Shape Reconstruction from Point Clouds Using Closed Form Solution of a Fourth-Order Partial Differential Equation

Authors: Zhu, Z., Chaudhry, E., Wang, S., Xia, Y., Iglesias, A., You, L. and Zhang, J.J.

Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volume: 12746 LNCS

Pages: 207-220

eISSN: 1611-3349

ISBN: 9783030779764

ISSN: 0302-9743

DOI: 10.1007/978-3-030-77977-1_16

Abstract:

Partial differential equation (PDE) based geometric modelling has a number of advantages such as fewer design variables, avoidance of stitching adjacent patches together to achieve required continuities, and physics-based nature. Although a lot of papers have investigated PDE-based shape creation, shape manipulation, surface blending and volume blending as well as surface reconstruction using implicit PDE surfaces, there is little work of investigating PDE-based shape reconstruction using explicit PDE surfaces, specially satisfying the constraints on four boundaries of a PDE surface patch. In this paper, we propose a new method of using an accurate closed form solution to a fourth-order partial differential equation to reconstruct 3D surfaces from point clouds. It includes selecting a fourth-order partial differential equation, obtaining the closed form solutions of the equation, investigating the errors of using one of the obtained closed form solutions to reconstruct PDE surfaces from differential number of 3D points.

http://eprints.bournemouth.ac.uk/35893/

Source: Scopus

Shape Reconstruction from Point Clouds Using Closed Form Solution of a Fourth-Order Partial Differential Equation

Authors: Zhu, Z., Chaudhry, E., Wang, S., Xia, Y., Iglesias, A., You, L. and Zhang, J.J.

Conference: ICCS 2021: International Conference on Computational Science

Pages: 207-220

ISBN: 9783030779764

ISSN: 0302-9743

Abstract:

Partial differential equation (PDE) based geometric modelling has a number of advantages such as fewer design variables, avoidance of stitching adjacent patches together to achieve required continuities, and physics-based nature. Although a lot of papers have investigated PDE-based shape creation, shape manipulation, surface blending and volume blending as well as surface reconstruction using implicit PDE surfaces, there is little work of investigating PDE-based shape reconstruction using explicit PDE surfaces, specially satisfying the constraints on four boundaries of a PDE surface patch. In this paper, we propose a new method of using an accurate closed form solution to a fourth-order partial differential equation to reconstruct 3D surfaces from point clouds. It includes selecting a fourth-order partial differential equation, obtaining the closed form solutions of the equation, investigating the errors of using one of the obtained closed form solutions to reconstruct PDE surfaces from differential number of 3D points.

http://eprints.bournemouth.ac.uk/35893/

Source: BURO EPrints