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A simple algorithm for computing positively weighted straight skeletons of monotone polygons.
Therese Biedl1, Martin Held2, Stefan Huber3
1David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 1A2, Canada.
Information Processing Letters
|February 5, 2015
Summary
This study analyzes straight skeletons of monotone polygonal chains to develop an efficient algorithm for computing weighted straight skeletons of monotone polygons. The new method achieves optimal time and space complexity for polygon vertex count.
Area of Science:
- Computational Geometry
- Geometric Algorithms
Background:
- Straight skeletons are fundamental geometric structures with applications in computer graphics and mesh generation.
- Monotone polygons and chains are specific classes of polygons with simplified structures, often used in geometric algorithms.
Purpose of the Study:
- To investigate the properties of straight skeletons specifically for monotone polygonal chains.
- To develop an efficient algorithm for computing positively weighted straight skeletons of monotone polygons.
Main Methods:
- Characterization of straight skeletons for monotone polygonal chains.
- Design and analysis of a novel algorithm based on these characteristics.
Main Results:
- The algorithm computes positively weighted straight skeletons of monotone polygons.
- The algorithm achieves a time complexity of O(n) and a space complexity of O(n), where n is the number of vertices.
Conclusions:
- The study provides an efficient method for computing weighted straight skeletons of monotone polygons.
- The algorithm's linear time and space complexity make it practical for applications involving large datasets.
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