A UNIFIED APPROACH TO GEOMETRIC MODELING OF CURVES AND SURFACES

L. H. You, Jian J. Zhang

2011

Abstract

A unified approach to geometric modeling of curves and surfaces is given. Both a vector-valued fourth and sixth order partial differential equations (PDEs) of motion are proposed. The fourth order PDE covers all existing PDEs used for surface modeling, and the sixth order PDE considers the curvature effect on curves and surfaces. In order to apply these PDEs to create curves and surfaces in real time, we have presented a composite power series method which guarantees the exact satisfaction of boundary conditions, and represents curves and surfaces with analytical mathematical formulae. We have examined the accuracy and efficiency of the proposed method, and employed it to a number of applications of static and dynamic modeling of curves and surfaces, including free-form surface generation and surface blending. It is found that this method has similar computational accuracy and efficiency to the corresponding closed form solution method, and creates curves and surfaces far more efficiently and accurately than numerical methods. In addition, it can deal with complicated shape modeling problems..

Paper Citation

in Harvard Style

You L. and Zhang J. (2011). A UNIFIED APPROACH TO GEOMETRIC MODELING OF CURVES AND SURFACES . In Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2011) ISBN 978-989-8425-45-4, pages 23-30. DOI: 10.5220/0003316300230030

in Bibtex Style

@conference{grapp11,
author={L. H. You and Jian J. Zhang},
title={A UNIFIED APPROACH TO GEOMETRIC MODELING OF CURVES AND SURFACES},
booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2011)},
year={2011},
pages={23-30},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003316300230030},
isbn={978-989-8425-45-4},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2011)
TI - A UNIFIED APPROACH TO GEOMETRIC MODELING OF CURVES AND SURFACES
SN - 978-989-8425-45-4
AU - You L.
AU - Zhang J.
PY - 2011
SP - 23
EP - 30
DO - 10.5220/0003316300230030