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Euler Spiral Construction
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This software reduces the construction of an Euler spiral from a pair of points and tangents at these points to solving a nonlinear system of equations involving Fresnel Integrals whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions. Since the choice of an appropriate initial curve is critical in this optimization, an optimal solution is analytically derived in the class of biarc curves, which is then used as the initial curve. The resulting interpolations yield intuitive interpolation across gaps and occlusions, and are extensible, in contrast to the scale-invariant version of elastica.
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