From e83776572cac2ceaa392e6ba976eec5ac925bdd7 Mon Sep 17 00:00:00 2001 From: Christian Rohlfs Date: Wed, 28 Dec 2022 07:25:30 +0500 Subject: [PATCH] Round joins fix (spline_cusp_tolerance) https://gitlab.freedesktop.org/cairo/cairo/-/issues/520 --- src/cairo-path-stroke-polygon.c | 95 ++++++++++++++++++++++++++------- src/cairo-path-stroke-traps.c | 32 +++++++---- 2 files changed, 99 insertions(+), 28 deletions(-) diff --git a/src/cairo-path-stroke-polygon.c b/src/cairo-path-stroke-polygon.c index 3f7c49802..44b6675e8 100644 --- a/src/cairo-path-stroke-polygon.c +++ b/src/cairo-path-stroke-polygon.c @@ -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; diff --git a/src/cairo-path-stroke-traps.c b/src/cairo-path-stroke-traps.c index eab978235..4eabf6583 100644 --- a/src/cairo-path-stroke-traps.c +++ b/src/cairo-path-stroke-traps.c @@ -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;