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Directly check the miter corner to detect wild miters.

Browse source 
The original test for wild miters would only work with a square transform
(and, in fact, the original code required an identity transform). Instead of
fixing that, I replaced it with a more obvious test which makes sure the
miter corner lies between the two faces and not out in space somewhere.
This commit is contained in:
Keith Packard 2008-01-03 18:37:53 -08:00 • committed by Carl Worth
parent 81e029edda
commit 7cf9a6e4e3
1 changed files with 57 additions and 82 deletions
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139
src/cairo-path-stroke.c
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@ -205,6 +205,22 @@ _cairo_stroker_face_clockwise (cairo_stroke_face_t *in, cairo_stroke_face_t *out
return _cairo_slope_clockwise (&in_slope, &out_slope);
}
/**
* _cairo_slope_compare_sgn
*
* Return -1, 0 or 1 depending on the relative slopes of
* two lines.
*/
static int
_cairo_slope_compare_sgn (double dx1, double dy1, double dx2, double dy2)
{
double c = (dx1 * dy2 - dx2 * dy1);
if (c > 0) return 1;
if (c < 0) return -1;
return 0;
}
static cairo_status_t
_cairo_stroker_join (cairo_stroker_t *stroker, cairo_stroke_face_t *in, cairo_stroke_face_t *out)
{
@ -272,9 +288,6 @@ _cairo_stroker_join (cairo_stroker_t *stroker, cairo_stroke_face_t *in, cairo_st
double in_dot_out = ((-in->usr_vector.x * out->usr_vector.x)+
(-in->usr_vector.y * out->usr_vector.y));
double ml = stroker->style->miter_limit;
double tolerance_squared = stroker->tolerance * stroker->tolerance;
double line_width_squared = (stroker->style->line_width *
stroker->style->line_width);
/* Check the miter limit -- lines meeting at an acute angle
* can generate long miters, the limit converts them to bevel
@ -332,84 +345,17 @@ _cairo_stroker_join (cairo_stroker_t *stroker, cairo_stroke_face_t *in, cairo_st
*
* 2 <= ml² (1 - in · out)
*
*
* That gives us the condition to avoid generating miters that
* are too large from angles that are too large. But we also
* need to avoid generating miters when the angle is very small.
*
* The miter formed from a tiny angle is also tiny, so the
* miter limit is not a concern. But with a tiny angle we will
* be computing the intersection of two lines that are very
* near parallel. Also, the limits of the fixed-point grid on
* the input face coordinates mean that the resulting
* intersection could be wildly wrong. (See the
* get-path-extents test case for a call to cairo_arc that
* results in two problematic faces.)
*
* Fortunately we can also derive an expression for when using
* a bevel join instead of a miter will introduce an error no
* larger than the tolerance. Consider the same join from
* before but with the miter now chopped off and replaced with
* a bevel join. The drawing is zoomed in a bit again, the
* point marked as '*' is the center of the stroke---the point
* where the two line segments of interest intersect:
*
* ----- .
* ^ ..
* | . .
* | . .
* 1/2 . .
* miter . . |
* length . . |
* | .______. ___v___
* | | . \ 1/2 bevel
* v | . \ width
* ---- * \ -------
* | \ ^
*
*
* The length of interest here is the vertical length of the
* miter that is eliminated. It's length can be obtained by
* starting with 1/2 the miter length and the subtracting off
* the vertical length that is included by the bevel join,
* (here termed 1/2 bevel width). To determine this new bevel
* width, we have a small right triangle shown, the hypotenuse
* of which has a length of 1/2 the line width, and the small
* angle at the upper right of the figure is psi/2.
*
* So we have:
*
* sin (psi/2) = (bevel_width / 2) / (line_width / 2)
*
* And we can determine when the miter is required by
* calculating when the eliminated portion of the miter is
* greater than the tolerance:
*
* (miter_length / 2) - (bevel_width / 2) > tolerance
*
* Substituting in the above expressions for miter_length and
* bevel_width:
*
* (line_width/2) / sin (psi/2) - (line_width/2) * sin (psi/2) > tolerance
* 1 / sin(psi/2) - sin (psi/2) > 2 * tolerance / line_width
* 1 / sin²(psi/2) -2 + sin²(psi/2) > 4 * (tolerance/line_width)²
*
* Use identity: sin²(psi/2) = (1-cos(psi))/2
* 2/(1 - cos(psi)) - 2 + (1-cos(psi))/2 > 4 * (tolerance/line_width)²
* 4/(1 - cos(psi)) - 4 + (1-cos(psi)) > 8 * (tolerance/line_width)²
* 4/(1 - cos(psi)) + (1-cos(psi)) > 8 * ((tolerance/line_width)² + 0.5)
*/
if ((2 <= ml * ml * (1 - in_dot_out)) &&
((8 * (tolerance_squared / line_width_squared + 0.5)) <
4 / (1 - in_dot_out) + (1 - in_dot_out))
)
if (2 <= ml * ml * (1 - in_dot_out))
{
double x1, y1, x2, y2;
double mx, my;
double dx1, dx2, dy1, dy2;
cairo_point_t outer;
cairo_point_t quad[4];
double ix, iy;
double fdx1, fdy1, fdx2, fdy2;
double mdx, mdy;
/*
* we've got the points already transformed to device
@ -447,17 +393,46 @@ _cairo_stroker_join (cairo_stroker_t *stroker, cairo_stroke_face_t *in, cairo_st
mx = (my - y2) * dx2 / dy2 + x2;
/*
* Draw the quadrilateral
* When the two outer edges are nearly parallel, slight
* perturbations in the position of the outer points of the lines
* caused by representing them in fixed point form can cause the
* intersection point of the miter to move a large amount. If
* that moves the miter intersection from between the two faces,
* then draw a bevel instead.
*/
outer.x = _cairo_fixed_from_double (mx);
outer.y = _cairo_fixed_from_double (my);
quad[0] = in->point;
quad[1] = *inpt;
quad[2] = outer;
quad[3] = *outpt;
ix = _cairo_fixed_to_double (in->point.x);
iy = _cairo_fixed_to_double (in->point.y);
return _cairo_traps_tessellate_convex_quad (stroker->traps, quad);
/* slope of one face */
fdx1 = x1 - ix; fdy1 = y1 - iy;
/* slope of the other face */
fdx2 = x2 - ix; fdy2 = y2 - iy;
/* slope from the intersection to the miter point */
mdx = mx - ix; mdy = my - iy;
/*
* Make sure the miter point line lies between the two
* faces by comparing the slopes
*/
if (_cairo_slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=
_cairo_slope_compare_sgn (fdx2, fdy2, mdx, mdy))
{
/*
* Draw the quadrilateral
*/
outer.x = _cairo_fixed_from_double (mx);
outer.y = _cairo_fixed_from_double (my);
quad[0] = in->point;
quad[1] = *inpt;
quad[2] = outer;
quad[3] = *outpt;
return _cairo_traps_tessellate_convex_quad (stroker->traps, quad);
}
}
/* fall through ... */
}