A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
The Mathematica book (4th edition)
The Mathematica book (4th edition)
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
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The reconstruction of curves from their curvature is a problem not very well-solved in cartographic generalization of roads. Frenet's formulas theoretically solve this problem. The result shows that there exists a curve (up to rigid motion) with prefixed curvature function and torsion. By the use of the curvature and torsion functions, in closed forms, it is possible to obtain many beautiful examples in connection with this classical construction. In the case of plane curves, the torsion is equal to zero and the curve is characterized by the curvature. Nevertheless, if our starting point is a discrete set of arc length curvature experimental measures, the application of the Frenet frame is not straightforward. This study aims to describe how to adapt the classical Frenet frame to more realistic contexts derived from practical requirements. Our approach is applied to numerical measures derived from roads defined by Spanish Cartography, more precisely, by the Mapa Topografico Nacional 1:25.000 (MTN25). The method described will be used to obtain generalizations of the original road by performing a standard wavelet decomposition on the curvature before the application of the Frenet frame for plane curves.