A new class of non-stationary interpolatory subdivision schemes based on exponential polynomials

Authors:
Yoo-Joo Choi;Yeon-Ju Lee;Jungho Yoon;Byung-Gook Lee;Young J. Kim
Affiliations:
Dept. of CS., Seoul Univ. of Venture and Info., Seoul, Korea;Dept. of Math., Ewha Womans Univ., Seoul, Korea;Dept. of Math., Ewha Womans Univ., Seoul, Korea;Div. of Internet Engineering, Dongseo Univ., Busan, Korea;Dept. of CS., Ewha Womans Univ., Seoul, Korea
Venue:
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Year:
2006

Citing 9
Cited 2

A butterfly subdivision scheme for surface interpolation with tension control

ACM Transactions on Graphics (TOG)
Piecewise smooth surface reconstruction

SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
The lifting scheme: a construction of second generation wavelets

SIAM Journal on Mathematical Analysis
Multiresolution signal processing for meshes

Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A subdivision algorithm for trigonometric spline curves

Computer Aided Geometric Design
DSP First: A Multimedia Approach

DSP First: A Multimedia Approach
Subdivision Methods for Geometric Design: A Constructive Approach

Subdivision Methods for Geometric Design: A Constructive Approach
A non-stationary subdivision scheme for generalizing trigonometric spline surfaces to arbitrary meshes

Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution

Computer Aided Geometric Design

Bi-3 C2 polar subdivision

ACM SIGGRAPH 2009 papers
Non-stationary subdivision schemes for surface interpolation based on exponential polynomials

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a new class of non-stationary, interpolatory subdivision schemes that can exactly reconstruct parametric surfaces including exponential polynomials. The subdivision rules in our scheme are interpolatory and are obtained using the property of reproducing exponential polynomials which constitute a shift-invariant space. It enables our scheme to exactly reproduce rotational features in surfaces which have trigonometric polynomials in their parametric equations. And the mask of our scheme converges to that of the polynomial-based scheme, so that the analytical smoothness of our scheme can be inferred from the smoothness of the polynomial based scheme.