A new method using the cubic B-spline curves with nominal uniform knot set to parameterize the geometry is proposed to deal with shape optimization problems. In the method, the control points of the B-spline curves are set to be the design variables in the optimization scheme. A knot insertion algorithm has been introduced in order to keep the geometry unchanged whilst increasing the number of ...

Traditionally, texture coordinates have been generated based solely on the model’s geometry, often even before a model’s textures have been created. With the arrival of new technologies, such as 3D paint programs, weaknesses of a static optimization pre-process are becoming apparent. These weaknesses arise from constructing a parameterization based solely on the model’s geometry, ignoring the f...

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in var...

We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?” We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem re...

In this paper, the feasible study of the optimal control techniques for the cardiac defibrillation on the anatomical three spatial dimensional rabbit ventricle geometry in the presence of bilateral control constraints. The present work addresses the numerical treatment of multiscale and multidomain simulations of bidomain equations, the description of deriving optimality system, the applicabili...

Improving the efficiency of compressors has been one of the most important goals of researchers over the years. In this paper, three different methods are presented for parameterization and blade optimization of axial flow compressor. All methods consist of flow analysis tool, optimization algorithms, and parametric geometry generation tool, that are different in each approach. Objective functi...

In this paper, we present an approach that extends isogeometric shape optimization from optimization of rectangular-like NURBS patches to the optimization of topologically complex geometries. We have successfully applied this approach in designing photonic crystals where complex geometries have been optimized to maximize the band gaps. Salient features of this approach include the following: 1)...

for Picof 2012 "Shape optimization in industry" Ecole Polytechnique, Paris, France, April 2-4, 2012 SHAPE OPTIMIZATION OF AUTOMOTIVE EXHAUST SYSTEMS WITH CONTINUOUS ADJOINT FLOW SOLVERS C. Hinterberger, M. Olesen Faurecia Emissions Control Technologies, Germany GmbH [email protected] [email protected] ABSTRACT Meeting backpressure and flow uniformity requirements within ...

This study focuses on the topology optimization of structures using a hybrid of level set method (LSM) incorporating sensitivity analysis and isogeometric analysis (IGA). First, the topology optimization problem is formulated using the LSM based on the shape gradient. The shape gradient easily handles boundary propagation with topological changes. In the LSM, the topological gradient method as ...