geissdoerfer / polyprox

Polygonal curve approximation for python

Polygonal Curve approximation

Fast implementation of solutions to the min-num and min-e problems of digital curve approximation.

Both approximate a planar curve given as a series of points by a subset of these points with the minimum maximum euclidean distance between the original curve and the linearly interpolated approximation. This distance is calculated according to the tolerance zone criterion, described in Alexander Kolesnikov's thesis

Both algorithms use the Ramer-Douglas-Peucker (RDP) algorithm as a subroutine. This algorithm is fast and usually ends up with good approximations, but does not guarantee optimality of the solution.

The min-e problem takes the length of the subset, i.e. the number of approximating points and calculates the solution with the minimum maximum error. Note that, due to the nature of the algorithm, the resulting subset length can differ slightly from the required number of points. The min-num problem takes an upper error bound and approximates the curve with the minimum length subset meeting this error criterion.

The algorithms are implemented in C and accessible by a pythonic interface. The min-num implementation offers similar functionality as the RDP implementations by sebleier and fhirschmann, but can be orders of magnitudes faster and more suitable for large curves. The present implementation uses a different error measure than these implementations (tolerance zone vs infinite beam).

Installation

pip install polyprox

Usage

import numpy
import polyprox

G = numpy.array([[0, 0], [0.9, 0], [1.1, 1.3], [2.5, 1.0], [2.2, 2.4]])
polyprox.min_e(G, m=2)
polyprox.min_num(G, epsilon=0.75)

Credits

Kun Zhao: initial python implementation

License

CSIRO Open Source Software License Agreement (variation of the BSD/MIT License)

References

H. Imai and M. Iri. 1988. "Polygonal approximations of a curve - formulations and algorithms." In: Computational Morphology: A Computational Geometric Approach to the Analysis of Form: 71–86.

W. S. Chan and F. Chin. 1996. "Approximation of polygonal curves with minimum number of line segments or minimum error." In: International Journal of Computational Geometry & Applications, 6 (01): 59–77

Douglas, David H, and Thomas K Peucker. 1973. “Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or Its Caricature.” In: Cartographica: The International Journal for Geographic Information and Geovisualization 10 (2): 112–122.