Hi Denis,
On 10/18/2010 2:21 PM, Denis Lila wrote:
I introduced a drawRoundCap method. This eliminated the side argument from
the round join drawing, which made it easier to eliminate the trig function
calls. I did this by using dot products to compute cosines (which was possible
because now Stroker takes only untransformed paths, and all lineWidths are the
same), and I used the double angle identities to compute any sines.
I came up with my own ways of detecting acute/obtuse angles and finding the
centres
of angles ("my own" meaning I didn't look at any websites), and they consist of:
1. if (omx * mx + omy * my)>= 0 then the angle is acute (line 200).
2. I explain this in a comment in the file (line 208).
The new trig-less round join code looks great! I don't see any errors,
but a couple of nit comments:
One comment on the comment. Isn't the upper bound on the ratio equal to
sqrt(2)/2? The radius (lineWidth2) is never greater than this chord
length for any angle >90.
When would the isCW test trigger? Does it track "rev"? What happens at
180 degrees (is that test reliable for the randomization that might
happen when omxy are directly opposite mxy)? The only reason I ask is
because I think the sign of mmxy is probably controllable by
understanding the input conditions, but this test should be safe (modulo
if it really works at 180 degrees). If it has failure modes at 180
degrees then reworking the math to produce the right sign in the first
place may be more robust for that case. A test for this is to render
"(0,0) -> (100,0) -> (0,0)" with round caps and then rotate it through
360 degrees and see if the round caps invert at various angles.
Also, line 256 - does that track "rev"?
My head started spinning when evaluating the parallel curve methods so
I'll stop here for now...
Sorry about that. Is there anything I can do to make it easier?
Actually I think I'm up to speed on all the math now. I mainly have to
double check the bookkeeping stuff a second time. Can you let me know
when you reach the end of my comment queue and I'll start the hopefully
final proofread?
...jim
