Euler B-spline for Curve Interpolation and Data Fitting

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Provided by: Binary Information Press
Topic: Big Data
Format: PDF
Euler spirals are a kind of fair curves that have linear curvatures in terms of arc length. However, Euler spirals cannot be represented by polynomials exactly. In this paper, the authors propose an algorithm for approximating a segment of Euler spiral which interpolates two specified points and two tangents at the points by a B-spline curve. The approximating B-spline curve is obtained as the solution to a differential equation which satisfies the boundary conditions. Similar to the exact interpolating Euler spiral, the interpolating B-spline curve is also fair and has approximate linear curvature.
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