Construction of G3 Conic Spline Interpolation
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Date
2014
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
In this paper, a new method to interpolate a sequence of ordered points with conic splines is presented. The degree
of continuity at joints of the resulting splines can reach G3 while the number of curvature extrema is reduced
to a minimum. The construction process is not based on parametrization, but basic geometric elements. A new
geometric concept called Chord-Tangent Ratio which is vital to determine the shape of conic splines is proposed.
The main idea of the construction is to merge the constraints of continuity into a function of tangent arguments and
Chord-Tangent Ratios, and construct an optimization function to eliminate the curvature extrema, then through
an iterative process, for the constraint function to reach its zero point and for the optimization function to reach
its minimum. Experiments show that splines constructed by the new method performs well not only in terms of
continuity, but also in smoothness.
Description
@inproceedings{:10.2312/sgp20141383,
booktitle = {Symposium on Geometry Processing 2014 - Posters},
editor = {Thomas Funkhouser and Shi-Min Hu},
title = {{Construction of G3 Conic Spline Interpolation}},
author = {Long Ma and Caiming Zhang},
year = {2014},
publisher = {The Eurographics Association},
ISSN = {-},
ISBN = {-},
DOI = {/10.2312/sgp20141383}
}