/**
* cairo_matrix_invert:
* @matrix: a #cairo_matrix_t
*
* Changes @matrix to be the inverse of it's original value. Not
* all transformation matrices have inverses; if the matrix
* collapses points together (it is <firstterm>degenerate</firstterm>),
* then it has no inverse and this function will fail.
*
* Returns: If @matrix has an inverse, modifies @matrix to
* be the inverse matrix and returns %CAIRO_STATUS_SUCCESS. Otherwise,
* returns %CAIRO_STATUS_INVALID_MATRIX.
**/
cairo_status_t
cairo_matrix_invert (cairo_matrix_t *matrix)
{
double det;
/* Simple scaling|translation matrices are quite common... */
if (matrix->xy == 0. && matrix->yx == 0.) {
matrix->x0 = -matrix->x0;
matrix->y0 = -matrix->y0;
if (matrix->xx != 1.) {
if (matrix->xx == 0.)
return _cairo_error (CAIRO_STATUS_INVALID_MATRIX);
matrix->xx = 1. / matrix->xx;
matrix->x0 *= matrix->xx;
}
if (matrix->yy != 1.) {
if (matrix->yy == 0.)
return _cairo_error (CAIRO_STATUS_INVALID_MATRIX);
matrix->yy = 1. / matrix->yy;
matrix->y0 *= matrix->yy;
}
return CAIRO_STATUS_SUCCESS;
}
/* inv (A) = 1/det (A) * adj (A) */
det = _cairo_matrix_compute_determinant (matrix);
if (! ISFINITE (det))
return _cairo_error (CAIRO_STATUS_INVALID_MATRIX);
if (det == 0)
return _cairo_error (CAIRO_STATUS_INVALID_MATRIX);
_cairo_matrix_compute_adjoint (matrix);
_cairo_matrix_scalar_multiply (matrix, 1 / det);
return CAIRO_STATUS_SUCCESS;
}
/* Compute the amount that each basis vector is scaled by. */
cairo_status_t
_cairo_matrix_compute_scale_factors (const cairo_matrix_t *matrix,
double *sx, double *sy, int x_major)
{
double det;
_cairo_matrix_compute_determinant (matrix, &det);
if (det == 0)
{
*sx = *sy = 0;
}
else
{
double x = x_major != 0;
double y = x == 0;
double major, minor;
cairo_matrix_transform_distance (matrix, &x, &y);
major = sqrt(x*x + y*y);
/*
* ignore mirroring
*/
if (det < 0)
det = -det;
if (major)
minor = det / major;
else
minor = 0.0;
if (x_major)
{
*sx = major;
*sy = minor;
}
else
{
*sx = minor;
*sy = major;
}
}
return CAIRO_STATUS_SUCCESS;
}
static cairo_status_t
_cairo_stroker_init (cairo_stroker_t *stroker,
const cairo_path_fixed_t *path,
const cairo_stroke_style_t *stroke_style,
const cairo_matrix_t *ctm,
const cairo_matrix_t *ctm_inverse,
double tolerance,
const cairo_box_t *limits,
int num_limits)
{
cairo_status_t status;
stroker->style = *stroke_style;
stroker->ctm = ctm;
stroker->ctm_inverse = ctm_inverse;
stroker->tolerance = tolerance;
stroker->ctm_determinant = _cairo_matrix_compute_determinant (stroker->ctm);
stroker->ctm_det_positive = stroker->ctm_determinant >= 0.0;
status = _cairo_pen_init (&stroker->pen,
stroke_style->line_width / 2.0,
tolerance, ctm);
if (unlikely (status))
return status;
stroker->has_current_face = FALSE;
stroker->has_first_face = FALSE;
stroker->has_initial_sub_path = FALSE;
_cairo_stroker_dash_init (&stroker->dash, stroke_style);
stroker->add_external_edge = NULL;
stroker->has_bounds = FALSE;
if (num_limits)
_cairo_stroker_limit (stroker, path, limits, num_limits);
return CAIRO_STATUS_SUCCESS;
}
cairo_status_t
_cairo_path_fixed_stroke_to_polygon (const cairo_path_fixed_t *path,
const cairo_stroke_style_t *style,
const cairo_matrix_t *ctm,
const cairo_matrix_t *ctm_inverse,
double tolerance,
cairo_polygon_t *polygon)
{
struct stroker stroker;
cairo_status_t status;
if (style->num_dashes) {
return _cairo_path_fixed_stroke_dashed_to_polygon (path,
style,
ctm,
ctm_inverse,
tolerance,
polygon);
}
stroker.has_bounds = polygon->num_limits;
if (stroker.has_bounds) {
/* Extend the bounds in each direction to account for the maximum area
* we might generate trapezoids, to capture line segments that are
* outside of the bounds but which might generate rendering that's
* within bounds.
*/
double dx, dy;
cairo_fixed_t fdx, fdy;
int i;
stroker.bounds = polygon->limits[0];
for (i = 1; i < polygon->num_limits; i++)
_cairo_box_add_box (&stroker.bounds, &polygon->limits[i]);
_cairo_stroke_style_max_distance_from_path (style, path, ctm, &dx, &dy);
fdx = _cairo_fixed_from_double (dx);
fdy = _cairo_fixed_from_double (dy);
stroker.bounds.p1.x -= fdx;
stroker.bounds.p2.x += fdx;
stroker.bounds.p1.y -= fdy;
stroker.bounds.p2.y += fdy;
}
stroker.style = *style;
stroker.ctm = ctm;
stroker.ctm_inverse = ctm_inverse;
stroker.tolerance = tolerance;
stroker.half_line_width = style->line_width / 2.;
/* To test whether we need to join two segments of a spline using
* a round-join or a bevel-join, we can inspect the angle between the
* two segments. If the difference between the chord distance
* (half-line-width times the cosine of the bisection angle) and the
* half-line-width itself is greater than tolerance then we need to
* inject a point.
*/
stroker.spline_cusp_tolerance = 1 - tolerance / stroker.half_line_width;
stroker.spline_cusp_tolerance *= stroker.spline_cusp_tolerance;
stroker.spline_cusp_tolerance *= 2;
stroker.spline_cusp_tolerance -= 1;
stroker.ctm_det_positive =
_cairo_matrix_compute_determinant (ctm) >= 0.0;
stroker.pen.num_vertices = 0;
if (path->has_curve_to ||
style->line_join == CAIRO_LINE_JOIN_ROUND ||
style->line_cap == CAIRO_LINE_CAP_ROUND) {
status = _cairo_pen_init (&stroker.pen,
stroker.half_line_width,
tolerance, ctm);
if (unlikely (status))
return status;
/* If the line width is so small that the pen is reduced to a
single point, then we have nothing to do. */
if (stroker.pen.num_vertices <= 1)
return CAIRO_STATUS_SUCCESS;
}
stroker.has_current_face = FALSE;
stroker.has_first_face = FALSE;
stroker.has_initial_sub_path = FALSE;
#if DEBUG
remove ("contours.txt");
remove ("polygons.txt");
_cairo_contour_init (&stroker.path, 0);
#endif
_cairo_contour_init (&stroker.cw.contour, 1);
_cairo_contour_init (&stroker.ccw.contour, -1);
tolerance *= CAIRO_FIXED_ONE;
tolerance *= tolerance;
stroker.contour_tolerance = tolerance;
stroker.polygon = polygon;
status = _cairo_path_fixed_interpret (path,
move_to,
line_to,
curve_to,
close_path,
&stroker);
/* Cap the start and end of the final sub path as needed */
if (likely (status == CAIRO_STATUS_SUCCESS))
add_caps (&stroker);
_cairo_contour_fini (&stroker.cw.contour);
_cairo_contour_fini (&stroker.ccw.contour);
if (stroker.pen.num_vertices)
_cairo_pen_fini (&stroker.pen);
#if DEBUG
{
FILE *file = fopen ("polygons.txt", "a");
_cairo_debug_print_polygon (file, polygon);
fclose (file);
}
#endif
return status;
}
cairo_status_t
_cairo_path_fixed_stroke_to_polygon (const cairo_path_fixed_t *path,
const cairo_stroke_style_t *style,
const cairo_matrix_t *ctm,
const cairo_matrix_t *ctm_inverse,
double tolerance,
cairo_polygon_t *polygon)
{
struct stroker stroker;
cairo_status_t status;
if (style->num_dashes) {
return _cairo_path_fixed_stroke_dashed_to_polygon (path,
style,
ctm,
ctm_inverse,
tolerance,
polygon);
}
stroker.style = *style;
stroker.ctm = ctm;
stroker.ctm_inverse = ctm_inverse;
stroker.tolerance = tolerance;
stroker.ctm_det_positive =
_cairo_matrix_compute_determinant (ctm) >= 0.0;
stroker.pen.num_vertices = 0;
if (path->has_curve_to ||
style->line_join == CAIRO_LINE_JOIN_ROUND ||
style->line_cap == CAIRO_LINE_CAP_ROUND) {
status = _cairo_pen_init (&stroker.pen,
style->line_width / 2.0,
tolerance, ctm);
if (unlikely (status))
return status;
/* If the line width is so small that the pen is reduced to a
single point, then we have nothing to do. */
if (stroker.pen.num_vertices <= 1)
return CAIRO_STATUS_SUCCESS;
}
stroker.has_current_face = FALSE;
stroker.has_first_face = FALSE;
stroker.has_initial_sub_path = FALSE;
#if DEBUG
remove ("contours.txt");
remove ("polygons.txt");
_cairo_contour_init (&stroker.path, 0);
#endif
_cairo_contour_init (&stroker.cw.contour, 1);
_cairo_contour_init (&stroker.ccw.contour, -1);
tolerance *= CAIRO_FIXED_ONE;
tolerance *= tolerance;
stroker.contour_tolerance = tolerance;
stroker.polygon = polygon;
status = _cairo_path_fixed_interpret (path,
move_to,
line_to,
curve_to,
close_path,
&stroker);
/* Cap the start and end of the final sub path as needed */
if (likely (status == CAIRO_STATUS_SUCCESS))
add_caps (&stroker);
_cairo_contour_fini (&stroker.cw.contour);
_cairo_contour_fini (&stroker.ccw.contour);
if (stroker.pen.num_vertices)
_cairo_pen_fini (&stroker.pen);
#if DEBUG
{
FILE *file = fopen ("polygons.txt", "a");
_cairo_debug_print_polygon (file, polygon);
fclose (file);
}
#endif
return status;
}
