Hello. I working on some bezier-related algorithms and need to be able to provide the curvature of a bezier at any queried point. Now when cubic beziers have cusps, their curvature is infinite. However the infinity can be positive or negative. The question is how to find out the sign of this infinity.
Now it is a fundamental property of cusps that the sign of curvature on either side of the cusp is the same, so it stands to reason that if the curvature sign on the sides is positive then the curvature at the cusp is positive infinity and likewise for negative. So one method to find the sign of the infinity is to evaluate the sign at a nearby point. However I'd like to do it analytically. As the attached SymPy script demonstrates, it is possible to evaluate the limit of the curvature and determine whether the infinity is positive or negative. However, L'Hopital's rule seems to fail. What is the method by which SymPy arrives at this result? Thank you! -- Shriramana Sharma ஶ்ரீரமணஶர்மா श्रीरमणशर्मा -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
bezier-cusp-curvature-limit.py
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