path: Implement SVG arcs
This is elliptical arc implementation according to the SVG spec. The code is mostly taken from librsvg, but pretty directly follows the SVG spec implementation notes. 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. It will be used in parsing SVG path syntax.
This commit is contained in:
Matthias Clasen
@@ -568,3 +568,166 @@ gsk_path_builder_close (GskPathBuilder *builder)
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gsk_path_builder_end_current (builder);
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}
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static void
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arc_segment (GskPathBuilder *builder,
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double cx,
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double cy,
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double rx,
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double ry,
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double sin_phi,
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double cos_phi,
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double sin_th0,
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double cos_th0,
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double sin_th1,
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double cos_th1,
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double t)
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{
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double x1, y1, x2, y2, x3, y3;
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x1 = rx * (cos_th0 - t * sin_th0);
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y1 = ry * (sin_th0 + t * cos_th0);
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x3 = rx * cos_th1;
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y3 = ry * sin_th1;
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x2 = x3 + rx * (t * sin_th1);
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y2 = y3 + ry * (-t * cos_th1);
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gsk_path_builder_curve_to (builder,
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cx + cos_phi * x1 - sin_phi * y1,
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cy + sin_phi * x1 + cos_phi * y1,
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cx + cos_phi * x2 - sin_phi * y2,
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cy + sin_phi * x2 + cos_phi * y2,
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cx + cos_phi * x3 - sin_phi * y3,
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cy + sin_phi * x3 + cos_phi * y3);
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}
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void
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gsk_path_builder_svg_arc_to (GskPathBuilder *builder,
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float rx,
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float ry,
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float x_axis_rotation,
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gboolean large_arc,
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gboolean positive_sweep,
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float x,
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float y)
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{
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graphene_point_t *current;
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double x1, y1, x2, y2;
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double phi, sin_phi, cos_phi;
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double mid_x, mid_y;
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double lambda;
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double d;
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double k;
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double x1_, y1_;
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double cx_, cy_;
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double cx, cy;
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double ux, uy, u_len;
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double cos_theta1, theta1;
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double vx, vy, v_len;
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double dp_uv;
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double cos_delta_theta, delta_theta;
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int i, n_segs;
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double d_theta, theta;
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double sin_th0, cos_th0;
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double sin_th1, cos_th1;
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double th_half;
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double t;
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if (builder->points->len > 0)
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{
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current = &g_array_index (builder->points, graphene_point_t, builder->points->len - 1);
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x1 = current->x;
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y1 = current->y;
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}
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else
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{
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x1 = 0;
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y1 = 0;
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}
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x2 = x;
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y2 = y;
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phi = x_axis_rotation * M_PI / 180.0;
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sincos (phi, &sin_phi, &cos_phi);
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rx = fabs (rx);
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ry = fabs (ry);
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mid_x = (x1 - x2) / 2;
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mid_y = (y1 - y2) / 2;
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x1_ = cos_phi * mid_x + sin_phi * mid_y;
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y1_ = - sin_phi * mid_x + cos_phi * mid_y;
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lambda = (x1_ / rx) * (x1_ / rx) + (y1_ / ry) * (y1_ / ry);
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if (lambda > 1)
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{
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lambda = sqrt (lambda);
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rx *= lambda;
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ry *= lambda;
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}
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d = (rx * y1_) * (rx * y1_) + (ry * x1_) * (ry * x1_);
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if (d == 0)
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return;
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k = sqrt (fabs ((rx * ry) * (rx * ry) / d - 1.0));
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if (positive_sweep == large_arc)
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k = -k;
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cx_ = k * rx * y1_ / ry;
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cy_ = -k * ry * x1_ / rx;
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cx = cos_phi * cx_ - sin_phi * cy_ + (x1 + x2) / 2;
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cy = sin_phi * cx_ + cos_phi * cy_ + (y1 + y2) / 2;
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ux = (x1_ - cx_) / rx;
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uy = (y1_ - cy_) / ry;
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u_len = sqrt (ux * ux + uy * uy);
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if (u_len == 0)
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return;
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cos_theta1 = CLAMP (ux / u_len, -1, 1);
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theta1 = acos (cos_theta1);
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if (uy < 0)
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theta1 = - theta1;
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vx = (- x1_ - cx_) / rx;
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vy = (- y1_ - cy_) / ry;
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v_len = sqrt (vx * vx + vy * vy);
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if (v_len == 0)
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return;
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dp_uv = ux * vx + uy * vy;
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cos_delta_theta = CLAMP (dp_uv / (u_len * v_len), -1, 1);
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delta_theta = acos (cos_delta_theta);
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if (ux * vy - uy * vx < 0)
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delta_theta = - delta_theta;
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if (positive_sweep && delta_theta < 0)
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delta_theta += 2 * M_PI;
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else if (!positive_sweep && delta_theta > 0)
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delta_theta -= 2 * M_PI;
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n_segs = ceil (fabs (delta_theta / (M_PI_2 + 0.001)));
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d_theta = delta_theta / n_segs;
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theta = theta1;
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sincos (theta1, &sin_th1, &cos_th1);
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th_half = d_theta / 2;
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t = (8.0 / 3.0) * sin (th_half / 2) * sin (th_half / 2) / sin (th_half);
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for (i = 0; i < n_segs; i++)
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{
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theta = theta1;
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theta1 = theta + d_theta;
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sin_th0 = sin_th1;
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cos_th0 = cos_th1;
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sincos (theta1, &sin_th1, &cos_th1);
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arc_segment (builder,
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cx, cy, rx, ry,
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sin_phi, cos_phi,
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sin_th0, cos_th0,
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sin_th1, cos_th1,
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t);
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}
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}
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@@ -101,6 +101,15 @@ void gsk_contour_add_segment (const GskContou
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void gsk_path_builder_add_contour (GskPathBuilder *builder,
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GskContour *contour);
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void gsk_path_builder_svg_arc_to (GskPathBuilder *builder,
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float rx,
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float ry,
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float x_axis_rotation,
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gboolean large_arc,
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gboolean positive_sweep,
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float x,
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float y);
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G_END_DECLS
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#endif /* __GSK_PATH_PRIVATE_H__ */
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