On Wed, Apr 22, 2020 at 9:30 AM Taco Hoekwater <t...@elvenkind.com> wrote:
> > In contrast, intersectionpoint finds the first intersection on the > non-reversed paths, which > is the base of the arrowhead. > > IIrc , it's the first in shuffle order @ Incidentally, if the given cubics intersect more than once, the process just sketched will not necessarily find the lexicographically smallest pair $(t_1,t_2)$. The solution actually obtained will be smallest in ``shuffled order''; i.e., if $t_1=(.a_1a_2\ldots a_{16})_2$ and $t_2=(.b_1b_2\ldots b_{16})_2$, then we will minimize $a_1b_1a_2b_2\ldots a_{16}b_{16}$, not $a_1a_2\ldots a_{16}b_1b_2\ldots b_{16}$. Shuffled order agrees with lexicographic order if all pairs of solutions $(t_1,t_2)$ and $(t_1',t_2')$ have the property that $t_1<t_1'$ iff $t_2<t_2'$; but in general, lexicographic order can be quite different, and the bisection algorithm would be substantially less efficient if it were constrained by lexicographic order. -- luigi
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