Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products

03/21/2019
by   Fady Massarwi, et al.
0

3D objects, modeled using Computer Aided Geometric Design tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physical analysis, in isogeometric analysis (IGA) in specific, necessitates a volumetric parametrization of the interior of the object. IGA is performed directly by integrating over the spline spaces of the volumetric spline representation of the object. Typically, tensor-product B-spline trivariates are used to parameterize the volumetric domain. A general 3D object, that can be modeled in contemporary B-rep CAD tools, is typically represented using trimmed B-spline surfaces. In order to capture the generality of the contemporary B-rep modeling space, while supporting IGA needs, Massarwi and Elber (2016) proposed the use of trimmed trivariates volumetric elements. However, the use of trimmed geometry makes the integration process more difficult since integration over trimmed B-spline basis functions is a highly challenging task. In this work, we propose an algorithm that precisely decomposes a trimmed B-spline trivariate into a set of (singular only on the boundary) tensor-product B-spline trivariates, that can be utilized to simplify the integration process in IGA. The trimmed B-spline trivariate is first subdivided into a set of trimmed Bézier trivariates, at all its internal knots. Then, each trimmed Bézier trivariate, is decomposed into a set of mutually exclusive tensor-product B-spline trivariates, that precisely cover the entire trimmed domain. This process, denoted untrimming, can be performed in either the Euclidean space or the parametric space of the trivariate. We present examples on complex trimmed trivariates' based geometry, and we demonstrate the effectiveness of the method by applying IGA over the (untrimmed) results.

READ FULL TEXT

page 3

page 7

page 9

page 12

page 13

page 14

page 16

research
08/05/2013

A Spline-based Volumetric Data Modeling Framework and Its Applications

In this dissertation, we concentrate on the challenging research issue o...
research
06/19/2021

Isogeometric de Rham complex discretization in solid toroidal domains

In this work we define a spline complex preserving the cohomological str...
research
03/17/2017

Volumetric parametrization from a level set boundary representation with PHT Splines

A challenge in isogeometric analysis is constructing analysis-suitable v...
research
06/09/2016

Isogeometric computation reuse method for complex objects with topology-consistent volumetric parameterization

Volumetric spline parameterization and computational efficiency are two ...
research
12/10/2021

The 3D Motorcycle Complex for Structured Volume Decomposition

The so-called motorcycle graph has been employed in recent years for var...
research
09/28/2018

From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry

During the last ten years, increasing efforts were made to improve and s...
research
02/01/2021

PAVEL: Decorative Patterns with Packed Volumetric Elements

Many real-world hand-crafted objects are decorated with elements that ar...

Please sign up or login with your details

Forgot password? Click here to reset