Add GskPathMeasure

An object to do measuring operations on paths - determining
their length, cutting off subpaths, things like that.

gsk/gsk.h

@@ -22,6 +22,8 @@
 #include <gsk/gskenums.h>
 #include <gsk/gskpath.h>
 #include <gsk/gskpathbuilder.h>
+#include <gsk/gskpathmeasure.h>
+#include <gsk/gskpathpoint.h>
 #include <gsk/gskrenderer.h>
 #include <gsk/gskrendernode.h>
 #include <gsk/gskroundedrect.h>

gsk/gskcontourprivate.h

@@ -58,6 +58,11 @@ void                    gsk_contour_print                       (const GskContou
                                                                  GString                *string);
 gboolean                gsk_contour_get_bounds                  (const GskContour       *self,
                                                                  graphene_rect_t        *bounds);
+gpointer                gsk_contour_init_measure                (const GskContour       *self,
+                                                                 float                   tolerance,
+                                                                 float                  *out_length);
+void                    gsk_contour_free_measure                (const GskContour       *self,
+                                                                 gpointer                data);
 gboolean                gsk_contour_foreach                     (const GskContour       *self,
                                                                  float                   tolerance,
                                                                  GskPathForeachFunc      func,
@@ -65,5 +70,34 @@ gboolean                gsk_contour_foreach                     (const GskContou
 void                    gsk_contour_get_start_end               (const GskContour       *self,
                                                                  graphene_point_t       *start,
                                                                  graphene_point_t       *end);
+void                    gsk_contour_get_point                   (const GskContour       *self,
+                                                                 gpointer                measure_data,
+                                                                 float                   distance,
+                                                                 GskPathDirection        direction,
+                                                                 graphene_point_t       *pos,
+                                                                 graphene_vec2_t        *tangent);
+gboolean                gsk_contour_get_closest_point           (const GskContour       *self,
+                                                                 gpointer                measure_data,
+                                                                 float                   tolerance,
+                                                                 const graphene_point_t *point,
+                                                                 float                   threshold,
+                                                                 float                  *out_distance,
+                                                                 graphene_point_t       *out_pos,
+                                                                 float                  *out_offset,
+                                                                 graphene_vec2_t        *out_tangent);
+int                     gsk_contour_get_winding                 (const GskContour       *self,
+                                                                 gpointer                measure_data,
+                                                                 const graphene_point_t *point);
+void                    gsk_contour_add_segment                 (const GskContour       *self,
+                                                                 GskPathBuilder         *builder,
+                                                                 gpointer                measure_data,
+                                                                 gboolean                emit_move_to,
+                                                                 float                   start,
+                                                                 float                   end);
+float                   gsk_contour_get_curvature               (const GskContour       *self,
+                                                                 gpointer                measure_data,
+                                                                 float                   distance,
+                                                                 graphene_point_t       *center);
+
 
 G_END_DECLS

gsk/gskcurve.c

@@ -51,6 +51,8 @@ struct _GskCurveClass
                                                          graphene_vec2_t        *tangent);
   void                          (* reverse)             (const GskCurve         *curve,
                                                          GskCurve               *reverse);
+  float                         (* get_curvature)       (const GskCurve         *curve,
+                                                         float                   t);
   void                          (* split)               (const GskCurve         *curve,
                                                          float                   progress,
                                                          GskCurve               *result1,
@@ -221,6 +223,13 @@ gsk_line_curve_get_tangent (const GskCurve  *curve,
   get_tangent (&self->points[0], &self->points[1], tangent);
 }
 
+static float
+gsk_line_curve_get_curvature (const GskCurve *curve,
+                              float           t)
+{
+  return 0;
+}
+
 static void
 gsk_line_curve_reverse (const GskCurve *curve,
                         GskCurve       *reverse)
@@ -299,6 +308,7 @@ static const GskCurveClass GSK_LINE_CURVE_CLASS = {
   gsk_line_curve_get_point,
   gsk_line_curve_get_tangent,
   gsk_line_curve_reverse,
+  gsk_line_curve_get_curvature,
   gsk_line_curve_split,
   gsk_line_curve_segment,
   gsk_line_curve_decompose,
@@ -441,6 +451,17 @@ gsk_quad_curve_get_tangent (const GskCurve   *curve,
   graphene_vec2_normalize (tangent, tangent);
 }
 
+
+static float gsk_cubic_curve_get_curvature (const GskCurve *curve,
+                                            float           t);
+
+static float
+gsk_quad_curve_get_curvature (const GskCurve *curve,
+                              float           t)
+{
+  return gsk_cubic_curve_get_curvature (curve, t);
+}
+
 static void
 gsk_quad_curve_reverse (const GskCurve *curve,
                         GskCurve       *reverse)
@@ -600,6 +621,7 @@ static const GskCurveClass GSK_QUAD_CURVE_CLASS = {
   gsk_quad_curve_get_point,
   gsk_quad_curve_get_tangent,
   gsk_quad_curve_reverse,
+  gsk_quad_curve_get_curvature,
   gsk_quad_curve_split,
   gsk_quad_curve_segment,
   gsk_quad_curve_decompose,
@@ -775,6 +797,105 @@ gsk_cubic_curve_reverse (const GskCurve *curve,
   reverse->cubic.has_coefficients = FALSE;
 }
 
+static void
+gsk_curve_get_derivative (const GskCurve *curve,
+                          GskCurve       *deriv)
+{
+  switch (curve->op)
+    {
+    case GSK_PATH_LINE:
+      {
+        const GskLineCurve *self = &curve->line;
+        graphene_point_t p;
+
+        p.x = self->points[1].x - self->points[0].x;
+        p.y = self->points[1].y - self->points[0].y;
+
+        gsk_line_curve_init_from_points (&deriv->line, GSK_PATH_LINE, &p, &p);
+      }
+      break;
+
+    case GSK_PATH_QUAD:
+      {
+        const GskQuadCurve *self = &curve->quad;
+        graphene_point_t p[2];
+
+        p[0].x = 2.f * (self->points[1].x - self->points[0].x);
+        p[0].y = 2.f * (self->points[1].y - self->points[0].y);
+        p[1].x = 2.f * (self->points[2].x - self->points[1].x);
+        p[1].y = 2.f * (self->points[2].y - self->points[1].y);
+
+        gsk_line_curve_init_from_points (&deriv->line, GSK_PATH_LINE, &p[0], &p[1]);
+      }
+      break;
+
+    case GSK_PATH_CUBIC:
+      {
+        const GskCubicCurve *self = &curve->cubic;
+        graphene_point_t p[3];
+
+        p[0].x = 3.f * (self->points[1].x - self->points[0].x);
+        p[0].y = 3.f * (self->points[1].y - self->points[0].y);
+        p[1].x = 3.f * (self->points[2].x - self->points[1].x);
+        p[1].y = 3.f * (self->points[2].y - self->points[1].y);
+        p[2].x = 3.f * (self->points[3].x - self->points[2].x);
+        p[2].y = 3.f * (self->points[3].y - self->points[2].y);
+
+        gsk_quad_curve_init_from_points (&deriv->quad, p);
+      }
+      break;
+
+    case GSK_PATH_MOVE:
+    case GSK_PATH_CLOSE:
+    case GSK_PATH_CONIC:
+    default:
+      g_assert_not_reached ();
+    }
+}
+
+static inline float
+cross (const graphene_vec2_t *v1,
+       const graphene_vec2_t *v2)
+{
+  return graphene_vec2_get_x (v1) * graphene_vec2_get_y (v2)
+         - graphene_vec2_get_y (v1) * graphene_vec2_get_x (v2);
+}
+
+static inline float
+pow3 (float w)
+{
+  return w * w * w;
+}
+
+static float
+gsk_cubic_curve_get_curvature (const GskCurve *curve,
+                               float           t)
+{
+  GskCurve c1, c2;
+  graphene_point_t p, pp;
+  graphene_vec2_t d, dd;
+  float num, denom;
+
+  gsk_curve_get_derivative (curve, &c1);
+  gsk_curve_get_derivative (&c1, &c2);
+
+  gsk_curve_get_point (&c1, t, &p);
+  gsk_curve_get_point (&c2, t, &pp);
+
+  graphene_vec2_init (&d, p.x, p.y);
+  graphene_vec2_init (&dd, pp.x, pp.y);
+
+  num = cross (&d, &dd);
+  if (num == 0)
+    return 0;
+
+  denom = pow3 (graphene_vec2_length (&d));
+  if (denom == 0)
+    return 0;
+
+  return num / denom;
+}
+
 static void
 gsk_cubic_curve_split (const GskCurve   *curve,
                        float             progress,
@@ -895,6 +1016,7 @@ static const GskCurveClass GSK_CUBIC_CURVE_CLASS = {
   gsk_cubic_curve_get_point,
   gsk_cubic_curve_get_tangent,
   gsk_cubic_curve_reverse,
+  gsk_cubic_curve_get_curvature,
   gsk_cubic_curve_split,
   gsk_cubic_curve_segment,
   gsk_cubic_curve_decompose,
@@ -1094,6 +1216,38 @@ gsk_conic_curve_get_tangent (const GskCurve   *curve,
   graphene_vec2_normalize (tangent, tangent);
 }
 
+/* See M. Floater, Derivatives of rational Bezier curves */
+static float
+gsk_conic_curve_get_curvature (const GskCurve *curve,
+                               float           t)
+{
+  graphene_point_t p[3], p1[2];
+  float w, w1[2], w2;
+  graphene_vec2_t t1, t2, t3;
+
+  w = curve->conic.points[2].x;
+
+  p[0] = curve->conic.points[0];
+  p[1] = curve->conic.points[1];
+  p[2] = curve->conic.points[3];
+
+  w1[0] = (1 - t) + t*w;
+  w1[1] = (1 - t)*w + t;
+
+  w2 = (1 - t)*w1[0] + t*w1[1];
+
+  p1[0].x = ((1 - t)*p[0].x + t*w*p[1].x)/w1[0];
+  p1[0].y = ((1 - t)*p[0].y + t*w*p[1].y)/w1[0];
+  p1[1].x = ((1 - t)*w*p[1].x + t*p[2].x)/w1[1];
+  p1[1].y = ((1 - t)*w*p[1].y + t*p[2].y)/w1[1];
+
+  graphene_vec2_init (&t1, p[1].x - p[0].x, p[1].y - p[0].y);
+  graphene_vec2_init (&t2, p[2].x - p[1].x, p[2].y - p[1].y);
+  graphene_vec2_init (&t3, p1[1].x - p1[0].x, p1[1].y - p1[0].y);
+
+  return 0.5 * ((w*pow3 (w2))/(pow3 (w1[0])*pow3 (w1[1]))) * (cross (&t1, &t2) / pow3 (graphene_vec2_length (&t3)));
+}
+
 static void
 gsk_conic_curve_reverse (const GskCurve *curve,
                          GskCurve       *reverse)
@@ -1443,6 +1597,7 @@ static const GskCurveClass GSK_CONIC_CURVE_CLASS = {
   gsk_conic_curve_get_point,
   gsk_conic_curve_get_tangent,
   gsk_conic_curve_reverse,
+  gsk_conic_curve_get_curvature,
   gsk_conic_curve_split,
   gsk_conic_curve_segment,
   gsk_conic_curve_decompose,
@@ -1550,6 +1705,31 @@ gsk_curve_get_tangent (const GskCurve   *curve,
   get_class (curve->op)->get_tangent (curve, progress, tangent);
 }
 
+float
+gsk_curve_get_curvature (const GskCurve   *curve,
+                         float             t,
+                         graphene_point_t *center)
+{
+  float k;
+
+  k = get_class (curve->op)->get_curvature (curve, t);
+
+  if (center != NULL && k != 0)
+    {
+      graphene_point_t p;
+      graphene_vec2_t tangent;
+      float r;
+
+      r = 1/k;
+      gsk_curve_get_point (curve, t, &p);
+      gsk_curve_get_tangent (curve, t, &tangent);
+      center->x = p.x - r * graphene_vec2_get_y (&tangent);
+      center->y = p.y + r * graphene_vec2_get_x (&tangent);
+    }
+
+  return k;
+}
+
 void
 gsk_curve_reverse (const GskCurve *curve,
                    GskCurve       *reverse)

gsk/gskcurveprivate.h

@@ -155,5 +155,9 @@ gboolean                gsk_curve_decompose_curve               (const GskCurve
 
 #define gsk_curve_builder_to(curve, builder) gsk_path_builder_pathop_to ((builder), gsk_curve_pathop (curve))
 
+float                   gsk_curve_get_curvature                 (const GskCurve         *curve,
+                                                                 float                   t,
+                                                                 graphene_point_t       *center);
+
 G_END_DECLS
 

gsk/gskpathbuilder.h

@@ -75,6 +75,12 @@ void                    gsk_path_builder_add_ellipse            (GskPathBuilder
                                                                  const graphene_point_t *center,
                                                                  const graphene_size_t  *radius);
 
+GDK_AVAILABLE_IN_ALL
+void                    gsk_path_builder_add_segment            (GskPathBuilder         *self,
+                                                                 GskPathMeasure         *measure,
+                                                                 float                   start,
+                                                                 float                   end);
+
 GDK_AVAILABLE_IN_ALL
 void                    gsk_path_builder_move_to                (GskPathBuilder         *self,
                                                                  float                   x,

gsk/gskpathmeasure.c

@@ -0,0 +1,489 @@
+/*
+ * 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 "gskpathmeasure.h"
+
+#include "gskpathbuilder.h"
+#include "gskpathpointprivate.h"
+#include "gskpathprivate.h"
+
+/**
+ * `GskPathMeasure` is an object that allows measurements
+ * on `GskPath`s such as determining the length of the path.
+ *
+ * Many measuring operations require approximating the path
+ * with simpler shapes. Therefore, a `GskPathMeasure` has
+ * a tolerance that determines what amount is required
+ * for such approximations.
+ *
+ * A `GskPathMeasure` struct is a reference counted struct
+ * and should be treated as opaque.
+ */
+
+typedef struct _GskContourMeasure GskContourMeasure;
+
+struct _GskContourMeasure
+{
+  float length;
+  gpointer contour_data;
+};
+
+struct _GskPathMeasure
+{
+  /*< private >*/
+  guint ref_count;
+
+  GskPath *path;
+  float tolerance;
+
+  float length;
+  gsize n_contours;
+  GskContourMeasure measures[];
+};
+
+G_DEFINE_BOXED_TYPE (GskPathMeasure, gsk_path_measure,
+                     gsk_path_measure_ref,
+                     gsk_path_measure_unref)
+
+/**
+ * gsk_path_measure_new:
+ * @path: the path to measure
+ *
+ * Creates a measure object for the given @path.
+ *
+ * Returns: a new `GskPathMeasure` representing @path
+ */
+GskPathMeasure *
+gsk_path_measure_new (GskPath *path)
+{
+  return gsk_path_measure_new_with_tolerance (path, GSK_PATH_TOLERANCE_DEFAULT);
+}
+
+/**
+ * gsk_path_measure_new_with_tolerance:
+ * @path: the path to measure
+ * @tolerance: the tolerance for measuring operations
+ *
+ * Creates a measure object for the given @path and @tolerance.
+ *
+ * Returns: a new `GskPathMeasure` representing @path
+ */
+GskPathMeasure *
+gsk_path_measure_new_with_tolerance (GskPath *path,
+                                     float    tolerance)
+{
+  GskPathMeasure *self;
+  gsize i, n_contours;
+
+  g_return_val_if_fail (path != NULL, NULL);
+  g_return_val_if_fail (tolerance > 0, NULL);
+
+  n_contours = gsk_path_get_n_contours (path);
+
+  self = g_malloc0 (sizeof (GskPathMeasure) + n_contours * sizeof (GskContourMeasure));
+
+  self->ref_count = 1;
+  self->path = gsk_path_ref (path);
+  self->tolerance = tolerance;
+  self->n_contours = n_contours;
+
+  for (i = 0; i < n_contours; i++)
+    {
+      self->measures[i].contour_data = gsk_contour_init_measure (gsk_path_get_contour (path, i),
+                                                                 self->tolerance,
+                                                                 &self->measures[i].length);
+      self->length += self->measures[i].length;
+    }
+
+  return self;
+}
+
+/**
+ * gsk_path_measure_ref:
+ * @self: a `GskPathMeasure`
+ *
+ * Increases the reference count of a `GskPathMeasure` by one.
+ *
+ * Returns: the passed in `GskPathMeasure`.
+ */
+GskPathMeasure *
+gsk_path_measure_ref (GskPathMeasure *self)
+{
+  g_return_val_if_fail (self != NULL, NULL);
+
+  self->ref_count++;
+
+  return self;
+}
+
+/**
+ * gsk_path_measure_unref:
+ * @self: a `GskPathMeasure`
+ *
+ * Decreases the reference count of a `GskPathMeasure` by one.
+ *
+ * If the resulting reference count is zero, frees the object.
+ */
+void
+gsk_path_measure_unref (GskPathMeasure *self)
+{
+  gsize i;
+
+  g_return_if_fail (self != NULL);
+  g_return_if_fail (self->ref_count > 0);
+
+  self->ref_count--;
+  if (self->ref_count > 0)
+    return;
+
+  for (i = 0; i < self->n_contours; i++)
+    {
+      gsk_contour_free_measure (gsk_path_get_contour (self->path, i),
+                                self->measures[i].contour_data);
+    }
+
+  gsk_path_unref (self->path);
+  g_free (self);
+}
+
+/**
+ * gsk_path_measure_get_path:
+ * @self: a `GskPathMeasure`
+ *
+ * Returns the path that the measure was created for.
+ *
+ * Returns: (transfer none): the path of @self
+ */
+GskPath *
+gsk_path_measure_get_path (GskPathMeasure *self)
+{
+  return self->path;
+}
+
+/**
+ * gsk_path_measure_get_tolerance:
+ * @self: a `GskPathMeasure`
+ *
+ * Returns the tolerance that the measure was created with.
+ *
+ * Returns: the tolerance of @self
+ */
+float
+gsk_path_measure_get_tolerance (GskPathMeasure *self)
+{
+  return self->tolerance;
+}
+
+/**
+ * gsk_path_measure_get_length:
+ * @self: a `GskPathMeasure`
+ *
+ * Gets the length of the path being measured.
+ *
+ * The length is cached, so this function does not do any work.
+ *
+ * Returns: The length of the path measured by @self
+ */
+float
+gsk_path_measure_get_length (GskPathMeasure *self)
+{
+  g_return_val_if_fail (self != NULL, 0);
+
+  return self->length;
+}
+
+/**
+ * gsk_path_measure_is_closed:
+ * @self: a `GskPathMeasure`
+ *
+ * Returns if the path being measured represents a single closed
+ * contour.
+ *
+ * Returns: `TRUE` if the current path is closed
+ */
+gboolean
+gsk_path_measure_is_closed (GskPathMeasure *self)
+{
+  const GskContour *contour;
+
+  g_return_val_if_fail (self != NULL, FALSE);
+
+  /* XXX: is the empty path closed? Currently it's not */
+  if (self->n_contours != 1)
+    return FALSE;
+
+  contour = gsk_path_get_contour (self->path, 0);
+  return gsk_contour_get_flags (contour) & GSK_PATH_CLOSED ? TRUE : FALSE;
+}
+
+static float
+gsk_path_measure_clamp_distance (GskPathMeasure *self,
+                                 float           distance)
+{
+  if (isnan (distance))
+    return 0;
+
+  return CLAMP (distance, 0, self->length);
+}
+
+/**
+ * gsk_path_measure_in_fill:
+ * @self: a `GskPathMeasure`
+ * @point: the point to test
+ * @fill_rule: the fill rule to follow
+ *
+ * Returns whether the given point is inside the area
+ * that would be affected if the path was filled according
+ * to @fill_rule.
+ *
+ * Returns: `TRUE` if @point is inside
+ */
+gboolean
+gsk_path_measure_in_fill (GskPathMeasure         *self,
+                          const graphene_point_t *point,
+                          GskFillRule             fill_rule)
+{
+  int winding = 0;
+  int i;
+
+  for (i = 0; i < self->n_contours; i++)
+    winding += gsk_contour_get_winding (gsk_path_get_contour (self->path, i),
+                                        self->measures[i].contour_data,
+                                        point);
+
+  switch (fill_rule)
+    {
+    case GSK_FILL_RULE_EVEN_ODD:
+      return winding & 1;
+    case GSK_FILL_RULE_WINDING:
+      return winding != 0;
+    default:
+      g_assert_not_reached ();
+    }
+}
+
+static void
+gsk_path_builder_add_segment_chunk (GskPathBuilder *self,
+                                    GskPathMeasure *measure,
+                                    gboolean        emit_move_to,
+                                    float           start,
+                                    float           end)
+{
+  g_assert (start < end);
+
+  for (gsize i = 0; i < measure->n_contours; i++)
+    {
+      if (measure->measures[i].length < start)
+        {
+          start -= measure->measures[i].length;
+          end -= measure->measures[i].length;
+        }
+      else if (start > 0 || end < measure->measures[i].length)
+        {
+          float len = MIN (end, measure->measures[i].length);
+          gsk_contour_add_segment (gsk_path_get_contour (measure->path, i),
+                                   self,
+                                   measure->measures[i].contour_data,
+                                   emit_move_to,
+                                   start,
+                                   len);
+          end -= len;
+          start = 0;
+          if (end <= 0)
+            break;
+        }
+      else
+        {
+          end -= measure->measures[i].length;
+          gsk_path_builder_add_contour (self, gsk_contour_dup (gsk_path_get_contour (measure->path, i)));
+        }
+      emit_move_to = TRUE;
+    }
+}
+
+/**
+ * gsk_path_builder_add_segment:
+ * @self: a `GskPathBuilder`
+ * @measure: the `GskPathMeasure` to take the segment to
+ * @start: start distance into the path
+ * @end: end distance into the path
+ *
+ * Adds to @self the segment of @measure from @start to @end.
+ *
+ * The distances are given relative to the length of @measure's path,
+ * from 0 for the beginning of the path to its length for the end
+ * of the path. The values will be clamped to that range. The length
+ * can be obtained with [method@Gsk.PathMeasure.get_length].
+ *
+ * If @start >= @end after clamping, the path will first add the segment
+ * from @start to the end of the path, and then add the segment from
+ * the beginning to @end. If the path is closed, these segments will
+ * be connected.
+ */
+void
+gsk_path_builder_add_segment (GskPathBuilder *self,
+                              GskPathMeasure *measure,
+                              float           start,
+                              float           end)
+{
+  g_return_if_fail (self != NULL);
+  g_return_if_fail (measure != NULL);
+
+  start = gsk_path_measure_clamp_distance (measure, start);
+  end = gsk_path_measure_clamp_distance (measure, end);
+
+  if (start < end)
+    {
+      gsk_path_builder_add_segment_chunk (self, measure, TRUE, start, end);
+    }
+  else
+    {
+      /* If the path is closed, we can connect the 2 subpaths. */
+      gboolean closed = gsk_path_measure_is_closed (measure);
+      gboolean need_move_to = !closed;
+
+      if (start < measure->length)
+        gsk_path_builder_add_segment_chunk (self, measure,
+                                            TRUE,
+                                            start, measure->length);
+      else
+        need_move_to = TRUE;
+
+      if (end > 0)
+        gsk_path_builder_add_segment_chunk (self, measure,
+                                            need_move_to,
+                                            0, end);
+      if (start == end && closed)
+        gsk_path_builder_close (self);
+    }
+}
+
+/**
+ * gsk_path_measure_get_point:
+ * @self: a `GskPathMeasure`
+ * @distance: the distance
+ *
+ * Returns a `GskPathPoint` representing the point at the given
+ * distance into the path.
+ *
+ * An empty path has no points, so `NULL` is returned in that case.
+ *
+ * Returns: (transfer full) (nullable): a newly allocated `GskPathPoint`
+ */
+GskPathPoint *
+gsk_path_measure_get_point (GskPathMeasure *self,
+                            float           distance)
+{
+  gsize i;
+  float contour_offset;
+  float offset;
+  const GskContour *contour;
+
+  g_return_val_if_fail (self != NULL, NULL);
+
+  if (self->n_contours == 0)
+    return NULL;
+
+  contour_offset = 0;
+  offset = gsk_path_measure_clamp_distance (self, distance);
+
+  for (i = 0; i < self->n_contours - 1; i++)
+    {
+      if (offset < self->measures[i].length)
+        break;
+
+      contour_offset += self->measures[i].length;
+      offset -= self->measures[i].length;
+    }
+
+  g_assert (0 <= i && i < self->n_contours);
+
+  offset = CLAMP (offset, 0, self->measures[i].length);
+
+  contour = gsk_path_get_contour (self->path, i);
+
+  return gsk_path_point_new (self,
+                             contour, self->measures[i].contour_data,
+                             contour_offset, offset);
+}
+
+/**
+ * gsk_path_measure_get_closest_point:
+ * @self: a `GskPathMeasure`
+ * @point: the point to fond the closest point to
+ * @threshold: The maximum allowed distance between the path and @point.
+ *   Use `INFINITY` to look for any point.
+ *
+ * Returns a `GskPathPoint` representing the point on the path
+ * that is closest to the given point.
+ *
+ * If no point on the path is closer than @threshold, `NULL` is returned.
+ *
+ * Returns: (transfer full) (nullable): a newly allocated `GskPathPoint`
+ */
+GskPathPoint *
+gsk_path_measure_get_closest_point (GskPathMeasure         *self,
+                                    const graphene_point_t *point,
+                                    float                   threshold)
+{
+  gssize best_idx;
+  float best_offset;
+  float best_contour_offset;
+  float contour_offset;
+
+  contour_offset = 0;
+  best_idx = -1;
+
+  for (gsize i = 0; i < self->n_contours; i++)
+    {
+      float distance, offset;
+
+      if (gsk_contour_get_closest_point (gsk_path_get_contour (self->path, i),
+                                         self->measures[i].contour_data,
+                                         self->tolerance,
+                                         point,
+                                         threshold,
+                                         &distance,
+                                         NULL,
+                                         &offset,
+                                         NULL))
+        {
+          best_idx = i;
+          best_offset = offset;
+          best_contour_offset = contour_offset;
+
+          if (distance < self->tolerance)
+            break;
+
+          threshold = distance - self->tolerance;
+        }
+
+      contour_offset += self->measures[i].length;
+    }
+
+  if (best_idx != -1)
+    return gsk_path_point_new (self,
+                               gsk_path_get_contour (self->path, best_idx),
+                               self->measures[best_idx].contour_data,
+                               best_contour_offset, best_offset);
+
+  return NULL;
+}

gsk/gskpathmeasure.h

@@ -0,0 +1,73 @@
+/*
+ * 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>
+ */
+
+#pragma once
+
+#if !defined (__GSK_H_INSIDE__) && !defined (GTK_COMPILATION)
+#error "Only <gsk/gsk.h> can be included directly."
+#endif
+
+
+#include <gsk/gskpath.h>
+#include <gsk/gskpathpoint.h>
+
+G_BEGIN_DECLS
+
+#define GSK_TYPE_PATH_MEASURE (gsk_path_measure_get_type ())
+
+GDK_AVAILABLE_IN_ALL
+GType                   gsk_path_measure_get_type               (void) G_GNUC_CONST;
+GDK_AVAILABLE_IN_ALL
+GskPathMeasure *        gsk_path_measure_new                    (GskPath                *path);
+GDK_AVAILABLE_IN_ALL
+GskPathMeasure *        gsk_path_measure_new_with_tolerance     (GskPath                *path,
+                                                                 float                   tolerance);
+
+GDK_AVAILABLE_IN_ALL
+GskPathMeasure *        gsk_path_measure_ref                    (GskPathMeasure         *self);
+GDK_AVAILABLE_IN_ALL
+void                    gsk_path_measure_unref                  (GskPathMeasure         *self);
+
+GDK_AVAILABLE_IN_ALL
+GskPath *               gsk_path_measure_get_path               (GskPathMeasure         *self) G_GNUC_PURE;
+GDK_AVAILABLE_IN_ALL
+float                   gsk_path_measure_get_tolerance          (GskPathMeasure         *self) G_GNUC_PURE;
+
+GDK_AVAILABLE_IN_ALL
+float                   gsk_path_measure_get_length             (GskPathMeasure         *self);
+GDK_AVAILABLE_IN_ALL
+gboolean                gsk_path_measure_is_closed              (GskPathMeasure         *self);
+
+GDK_AVAILABLE_IN_ALL
+gboolean                gsk_path_measure_in_fill                (GskPathMeasure         *self,
+                                                                 const graphene_point_t *point,
+                                                                 GskFillRule             fill_rule);
+
+GDK_AVAILABLE_IN_ALL
+GskPathPoint *          gsk_path_measure_get_point              (GskPathMeasure         *self,
+                                                                 float                   distance);
+
+GDK_AVAILABLE_IN_ALL
+GskPathPoint *          gsk_path_measure_get_closest_point      (GskPathMeasure         *self,
+                                                                 const graphene_point_t *point,
+                                                                 float                   threshold);
+
+G_DEFINE_AUTOPTR_CLEANUP_FUNC(GskPathMeasure, gsk_path_measure_unref)
+
+G_END_DECLS

gsk/gskpathpoint.c

@@ -0,0 +1,195 @@
+#include "config.h"
+
+#include "gskpathpointprivate.h"
+
+#include "gskcontourprivate.h"
+#include "gskpathmeasure.h"
+
+#include "gdk/gdkprivate.h"
+
+
+/**
+ * GskPathPoint:
+ *
+ * `GskPathPoint` is an opaque, immutable type representing a point on a path.
+ *
+ * It can be queried for properties of the path at that point, such as its
+ * tangent or its curvature.
+ *
+ * To obtain a `GskPathPoint`, use [method@Gsk.PathMeasure.get_path_point]
+ * or [method@Gsk.PathMeasure.get_closest_point].
+ */
+
+struct _GskPathPoint
+{
+  guint ref_count;
+
+  GskPathMeasure *measure;
+  const GskContour *contour;
+  gpointer measure_data;
+  float contour_offset;  /* distance from beginning of path to contour */
+  float offset;          /* offset of point inside contour */
+};
+
+G_DEFINE_BOXED_TYPE (GskPathPoint, gsk_path_point,
+                     gsk_path_point_ref,
+                     gsk_path_point_unref)
+
+GskPathPoint *
+gsk_path_point_new (GskPathMeasure   *measure,
+                    const GskContour *contour,
+                    gpointer          measure_data,
+                    float             contour_offset,
+                    float             offset)
+{
+  GskPathPoint *self;
+
+  self = g_new0 (GskPathPoint, 1);
+
+  self->ref_count = 1;
+
+  self->measure = gsk_path_measure_ref (measure);
+  self->contour = contour;
+  self->measure_data = measure_data;
+  self->contour_offset = contour_offset;
+  self->offset = offset;
+
+  return self;
+}
+
+/**
+ * gsk_path_point_ref:
+ * @self: a `GskPathPoint`
+ *
+ * Increases the reference count of a `GskPathPoint` by one.
+ *
+ * Returns: the passed in `GskPathPoint`
+ */
+GskPathPoint *
+gsk_path_point_ref (GskPathPoint *self)
+{
+  g_return_val_if_fail (self != NULL, NULL);
+
+  self->ref_count++;
+
+  return self;
+}
+
+/**
+ * gsk_path_point_unref:
+ * @self: a `GskPathPoint`
+ *
+ * Decreases the reference count of a `GskPathPoint` by one.
+ *
+ * If the resulting reference count is zero, frees the path_measure.
+ */
+void
+gsk_path_point_unref (GskPathPoint *self)
+{
+  g_return_if_fail (self != NULL);
+  g_return_if_fail (self->ref_count > 0);
+
+  self->ref_count--;
+  if (self->ref_count > 0)
+    return;
+
+  gsk_path_measure_unref (self->measure);
+
+  g_free (self);
+}
+
+GskPathMeasure *
+gsk_path_point_get_measure (GskPathPoint *self)
+{
+  return self->measure;
+}
+
+/**
+ * gsk_path_point_get_distance:
+ * @self: a `GskPathPoint`
+ *
+ * Returns the distance of the given point from the start of the path.
+ *
+ * This is the length of the contour from the beginning of the path
+ * to the point.
+ *
+ * Returns: The offset of point in path
+ */
+float
+gsk_path_point_get_distance (GskPathPoint *self)
+{
+  return self->contour_offset + self->offset;
+}
+
+/**
+ * gsk_path_point_get_position:
+ * @self: a `GskPathPoint`
+ * @position: (out caller-allocates): Return location for
+ *   the coordinates of the point
+ *
+ * Gets the position of the point.
+ */
+void
+gsk_path_point_get_position (GskPathPoint     *self,
+                             graphene_point_t *position)
+{
+  gsk_contour_get_point (self->contour,
+                         self->measure_data,
+                         self->offset,
+                         GSK_PATH_END,
+                         position, NULL);
+}
+
+/**
+ * gsk_path_point_get_tangent:
+ * @self: a `GskPathPoint`
+ * @direction: the direction for which to return the tangent
+ * @tangent: (out caller-allocates): Return location for
+ *   the tangent at the point
+ *
+ * Gets the tangent of the path at the point.
+ *
+ * Note that certain points on a path may not have a single
+ * tangent, such as sharp turns. At such points, there are
+ * two tangents -- the direction of the path going into the
+ * point, and the direction coming out of it.
+ *
+ * The @direction argument lets you choose which one to get.
+ */
+void
+gsk_path_point_get_tangent (GskPathPoint     *self,
+                            GskPathDirection  direction,
+                            graphene_vec2_t  *tangent)
+{
+  gsk_contour_get_point (self->contour,
+                         self->measure_data,
+                         self->offset,
+                         direction,
+                         NULL, tangent);
+}
+
+/**
+ * gsk_path_point_get_curvature:
+ * @self: a `GskPathPoint`
+ * @center: (out caller-allocates): Return location for
+ *   the center of the osculating circle
+ *
+ * Calculates the curvature at the point @distance units into
+ * the path.
+ *
+ * Optionally, returns the center of the osculating circle as well.
+ *
+ * If the curvature is infinite (at line segments), zero is returned,
+ * and @center is not modified.
+ *
+ * Returns: The curvature of the path at the given point
+ */
+float
+gsk_path_point_get_curvature (GskPathPoint     *self,
+                              graphene_point_t *center)
+{
+  return gsk_contour_get_curvature (self->contour,
+                                    self->measure_data,
+                                    self->offset,
+                                    center);
+}

gsk/gskpathpoint.h

@@ -0,0 +1,43 @@
+#pragma once
+
+#if !defined (__GSK_H_INSIDE__) && !defined (GTK_COMPILATION)
+#error "Only <gsk/gsk.h> can be included directly."
+#endif
+
+
+#include <gsk/gsktypes.h>
+
+G_BEGIN_DECLS
+
+#define GSK_TYPE_PATH_POINT (gsk_path_point_get_type ())
+
+GDK_AVAILABLE_IN_ALL
+GType                   gsk_path_point_get_type        (void) G_GNUC_CONST;
+
+GDK_AVAILABLE_IN_ALL
+GskPathPoint *          gsk_path_point_ref             (GskPathPoint *self);
+GDK_AVAILABLE_IN_ALL
+void                    gsk_path_point_unref           (GskPathPoint *self);
+
+GDK_AVAILABLE_IN_ALL
+GskPathMeasure *        gsk_path_point_get_measure     (GskPathPoint     *self);
+
+GDK_AVAILABLE_IN_ALL
+float                   gsk_path_point_get_distance    (GskPathPoint     *self);
+
+GDK_AVAILABLE_IN_ALL
+void                    gsk_path_point_get_position    (GskPathPoint     *self,
+                                                        graphene_point_t *position);
+
+GDK_AVAILABLE_IN_ALL
+void                    gsk_path_point_get_tangent     (GskPathPoint     *self,
+                                                        GskPathDirection  direction,
+                                                        graphene_vec2_t  *tangent);
+
+GDK_AVAILABLE_IN_ALL
+float                   gsk_path_point_get_curvature   (GskPathPoint     *self,
+                                                        graphene_point_t *center);
+
+G_DEFINE_AUTOPTR_CLEANUP_FUNC(GskPathPoint, gsk_path_point_unref)
+
+G_END_DECLS

gsk/gskpathpointprivate.h

@@ -0,0 +1,16 @@
+#pragma once
+
+#include "gskpathpoint.h"
+#include "gskcontourprivate.h"
+#include "gskpathmeasure.h"
+
+G_BEGIN_DECLS
+
+GskPathPoint * gsk_path_point_new (GskPathMeasure *measure,
+                                   const GskContour *contour,
+                                   gpointer          measure_data,
+                                   float             contour_offset,
+                                   float             offset);
+
+G_END_DECLS
+

gsk/gsktypes.h

@@ -27,6 +27,8 @@
 
 typedef struct _GskPath                 GskPath;
 typedef struct _GskPathBuilder          GskPathBuilder;
+typedef struct _GskPathMeasure          GskPathMeasure;
+typedef struct _GskPathPoint            GskPathPoint;
 typedef struct _GskRenderer             GskRenderer;
 typedef struct _GskTransform            GskTransform;
 

gsk/meson.build

@@ -28,6 +28,8 @@ gsk_public_sources = files([
   'gskglshader.c',
   'gskpath.c',
   'gskpathbuilder.c',
+  'gskpathmeasure.c',
+  'gskpathpoint.c',
   'gskrenderer.c',
   'gskrendernode.c',
   'gskrendernodeimpl.c',
@@ -73,6 +75,8 @@ gsk_public_headers = files([
   'gskglshader.h',
   'gskpath.h',
   'gskpathbuilder.h',
+  'gskpathmeasure.h',
+  'gskpathpoint.h',
   'gskrenderer.h',
   'gskrendernode.h',
   'gskroundedrect.h',