Re: [OpenJDK 2D-Dev] X11 uniform scaled wide lines and dashed lines; STROKE_CONTROL in Pisces
Hi Denis, One clarification: On 10/20/10 7:11 AM, Denis Lila wrote: 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)? isCw is used for computing the arc bisector by testing whether the computed point is on the side it should be (and multiplying by -1 if not), it is used to compute the sign of cv in drawBezApproxForArc, and for computing rev. 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. I already did that. I drew 100 lines like the one you describe. I attached the results. It never fails. It is still possible that there could be some case where it fails, but this does prove that such a case would be very rare. Also, line 256 - does that track rev? It does. I changed the test to if(rev). Cool, but above I was also asking the same question about line 231, and you provided a lot of information about line 231 (and a test to verify it), but didn't answer if the test in line 231 also tracks rev the same way...? ...jim
Re: [OpenJDK 2D-Dev] X11 uniform scaled wide lines and dashed lines; STROKE_CONTROL in Pisces
On 10/20/10 7:54 AM, Denis Lila wrote: In #2, you have a bunch of I'() || B'() which I read as the slope of the derivative (i.e. acceleration) is equal, don't you really mean I() || B() which would mean the original curves should be parallel? Otherwise you could say I'() == B'(), but I think you want to show parallels because that shows how you can use the dxy1,dxy4 values as the parallel equivalents. Not really. I've updated the comment explaining what || does, and it should be clearer now. Basically, A(t) || B(t) means that vectors A(t) and B(t) are parallel (i.e. A(t) = c*B(t), for some nonzero t), not that curves A and B are parallel at t. I'm not sure we are on the same page here. I'() is usually the symbol indicating the derivative of I(). My issue is not with the || operator, but with the fact that you are applying it to the I'() instead of I(). Also, how is A(t) and B(t) are parallel not the same as the curves A and B are parallel at t? Also, A(t) = c*B(t) is always true for all A and B and all t if you take a sample in isolation. Parallel means something like A(t) = c*B(t) with the same value of c for some interval around t, not that the values at t can be expressed as a multiple. Again, I'() || B'() says to me that the derivative curves are parallel, not that the original curves are parallel... ...jim
Re: [OpenJDK 2D-Dev] X11 uniform scaled wide lines and dashed lines; STROKE_CONTROL in Pisces
Cool, but above I was also asking the same question about line 231, and you provided a lot of information about line 231 (and a test to verify it), but didn't answer if the test in line 231 also tracks rev the same way...? Oh, no, line 231 isn't mean to be related to rev at all. It just checks to see on which side of the (omx,omy),(mx,my) chord the computed (mmx, mmy) is. Regards, Denis. - Jim Graham james.gra...@oracle.com wrote: Hi Denis, One clarification: On 10/20/10 7:11 AM, Denis Lila wrote: 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)? isCw is used for computing the arc bisector by testing whether the computed point is on the side it should be (and multiplying by -1 if not), it is used to compute the sign of cv in drawBezApproxForArc, and for computing rev. 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. I already did that. I drew 100 lines like the one you describe. I attached the results. It never fails. It is still possible that there could be some case where it fails, but this does prove that such a case would be very rare. Also, line 256 - does that track rev? It does. I changed the test to if(rev). ...jim
Re: [OpenJDK 2D-Dev] X11 uniform scaled wide lines and dashed lines; STROKE_CONTROL in Pisces
Also, how is A(t) and B(t) are parallel not the same as the curves A and B are parallel at t? Well, suppose A and B are lines with endpoints (0,0), (2,0) for A and (0,1),(2,1) for B. Obviously, for all t, A and B are parallel at t. However let t = 0.5. Then A(t) = (1,0) and B(t) = (1, 1). The vectors (1,0) and (1,1) are not parallel, so saying A(t) || B(t) is the same as saying that there exists c such that (1,0) = c*(1,1), which isn't true. However, A'(t)=(2,0) and B'(t)=(2,0), and the vectors (2,0) and (2,0) are parallel. Does this make more sense? Regards, Denis. - Jim Graham james.gra...@oracle.com wrote: On 10/20/10 7:54 AM, Denis Lila wrote: In #2, you have a bunch of I'() || B'() which I read as the slope of the derivative (i.e. acceleration) is equal, don't you really mean I() || B() which would mean the original curves should be parallel? Otherwise you could say I'() == B'(), but I think you want to show parallels because that shows how you can use the dxy1,dxy4 values as the parallel equivalents. Not really. I've updated the comment explaining what || does, and it should be clearer now. Basically, A(t) || B(t) means that vectors A(t) and B(t) are parallel (i.e. A(t) = c*B(t), for some nonzero t), not that curves A and B are parallel at t. I'm not sure we are on the same page here. I'() is usually the symbol indicating the derivative of I(). My issue is not with the || operator, but with the fact that you are applying it to the I'() instead of I(). Also, A(t) = c*B(t) is always true for all A and B and all t if you take a sample in isolation. Parallel means something like A(t) = c*B(t) with the same value of c for some interval around t, not that the values at t can be expressed as a multiple. Again, I'() || B'() says to me that the derivative curves are parallel, not that the original curves are parallel... ...jim
Re: [OpenJDK 2D-Dev] X11 uniform scaled wide lines and dashed lines; STROKE_CONTROL in Pisces
Right, but it seemed to me that if omxy was the from vector and mxy was the to vector, that the computed mmxy should always be predictably on the same side of it, no? If it was on the wrong side then it wouldn't be a random occurence, it must be related to the input data. So either it is always on the right side, always on the wrong side (i.e. just reverse the rotation in the math), or always on the right/wrong side depending on the CWness of the join angle - which would be reflected in rev... No? ...jim On 10/20/10 10:29 AM, Denis Lila wrote: Cool, but above I was also asking the same question about line 231, and you provided a lot of information about line 231 (and a test to verify it), but didn't answer if the test in line 231 also tracks rev the same way...? Oh, no, line 231 isn't mean to be related to rev at all. It just checks to see on which side of the (omx,omy),(mx,my) chord the computed (mmx, mmy) is. Regards, Denis. - Jim Grahamjames.gra...@oracle.com wrote: Hi Denis, One clarification: On 10/20/10 7:11 AM, Denis Lila wrote: 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)? isCw is used for computing the arc bisector by testing whether the computed point is on the side it should be (and multiplying by -1 if not), it is used to compute the sign of cv in drawBezApproxForArc, and for computing rev. 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. I already did that. I drew 100 lines like the one you describe. I attached the results. It never fails. It is still possible that there could be some case where it fails, but this does prove that such a case would be very rare. Also, line 256 - does that track rev? It does. I changed the test to if(rev). ...jim
Re: [OpenJDK 2D-Dev] X11 uniform scaled wide lines and dashed lines; STROKE_CONTROL in Pisces
OK, I can see how your terminology works now, but it seems odd to me. I never consider re-expressing the coordinates on a curve as a vector and basing geometric properties on those constructed vectors. I either consider the points on the curve, or its tangent or its normal - none of which is the value you are expressing. You are, essentially, operating on tangent vectors, but you aren't calling them that, you are calling them something like the vector of the derivative which is a relative (direction only) version of the tangent vector (which has location and direction). When one talks about curves and being parallel, my mind tends to think of the tangents of the curves being parallel and tangents are directed by the first derivative. Also, if you are going to use your definition of vector then parallel is an odd term to use for values that originate from the same point (points considered as a vector are taken to originate from 0,0) - really you want those vectors to be collinear, not (just) parallel. So, either || means the coordinates of the curves expressed as vectors are collinear or it means the curves (i.e. the tangents of the curve at the indicated point) are parallel. Saying vector I() is parallel to vector B() didn't really have meaning to me based on the above biases. So, I get your comment now and all of the math makes sense, but the terminology seemed foreign to me... ...jim On 10/20/10 10:48 AM, Denis Lila wrote: Also, how is A(t) and B(t) are parallel not the same as the curves A and B are parallel at t? Well, suppose A and B are lines with endpoints (0,0), (2,0) for A and (0,1),(2,1) for B. Obviously, for all t, A and B are parallel at t. However let t = 0.5. Then A(t) = (1,0) and B(t) = (1, 1). The vectors (1,0) and (1,1) are not parallel, so saying A(t) || B(t) is the same as saying that there exists c such that (1,0) = c*(1,1), which isn't true. However, A'(t)=(2,0) and B'(t)=(2,0), and the vectors (2,0) and (2,0) are parallel. Does this make more sense? Regards, Denis. - Jim Grahamjames.gra...@oracle.com wrote: On 10/20/10 7:54 AM, Denis Lila wrote: In #2, you have a bunch of I'() || B'() which I read as the slope of the derivative (i.e. acceleration) is equal, don't you really mean I() || B() which would mean the original curves should be parallel? Otherwise you could say I'() == B'(), but I think you want to show parallels because that shows how you can use the dxy1,dxy4 values as the parallel equivalents. Not really. I've updated the comment explaining what || does, and it should be clearer now. Basically, A(t) || B(t) means that vectors A(t) and B(t) are parallel (i.e. A(t) = c*B(t), for some nonzero t), not that curves A and B are parallel at t. I'm not sure we are on the same page here. I'() is usually the symbol indicating the derivative of I(). My issue is not with the || operator, but with the fact that you are applying it to the I'() instead of I(). Also, A(t) = c*B(t) is always true for all A and B and all t if you take a sample in isolation. Parallel means something like A(t) = c*B(t) with the same value of c for some interval around t, not that the values at t can be expressed as a multiple. Again, I'() || B'() says to me that the derivative curves are parallel, not that the original curves are parallel... ...jim
