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Add figure illustrating derivation of miter limit

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And use sin in the first place rather than the more awkward
secant.
This commit is contained in:
Carl Worth 2007-10-29 16:24:13 -07:00
parent abeba1e69b
commit 9bf0a640d2
1 changed files with 36 additions and 7 deletions
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43
src/cairo-path-stroke.c
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@ -273,18 +273,47 @@ _cairo_stroker_join (cairo_stroker_t *stroker, cairo_stroke_face_t *in, cairo_st
(-in->usr_vector.y * out->usr_vector.y));
double ml = stroker->style->miter_limit;
/*
* Check the miter limit -- lines meeting at an acute angle
/* Check the miter limit -- lines meeting at an acute angle
* can generate long miters, the limit converts them to bevel
*
* We want to know when the miter is within the miter limit.
* That's straightforward to specify:
* Consider the miter join formed when two line segments
* meet at an angle psi:
*
* secant (psi / 2) <= ml
* /.\
* /. .\
* /./ \.\
* /./psi\.\
*
* where psi is the angle between in and out
* We can zoom in on the right half of that to see:
*
* |\
* | \ psi/2
* | \
* | \
* | \
* | \
* miter \
* length \
* | \
* | .\
* | . \
* |. line \
* \ width \
* \ \
*
*
* The right triangle in that figure, (the line-width side is
* shown faintly with three '.' characters), gives us the
* following expression relating miter length, angle and line
* width:
*
* 1 /sin (psi/2) = miter_length / line_width
*
* The right-hand side of this relationship is the same ratio
* in which the miter limit (ml) is expressed. We want to know
* when the miter length is within the miter limit. That is
* when the following condition holds:
*
* secant(psi/2) = 1/sin(psi/2)
* 1/sin(psi/2) <= ml
* 1 <= ml sin(psi/2)
* 1 <= ml² sin²(psi/2)