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Related Experiment Video

Updated: May 23, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

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Restricted trivariate polycube splines for volumetric data modeling.

Kexiang Wang¹, Xin Li, Bo Li

¹Department of Computer Science, Stony Brook University, Stony Brook, NY 11790-4400, USA. kwang@cs.sunysb.edu

IEEE Transactions on Visualization and Computer Graphics

|March 24, 2012

Summary

This study introduces restricted trivariate polycube splines (RTP-splines), a novel volumetric modeling method. RTP-splines efficiently represent complex solid objects with improved computational performance for scientific applications.

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Area of Science:

Computer-Aided Design (CAD)
Geometric Modeling
Scientific Computing

Background:

Existing spline schemes like trivariate T-splines and tensor-product B-splines have limitations in modeling complex solid objects.
There is a need for a unified spline representation that can handle intricate topologies and ensure efficient computations.

Purpose of the Study:

To introduce a novel volumetric modeling framework using restricted trivariate polycube splines (RTP-splines).
To generalize existing spline methods by utilizing a solid polycube structure for underlying parametric domains.
To demonstrate the advantages of RTP-splines for modeling complex geometries and for applications like isogeometric analysis.

Main Methods:

A top-down construction process involving four key steps: domain extension, B-spline volume construction with restricted boundaries, knot insertion via anchor points for local refinement, and removal of exterior cells.
Utilizing a solid polycube structure as the basis for parametric domains.
Implementing restricted support regions for blending functions.

Main Results:

RTP-splines naturally model solid objects with complex topologies and bifurcations using a single, continuous representation, eliminating the need for domain trimming or patching.
Guaranteed semistandardness ensures efficient evaluation of functions and derivatives.
Restricted support regions prevent unintended influence of control points on distant domain areas, beneficial for applications like isogeometric analysis.

Conclusions:

RTP-splines offer a powerful and promising tool for volumetric modeling of complex solid objects.
The proposed spline scheme demonstrates significant advantages for scientific and engineering applications involving multi-attribute datasets.
Extensive experiments confirm the efficacy of converting complicated solid models into the RTP-spline representation.