Hi,
I have a somewhat-involved question regarding getting an exact representation of a Cartesian oval refracting surface as a rational Bezier curve. More specifically, I'm looking for a particular parameterization that:
Article Superconical aplanatic ovoid singlet lenses
)Article Curves with chord length parameterization
)Due to the way the Cartesian oval is parameterized in 1), it would naturally follow that there would exist an exact Bezier representation that is chord-length. Indeed, there already exists such a chord-length Bezier representation of a limaçon, a special case of the Cartesian oval. But, how does one translate the parameterization given by Silva and Torres to an equivalent chord-length parameterization? The endpoints and their tangents are easy enough to derive, as well as obtaining the maximum chord length of the Cartesian oval, but the determination of the three inner control points, and their weights, I have no clue.
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