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Computing Contour Trees for 2D Piecewise Polynomial Functions
Author(s) -
Nucha Girijanandan,
Bonneau GeorgesPierre,
Hahmann Stefanie,
Natarajan Vijay
Publication year - 2017
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13165
Subject(s) - isosurface , parallelizable manifold , monotone polygon , scalar field , mathematics , scalar (mathematics) , algorithm , computer science , polygon (computer graphics) , marching cubes , topology (electrical circuits) , visualization , geometry , artificial intelligence , combinatorics , telecommunications , frame (networking) , mathematical physics
Abstract Contour trees are extensively used in scalar field analysis. The contour tree is a data structure that tracks the evolution of level set topology in a scalar field. Scalar fields are typically available as samples at vertices of a mesh and are linearly interpolated within each cell of the mesh. A more suitable way of representing scalar fields, especially when a smoother function needs to be modeled, is via higher order interpolants. We propose an algorithm to compute the contour tree for such functions. The algorithm computes a local structure by connecting critical points using a numerically stable monotone path tracing procedure. Such structures are computed for each cell and are stitched together to obtain the contour tree of the function. The algorithm is scalable to higher degree interpolants whereas previous methods were restricted to quadratic or linear interpolants. The algorithm is intrinsically parallelizable and has potential applications to isosurface extraction.