fdo-mirrors/cairo
1
0
Fork 0
mirror of https://gitlab.freedesktop.org/cairo/cairo.git synced 2026-03-17 18:20:41 +01:00
Code Issues Projects Releases Packages Wiki Activity Actions

Round joins fix (spline_cusp_tolerance)

Browse source 
https://gitlab.freedesktop.org/cairo/cairo/-/issues/520
This commit is contained in:
Christian Rohlfs 2022-12-28 07:25:30 +05:00
parent 805897b1f7
commit e83776572c
2 changed files with 99 additions and 28 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

95
src/cairo-path-stroke-polygon.c
View file

@ -399,16 +399,16 @@ outer_close (struct stroker *stroker,
switch (stroker->style.line_join) {
case CAIRO_LINE_JOIN_ROUND:
/* construct a fan around the common midpoint */
if ((in->dev_slope.x * out->dev_slope.x +
in->dev_slope.y * out->dev_slope.y) < stroker->spline_cusp_tolerance)
{
/* construct a fan around the common midpoint */
add_fan (stroker,
&in->dev_vector, &out->dev_vector, &in->point,
clockwise, outer);
break;
}
/* else fall through */
} /* else: bevel join */
break;
case CAIRO_LINE_JOIN_MITER:
default: {
/* dot product of incoming slope vector with outgoing slope vector */
@ -587,10 +587,14 @@ outer_join (struct stroker *stroker,
switch (stroker->style.line_join) {
case CAIRO_LINE_JOIN_ROUND:
/* construct a fan around the common midpoint */
add_fan (stroker,
&in->dev_vector, &out->dev_vector, &in->point,
clockwise, outer);
if ((in->dev_slope.x * out->dev_slope.x +
in->dev_slope.y * out->dev_slope.y) < stroker->spline_cusp_tolerance)
{
/* construct a fan around the common midpoint */
add_fan (stroker,
&in->dev_vector, &out->dev_vector, &in->point,
clockwise, outer);
} /* else: bevel join */
break;
case CAIRO_LINE_JOIN_MITER:
@ -1291,17 +1295,72 @@ _cairo_path_fixed_stroke_to_polygon (const cairo_path_fixed_t *path,
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.
/* If `CAIRO_LINE_JOIN_ROUND` is selected and a joint's `arc height`
* is greater than `tolerance` then two segments are joined with
* round-join, otherwise bevel-join is used.
*
* (See https://gitlab.freedesktop.org/cairo/cairo/-/merge_requests/372#note_1698225
* for an illustration.)
*
* `Arc height` is the distance from the center of arc's chord to
* the center of the arc. It is also the difference of arc's radius
* and the "distance from a point where segments are joined to the
* chord" (distance to the chord). Arc's radius is the half of a line
* width and the "distance to the chord" is equal to "half of a line width"
* times `cos(half the angle between segment vectors)`. So
*
* arc_height = w/2 - w/2 * cos(phi/2),
*
* where `w/2` is the "half of a line width".
*
* Using the double angle cosine formula we can express the `cos(phi/2)`
* with just `cos(phi)` which is also the dot product of segments'
* unit vectors.
*
* cos(phi/2) = sqrt ( (1 + cos(phi)) / 2 );
* cos(phi/2) is in [0; 1] range, cannot be negative;
*
* cos(phi) = a . b = (ax * bx + ay * by),
*
* where `a` and `b` are unit vectors of the segments to be joined.
*
* Since `arc height` should be greater than the `tolerance` to produce
* a round-join we can write
*
* w/2 * (1 - cos(phi/2)) > tolerance;
* 1 - tolerance / (w/2) > cos(phi/2); [!]
*
* which can be rewritten with the above double angle formula to
*
* cos(phi) < 2 * ( 1 - tolerance / (w/2) )^2 - 1,
*
* [!] Note that `w/2` is in [tolerance; +inf] range, since `cos(phi/2)`
* cannot be negative. The left part of the above inequality is the
* dot product and the right part is the `spline_cusp_tolerance`:
*
* (ax * bx + ay * by) < spline_cusp_tolerance.
*
* In the code below only the `spline_cusp_tolerance` is calculated.
* The dot product is calculated later, in the condition expression
* itself. "Half of a line width" must be scaled with CTM for tolerance
* condition to be properly met. Also, since `arch height` cannot exceed
* the "half of a line width" and since `cos(phi/2)` cannot be negative,
* when `tolerance` is greater than the "half of a line width" the
* bevel-join should be produced.
*/
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;
double scaled_hlw = hypot(stroker.half_line_width * ctm->xx,
stroker.half_line_width * ctm->yx);
if (scaled_hlw <= tolerance) {
stroker.spline_cusp_tolerance = -1.0;
} else {
stroker.spline_cusp_tolerance = 1 - tolerance / scaled_hlw;
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;

32
src/cairo-path-stroke-traps.c
View file

@ -102,17 +102,29 @@ stroker_init (struct stroker *stroker,
stroker->tolerance = tolerance;
stroker->traps = traps;
/* 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.
/* If `CAIRO_LINE_JOIN_ROUND` is selected and a joint's `arc height`
* is greater than `tolerance` then two segments are joined with
* round-join, otherwise bevel-join is used.
*
* `Arc height` is the difference of the "half of a line width" and
* the "half of a line width" times `cos(half the angle between segment vectors)`.
*
* See detailed description in the `_cairo_path_fixed_stroke_to_polygon()`
* function in the `cairo-path-stroke-polygon.c` file or follow the
* https://gitlab.freedesktop.org/cairo/cairo/-/merge_requests/372#note_1698225
* link to see the detailed description with an illustration.
*/
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;
double scaled_hlw = hypot(stroker->half_line_width * ctm->xx,
stroker->half_line_width * ctm->yx);
if (scaled_hlw <= tolerance) {
stroker->spline_cusp_tolerance = -1.0;
} else {
stroker->spline_cusp_tolerance = 1 - tolerance / scaled_hlw;
stroker->spline_cusp_tolerance *= stroker->spline_cusp_tolerance;
stroker->spline_cusp_tolerance *= 2;
stroker->spline_cusp_tolerance -= 1;
}
stroker->ctm_determinant = _cairo_matrix_compute_determinant (stroker->ctm);
stroker->ctm_det_positive = stroker->ctm_determinant >= 0.0;