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gtk/gsk/gskcurve.c
Simon McVittie 214f5a6f98 gskpathop: Introduce a type to represent an aligned graphene_point_t 
When we allocate a graphene_point_t on the stack, there's no guarantee
that it will be aligned at an 8-byte boundary, which is an assumption
made by gsk_pathop_encode() (which wants to use the lowest 3 bits to
encode the operation). In the places where it matters, force the
points on the stack and embedded in structs to be nicely aligned.

By using a distinct type for this (a union with a suitable size and
alignment), we ensure that the compiler will warn or error whenever we
can't prove that a particular point is, in fact, suitably aligned.
We can go from a `GskAlignedPoint *` to a `graphene_point_t *`
(which is always valid, because the `GskAlignedPoint` is aligned)
via &aligned_points[0].pt, but we cannot go back the other way
(which is not always valid, because the `graphene_point_t` is not
necessarily aligned nicely) without a cast.

In practice, it seems that a graphene_point_t on x86_64 *is* usually
placed at an 8-byte boundary, but this is not the case on 32-bit
architectures or on s390x.

In many cases we can avoid needing an explicit reference to the more
complicated type by making use of a transparent union. There's already
at least one transparent union in GSK's public API, so it's presumably
portable enough to match GTK's requirements.

Increasing the alignment of GskAlignedPoint also requires adjusting how
a GskStandardContour is allocated and initialized. This data structure
allocates extra memory to hold an array of GskAlignedPoint outside the
bounds of the struct itself, and that array now needs to be aligned
suitably. Previously the array started with at next byte after the
flexible array of gskpathop, but the alignment of a gskpathop is only
4 bytes on 32-bit architectures, so depending on the number of gskpathop
in the trailing flexible array, that pointer might be an unsuitable
location to allocate a GskAlignedPoint.

Resolves: https://gitlab.gnome.org/GNOME/gtk/-/issues/6395
Signed-off-by: Simon McVittie <smcv@debian.org>
2024-07-28 17:31:41 +01:00

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/*
* Copyright © 2020 Benjamin Otte
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library. If not, see <http://www.gnu.org/licenses/>.
*
* Authors: Benjamin Otte <otte@gnome.org>
*/
#include "config.h"
#include "gskcurveprivate.h"
#include "gskboundingboxprivate.h"
/* GskCurve collects all the functionality we need for Bézier segments */
#define MIN_PROGRESS (1/1024.f)
typedef struct _GskCurveClass GskCurveClass;
struct _GskCurveClass
{
void (* init) (GskCurve *curve,
gskpathop op);
void (* init_foreach) (GskCurve *curve,
GskPathOperation op,
const graphene_point_t *pts,
gsize n_pts,
float weight);
void (* print) (const GskCurve *curve,
GString *string);
gskpathop (* pathop) (const GskCurve *curve);
const graphene_point_t * (* get_start_point) (const GskCurve *curve);
const graphene_point_t * (* get_end_point) (const GskCurve *curve);
void (* get_start_tangent) (const GskCurve *curve,
graphene_vec2_t *tangent);
void (* get_end_tangent) (const GskCurve *curve,
graphene_vec2_t *tangent);
void (* get_point) (const GskCurve *curve,
float t,
graphene_point_t *pos);
void (* get_tangent) (const GskCurve *curve,
float t,
graphene_vec2_t *tangent);
void (* reverse) (const GskCurve *curve,
GskCurve *reverse);
float (* get_curvature) (const GskCurve *curve,
float t);
void (* split) (const GskCurve *curve,
float progress,
GskCurve *result1,
GskCurve *result2);
void (* segment) (const GskCurve *curve,
float start,
float end,
GskCurve *segment);
gboolean (* decompose) (const GskCurve *curve,
float tolerance,
GskCurveAddLineFunc add_line_func,
gpointer user_data);
gboolean (* decompose_curve) (const GskCurve *curve,
GskPathForeachFlags flags,
float tolerance,
GskCurveAddCurveFunc add_curve_func,
gpointer user_data);
void (* get_bounds) (const GskCurve *curve,
GskBoundingBox *bounds);
void (* get_tight_bounds) (const GskCurve *curve,
GskBoundingBox *bounds);
void (* get_derivative_at) (const GskCurve *curve,
float t,
graphene_point_t *value);
int (* get_crossing) (const GskCurve *curve,
const graphene_point_t *point);
float (* get_length_to) (const GskCurve *curve,
float t);
float (* get_at_length) (const GskCurve *curve,
float distance,
float epsilon);
};
/* {{{ Utilities */
#define RAD_TO_DEG(r) ((r)*180.f/M_PI)
#define DEG_TO_RAD(d) ((d)*M_PI/180.f)
static void
get_tangent (const graphene_point_t *p0,
const graphene_point_t *p1,
graphene_vec2_t *t)
{
graphene_vec2_init (t, p1->x - p0->x, p1->y - p0->y);
graphene_vec2_normalize (t, t);
}
static int
line_get_crossing (const graphene_point_t *p,
const graphene_point_t *p1,
const graphene_point_t *p2)
{
if (p1->y <= p->y)
{
if (p2->y > p->y)
{
if ((p2->x - p1->x) * (p->y - p1->y) - (p->x - p1->x) * (p2->y - p1->y) > 0)
return 1;
}
}
else if (p2->y <= p->y)
{
if ((p2->x - p1->x) * (p->y - p1->y) - (p->x - p1->x) * (p2->y - p1->y) < 0)
return -1;
}
return 0;
}
static int
get_crossing_by_bisection (const GskCurve *curve,
const graphene_point_t *point)
{
GskBoundingBox bounds;
GskCurve c1, c2;
gsk_curve_get_bounds (curve, &bounds);
if (bounds.max.y < point->y || bounds.min.y > point->y || bounds.max.x < point->x)
return 0;
if (bounds.min.x > point->x)
return line_get_crossing (point, gsk_curve_get_start_point (curve), gsk_curve_get_end_point (curve));
if (graphene_point_distance (&bounds.min, &bounds.max, NULL, NULL) < 0.001)
return line_get_crossing (point, gsk_curve_get_start_point (curve), gsk_curve_get_end_point (curve));
gsk_curve_split (curve, 0.5, &c1, &c2);
return gsk_curve_get_crossing (&c1, point) + gsk_curve_get_crossing (&c2, point);
}
/* Replace a line by an equivalent quad,
* and a quad by an equivalent cubic.
*/
static void
gsk_curve_elevate (const GskCurve *curve,
GskCurve *elevated)
{
if (curve->op == GSK_PATH_LINE)
{
GskAlignedPoint p[3];
p[0].pt = curve->line.points[0];
graphene_point_interpolate (&curve->line.points[0],
&curve->line.points[1],
0.5,
&p[1].pt);
p[2].pt = curve->line.points[1];
gsk_curve_init (elevated, gsk_pathop_encode (GSK_PATH_QUAD, p));
}
else if (curve->op == GSK_PATH_QUAD)
{
GskAlignedPoint p[4];
p[0].pt = curve->quad.points[0];
graphene_point_interpolate (&curve->quad.points[0],
&curve->quad.points[1],
2/3.,
&p[1].pt);
graphene_point_interpolate (&curve->quad.points[2],
&curve->quad.points[1],
2/3.,
&p[2].pt);
p[3].pt = curve->quad.points[2];
gsk_curve_init (elevated, gsk_pathop_encode (GSK_PATH_CUBIC, p));
}
else
g_assert_not_reached ();
}
/* Compute arclength by using Gauss quadrature on
*
* \int_0^z \sqrt{ (dx/dt)^2 + (dy/dt)^2 } dt
*/
#include "gskcurve-ct-values.c"
static float
get_length_by_approximation (const GskCurve *curve,
float t)
{
double z = t / 2;
double sum = 0;
graphene_point_t d;
for (unsigned int i = 0; i < G_N_ELEMENTS (T); i++)
{
gsk_curve_get_derivative_at (curve, z * T[i] + z, &d);
sum += C[i] * sqrt (d.x * d.x + d.y * d.y);
}
return z * sum;
}
/* Compute the inverse of the arclength using bisection,
* to a given precision
*/
static float
get_t_by_bisection (const GskCurve *curve,
float length,
float epsilon)
{
float t1, t2, t, l;
GskCurve c1;
g_assert (epsilon >= FLT_EPSILON);
t1 = 0;
t2 = 1;
do
{
t = (t1 + t2) / 2;
if (t == t1 || t == t2)
break;
gsk_curve_split (curve, t, &c1, NULL);
l = gsk_curve_get_length (&c1);
if (fabsf (length - l) < epsilon)
break;
else if (l < length)
t1 = t;
else
t2 = t;
}
while (t1 < t2);
return t;
}
/* }}} */
/* {{{ Line */
static void
gsk_line_curve_init_from_points (GskLineCurve *self,
GskPathOperation op,
const graphene_point_t *start,
const graphene_point_t *end)
{
self->op = op;
self->points[0] = *start;
self->points[1] = *end;
}
static void
gsk_line_curve_init (GskCurve *curve,
gskpathop op)
{
GskLineCurve *self = &curve->line;
const graphene_point_t *pts = gsk_pathop_points (op);
gsk_line_curve_init_from_points (self, gsk_pathop_op (op), &pts[0], &pts[1]);
}
static void
gsk_line_curve_init_foreach (GskCurve *curve,
GskPathOperation op,
const graphene_point_t *pts,
gsize n_pts,
float weight)
{
GskLineCurve *self = &curve->line;
g_assert (n_pts == 2);
gsk_line_curve_init_from_points (self, op, &pts[0], &pts[1]);
}
static void
gsk_line_curve_print (const GskCurve *curve,
GString *string)
{
g_string_append_printf (string,
"M %g %g L %g %g",
curve->line.points[0].x, curve->line.points[0].y,
curve->line.points[1].x, curve->line.points[1].y);
}
static gskpathop
gsk_line_curve_pathop (const GskCurve *curve)
{
const GskLineCurve *self = &curve->line;
return gsk_pathop_encode (self->op, self->aligned_points);
}
static const graphene_point_t *
gsk_line_curve_get_start_point (const GskCurve *curve)
{
const GskLineCurve *self = &curve->line;
return &self->points[0];
}
static const graphene_point_t *
gsk_line_curve_get_end_point (const GskCurve *curve)
{
const GskLineCurve *self = &curve->line;
return &self->points[1];
}
static void
gsk_line_curve_get_start_end_tangent (const GskCurve *curve,
graphene_vec2_t *tangent)
{
const GskLineCurve *self = &curve->line;
get_tangent (&self->points[0], &self->points[1], tangent);
}
static void
gsk_line_curve_get_point (const GskCurve *curve,
float t,
graphene_point_t *pos)
{
const GskLineCurve *self = &curve->line;
graphene_point_interpolate (&self->points[0], &self->points[1], t, pos);
}
static void
gsk_line_curve_get_tangent (const GskCurve *curve,
float t,
graphene_vec2_t *tangent)
{
const GskLineCurve *self = &curve->line;
get_tangent (&self->points[0], &self->points[1], tangent);
}
static float
gsk_line_curve_get_curvature (const GskCurve *curve,
float t)
{
return 0;
}
static void
gsk_line_curve_reverse (const GskCurve *curve,
GskCurve *reverse)
{
const GskLineCurve *self = &curve->line;
reverse->op = GSK_PATH_LINE;
reverse->line.points[0] = self->points[1];
reverse->line.points[1] = self->points[0];
}
static void
gsk_line_curve_split (const GskCurve *curve,
float progress,
GskCurve *start,
GskCurve *end)
{
const GskLineCurve *self = &curve->line;
graphene_point_t point;
graphene_point_interpolate (&self->points[0], &self->points[1], progress, &point);
if (start)
gsk_line_curve_init_from_points (&start->line, GSK_PATH_LINE, &self->points[0], &point);
if (end)
gsk_line_curve_init_from_points (&end->line, GSK_PATH_LINE, &point, &self->points[1]);
}
static void
gsk_line_curve_segment (const GskCurve *curve,
float start,
float end,
GskCurve *segment)
{
const GskLineCurve *self = &curve->line;
const graphene_point_t *pts = self->points;
graphene_point_t p0, p1;
graphene_point_interpolate (&pts[0], &pts[1], start, &p0);
graphene_point_interpolate (&pts[0], &pts[1], end, &p1);
gsk_line_curve_init_from_points (&segment->line, GSK_PATH_LINE, &p0, &p1);
}
static gboolean
gsk_line_curve_decompose (const GskCurve *curve,
float tolerance,
GskCurveAddLineFunc add_line_func,
gpointer user_data)
{
const GskLineCurve *self = &curve->line;
const graphene_point_t *pts = self->points;
return add_line_func (&pts[0], &pts[1], 0.f, 1.f, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
}
static gboolean
gsk_line_curve_decompose_curve (const GskCurve *curve,
GskPathForeachFlags flags,
float tolerance,
GskCurveAddCurveFunc add_curve_func,
gpointer user_data)
{
const GskLineCurve *self = &curve->line;
return add_curve_func (GSK_PATH_LINE, self->points, 2, 0.f, user_data);
}
static void
gsk_line_curve_get_bounds (const GskCurve *curve,
GskBoundingBox *bounds)
{
const GskLineCurve *self = &curve->line;
const graphene_point_t *pts = self->points;
gsk_bounding_box_init (bounds, &pts[0], &pts[1]);
}
static void
gsk_line_curve_get_derivative_at (const GskCurve *curve,
float t,
graphene_point_t *value)
{
const GskLineCurve *self = &curve->line;
const graphene_point_t *pts = self->points;
value->x = pts[1].x - pts[0].x;
value->y = pts[1].y - pts[0].y;
}
static int
gsk_line_curve_get_crossing (const GskCurve *curve,
const graphene_point_t *point)
{
const GskLineCurve *self = &curve->line;
const graphene_point_t *pts = self->points;
return line_get_crossing (point, &pts[0], &pts[1]);
}
static float
gsk_line_curve_get_length_to (const GskCurve *curve,
float t)
{
const GskLineCurve *self = &curve->line;
const graphene_point_t *pts = self->points;
return t * graphene_point_distance (&pts[0], &pts[1], NULL, NULL);
}
static float
gsk_line_curve_get_at_length (const GskCurve *curve,
float distance,
float epsilon)
{
const GskLineCurve *self = &curve->line;
const graphene_point_t *pts = self->points;
float length;
length = graphene_point_distance (&pts[0], &pts[1], NULL, NULL);
if (length == 0)
return 0;
return CLAMP (distance / length, 0, 1);
}
static const GskCurveClass GSK_LINE_CURVE_CLASS = {
gsk_line_curve_init,
gsk_line_curve_init_foreach,
gsk_line_curve_print,
gsk_line_curve_pathop,
gsk_line_curve_get_start_point,
gsk_line_curve_get_end_point,
gsk_line_curve_get_start_end_tangent,
gsk_line_curve_get_start_end_tangent,
gsk_line_curve_get_point,
gsk_line_curve_get_tangent,
gsk_line_curve_reverse,
gsk_line_curve_get_curvature,
gsk_line_curve_split,
gsk_line_curve_segment,
gsk_line_curve_decompose,
gsk_line_curve_decompose_curve,
gsk_line_curve_get_bounds,
gsk_line_curve_get_bounds,
gsk_line_curve_get_derivative_at,
gsk_line_curve_get_crossing,
gsk_line_curve_get_length_to,
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->aligned_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->aligned_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->aligned_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];
GskAlignedPoint 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].pt = GRAPHENE_POINT_INIT (l[0].x / l[0].z, l[0].y / l[0].z);
left[1].pt = GRAPHENE_POINT_INIT (l[1].x / l[1].z, l[1].y / l[1].z);
left[3].pt = GRAPHENE_POINT_INIT (l[2].x / l[2].z, l[2].y / l[2].z);
right[0].pt = GRAPHENE_POINT_INIT (r[0].x / r[0].z, r[0].y / r[0].z);
right[1].pt = GRAPHENE_POINT_INIT (r[1].x / r[1].z, r[1].y / r[1].z);
right[3].pt = 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].pt = GRAPHENE_POINT_INIT (l[1].z / sqrt (l[2].z), 0);
right[2].pt = 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 || end >= 1.0f)
{
if (start <= 0.0f)
gsk_conic_curve_split (curve, end, segment, NULL);
else if (end >= 1.0f)
gsk_conic_curve_split (curve, start, NULL, segment);
return;
}
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;
GskAlignedPoint 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].pt = self->points[0];
p[3].pt = self->points[3];
graphene_point_interpolate (&self->points[0], &self->points[1], lambda, &p[1].pt);
graphene_point_interpolate (&self->points[3], &self->points[1], lambda, &p[2].pt);
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, &center);
if (graphene_point_distance (&center, 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);
}
/* Find cusps inside the open interval from 0 to 1.
*
* According to Stone & deRose, A Geometric Characterization
* of Parametric Cubic curves, a necessary and sufficient
* condition is that the first derivative vanishes.
*/
int
gsk_curve_get_cusps (const GskCurve *curve,
float t[2])
{
const graphene_point_t *pts = curve->cubic.points;
graphene_point_t p[3];
float ax, bx, cx;
float ay, by, cy;
float tx[3];
int nx;
int n = 0;
if (curve->op != GSK_PATH_CUBIC)
return 0;
p[0].x = 3 * (pts[1].x - pts[0].x);
p[0].y = 3 * (pts[1].y - pts[0].y);
p[1].x = 3 * (pts[2].x - pts[1].x);
p[1].y = 3 * (pts[2].y - pts[1].y);
p[2].x = 3 * (pts[3].x - pts[2].x);
p[2].y = 3 * (pts[3].y - pts[2].y);
ax = p[0].x - 2 * p[1].x + p[2].x;
bx = - 2 * p[0].x + 2 * p[1].x;
cx = p[0].x;
nx = solve_quadratic (ax, bx, cx, tx);
nx = filter_allowable (tx, nx);
ay = p[0].y - 2 * p[1].y + p[2].y;
by = - 2 * p[0].y + 2 * p[1].y;
cy = p[0].y;
for (int i = 0; i < nx; i++)
{
float ti = tx[i];
if (0 < ti && ti < 1 &&
fabsf (ay * ti * ti + by * ti + cy) < 0.001)
t[n++] = ti;
}
return n;
}
/* }}} */
/* vim:set foldmethod=marker expandtab: */
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