f * pts[2].y + 3.0f * pts[1].y - pts[0].y);
-  coeffs[1] = GRAPHENE_POINT_INIT (3.0f * pts[2].x - 6.0f * pts[1].x + 3.0f * pts[0].x,
-                                   3.0f * pts[2].y - 6.0f * pts[1].y + 3.0f * pts[0].y);
-  coeffs[2] = GRAPHENE_POINT_INIT (3.0f * pts[1].x - 3.0f * pts[0].x,
-                                   3.0f * pts[1].y - 3.0f * pts[0].y);
-  coeffs[3] = pts[0];
-}
-
-void
-gsk_spline_get_point_cubic (const graphene_point_t  pts[4],
-                            float                   progress,
-                            graphene_point_t       *pos,
-                            graphene_vec2_t        *tangent)
-{
-  graphene_point_t c[4];
-
-  gsk_spline_cubic_get_coefficients (c, pts);
-
-  if (pos)
-    *pos = GRAPHENE_POINT_INIT (((c[0].x * progress + c[1].x) * progress +c[2].x) * progress + c[3].x,
-                                ((c[0].y * progress + c[1].y) * progress +c[2].y) * progress + c[3].y);
-  if (tangent)
-    {
-      graphene_vec2_init (tangent,
-                          (3.0f * c[0].x * progress + 2.0f * c[1].x) * progress + c[2].x,
-                          (3.0f * c[0].y * progress + 2.0f * c[1].y) * progress + c[2].y);
-      graphene_vec2_normalize (tangent, tangent);
-    }
-}
-
-void
-gsk_spline_split_cubic (const graphene_point_t pts[4],
-                        graphene_point_t       result1[4],
-                        graphene_point_t       result2[4],
-                        float                  progress)
-{
-    graphene_point_t ab, bc, cd;
-    graphene_point_t abbc, bccd;
-    graphene_point_t final;
-
-    graphene_point_interpolate (&pts[0], &pts[1], progress, &ab);
-    graphene_point_interpolate (&pts[1], &pts[2], progress, &bc);
-    graphene_point_interpolate (&pts[2], &pts[3], progress, &cd);
-    graphene_point_interpolate (&ab, &bc, progress, &abbc);
-    graphene_point_interpolate (&bc, &cd, progress, &bccd);
-    graphene_point_interpolate (&abbc, &bccd, progress, &final);
-
-    memcpy (result1, (graphene_point_t[4]) { pts[0], ab, abbc, final }, sizeof (graphene_point_t[4]));
-    memcpy (result2, (graphene_point_t[4]) { final, bccd, cd, pts[3] }, sizeof (graphene_point_t[4]));
-}
-
-#if 0
-/* Return an upper bound on the error (squared) that could result from
- * approximating a spline as a line segment connecting the two endpoints. */
-static float
-gsk_spline_error_squared (const graphene_point_t pts[4])
-{
-  float bdx, bdy, berr;
-  float cdx, cdy, cerr;
-
-  /* We are going to compute the distance (squared) between each of the the b
-   * and c control points and the segment a-b. The maximum of these two
-   * distances will be our approximation error. */
-
-  bdx = pts[1].x - pts[0].x;
-  bdy = pts[1].y - pts[0].y;
-
-  cdx = pts[2].x - pts[0].x;
-  cdy = pts[2].y - pts[0].y;
-
-  if (!graphene_point_equal (&pts[0], &pts[3]))
-    {
-      float dx, dy, u, v;
-
-      /* Intersection point (px):
-       *     px = p1 + u(p2 - p1)
-       *     (p - px) ∙ (p2 - p1) = 0
-       * Thus:
-       *     u = ((p - p1) ∙ (p2 - p1)) / ∥p2 - p1∥²;
-       */
-
-      dx = pts[3].x - pts[0].x;
-      dy = pts[3].y - pts[0].y;
-      v = dx * dx + dy * dy;
-
-      u = bdx * dx + bdy * dy;
-      if (u <= 0)
-        {
-          /* bdx -= 0;
-           * bdy -= 0;
-           */
-        }
-      else if (u >= v)
-        {
-          bdx -= dx;
-          bdy -= dy;
-        }
-      else
-        {
-          bdx -= u/v * dx;
-          bdy -= u/v * dy;
-        }
-
-      u = cdx * dx + cdy * dy;
-      if (u <= 0)
-        {
-          /* cdx -= 0;
-           * cdy -= 0;
-           */
-        }
-      else if (u >= v)
-        {
-          cdx -= dx;
-          cdy -= dy;
-        }
-      else
-        {
-          cdx -= u/v * dx;
-          cdy -= u/v * dy;
-        }
-    }
-
-    berr = bdx * bdx + bdy * bdy;
-    cerr = cdx * cdx + cdy * cdy;
-    if (berr > cerr)
-      return berr;
-    else
-      return cerr;
-}
-#endif
-
-/* taken from Skia, including the very descriptive name */
-static gboolean
-gsk_spline_cubic_too_curvy (const graphene_point_t pts[4],
-                            float                  tolerance)
-{
-  graphene_point_t p;
-
-  graphene_point_interpolate (&pts[0], &pts[3], 1.0f / 3, &p);
-  if (ABS (p.x - pts[1].x) + ABS (p.y - pts[1].y)  > tolerance)
-    return TRUE;
-
-  graphene_point_interpolate (&pts[0], &pts[3], 2.0f / 3, &p);
-  if (ABS (p.x - pts[2].x) + ABS (p.y - pts[2].y)  > tolerance)
-    return TRUE;
-
-  return FALSE;
-}
-
-static void
-gsk_spline_cubic_decompose (GskCubicDecomposition  *d,
-                            const graphene_point_t  pts[4],
-                            float                   progress)
-{
-  graphene_point_t left[4], right[4];
-
-  if (!gsk_spline_cubic_too_curvy (pts, d->tolerance) || progress < MIN_PROGRESS)
-    {
-      gsk_spline_decompose_add_point (&d->decomp, &pts[3], progress);
-      return;
-    }
-
-  gsk_spline_split_cubic (pts, left, right, 0.5);
-
-  gsk_spline_cubic_decompose (d, left, progress / 2);
-  gsk_spline_cubic_decompose (d, right, progress / 2);
-}
-
-void 
-gsk_spline_decompose_cubic (const graphene_point_t pts[4],
-                            float                  tolerance,
-                            GskSplineAddPointFunc  add_point_func,
-                            gpointer               user_data)
-{
-  GskCubicDecomposition decomp = { { pts[0], 0.0f, add_point_func, user_data }, tolerance };
-
-  gsk_spline_cubic_decompose (&decomp, pts, 1.0f);
-
-  gsk_spline_decompose_finish (&decomp.decomp, &pts[3]);
-}
-
-/* CONIC */
-
-typedef struct {
-  graphene_point_t num[3];
-  graphene_point_t denom[3];
-} ConicCoefficients;
-
-typedef struct
-{
-  GskSplineDecompose decomp;
-  float tolerance;
-  ConicCoefficients c;
-} GskConicDecomposition;
-
-
-static void
-gsk_spline_conic_get_coefficents (ConicCoefficients      *c,
-                                  const graphene_point_t  pts[4])
-{
-  float w = pts[2].x;
-  graphene_point_t pw = GRAPHENE_POINT_INIT (w * pts[1].x, w * pts[1].y);
-
-  c->num[2] = pts[0];
-  c->num[1] = GRAPHENE_POINT_INIT (2 * (pw.x - pts[0].x),
-                                   2 * (pw.y - pts[0].y));
-  c->num[0] = GRAPHENE_POINT_INIT (pts[3].x - 2 * pw.x + pts[0].x,
-                                   pts[3].y - 2 * pw.y + pts[0].y);
-
-  c->denom[2] = GRAPHENE_POINT_INIT (1, 1);
-  c->denom[1] = GRAPHENE_POINT_INIT (2 * (w - 1), 2 * (w - 1));
-  c->denom[0] = GRAPHENE_POINT_INIT (-c->denom[1].x, -c->denom[1].y);
-}
-
-static inline void
-gsk_spline_eval_quad (const graphene_point_t quad[3],
-                      float                  progress,
-                      graphene_point_t      *result)
-{
-  *result = GRAPHENE_POINT_INIT ((quad[0].x * progress + quad[1].x) * progress + quad[2].x,
-                                 (quad[0].y * progress + quad[1].y) * progress + quad[2].y);
-}
-
-static inline void
-gsk_spline_eval_conic (const ConicCoefficients *c,
-                       float                    progress,
-                       graphene_point_t        *result)
-{
-  graphene_point_t num, denom;
-
-  gsk_spline_eval_quad (c->num, progress, &num);
-  gsk_spline_eval_quad (c->denom, progress, &denom);
-  *result = GRAPHENE_POINT_INIT (num.x / denom.x, num.y / denom.y);
-}
-                       
-void
-gsk_spline_get_point_conic (const graphene_point_t  pts[4],
-                            float                   progress,
-                            graphene_point_t       *pos,
-                            graphene_vec2_t        *tangent)
-{
-  ConicCoefficients c;
-
-  gsk_spline_conic_get_coefficents (&c, pts);
-
-  if (pos)
-    gsk_spline_eval_conic (&c, progress, pos);
-
-  if (tangent)
-    {
-      graphene_point_t tmp;
-      float w = pts[2].x;
-
-      /* The tangent will be 0 in these corner cases, just
-       * treat it like a line here. */
-      if ((progress <= 0.f && graphene_point_equal (&pts[0], &pts[1])) ||
-          (progress >= 1.f && graphene_point_equal (&pts[1], &pts[3])))
-        {
-          graphene_vec2_init (tangent, pts[3].x - pts[0].x, pts[3].y - pts[0].y);
-          return;
-        }
-
-      gsk_spline_eval_quad ((graphene_point_t[3]) {
-                              GRAPHENE_POINT_INIT ((w - 1) * (pts[3].x - pts[0].x),
-                                                   (w - 1) * (pts[3].y - pts[0].y)),
-                              GRAPHENE_POINT_INIT (pts[3].x - pts[0].x - 2 * w * (pts[1].x - pts[0].x),
-                                                   pts[3].y - pts[0].y - 2 * w * (pts[1].y - pts[0].y)),
-                              GRAPHENE_POINT_INIT (w * (pts[1].x - pts[0].x),
-                                                   w * (pts[1].y - pts[0].y))
-                            },
-                            progress,
-                            &tmp);
-      graphene_vec2_init (tangent, tmp.x, tmp.y);
-      graphene_vec2_normalize (tangent, tangent);
-    }
-}
-
-void
-gsk_spline_split_conic (const graphene_point_t pts[4],
-                        graphene_point_t       result1[4],
-                        graphene_point_t       result2[4],
-                        float                  progress)
-{
-  g_warning ("FIXME: Stop treating conics as lines");
-}
-
-/* taken from Skia, including the very descriptive name */
-static gboolean
-gsk_spline_conic_too_curvy (const graphene_point_t *start,
-                            const graphene_point_t *mid,
-                            const graphene_point_t *end,
-                            float                  tolerance)
-{
-  return fabs ((start->x + end->x) * 0.5 - mid->x) > tolerance
-      || fabs ((start->y + end->y) * 0.5 - mid->y) > tolerance;
-}
-
-static void
-gsk_spline_decompose_conic_subdivide (GskConicDecomposition  *d,
-                                      const graphene_point_t *start,
-                                      float                   start_progress,
-                                      const graphene_point_t *end,
-                                      float                   end_progress)
-{
-  graphene_point_t mid;
-  float mid_progress;
-
-  mid_progress = (start_progress + end_progress) / 2;
-  gsk_spline_eval_conic (&d->c, mid_progress, &mid);
-
-  if (end_progress - start_progress < MIN_PROGRESS ||
-      !gsk_spline_conic_too_curvy (start, &mid, end, d->tolerance))
-    {
-      gsk_spline_decompose_add_point (&d->decomp, end, end_progress - start_progress);
-      return;
-    }
-
-  gsk_spline_decompose_conic_subdivide (d, start, start_progress, &mid, mid_progress);
-  gsk_spline_decompose_conic_subdivide (d, &mid, mid_progress, end, end_progress);
-}
-
-void
-gsk_spline_decompose_conic (const graphene_point_t pts[4],
-                            float                  tolerance,
-                            GskSplineAddPointFunc  add_point_func,
-                            gpointer               user_data)
-{
-  GskConicDecomposition d = { { pts[0], 0.0f, add_point_func, user_data }, tolerance, };
-
-  gsk_spline_conic_get_coefficents (&d.c, pts);
-
-  gsk_spline_decompose_conic_subdivide (&d, &pts[0], 0.0f, &pts[3], 1.0f);
-
-  gsk_spline_decompose_finish (&d.decomp, &pts[3]);
-}
-
 /* Spline deviation from the circle in radius would be given by:
 
         error = sqrt (x**2 + y**2) - 1
diff --git a/gsk/gsksplineprivate.h b/gsk/gsksplineprivate.h
index 02556937ce..c9da32734c 100644
--- a/gsk/gsksplineprivate.h
+++ b/gsk/gsksplineprivate.h
@@ -25,38 +25,6 @@
 
 G_BEGIN_DECLS
 
-typedef void (* GskSplineAddPointFunc) (const graphene_point_t *from,
-                                        const graphene_point_t *to,
-                                        float                   from_progress,
-                                        float                   to_progress,
-                                        gpointer                user_data);
-
-void                    gsk_spline_get_point_cubic              (const graphene_point_t  pts[4],
-                                                                 float                   progress,
-                                                                 graphene_point_t       *pos,
-                                                                 graphene_vec2_t        *tangent);
-void                    gsk_spline_split_cubic                  (const graphene_point_t  pts[4],
-                                                                 graphene_point_t        result1[4],
-                                                                 graphene_point_t        result2[4],
-                                                                 float                   progress);
-void                    gsk_spline_decompose_cubic              (const graphene_point_t  pts[4],
-                                                                 float                   tolerance,
-                                                                 GskSplineAddPointFunc   add_point_func,
-                                                                 gpointer                user_data);
-
-void                    gsk_spline_get_point_conic              (const graphene_point_t  pts[4],
-                                                                 float                   progress,
-                                                                 graphene_point_t       *pos,
-                                                                 graphene_vec2_t        *tangent);
-void                    gsk_spline_split_conic                  (const graphene_point_t  pts[4],
-                                                                 graphene_point_t        result1[4],
-                                                                 graphene_point_t        result2[4],
-                                                                 float                   progress);
-void                    gsk_spline_decompose_conic              (const graphene_point_t  pts[4],
-                                                                 float                   tolerance,
-                                                                 GskSplineAddPointFunc   add_point_func,
-                                                                 gpointer                user_data);
-
 typedef gboolean (* GskSplineAddCurveFunc) (const graphene_point_t curve[4],
                                             gpointer               user_data);
 gboolean                gsk_spline_decompose_arc                (const graphene_point_t *center,
diff --git a/gsk/meson.build b/gsk/meson.build
index 55f37e1c3e..78e3e88876 100644
--- a/gsk/meson.build
+++ b/gsk/meson.build
@@ -21,8 +21,8 @@ gsk_private_gl_shaders = [
 ]
 
 gsk_public_sources = files([
-  'gskdiff.c',
   'gskcairorenderer.c',
+  'gskdiff.c',
   'gskglshader.c',
   'gskpath.c',
   'gskpathbuilder.c',
@@ -40,6 +40,7 @@ gsk_public_sources = files([
 gsk_private_sources = files([
   'gskcairoblur.c',
   'gskcontour.c',
+  'gskcurve.c',
   'gskdebug.c',
   'gskprivate.c',
   'gskprofiler.c',