Tuesday, June 07, 2016

[hpgosidz] Arc length parametrization

Given a vector valued function F(t), derive its arc length parameterization, that is a function T(s) such that F(T(s)) moves along the arc at constant speed as s increases at a constant rate.  We need automatic or numerical differentiation, quadrature, and root finding to invert the arc length integral.  There might be a trick of inverting before integrating (implicit differentiation) to avoid needing root finding.

The motivation was for a color wheel (future post), needing to have a path that moves in CIELab color space at constant speed along a path that was specified in RGB space.

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