A technique for smoothing scattered data with conic sections |
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Affiliation: | 1. School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China |
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Abstract: | Piecewise rational quadratic curves are frequently used in many fields of computer science to represent curved shapes. For a large number of applications of computer aided design, the representation of data with a piecewise parametric curve that lies close to the data is an important consideration. This paper presents a geometric solution to the problem of automatically generating piecewise parametric rational quadratic polynomial approximations to shapes from sampled data. The algorithm takes a set of sample points, automatically generates tangents at some points and derives a piecewise rational quadratic curve that lies close to the data points. Combining this algorithm with the biquadratic search to subdivide the data if it cannot be represented with a single arc, we have a very stable algorithm that gives good results over a range of shapes and applications. |
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