NURBS solid modeling for the three-dimensional limit analysis of curved rigid block structures

N Grillanda, A Chiozzi, G Milani, A Tralli - Computer Methods in Applied …, 2022‏ - Elsevier
In this paper, we present a novel computational approach for the generalized three-
dimensional upper bound limit analysis of curved rigid block structures. This approach …

Singularity computation for rational parametric surfaces using moving planes

X Jia, F Chen, S Yao - ACM Transactions on Graphics (TOG), 2022‏ - dl.acm.org
Singularity computation is a fundamental problem in Computer Graphics and Computer
Aided Geometric Design, since it is closely related to topology determination, intersection …

[HTML][HTML] Survey on the theory and applications of μ-bases for rational curves and surfaces

X Jia, X Shi, F Chen - Journal of Computational and Applied Mathematics, 2018‏ - Elsevier
Abstract μ-Bases are new representations for rational curves and surfaces which serve as a
bridge between their parametric forms and implicit forms. Geometrically, μ-bases are …

μ-bases and singularities of rational planar curves

X Jia, R Goldman - Computer Aided Geometric Design, 2009‏ - Elsevier
We provide a technique to detect the singularities of rational planar curves and to compute
the correct order of each singularity including the infinitely near singularities without …

Role of moving planes and moving spheres following Dupin cyclides

X Jia - Computer Aided Geometric Design, 2014‏ - Elsevier
We provide explicit representations of three moving planes that form a μ-basis for a standard
Dupin cyclide. We also show how to compute μ-bases for Dupin cyclides in general position …

Computing the singularities of rational surfaces

S Pérez-Díaz, J Sendra, C Villarino - Mathematics of Computation, 2015‏ - ams.org
Given a rational projective parametrization $\mathcal {P}(\mathfrak {s},\mathfrak {t},\mathfrak
{v}) $ of a rational projective surface $\mathcal {S} $ we present an algorithm such that, with …

Computing μ-bases from algebraic ruled surfaces

LY Shen - Computer Aided Geometric Design, 2016‏ - Elsevier
We find a μ-basis for a rational ruled surface, starting from its implicit representation. A
parametrization for this ruled surface is then deduced form this μ-basis. This parametrization …

Implicitization, parameterization and singularity computation of Steiner surfaces using moving surfaces

X Wang, F Chen - Journal of Symbolic Computation, 2012‏ - Elsevier
A Steiner surface is a quadratically parameterizable surface without base points. To make
Steiner surfaces more applicable in Computer Aided Geometric Design and Geometric …

Computing μ-Bases of Univariate Polynomial Matrices Using Polynomial Matrix Factorization

B Huang, F Chen - Journal of Systems Science and Complexity, 2021‏ - Springer
This paper extends the notion of μ-bases to arbitrary univariate polynomial matrices and
present an efficient algorithm to compute a μ-basis for a univariate polynomial matrix based …

B-Lift curves and its ruled surfaces

A Altınkaya, M Çalışkan - … Faculty of Sciences University of Ankara …, 2023‏ - dergipark.org.tr
In this paper, we have described the B-Lift curve in Euclidean space as a curve obtained by
combining the endpoints of the binormal vector of a unit speed curve. Subsequently, we …