Concept

Bézier surface

Related publications (28)

Synthesis and Analysis of 3D shapes with Geometric Deep Learning in Computer-Aided Engineering

In this thesis, we advocate that Computer-Aided Engineering could benefit from a Geometric Deep Learning revolution, similarly to the way that Deep Learning revolutionized Computer Vision. To do so, we consider a variety of Computer-Aided Engineering pro ...

EPFL2022

Overlapping Multipatch Isogeometric Method With Minimal Stabilization

Annalisa Buffa, Pablo Antolin Sanchez, Xiaodong Wei, Riccardo Puppi

We present a novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference (i.e., trimming), union, and intersection. Particularly, this work focuses on the union operation, which involve ...

SIAM PUBLICATIONS2021

Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries

Rafael Vazquez Hernandez

Adaptive isogeometric methods for the solution of partial diifferential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical spline ...

2020

A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries

Annalisa Buffa, Rafael Vazquez Hernandez, Riccardo Puppi

Trimming is a common operation in computer aided design and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming, the geometric description of the patch remains ...

2020

MATHICSE Technical Report : Isogeometric analysis with $C^1$ hierarchical functions on planar two-patch geometries

Rafael Vazquez Hernandez

MATHICSE2019

MATHICSE Technical Report : A minimal stabilization procedure for isogeometric methods on trimmed geometries

Annalisa Buffa, Rafael Vazquez Hernandez, Riccardo Puppi

Trimming is a common operation in CAD, and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming the geometric description of the patch remains unchanged, but the ...

MATHICSE2019

Landmark-Based Shape Encoding and Sparse-Dictionary Learning in the Continuous Domain

Michaël Unser, Daniel Andreas Schmitter

We provide a generic framework to learn shape dictionaries of landmark-based curves that are defined in the continuous domain. We first present an unbiased alignment method that involves the construction of a mean shape as well as training sets whose eleme ...

2018

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Michaël Unser, Julien René Pierre Fageot, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that interpolate the shape ...

2017

Toward design optimization of a Pelton turbine runner

François Avellan, Loïc Andolfatto, Christian Vessaz, Christophe Tournier

The objective of the present paper is to propose a strategy to optimize the performance of a Pelton runner based on a parametric model of the bucket geometry, massive particle based numerical simulations and advanced optimization strategies to reduce the d ...

Springer Verlag2017

Motion Planning for Urban Autonomous Driving using Bezier Curves and MPC

Inaki Navarro Oiza, Arnaud de La Fortelle

This paper presents a real-time motion planning scheme for urban autonomous driving that will be deployed as a basis for cooperative maneuvers defined in the European project AutoNet2030. We use a path-velocity decomposition approach to separate the motion ...

Ieee2016

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