[gtk/matthiasc/lottie2: 1/6] path: Implement arcs

[Matthias Clasen <matthiasc src gnome org>]

commit 4113869970cae1d598285cc9589d7c2677f1f0e9
Author: Matthias Clasen <mclasen redhat com>
Date:   Tue Nov 24 19:59:46 2020 -0500

    path: Implement arcs
    
    This is an elliptical arc implementation according
    to the SVG spec. The code is mostly taken from
    librsvg, but pretty directly follows the SVG spec
    implementation notes. This will be used in subsequent
    commits.
    
    We don't export this, since the parametrization
    is inconvenient. We do want an arc_to API, but
    these are not the arcs we are looking for.

 gsk/gskpath.c | 162 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 gsk/gskpath.h |   1 +
 2 files changed, 163 insertions(+)
---
diff --git a/gsk/gskpath.c b/gsk/gskpath.c
index 6f3a988c62..b4006233fa 100644
--- a/gsk/gskpath.c
+++ b/gsk/gskpath.c
@@ -2168,3 +2168,165 @@ gsk_path_builder_close (GskPathBuilder *builder)
   gsk_path_builder_end_current (builder);
 }
 
+static void
+arc_segment (GskPathBuilder *builder,
+             double          cx,
+             double          cy,
+             double          rx,
+             double          ry,
+             double          sin_phi,
+             double          cos_phi,
+             double          sin_th0,
+             double          cos_th0,
+             double          sin_th1,
+             double          cos_th1,
+             double          t)
+{
+  double x1, y1, x2, y2, x3, y3;
+
+  x1 = rx * (cos_th0 - t * sin_th0);
+  y1 = ry * (sin_th0 + t * cos_th0);
+  x3 = rx * cos_th1;
+  y3 = ry * sin_th1;
+  x2 = x3 + rx * (t * sin_th1);
+  y2 = y3 + ry * (-t * cos_th1);
+
+  gsk_path_builder_curve_to (builder,
+                             cx + cos_phi * x1 - sin_phi * y1,
+                             cy + sin_phi * x1 + cos_phi * y1,
+                             cx + cos_phi * x2 - sin_phi * y2,
+                             cy + sin_phi * x2 + cos_phi * y2,
+                             cx + cos_phi * x3 - sin_phi * y3,
+                             cy + sin_phi * x3 + cos_phi * y3);
+}
+
+static void
+arc_to (GskPathBuilder *builder,
+        float           rx,
+        float           ry,
+        float           x_axis_rotation,
+        gboolean        large_arc,
+        gboolean        positive_sweep,
+        float           x,
+        float           y)
+{
+  graphene_point_t *current;
+  double x1, y1, x2, y2;
+  double phi, sin_phi, cos_phi;
+  double mid_x, mid_y;
+  double lambda;
+  double d;
+  double k;
+  double x1_, y1_;
+  double cx_, cy_;
+  double  cx, cy;
+  double ux, uy, u_len;
+  double cos_theta1, theta1;
+  double vx, vy, v_len;
+  double dp_uv;
+  double cos_delta_theta, delta_theta;
+  int i, n_segs;
+  double d_theta, theta;
+  double sin_th0, cos_th0;
+  double sin_th1, cos_th1;
+  double th_half;
+  double t;
+
+  if (builder->points->len > 0)
+    {
+      current = &g_array_index (builder->points, graphene_point_t, builder->points->len - 1);
+      x1 = current->x;
+      y1 = current->y;
+    }
+  else
+    {
+      x1 = 0;
+      y1 = 0;
+    }
+  x2 = x;
+  y2 = y;
+
+  phi = x_axis_rotation * M_PI / 180.0;
+  sincos (phi, &sin_phi, &cos_phi);
+
+  rx = fabs (rx);
+  ry = fabs (ry);
+
+  mid_x = (x1 - x2) / 2;
+  mid_y = (y1 - y2) / 2;
+
+  x1_ = cos_phi * mid_x + sin_phi * mid_y;
+  y1_ = - sin_phi * mid_x + cos_phi * mid_y;
+
+  lambda = (x1_ / rx) * (x1_ / rx) + (y1_ / ry) * (y1_ / ry);
+  if (lambda > 1)
+    {
+      lambda = sqrt (lambda);
+      rx *= lambda;
+      ry *= lambda;
+    }
+
+  d = (rx * y1_) * (rx * y1_) + (ry * x1_) * (ry * x1_);
+  if (d == 0)
+    return;
+
+  k = sqrt (fabs ((rx * ry) * (rx * ry) / d - 1.0));
+  if (positive_sweep == large_arc)
+    k = -k;
+
+  cx_ = k * rx * y1_ / ry;
+  cy_ = -k * ry * x1_ / rx;
+
+  cx = cos_phi * cx_ - sin_phi * cy_ + (x1 + x2) / 2;
+  cy = sin_phi * cx_ + cos_phi * cy_ + (y1 + y2) / 2;
+
+  ux = (x1_ - cx_) / rx;
+  uy = (y1_ - cy_) / ry;
+  u_len = sqrt (ux * ux + uy * uy);
+  if (u_len == 0)
+    return;
+
+  cos_theta1 = CLAMP (ux / u_len, -1, 1);
+  theta1 = acos (cos_theta1);
+  if (uy < 0)
+    theta1 = - theta1;
+
+  vx = (- x1_ - cx_) / rx;
+  vy = (- y1_ - cy_) / ry;
+  v_len = sqrt (vx * vx + vy * vy);
+  if (v_len == 0)
+    return;
+
+  dp_uv = ux * vx + uy * vy;
+  cos_delta_theta = CLAMP (dp_uv / (u_len * v_len), -1, 1);
+  delta_theta = acos (cos_delta_theta);
+  if (ux * vy - uy * vx < 0)
+    delta_theta = - delta_theta;
+  if (positive_sweep && delta_theta < 0)
+    delta_theta += 2 * M_PI;
+  else if (!positive_sweep && delta_theta > 0)
+    delta_theta -= 2 * M_PI;
+
+  n_segs = ceil (fabs (delta_theta / (M_PI_2 + 0.001)));
+  d_theta = delta_theta / n_segs;
+  theta = theta1;
+  sincos (theta1, &sin_th1, &cos_th1);
+
+  th_half = d_theta / 2;
+  t = (8.0 / 3.0) * sin (th_half / 2) * sin (th_half / 2) / sin (th_half);
+
+  for (i = 0; i < n_segs; i++)
+    {
+      theta = theta1;
+      theta1 = theta + d_theta;
+      sin_th0 = sin_th1;
+      cos_th0 = cos_th1;
+      sincos (theta1, &sin_th1, &cos_th1);
+      arc_segment (builder,
+                   cx, cy, rx, ry,
+                   sin_phi, cos_phi,
+                   sin_th0, cos_th0,
+                   sin_th1, cos_th1,
+                   t);
+    }
+}
diff --git a/gsk/gskpath.h b/gsk/gskpath.h
index f2010d5397..f590c4c452 100644
--- a/gsk/gskpath.h
+++ b/gsk/gskpath.h
@@ -131,6 +131,7 @@ void                    gsk_path_builder_curve_to               (GskPathBuilder
                                                                  float                 y2,
                                                                  float                 x3,
                                                                  float                 y3);
+
 GDK_AVAILABLE_IN_ALL
 void                    gsk_path_builder_close                  (GskPathBuilder       *builder);