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2587 lines
78 KiB
C
2587 lines
78 KiB
C
/*
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* Copyright © 2020 Benjamin Otte
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library. If not, see <http://www.gnu.org/licenses/>.
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*
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* Authors: Benjamin Otte <otte@gnome.org>
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*/
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#include "config.h"
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#include "gskcurveprivate.h"
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#include "gskboundingboxprivate.h"
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/* GskCurve collects all the functionality we need for Bézier segments */
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#define MIN_PROGRESS (1/1024.f)
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typedef struct _GskCurveClass GskCurveClass;
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struct _GskCurveClass
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{
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void (* init) (GskCurve *curve,
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gskpathop op);
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void (* init_foreach) (GskCurve *curve,
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GskPathOperation op,
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const graphene_point_t *pts,
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gsize n_pts,
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float weight);
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void (* print) (const GskCurve *curve,
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GString *string);
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gskpathop (* pathop) (const GskCurve *curve);
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const graphene_point_t * (* get_start_point) (const GskCurve *curve);
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const graphene_point_t * (* get_end_point) (const GskCurve *curve);
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void (* get_start_tangent) (const GskCurve *curve,
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graphene_vec2_t *tangent);
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void (* get_end_tangent) (const GskCurve *curve,
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graphene_vec2_t *tangent);
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void (* get_point) (const GskCurve *curve,
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float t,
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graphene_point_t *pos);
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void (* get_tangent) (const GskCurve *curve,
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float t,
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graphene_vec2_t *tangent);
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void (* reverse) (const GskCurve *curve,
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GskCurve *reverse);
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float (* get_curvature) (const GskCurve *curve,
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float t);
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void (* split) (const GskCurve *curve,
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float progress,
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GskCurve *result1,
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GskCurve *result2);
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void (* segment) (const GskCurve *curve,
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float start,
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float end,
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GskCurve *segment);
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gboolean (* decompose) (const GskCurve *curve,
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float tolerance,
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GskCurveAddLineFunc add_line_func,
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gpointer user_data);
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gboolean (* decompose_curve) (const GskCurve *curve,
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GskPathForeachFlags flags,
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float tolerance,
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GskCurveAddCurveFunc add_curve_func,
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gpointer user_data);
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void (* get_bounds) (const GskCurve *curve,
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GskBoundingBox *bounds);
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void (* get_tight_bounds) (const GskCurve *curve,
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GskBoundingBox *bounds);
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void (* get_derivative_at) (const GskCurve *curve,
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float t,
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graphene_point_t *value);
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int (* get_crossing) (const GskCurve *curve,
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const graphene_point_t *point);
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float (* get_length_to) (const GskCurve *curve,
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float t);
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float (* get_at_length) (const GskCurve *curve,
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float distance,
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float epsilon);
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};
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/* {{{ Utilities */
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#define RAD_TO_DEG(r) ((r)*180.f/M_PI)
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#define DEG_TO_RAD(d) ((d)*M_PI/180.f)
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static void
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get_tangent (const graphene_point_t *p0,
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const graphene_point_t *p1,
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graphene_vec2_t *t)
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{
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graphene_vec2_init (t, p1->x - p0->x, p1->y - p0->y);
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graphene_vec2_normalize (t, t);
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}
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static int
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line_get_crossing (const graphene_point_t *p,
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const graphene_point_t *p1,
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const graphene_point_t *p2)
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{
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if (p1->y <= p->y)
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{
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if (p2->y > p->y)
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{
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if ((p2->x - p1->x) * (p->y - p1->y) - (p->x - p1->x) * (p2->y - p1->y) > 0)
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return 1;
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}
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}
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else if (p2->y <= p->y)
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{
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if ((p2->x - p1->x) * (p->y - p1->y) - (p->x - p1->x) * (p2->y - p1->y) < 0)
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return -1;
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}
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return 0;
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}
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static int
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get_crossing_by_bisection (const GskCurve *curve,
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const graphene_point_t *point)
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{
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GskBoundingBox bounds;
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GskCurve c1, c2;
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gsk_curve_get_bounds (curve, &bounds);
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if (bounds.max.y < point->y || bounds.min.y > point->y || bounds.max.x < point->x)
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return 0;
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if (bounds.min.x > point->x)
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return line_get_crossing (point, gsk_curve_get_start_point (curve), gsk_curve_get_end_point (curve));
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if (graphene_point_distance (&bounds.min, &bounds.max, NULL, NULL) < 0.001)
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return line_get_crossing (point, gsk_curve_get_start_point (curve), gsk_curve_get_end_point (curve));
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gsk_curve_split (curve, 0.5, &c1, &c2);
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return gsk_curve_get_crossing (&c1, point) + gsk_curve_get_crossing (&c2, point);
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}
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/* Replace a line by an equivalent quad,
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* and a quad by an equivalent cubic.
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*/
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static void
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gsk_curve_elevate (const GskCurve *curve,
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GskCurve *elevated)
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{
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if (curve->op == GSK_PATH_LINE)
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{
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graphene_point_t p[3];
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p[0] = curve->line.points[0];
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graphene_point_interpolate (&curve->line.points[0],
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&curve->line.points[1],
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0.5,
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&p[1]);
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p[2] = curve->line.points[1];
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gsk_curve_init (elevated, gsk_pathop_encode (GSK_PATH_QUAD, p));
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}
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else if (curve->op == GSK_PATH_QUAD)
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{
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graphene_point_t p[4];
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p[0] = curve->quad.points[0];
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graphene_point_interpolate (&curve->quad.points[0],
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&curve->quad.points[1],
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2/3.,
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&p[1]);
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graphene_point_interpolate (&curve->quad.points[2],
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&curve->quad.points[1],
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2/3.,
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&p[2]);
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p[3] = curve->quad.points[2];
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gsk_curve_init (elevated, gsk_pathop_encode (GSK_PATH_CUBIC, p));
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}
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else
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g_assert_not_reached ();
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}
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/* Compute arclength by using Gauss quadrature on
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*
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* \int_0^z \sqrt{ (dx/dt)^2 + (dy/dt)^2 } dt
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*/
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#include "gskcurve-ct-values.c"
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static float
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get_length_by_approximation (const GskCurve *curve,
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float t)
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{
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double z = t / 2;
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double sum = 0;
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graphene_point_t d;
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for (unsigned int i = 0; i < G_N_ELEMENTS (T); i++)
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{
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gsk_curve_get_derivative_at (curve, z * T[i] + z, &d);
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sum += C[i] * sqrt (d.x * d.x + d.y * d.y);
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}
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return z * sum;
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}
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/* Compute the inverse of the arclength using bisection,
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* to a given precision
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*/
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static float
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get_t_by_bisection (const GskCurve *curve,
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float length,
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float epsilon)
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{
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float t1, t2, t, l;
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GskCurve c1;
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g_assert (epsilon >= FLT_EPSILON);
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t1 = 0;
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t2 = 1;
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while (t1 < t2)
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{
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t = (t1 + t2) / 2;
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if (t == t1 || t == t2)
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break;
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gsk_curve_split (curve, t, &c1, NULL);
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l = gsk_curve_get_length (&c1);
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if (fabsf (length - l) < epsilon)
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break;
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else if (l < length)
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t1 = t;
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else
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t2 = t;
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}
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return t;
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}
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/* }}} */
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/* {{{ Line */
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static void
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gsk_line_curve_init_from_points (GskLineCurve *self,
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GskPathOperation op,
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const graphene_point_t *start,
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const graphene_point_t *end)
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{
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self->op = op;
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self->points[0] = *start;
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self->points[1] = *end;
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}
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static void
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gsk_line_curve_init (GskCurve *curve,
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gskpathop op)
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{
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GskLineCurve *self = &curve->line;
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const graphene_point_t *pts = gsk_pathop_points (op);
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gsk_line_curve_init_from_points (self, gsk_pathop_op (op), &pts[0], &pts[1]);
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}
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static void
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gsk_line_curve_init_foreach (GskCurve *curve,
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GskPathOperation op,
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const graphene_point_t *pts,
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gsize n_pts,
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float weight)
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{
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GskLineCurve *self = &curve->line;
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g_assert (n_pts == 2);
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gsk_line_curve_init_from_points (self, op, &pts[0], &pts[1]);
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}
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static void
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gsk_line_curve_print (const GskCurve *curve,
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GString *string)
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{
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g_string_append_printf (string,
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"M %g %g L %g %g",
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curve->line.points[0].x, curve->line.points[0].y,
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curve->line.points[1].x, curve->line.points[1].y);
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}
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static gskpathop
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gsk_line_curve_pathop (const GskCurve *curve)
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{
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const GskLineCurve *self = &curve->line;
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return gsk_pathop_encode (self->op, self->points);
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}
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static const graphene_point_t *
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gsk_line_curve_get_start_point (const GskCurve *curve)
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{
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const GskLineCurve *self = &curve->line;
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return &self->points[0];
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}
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static const graphene_point_t *
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gsk_line_curve_get_end_point (const GskCurve *curve)
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{
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const GskLineCurve *self = &curve->line;
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return &self->points[1];
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}
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static void
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gsk_line_curve_get_start_end_tangent (const GskCurve *curve,
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graphene_vec2_t *tangent)
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{
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const GskLineCurve *self = &curve->line;
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get_tangent (&self->points[0], &self->points[1], tangent);
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}
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static void
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gsk_line_curve_get_point (const GskCurve *curve,
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float t,
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graphene_point_t *pos)
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{
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const GskLineCurve *self = &curve->line;
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graphene_point_interpolate (&self->points[0], &self->points[1], t, pos);
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}
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static void
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gsk_line_curve_get_tangent (const GskCurve *curve,
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float t,
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graphene_vec2_t *tangent)
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{
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const GskLineCurve *self = &curve->line;
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get_tangent (&self->points[0], &self->points[1], tangent);
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}
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static float
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gsk_line_curve_get_curvature (const GskCurve *curve,
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float t)
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{
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return 0;
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}
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static void
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gsk_line_curve_reverse (const GskCurve *curve,
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GskCurve *reverse)
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{
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const GskLineCurve *self = &curve->line;
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reverse->op = GSK_PATH_LINE;
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reverse->line.points[0] = self->points[1];
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reverse->line.points[1] = self->points[0];
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}
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static void
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gsk_line_curve_split (const GskCurve *curve,
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float progress,
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GskCurve *start,
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GskCurve *end)
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{
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const GskLineCurve *self = &curve->line;
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graphene_point_t point;
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graphene_point_interpolate (&self->points[0], &self->points[1], progress, &point);
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if (start)
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gsk_line_curve_init_from_points (&start->line, GSK_PATH_LINE, &self->points[0], &point);
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if (end)
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gsk_line_curve_init_from_points (&end->line, GSK_PATH_LINE, &point, &self->points[1]);
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}
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static void
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gsk_line_curve_segment (const GskCurve *curve,
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float start,
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float end,
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GskCurve *segment)
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{
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const GskLineCurve *self = &curve->line;
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const graphene_point_t *pts = self->points;
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graphene_point_t p0, p1;
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graphene_point_interpolate (&pts[0], &pts[1], start, &p0);
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graphene_point_interpolate (&pts[0], &pts[1], end, &p1);
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gsk_line_curve_init_from_points (&segment->line, GSK_PATH_LINE, &p0, &p1);
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}
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static gboolean
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gsk_line_curve_decompose (const GskCurve *curve,
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float tolerance,
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GskCurveAddLineFunc add_line_func,
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gpointer user_data)
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{
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const GskLineCurve *self = &curve->line;
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const graphene_point_t *pts = self->points;
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return add_line_func (&pts[0], &pts[1], 0.f, 1.f, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
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}
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static gboolean
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gsk_line_curve_decompose_curve (const GskCurve *curve,
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GskPathForeachFlags flags,
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float tolerance,
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GskCurveAddCurveFunc add_curve_func,
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gpointer user_data)
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{
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const GskLineCurve *self = &curve->line;
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return add_curve_func (GSK_PATH_LINE, self->points, 2, 0.f, user_data);
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}
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static void
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gsk_line_curve_get_bounds (const GskCurve *curve,
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GskBoundingBox *bounds)
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{
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const GskLineCurve *self = &curve->line;
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const graphene_point_t *pts = self->points;
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gsk_bounding_box_init (bounds, &pts[0], &pts[1]);
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}
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static void
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gsk_line_curve_get_derivative_at (const GskCurve *curve,
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float t,
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graphene_point_t *value)
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{
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const GskLineCurve *self = &curve->line;
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const graphene_point_t *pts = self->points;
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value->x = pts[1].x - pts[0].x;
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value->y = pts[1].y - pts[0].y;
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}
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static int
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gsk_line_curve_get_crossing (const GskCurve *curve,
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const graphene_point_t *point)
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{
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const GskLineCurve *self = &curve->line;
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const graphene_point_t *pts = self->points;
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return line_get_crossing (point, &pts[0], &pts[1]);
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}
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static float
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gsk_line_curve_get_length_to (const GskCurve *curve,
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float t)
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{
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const GskLineCurve *self = &curve->line;
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const graphene_point_t *pts = self->points;
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return t * graphene_point_distance (&pts[0], &pts[1], NULL, NULL);
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}
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static float
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gsk_line_curve_get_at_length (const GskCurve *curve,
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float distance,
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float epsilon)
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{
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const GskLineCurve *self = &curve->line;
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const graphene_point_t *pts = self->points;
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float length;
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length = graphene_point_distance (&pts[0], &pts[1], NULL, NULL);
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if (length == 0)
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return 0;
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return CLAMP (distance / length, 0, 1);
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}
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static const GskCurveClass GSK_LINE_CURVE_CLASS = {
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gsk_line_curve_init,
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gsk_line_curve_init_foreach,
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gsk_line_curve_print,
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gsk_line_curve_pathop,
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gsk_line_curve_get_start_point,
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gsk_line_curve_get_end_point,
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gsk_line_curve_get_start_end_tangent,
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gsk_line_curve_get_start_end_tangent,
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gsk_line_curve_get_point,
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gsk_line_curve_get_tangent,
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gsk_line_curve_reverse,
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gsk_line_curve_get_curvature,
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gsk_line_curve_split,
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gsk_line_curve_segment,
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gsk_line_curve_decompose,
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gsk_line_curve_decompose_curve,
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gsk_line_curve_get_bounds,
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gsk_line_curve_get_bounds,
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gsk_line_curve_get_derivative_at,
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gsk_line_curve_get_crossing,
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gsk_line_curve_get_length_to,
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|
gsk_line_curve_get_at_length,
|
|
};
|
|
|
|
/* }}} */
|
|
/* {{{ Quadratic */
|
|
|
|
static void
|
|
gsk_quad_curve_ensure_coefficients (const GskQuadCurve *curve)
|
|
{
|
|
GskQuadCurve *self = (GskQuadCurve *) curve;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
if (self->has_coefficients)
|
|
return;
|
|
|
|
self->coeffs[2] = pts[0];
|
|
self->coeffs[1] = GRAPHENE_POINT_INIT (2 * (pts[1].x - pts[0].x),
|
|
2 * (pts[1].y - pts[0].y));
|
|
self->coeffs[0] = GRAPHENE_POINT_INIT (pts[2].x - 2 * pts[1].x + pts[0].x,
|
|
pts[2].y - 2 * pts[1].y + pts[0].y);
|
|
|
|
self->has_coefficients = TRUE;
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_init_from_points (GskQuadCurve *self,
|
|
const graphene_point_t pts[3])
|
|
{
|
|
self->op = GSK_PATH_QUAD;
|
|
self->has_coefficients = FALSE;
|
|
memcpy (self->points, pts, sizeof (graphene_point_t) * 3);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_init (GskCurve *curve,
|
|
gskpathop op)
|
|
{
|
|
GskQuadCurve *self = &curve->quad;
|
|
|
|
gsk_quad_curve_init_from_points (self, gsk_pathop_points (op));
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts,
|
|
float weight)
|
|
{
|
|
GskQuadCurve *self = &curve->quad;
|
|
|
|
g_assert (n_pts == 3);
|
|
|
|
gsk_quad_curve_init_from_points (self, pts);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
g_string_append_printf (string,
|
|
"M %g %g Q %g %g %g %g",
|
|
curve->quad.points[0].x, curve->quad.points[0].y,
|
|
curve->quad.points[1].x, curve->cubic.points[1].y,
|
|
curve->quad.points[2].x, curve->cubic.points[2].y);
|
|
}
|
|
|
|
static gskpathop
|
|
gsk_quad_curve_pathop (const GskCurve *curve)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
return gsk_pathop_encode (self->op, self->points);
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_quad_curve_get_start_point (const GskCurve *curve)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
return &self->points[0];
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_quad_curve_get_end_point (const GskCurve *curve)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
return &self->points[2];
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_start_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
get_tangent (&self->points[0], &self->points[1], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
get_tangent (&self->points[1], &self->points[2], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_point (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *pos)
|
|
{
|
|
GskQuadCurve *self = (GskQuadCurve *) &curve->quad;
|
|
const graphene_point_t *c = self->coeffs;
|
|
|
|
gsk_quad_curve_ensure_coefficients (self);
|
|
|
|
*pos = GRAPHENE_POINT_INIT ((c[0].x * t + c[1].x) * t + c[2].x,
|
|
(c[0].y * t + c[1].y) * t + c[2].y);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_tangent (const GskCurve *curve,
|
|
float t,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
GskQuadCurve *self = (GskQuadCurve *) &curve->quad;
|
|
const graphene_point_t *c = self->coeffs;
|
|
|
|
gsk_quad_curve_ensure_coefficients (self);
|
|
|
|
graphene_vec2_init (tangent,
|
|
2.0f * c[0].x * t + c[1].x,
|
|
2.0f * c[0].y * t + c[1].y);
|
|
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)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
reverse->op = GSK_PATH_QUAD;
|
|
reverse->cubic.points[0] = self->points[2];
|
|
reverse->cubic.points[1] = self->points[1];
|
|
reverse->cubic.points[2] = self->points[0];
|
|
reverse->cubic.has_coefficients = FALSE;
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_split (const GskCurve *curve,
|
|
float progress,
|
|
GskCurve *start,
|
|
GskCurve *end)
|
|
{
|
|
GskQuadCurve *self = (GskQuadCurve *) &curve->quad;
|
|
const graphene_point_t *pts = self->points;
|
|
graphene_point_t ab, bc;
|
|
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 (&ab, &bc, progress, &final);
|
|
|
|
if (start)
|
|
gsk_quad_curve_init_from_points (&start->quad, (graphene_point_t[3]) { pts[0], ab, final });
|
|
if (end)
|
|
gsk_quad_curve_init_from_points (&end->quad, (graphene_point_t[3]) { final, bc, pts[2] });
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
GskCurve tmp;
|
|
|
|
gsk_quad_curve_split (curve, start, NULL, &tmp);
|
|
gsk_quad_curve_split (&tmp, (end - start) / (1.0f - start), segment, NULL);
|
|
}
|
|
|
|
/* taken from Skia, including the very descriptive name */
|
|
static gboolean
|
|
gsk_quad_curve_too_curvy (const GskQuadCurve *self,
|
|
float tolerance)
|
|
{
|
|
const graphene_point_t *pts = self->points;
|
|
float dx, dy;
|
|
|
|
dx = fabs (pts[1].x / 2 - (pts[0].x + pts[2].x) / 4);
|
|
dy = fabs (pts[1].y / 2 - (pts[0].y + pts[2].y) / 4);
|
|
|
|
return MAX (dx, dy) > tolerance;
|
|
}
|
|
|
|
static gboolean
|
|
gsk_quad_curve_decompose_step (const GskCurve *curve,
|
|
float start_progress,
|
|
float end_progress,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
GskCurve left, right;
|
|
float mid_progress;
|
|
|
|
if (!gsk_quad_curve_too_curvy (self, tolerance))
|
|
return add_line_func (&self->points[0], &self->points[2], start_progress, end_progress, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
|
|
if (end_progress - start_progress <= MIN_PROGRESS)
|
|
return add_line_func (&self->points[0], &self->points[2], start_progress, end_progress, GSK_CURVE_LINE_REASON_SHORT, user_data);
|
|
|
|
gsk_quad_curve_split ((const GskCurve *) self, 0.5, &left, &right);
|
|
mid_progress = (start_progress + end_progress) / 2;
|
|
|
|
return gsk_quad_curve_decompose_step (&left, start_progress, mid_progress, tolerance, add_line_func, user_data)
|
|
&& gsk_quad_curve_decompose_step (&right, mid_progress, end_progress, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_quad_curve_decompose (const GskCurve *curve,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
return gsk_quad_curve_decompose_step (curve, 0.0, 1.0, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
typedef struct
|
|
{
|
|
GskCurveAddCurveFunc add_curve;
|
|
gpointer user_data;
|
|
} AddLineData;
|
|
|
|
static gboolean
|
|
gsk_curve_add_line_cb (const graphene_point_t *from,
|
|
const graphene_point_t *to,
|
|
float from_progress,
|
|
float to_progress,
|
|
GskCurveLineReason reason,
|
|
gpointer user_data)
|
|
{
|
|
AddLineData *data = user_data;
|
|
graphene_point_t p[2] = { *from, *to };
|
|
|
|
return data->add_curve (GSK_PATH_LINE, p, 2, 0.f, data->user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_quad_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_QUAD)
|
|
return add_curve_func (GSK_PATH_QUAD, self->points, 3, 0.f, user_data);
|
|
else if (graphene_point_equal (&curve->conic.points[0], &curve->conic.points[1]) ||
|
|
graphene_point_equal (&curve->conic.points[1], &curve->conic.points[2]))
|
|
{
|
|
if (!graphene_point_equal (&curve->conic.points[0], &curve->conic.points[2]))
|
|
return add_curve_func (GSK_PATH_LINE,
|
|
(graphene_point_t[2]) {
|
|
curve->conic.points[0],
|
|
curve->conic.points[2],
|
|
},
|
|
2, 0.f, user_data);
|
|
else
|
|
return TRUE;
|
|
}
|
|
else if (flags & GSK_PATH_FOREACH_ALLOW_CUBIC)
|
|
{
|
|
GskCurve c;
|
|
|
|
gsk_curve_elevate (curve, &c);
|
|
return add_curve_func (GSK_PATH_CUBIC, c.cubic.points, 4, 0.f, user_data);
|
|
}
|
|
else
|
|
{
|
|
return gsk_quad_curve_decompose (curve,
|
|
tolerance,
|
|
gsk_curve_add_line_cb,
|
|
&(AddLineData) { add_curve_func, user_data });
|
|
}
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[2]);
|
|
gsk_bounding_box_expand (bounds, &pts[1]);
|
|
}
|
|
|
|
/* Solve P' = 0 where P is
|
|
* P = (1-t)^2*pa + 2*t*(1-t)*pb + t^2*pc
|
|
*/
|
|
static int
|
|
get_quadratic_extrema (float pa, float pb, float pc, float t[1])
|
|
{
|
|
float d = pa - 2 * pb + pc;
|
|
|
|
if (fabs (d) > 0.0001)
|
|
{
|
|
t[0] = (pa - pb) / d;
|
|
return 1;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_tight_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
const graphene_point_t *pts = self->points;
|
|
float t[4];
|
|
int n;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[2]);
|
|
|
|
n = 0;
|
|
n += get_quadratic_extrema (pts[0].x, pts[1].x, pts[2].x, &t[n]);
|
|
n += get_quadratic_extrema (pts[0].y, pts[1].y, pts[2].y, &t[n]);
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
graphene_point_t p;
|
|
|
|
gsk_quad_curve_get_point (curve, t[i], &p);
|
|
gsk_bounding_box_expand (bounds, &p);
|
|
}
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_derivative (const GskCurve *curve,
|
|
GskCurve *deriv)
|
|
{
|
|
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]);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_derivative_at (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *value)
|
|
{
|
|
GskCurve d;
|
|
gsk_quad_curve_get_derivative (curve, &d);
|
|
gsk_curve_get_point (&d, t, value);
|
|
}
|
|
|
|
static int
|
|
gsk_quad_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return get_crossing_by_bisection (curve, point);
|
|
}
|
|
|
|
static float
|
|
gsk_quad_curve_get_length_to (const GskCurve *curve,
|
|
float t)
|
|
{
|
|
return get_length_by_approximation (curve, t);
|
|
}
|
|
|
|
static float
|
|
gsk_quad_curve_get_at_length (const GskCurve *curve,
|
|
float t,
|
|
float epsilon)
|
|
{
|
|
return get_t_by_bisection (curve, t, epsilon);
|
|
}
|
|
|
|
static const GskCurveClass GSK_QUAD_CURVE_CLASS = {
|
|
gsk_quad_curve_init,
|
|
gsk_quad_curve_init_foreach,
|
|
gsk_quad_curve_print,
|
|
gsk_quad_curve_pathop,
|
|
gsk_quad_curve_get_start_point,
|
|
gsk_quad_curve_get_end_point,
|
|
gsk_quad_curve_get_start_tangent,
|
|
gsk_quad_curve_get_end_tangent,
|
|
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,
|
|
gsk_quad_curve_decompose_curve,
|
|
gsk_quad_curve_get_bounds,
|
|
gsk_quad_curve_get_tight_bounds,
|
|
gsk_quad_curve_get_derivative_at,
|
|
gsk_quad_curve_get_crossing,
|
|
gsk_quad_curve_get_length_to,
|
|
gsk_quad_curve_get_at_length,
|
|
};
|
|
|
|
/* }}} */
|
|
/* {{{ Cubic */
|
|
|
|
static void
|
|
gsk_cubic_curve_ensure_coefficients (const GskCubicCurve *curve)
|
|
{
|
|
GskCubicCurve *self = (GskCubicCurve *) 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_cubic_curve_init_from_points (GskCubicCurve *self,
|
|
const graphene_point_t pts[4])
|
|
{
|
|
self->op = GSK_PATH_CUBIC;
|
|
self->has_coefficients = FALSE;
|
|
memcpy (self->points, pts, sizeof (graphene_point_t) * 4);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_init (GskCurve *curve,
|
|
gskpathop op)
|
|
{
|
|
GskCubicCurve *self = &curve->cubic;
|
|
|
|
gsk_cubic_curve_init_from_points (self, gsk_pathop_points (op));
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts,
|
|
float weight)
|
|
{
|
|
GskCubicCurve *self = &curve->cubic;
|
|
|
|
g_assert (n_pts == 4);
|
|
|
|
gsk_cubic_curve_init_from_points (self, pts);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
g_string_append_printf (string,
|
|
"M %f %f C %f %f %f %f %f %f",
|
|
curve->cubic.points[0].x, curve->cubic.points[0].y,
|
|
curve->cubic.points[1].x, curve->cubic.points[1].y,
|
|
curve->cubic.points[2].x, curve->cubic.points[2].y,
|
|
curve->cubic.points[3].x, curve->cubic.points[3].y);
|
|
}
|
|
|
|
static gskpathop
|
|
gsk_cubic_curve_pathop (const GskCurve *curve)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
return gsk_pathop_encode (self->op, self->points);
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_cubic_curve_get_start_point (const GskCurve *curve)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
return &self->points[0];
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_cubic_curve_get_end_point (const GskCurve *curve)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
return &self->points[3];
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_start_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
if (graphene_point_near (&self->points[0], &self->points[1], 0.0001))
|
|
{
|
|
if (graphene_point_near (&self->points[0], &self->points[2], 0.0001))
|
|
get_tangent (&self->points[0], &self->points[3], tangent);
|
|
else
|
|
get_tangent (&self->points[0], &self->points[2], tangent);
|
|
}
|
|
else
|
|
get_tangent (&self->points[0], &self->points[1], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
if (graphene_point_near (&self->points[2], &self->points[3], 0.0001))
|
|
{
|
|
if (graphene_point_near (&self->points[1], &self->points[3], 0.0001))
|
|
get_tangent (&self->points[0], &self->points[3], tangent);
|
|
else
|
|
get_tangent (&self->points[1], &self->points[3], tangent);
|
|
}
|
|
else
|
|
get_tangent (&self->points[2], &self->points[3], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_point (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *pos)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *c = self->coeffs;
|
|
|
|
gsk_cubic_curve_ensure_coefficients (self);
|
|
|
|
*pos = GRAPHENE_POINT_INIT (((c[0].x * t + c[1].x) * t +c[2].x) * t + c[3].x,
|
|
((c[0].y * t + c[1].y) * t +c[2].y) * t + c[3].y);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_tangent (const GskCurve *curve,
|
|
float t,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *c = self->coeffs;
|
|
|
|
gsk_cubic_curve_ensure_coefficients (self);
|
|
|
|
graphene_vec2_init (tangent,
|
|
(3.0f * c[0].x * t + 2.0f * c[1].x) * t + c[2].x,
|
|
(3.0f * c[0].y * t + 2.0f * c[1].y) * t + c[2].y);
|
|
graphene_vec2_normalize (tangent, tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_reverse (const GskCurve *curve,
|
|
GskCurve *reverse)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
reverse->op = GSK_PATH_CUBIC;
|
|
reverse->cubic.points[0] = self->points[3];
|
|
reverse->cubic.points[1] = self->points[2];
|
|
reverse->cubic.points[2] = self->points[1];
|
|
reverse->cubic.points[3] = self->points[0];
|
|
reverse->cubic.has_coefficients = FALSE;
|
|
}
|
|
|
|
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 void
|
|
gsk_cubic_curve_get_derivative (const GskCurve *curve,
|
|
GskCurve *deriv)
|
|
{
|
|
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);
|
|
}
|
|
|
|
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_cubic_curve_get_derivative (curve, &c1);
|
|
gsk_quad_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,
|
|
GskCurve *start,
|
|
GskCurve *end)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
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_cubic_curve_init_from_points (&start->cubic, (graphene_point_t[4]) { pts[0], ab, abbc, final });
|
|
if (end)
|
|
gsk_cubic_curve_init_from_points (&end->cubic, (graphene_point_t[4]) { final, bccd, cd, pts[3] });
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
GskCurve tmp;
|
|
|
|
gsk_cubic_curve_split (curve, start, NULL, &tmp);
|
|
gsk_cubic_curve_split (&tmp, (end - start) / (1.0f - start), segment, NULL);
|
|
}
|
|
|
|
/* taken from Skia, including the very descriptive name */
|
|
static gboolean
|
|
gsk_cubic_curve_too_curvy (const GskCubicCurve *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 (MAX (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 (MAX (ABS (p.x - pts[2].x), ABS (p.y - pts[2].y)) > tolerance)
|
|
return TRUE;
|
|
|
|
return FALSE;
|
|
}
|
|
|
|
static gboolean
|
|
gsk_cubic_curve_decompose_step (const GskCurve *curve,
|
|
float start_progress,
|
|
float end_progress,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
GskCurve left, right;
|
|
float mid_progress;
|
|
|
|
if (!gsk_cubic_curve_too_curvy (self, tolerance))
|
|
return add_line_func (&self->points[0], &self->points[3], start_progress, end_progress, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
|
|
if (end_progress - start_progress <= MIN_PROGRESS)
|
|
return add_line_func (&self->points[0], &self->points[3], start_progress, end_progress, GSK_CURVE_LINE_REASON_SHORT, user_data);
|
|
|
|
gsk_cubic_curve_split ((const GskCurve *) self, 0.5, &left, &right);
|
|
mid_progress = (start_progress + end_progress) / 2;
|
|
|
|
return gsk_cubic_curve_decompose_step (&left, start_progress, mid_progress, tolerance, add_line_func, user_data)
|
|
&& gsk_cubic_curve_decompose_step (&right, mid_progress, end_progress, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_cubic_curve_decompose (const GskCurve *curve,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
return gsk_cubic_curve_decompose_step (curve, 0.0, 1.0, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_cubic_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_CUBIC)
|
|
return add_curve_func (GSK_PATH_CUBIC, self->points, 4, 0.f, user_data);
|
|
|
|
/* FIXME: Quadratic or arc approximation */
|
|
return gsk_cubic_curve_decompose (curve,
|
|
tolerance,
|
|
gsk_curve_add_line_cb,
|
|
&(AddLineData) { add_curve_func, user_data });
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[3]);
|
|
gsk_bounding_box_expand (bounds, &pts[1]);
|
|
gsk_bounding_box_expand (bounds, &pts[2]);
|
|
}
|
|
|
|
static inline gboolean
|
|
acceptable (float t)
|
|
{
|
|
return 0 <= t && t <= 1;
|
|
}
|
|
|
|
/* Solve P' = 0 where P is
|
|
* P = (1-t)^3*pa + 3*t*(1-t)^2*pb + 3*t^2*(1-t)*pc + t^3*pd
|
|
*/
|
|
static int
|
|
get_cubic_extrema (float pa, float pb, float pc, float pd, float t[2])
|
|
{
|
|
float a, b, c;
|
|
float d, tt;
|
|
int n = 0;
|
|
|
|
a = 3 * (pd - 3*pc + 3*pb - pa);
|
|
b = 6 * (pc - 2*pb + pa);
|
|
c = 3 * (pb - pa);
|
|
|
|
if (fabs (a) > 0.0001)
|
|
{
|
|
if (b*b > 4*a*c)
|
|
{
|
|
d = sqrt (b*b - 4*a*c);
|
|
tt = (-b + d)/(2*a);
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
tt = (-b - d)/(2*a);
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
}
|
|
else
|
|
{
|
|
tt = -b / (2*a);
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
}
|
|
}
|
|
else if (fabs (b) > 0.0001)
|
|
{
|
|
tt = -c / b;
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
}
|
|
|
|
return n;
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_tight_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *pts = self->points;
|
|
float t[4];
|
|
int n;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[3]);
|
|
|
|
n = 0;
|
|
n += get_cubic_extrema (pts[0].x, pts[1].x, pts[2].x, pts[3].x, &t[n]);
|
|
n += get_cubic_extrema (pts[0].y, pts[1].y, pts[2].y, pts[3].y, &t[n]);
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
graphene_point_t p;
|
|
|
|
gsk_cubic_curve_get_point (curve, t[i], &p);
|
|
gsk_bounding_box_expand (bounds, &p);
|
|
}
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_derivative_at (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *value)
|
|
{
|
|
GskCurve d;
|
|
gsk_cubic_curve_get_derivative (curve, &d);
|
|
gsk_curve_get_point (&d, t, value);
|
|
}
|
|
|
|
static int
|
|
gsk_cubic_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return get_crossing_by_bisection (curve, point);
|
|
}
|
|
|
|
static float
|
|
gsk_cubic_curve_get_length_to (const GskCurve *curve,
|
|
float t)
|
|
{
|
|
return get_length_by_approximation (curve, t);
|
|
}
|
|
|
|
static float
|
|
gsk_cubic_curve_get_at_length (const GskCurve *curve,
|
|
float t,
|
|
float epsilon)
|
|
{
|
|
return get_t_by_bisection (curve, t, epsilon);
|
|
}
|
|
|
|
static const GskCurveClass GSK_CUBIC_CURVE_CLASS = {
|
|
gsk_cubic_curve_init,
|
|
gsk_cubic_curve_init_foreach,
|
|
gsk_cubic_curve_print,
|
|
gsk_cubic_curve_pathop,
|
|
gsk_cubic_curve_get_start_point,
|
|
gsk_cubic_curve_get_end_point,
|
|
gsk_cubic_curve_get_start_tangent,
|
|
gsk_cubic_curve_get_end_tangent,
|
|
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,
|
|
gsk_cubic_curve_decompose_curve,
|
|
gsk_cubic_curve_get_bounds,
|
|
gsk_cubic_curve_get_tight_bounds,
|
|
gsk_cubic_curve_get_derivative_at,
|
|
gsk_cubic_curve_get_crossing,
|
|
gsk_cubic_curve_get_length_to,
|
|
gsk_cubic_curve_get_at_length,
|
|
};
|
|
|
|
/* }}} */
|
|
/* {{{ Conic */
|
|
|
|
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 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 void
|
|
gsk_conic_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts,
|
|
float weight)
|
|
{
|
|
GskConicCurve *self = &curve->conic;
|
|
|
|
g_assert (n_pts == 3);
|
|
|
|
gsk_conic_curve_init_from_points (self,
|
|
(graphene_point_t[4]) {
|
|
pts[0],
|
|
pts[1],
|
|
GRAPHENE_POINT_INIT (weight, 0),
|
|
pts[2]
|
|
});
|
|
}
|
|
|
|
static void
|
|
gsk_conic_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
g_string_append_printf (string,
|
|
"M %g %g O %g %g %g %g %g",
|
|
curve->conic.points[0].x, curve->conic.points[0].y,
|
|
curve->conic.points[1].x, curve->conic.points[1].y,
|
|
curve->conic.points[3].x, curve->conic.points[3].y,
|
|
curve->conic.points[2].x);
|
|
}
|
|
|
|
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 void
|
|
gsk_conic_curve_get_start_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
|
|
get_tangent (&self->points[0], &self->points[1], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_conic_curve_get_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
|
|
get_tangent (&self->points[1], &self->points[3], tangent);
|
|
}
|
|
|
|
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_get_point (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *pos)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
|
|
gsk_conic_curve_ensure_coefficents (self);
|
|
|
|
gsk_conic_curve_eval_point (self, t, pos);
|
|
}
|
|
|
|
/* See M. Floater, Derivatives of rational Bezier curves */
|
|
static void
|
|
gsk_conic_curve_get_derivative_at (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *value)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
float w = gsk_conic_curve_get_weight (self);
|
|
const graphene_point_t *pts = self->points;
|
|
graphene_point_t p[3], p1[2];
|
|
float w1[2], w2;
|
|
|
|
/* The tangent will be 0 in these corner cases, just
|
|
* treat it like a line here.
|
|
*/
|
|
if ((t <= 0.f && graphene_point_equal (&pts[0], &pts[1])) ||
|
|
(t >= 1.f && graphene_point_equal (&pts[1], &pts[3])))
|
|
{
|
|
graphene_point_init (value, pts[3].x - pts[0].x, pts[3].y - pts[0].y);
|
|
return;
|
|
}
|
|
|
|
p[0] = pts[0];
|
|
p[1] = pts[1];
|
|
p[2] = pts[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];
|
|
|
|
value->x = 2 * (w1[0] * w1[1])/(w2*w2) * (p1[1].x - p1[0].x);
|
|
value->y = 2 * (w1[0] * w1[1])/(w2*w2) * (p1[1].y - p1[0].y);
|
|
}
|
|
|
|
static void
|
|
gsk_conic_curve_get_tangent (const GskCurve *curve,
|
|
float t,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
graphene_point_t tmp;
|
|
gsk_conic_curve_get_derivative_at (curve, t, &tmp);
|
|
graphene_vec2_init (tangent, tmp.x, tmp.y);
|
|
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)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
|
|
reverse->op = GSK_PATH_CONIC;
|
|
reverse->conic.points[0] = self->points[3];
|
|
reverse->conic.points[1] = self->points[1];
|
|
reverse->conic.points[2] = self->points[2];
|
|
reverse->conic.points[3] = self->points[0];
|
|
reverse->conic.has_coefficients = FALSE;
|
|
}
|
|
|
|
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));
|
|
}
|
|
|
|
static void
|
|
gsk_conic_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
graphene_point_t start_num, start_denom;
|
|
graphene_point_t mid_num, mid_denom;
|
|
graphene_point_t end_num, end_denom;
|
|
graphene_point_t ctrl_num, ctrl_denom;
|
|
float mid;
|
|
|
|
if (start <= 0.0f)
|
|
return gsk_conic_curve_split (curve, end, segment, NULL);
|
|
else if (end >= 1.0f)
|
|
return gsk_conic_curve_split (curve, start, NULL, segment);
|
|
|
|
gsk_conic_curve_ensure_coefficents (self);
|
|
|
|
gsk_curve_eval_quad (self->num, start, &start_num);
|
|
gsk_curve_eval_quad (self->denom, start, &start_denom);
|
|
mid = (start + end) / 2;
|
|
gsk_curve_eval_quad (self->num, mid, &mid_num);
|
|
gsk_curve_eval_quad (self->denom, mid, &mid_denom);
|
|
gsk_curve_eval_quad (self->num, end, &end_num);
|
|
gsk_curve_eval_quad (self->denom, end, &end_denom);
|
|
ctrl_num = GRAPHENE_POINT_INIT (2 * mid_num.x - (start_num.x + end_num.x) / 2,
|
|
2 * mid_num.y - (start_num.y + end_num.y) / 2);
|
|
ctrl_denom = GRAPHENE_POINT_INIT (2 * mid_denom.x - (start_denom.x + end_denom.x) / 2,
|
|
2 * mid_denom.y - (start_denom.y + end_denom.y) / 2);
|
|
|
|
gsk_conic_curve_init_from_points (&segment->conic,
|
|
(graphene_point_t[4]) {
|
|
GRAPHENE_POINT_INIT (start_num.x / start_denom.x,
|
|
start_num.y / start_denom.y),
|
|
GRAPHENE_POINT_INIT (ctrl_num.x / ctrl_denom.x,
|
|
ctrl_num.y / ctrl_denom.y),
|
|
GRAPHENE_POINT_INIT (ctrl_denom.x / sqrtf (start_denom.x * end_denom.x),
|
|
0),
|
|
GRAPHENE_POINT_INIT (end_num.x / end_denom.x,
|
|
end_num.y / end_denom.y)
|
|
});
|
|
|
|
}
|
|
|
|
/* 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 (!gsk_conic_curve_too_curvy (start, &mid, end, tolerance))
|
|
return add_line_func (start, end, start_progress, end_progress, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
|
|
if (end_progress - start_progress <= MIN_PROGRESS)
|
|
return add_line_func (start, end, start_progress, end_progress, GSK_CURVE_LINE_REASON_SHORT, 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;
|
|
graphene_point_t mid;
|
|
|
|
gsk_conic_curve_ensure_coefficents (self);
|
|
|
|
gsk_conic_curve_eval_point (self, 0.5, &mid);
|
|
|
|
return gsk_conic_curve_decompose_subdivide (self,
|
|
tolerance,
|
|
&self->points[0],
|
|
0.0f,
|
|
&mid,
|
|
0.5f,
|
|
add_line_func,
|
|
user_data)
|
|
&& gsk_conic_curve_decompose_subdivide (self,
|
|
tolerance,
|
|
&mid,
|
|
0.5f,
|
|
&self->points[3],
|
|
1.0f,
|
|
add_line_func,
|
|
user_data);
|
|
}
|
|
|
|
/* See Floater, M: An analysis of cubic approximation schemes
|
|
* for conic sections
|
|
*/
|
|
static void
|
|
cubic_approximation (const GskCurve *curve,
|
|
GskCurve *cubic)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
graphene_point_t p[4];
|
|
float w = self->points[2].x;
|
|
float w2 = w*w;
|
|
float lambda;
|
|
|
|
lambda = 2 * (6*w2 + 1 - sqrt (3*w2 + 1)) / (12*w2 + 3);
|
|
|
|
p[0] = self->points[0];
|
|
p[3] = self->points[3];
|
|
graphene_point_interpolate (&self->points[0], &self->points[1], lambda, &p[1]);
|
|
graphene_point_interpolate (&self->points[3], &self->points[1], lambda, &p[2]);
|
|
|
|
gsk_curve_init (cubic, gsk_pathop_encode (GSK_PATH_CUBIC, p));
|
|
}
|
|
|
|
static gboolean
|
|
gsk_conic_is_close_to_cubic (const GskCurve *conic,
|
|
const GskCurve *cubic,
|
|
float tolerance)
|
|
{
|
|
float t[] = { 0.1, 0.5, 0.9 };
|
|
graphene_point_t p0, p1;
|
|
|
|
for (int i = 0; i < G_N_ELEMENTS (t); i++)
|
|
{
|
|
gsk_curve_get_point (conic, t[i], &p0);
|
|
gsk_curve_get_point (cubic, t[i], &p1);
|
|
if (graphene_point_distance (&p0, &p1, NULL, NULL) > tolerance)
|
|
return FALSE;
|
|
}
|
|
|
|
return TRUE;
|
|
}
|
|
|
|
static gboolean gsk_conic_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data);
|
|
|
|
static gboolean
|
|
gsk_conic_curve_decompose_or_add (const GskCurve *curve,
|
|
const GskCurve *cubic,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
if (graphene_point_equal (&curve->conic.points[0], &curve->conic.points[1]) ||
|
|
graphene_point_equal (&curve->conic.points[1], &curve->conic.points[3]))
|
|
{
|
|
if (!graphene_point_equal (&curve->conic.points[0], &curve->conic.points[3]))
|
|
return add_curve_func (GSK_PATH_LINE,
|
|
(graphene_point_t[2]) {
|
|
curve->conic.points[0],
|
|
curve->conic.points[3],
|
|
},
|
|
2, 0.f, user_data);
|
|
else
|
|
return TRUE;
|
|
}
|
|
else if (gsk_conic_is_close_to_cubic (curve, cubic, tolerance))
|
|
return add_curve_func (GSK_PATH_CUBIC, cubic->cubic.points, 4, 0.f, user_data);
|
|
else
|
|
{
|
|
GskCurve c1, c2;
|
|
GskCurve cc1, cc2;
|
|
|
|
gsk_conic_curve_split (curve, 0.5, &c1, &c2);
|
|
|
|
cubic_approximation (&c1, &cc1);
|
|
cubic_approximation (&c2, &cc2);
|
|
|
|
return gsk_conic_curve_decompose_or_add (&c1, &cc1, tolerance, add_curve_func, user_data) &&
|
|
gsk_conic_curve_decompose_or_add (&c2, &cc2, tolerance, add_curve_func, user_data);
|
|
}
|
|
}
|
|
|
|
static gboolean
|
|
gsk_conic_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
GskCurve c;
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_CONIC)
|
|
return add_curve_func (GSK_PATH_CONIC,
|
|
(const graphene_point_t[3]) { self->points[0],
|
|
self->points[1],
|
|
self->points[3] },
|
|
3,
|
|
self->points[2].x,
|
|
user_data);
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_CUBIC)
|
|
{
|
|
cubic_approximation (curve, &c);
|
|
return gsk_conic_curve_decompose_or_add (curve, &c, tolerance, add_curve_func, user_data);
|
|
}
|
|
|
|
/* FIXME: Quadratic approximation */
|
|
return gsk_conic_curve_decompose (curve,
|
|
tolerance,
|
|
gsk_curve_add_line_cb,
|
|
&(AddLineData) { add_curve_func, user_data });
|
|
}
|
|
|
|
static void
|
|
gsk_conic_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[3]);
|
|
gsk_bounding_box_expand (bounds, &pts[1]);
|
|
}
|
|
|
|
/* Solve N = 0 where N is the numerator of (P/Q)', with
|
|
* P = (1-t)^2*a + 2*t*(1-t)*w*b + t^2*c
|
|
* Q = (1-t)^2 + 2*t*(1-t)*w + t^2
|
|
*/
|
|
static int
|
|
get_conic_extrema (float a, float b, float c, float w, float t[4])
|
|
{
|
|
float q, tt;
|
|
int n = 0;
|
|
float w2 = w*w;
|
|
float wac = (w - 1)*(a - c);
|
|
|
|
if (wac != 0)
|
|
{
|
|
q = - sqrt (a*a - 4*a*b*w2 + 4*a*c*w2 - 2*a*c + 4*b*b*w2 - 4*b*c*w2 + c*c);
|
|
|
|
tt = (- q + 2*a*w - a - 2*b*w + c)/(2*wac);
|
|
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
|
|
tt = (q + 2*a*w - a - 2*b*w + c)/(2*wac);
|
|
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
}
|
|
|
|
if (w * (b - c) != 0 && a == c)
|
|
t[n++] = 0.5;
|
|
|
|
if (w == 1 && a - 2*b + c != 0)
|
|
{
|
|
tt = (a - b) / (a - 2*b + c);
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
}
|
|
|
|
return n;
|
|
}
|
|
|
|
static void
|
|
gsk_conic_curve_get_tight_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskConicCurve *self = &curve->conic;
|
|
float w = gsk_conic_curve_get_weight (self);
|
|
const graphene_point_t *pts = self->points;
|
|
float t[8];
|
|
int n;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[3]);
|
|
|
|
n = 0;
|
|
n += get_conic_extrema (pts[0].x, pts[1].x, pts[3].x, w, &t[n]);
|
|
n += get_conic_extrema (pts[0].y, pts[1].y, pts[3].y, w, &t[n]);
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
graphene_point_t p;
|
|
|
|
gsk_conic_curve_get_point (curve, t[i], &p);
|
|
gsk_bounding_box_expand (bounds, &p);
|
|
}
|
|
}
|
|
|
|
static int
|
|
gsk_conic_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return get_crossing_by_bisection (curve, point);
|
|
}
|
|
|
|
static float
|
|
gsk_conic_curve_get_length_to (const GskCurve *curve,
|
|
float t)
|
|
{
|
|
return get_length_by_approximation (curve, t);
|
|
}
|
|
|
|
static float
|
|
gsk_conic_curve_get_at_length (const GskCurve *curve,
|
|
float t,
|
|
float epsilon)
|
|
{
|
|
return get_t_by_bisection (curve, t, epsilon);
|
|
}
|
|
|
|
static const GskCurveClass GSK_CONIC_CURVE_CLASS = {
|
|
gsk_conic_curve_init,
|
|
gsk_conic_curve_init_foreach,
|
|
gsk_conic_curve_print,
|
|
gsk_conic_curve_pathop,
|
|
gsk_conic_curve_get_start_point,
|
|
gsk_conic_curve_get_end_point,
|
|
gsk_conic_curve_get_start_tangent,
|
|
gsk_conic_curve_get_end_tangent,
|
|
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,
|
|
gsk_conic_curve_decompose_curve,
|
|
gsk_conic_curve_get_bounds,
|
|
gsk_conic_curve_get_tight_bounds,
|
|
gsk_conic_curve_get_derivative_at,
|
|
gsk_conic_curve_get_crossing,
|
|
gsk_conic_curve_get_length_to,
|
|
gsk_conic_curve_get_at_length,
|
|
};
|
|
|
|
/* }}} */
|
|
/* {{{ 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_QUAD] = &GSK_QUAD_CURVE_CLASS,
|
|
[GSK_PATH_CUBIC] = &GSK_CUBIC_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)
|
|
{
|
|
memset (curve, 0, sizeof (GskCurve));
|
|
get_class (gsk_pathop_op (op))->init (curve, op);
|
|
}
|
|
|
|
void
|
|
gsk_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts,
|
|
float weight)
|
|
{
|
|
memset (curve, 0, sizeof (GskCurve));
|
|
get_class (op)->init_foreach (curve, op, pts, n_pts, weight);
|
|
}
|
|
|
|
void
|
|
gsk_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
get_class (curve->op)->print (curve, string);
|
|
}
|
|
|
|
char *
|
|
gsk_curve_to_string (const GskCurve *curve)
|
|
{
|
|
GString *s = g_string_new ("");
|
|
gsk_curve_print (curve, s);
|
|
return g_string_free (s, FALSE);
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_start_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
get_class (curve->op)->get_start_tangent (curve, tangent);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
get_class (curve->op)->get_end_tangent (curve, tangent);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_point (const GskCurve *curve,
|
|
float progress,
|
|
graphene_point_t *pos)
|
|
{
|
|
get_class (curve->op)->get_point (curve, progress, pos);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_tangent (const GskCurve *curve,
|
|
float progress,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
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)
|
|
{
|
|
get_class (curve->op)->reverse (curve, reverse);
|
|
}
|
|
|
|
void
|
|
gsk_curve_split (const GskCurve *curve,
|
|
float progress,
|
|
GskCurve *start,
|
|
GskCurve *end)
|
|
{
|
|
get_class (curve->op)->split (curve, progress, start, end);
|
|
}
|
|
|
|
void
|
|
gsk_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
if (start <= 0 && end >= 1)
|
|
{
|
|
*segment = *curve;
|
|
return;
|
|
}
|
|
|
|
get_class (curve->op)->segment (curve, start, end, segment);
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
gboolean
|
|
gsk_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
return get_class (curve->op)->decompose_curve (curve, flags, tolerance, add_curve_func, user_data);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
get_class (curve->op)->get_bounds (curve, bounds);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_tight_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
get_class (curve->op)->get_tight_bounds (curve, bounds);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_derivative_at (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *value)
|
|
{
|
|
get_class (curve->op)->get_derivative_at (curve, t, value);
|
|
}
|
|
|
|
int
|
|
gsk_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return get_class (curve->op)->get_crossing (curve, point);
|
|
}
|
|
|
|
static gboolean
|
|
project_point_onto_line (const GskCurve *curve,
|
|
const graphene_point_t *point,
|
|
float threshold,
|
|
float *out_distance,
|
|
float *out_t)
|
|
{
|
|
const graphene_point_t *a = gsk_curve_get_start_point (curve);
|
|
const graphene_point_t *b = gsk_curve_get_end_point (curve);
|
|
graphene_vec2_t n, ap;
|
|
graphene_point_t p;
|
|
|
|
if (graphene_point_equal (a, b))
|
|
{
|
|
*out_t = 0;
|
|
*out_distance = graphene_point_distance (point, a, NULL, NULL);
|
|
}
|
|
else
|
|
{
|
|
graphene_vec2_init (&n, b->x - a->x, b->y - a->y);
|
|
graphene_vec2_init (&ap, point->x - a->x, point->y - a->y);
|
|
|
|
*out_t = graphene_vec2_dot (&n, &ap) / graphene_vec2_dot (&n, &n);
|
|
*out_t = CLAMP (*out_t, 0, 1);
|
|
|
|
graphene_point_interpolate (a, b, *out_t, &p);
|
|
*out_distance = graphene_point_distance (point, &p, NULL, NULL);
|
|
}
|
|
|
|
return *out_distance <= threshold;
|
|
}
|
|
|
|
static float
|
|
get_segment_bounding_sphere (const GskCurve *curve,
|
|
float t1,
|
|
float t2,
|
|
graphene_point_t *center)
|
|
{
|
|
GskCurve c;
|
|
GskBoundingBox bounds;
|
|
|
|
gsk_curve_segment (curve, t1, t2, &c);
|
|
gsk_curve_get_tight_bounds (&c, &bounds);
|
|
graphene_point_interpolate (&bounds.min, &bounds.max, 0.5, center);
|
|
return graphene_point_distance (center, &bounds.min, NULL, NULL);
|
|
}
|
|
|
|
static gboolean
|
|
find_closest_point (const GskCurve *curve,
|
|
const graphene_point_t *point,
|
|
float threshold,
|
|
float t1,
|
|
float t2,
|
|
float *out_distance,
|
|
float *out_t)
|
|
{
|
|
graphene_point_t center;
|
|
float radius;
|
|
float t, d, nt;
|
|
|
|
radius = get_segment_bounding_sphere (curve, t1, t2, ¢er);
|
|
if (graphene_point_distance (¢er, point, NULL, NULL) > threshold + radius)
|
|
return FALSE;
|
|
|
|
d = INFINITY;
|
|
t = (t1 + t2) / 2;
|
|
|
|
if (fabs (t1 - t2) < 0.001)
|
|
{
|
|
graphene_point_t p;
|
|
gsk_curve_get_point (curve, t, &p);
|
|
d = graphene_point_distance (point, &p, NULL, NULL);
|
|
nt = t;
|
|
}
|
|
else
|
|
{
|
|
float dd, tt;
|
|
|
|
dd = INFINITY;
|
|
nt = 0;
|
|
|
|
if (find_closest_point (curve, point, threshold, t1, t, &dd, &tt))
|
|
{
|
|
d = dd;
|
|
nt = tt;
|
|
}
|
|
|
|
if (find_closest_point (curve, point, MIN (dd, threshold), t, t2, &dd, &tt))
|
|
{
|
|
d = dd;
|
|
nt = tt;
|
|
}
|
|
}
|
|
|
|
if (d < threshold)
|
|
{
|
|
*out_distance = d;
|
|
*out_t = nt;
|
|
return TRUE;
|
|
}
|
|
else
|
|
{
|
|
*out_distance = INFINITY;
|
|
*out_t = 0;
|
|
return FALSE;
|
|
}
|
|
}
|
|
|
|
gboolean
|
|
gsk_curve_get_closest_point (const GskCurve *curve,
|
|
const graphene_point_t *point,
|
|
float threshold,
|
|
float *out_dist,
|
|
float *out_t)
|
|
{
|
|
if (curve->op == GSK_PATH_LINE || curve->op == GSK_PATH_CLOSE)
|
|
return project_point_onto_line (curve, point, threshold, out_dist, out_t);
|
|
else
|
|
return find_closest_point (curve, point, threshold, 0, 1, out_dist, out_t);
|
|
}
|
|
|
|
float
|
|
gsk_curve_get_length_to (const GskCurve *curve,
|
|
float t)
|
|
{
|
|
return get_class (curve->op)->get_length_to (curve, t);
|
|
}
|
|
|
|
float
|
|
gsk_curve_get_length (const GskCurve *curve)
|
|
{
|
|
return gsk_curve_get_length_to (curve, 1);
|
|
}
|
|
|
|
/* Compute the inverse of the arclength using bisection,
|
|
* to a given precision
|
|
*/
|
|
float
|
|
gsk_curve_at_length (const GskCurve *curve,
|
|
float length,
|
|
float epsilon)
|
|
{
|
|
return get_class (curve->op)->get_at_length (curve, length, epsilon);
|
|
}
|
|
|
|
static inline void
|
|
_sincosf (float angle,
|
|
float *out_s,
|
|
float *out_c)
|
|
{
|
|
#ifdef HAVE_SINCOSF
|
|
sincosf (angle, out_s, out_c);
|
|
#else
|
|
*out_s = sinf (angle);
|
|
*out_c = cosf (angle);
|
|
#endif
|
|
}
|
|
|
|
static void
|
|
align_points (const graphene_point_t *p,
|
|
const graphene_point_t *a,
|
|
const graphene_point_t *b,
|
|
graphene_point_t *q,
|
|
int n)
|
|
{
|
|
graphene_vec2_t n1;
|
|
float angle;
|
|
float s, c;
|
|
|
|
get_tangent (a, b, &n1);
|
|
angle = - atan2f (graphene_vec2_get_y (&n1), graphene_vec2_get_x (&n1));
|
|
_sincosf (angle, &s, &c);
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
q[i].x = (p[i].x - a->x) * c - (p[i].y - a->y) * s;
|
|
q[i].y = (p[i].x - a->x) * s + (p[i].y - a->y) * c;
|
|
}
|
|
}
|
|
|
|
static int
|
|
filter_allowable (float t[3],
|
|
int n)
|
|
{
|
|
float g[3];
|
|
int j = 0;
|
|
|
|
for (int i = 0; i < n; i++)
|
|
if (0 < t[i] && t[i] < 1)
|
|
g[j++] = t[i];
|
|
for (int i = 0; i < j; i++)
|
|
t[i] = g[i];
|
|
return j;
|
|
}
|
|
|
|
/* find solutions for at^2 + bt + c = 0 */
|
|
static int
|
|
solve_quadratic (float a, float b, float c, float t[2])
|
|
{
|
|
float d;
|
|
int n = 0;
|
|
|
|
if (fabsf (a) > 0.0001)
|
|
{
|
|
if (b*b > 4*a*c)
|
|
{
|
|
d = sqrtf (b*b - 4*a*c);
|
|
t[n++] = (-b + d)/(2*a);
|
|
t[n++] = (-b - d)/(2*a);
|
|
}
|
|
else
|
|
{
|
|
t[n++] = -b / (2*a);
|
|
}
|
|
}
|
|
else if (fabsf (b) > 0.0001)
|
|
{
|
|
t[n++] = -c / b;
|
|
}
|
|
|
|
return n;
|
|
}
|
|
|
|
int
|
|
gsk_curve_get_curvature_points (const GskCurve *curve,
|
|
float t[3])
|
|
{
|
|
const graphene_point_t *pts = curve->cubic.points;
|
|
graphene_point_t p[4];
|
|
float a, b, c, d;
|
|
float x, y, z;
|
|
int n;
|
|
|
|
if (curve->op != GSK_PATH_CUBIC)
|
|
return 0; /* FIXME */
|
|
|
|
align_points (pts, &pts[0], &pts[3], p, 4);
|
|
|
|
a = p[2].x * p[1].y;
|
|
b = p[3].x * p[1].y;
|
|
c = p[1].x * p[2].y;
|
|
d = p[3].x * p[2].y;
|
|
|
|
x = - 3*a + 2*b + 3*c - d;
|
|
y = 3*a - b - 3*c;
|
|
z = c - a;
|
|
|
|
n = solve_quadratic (x, y, z, t);
|
|
return filter_allowable (t, n);
|
|
}
|
|
|
|
/* }}} */
|
|
|
|
/* vim:set foldmethod=marker expandtab: */
|