Back to Search
Start Over
Computing the μ-bases of algebraic monoid curves and surfaces
- Source :
- Computers & Graphics. 97:78-87
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- The μ-basis is a developing algebraic tool to study the expressions of rational curves and surfaces. It can play a bridge role between the parametric forms and implicit forms and show some advantages in implicitization, inversion formulas and singularity computation. However, it is difficult and there are few works to compute the μ-basis from an implicit form. In this paper, we derive the explicit forms of μ-basis for implicit monoid curves and surfaces, including the conics and quadrics which are particular cases of these entities. Additionally, we also provide the explicit form of μ-basis for monoid curves and surfaces defined by any rational parametrization (not necessarily in standard proper form). Our technique is simply based on the linear coordinate transformation and standard forms of these curves and surfaces. As a practical application in numerical situation, if an exact multiple point can not be computed, we can consider the problem of computing “approximate μ-basis” as well as the error estimation.<br />Agencia Estatal de Investigación
- Subjects :
- Monoid
Conic
Pure mathematics
Quadric
Basis (linear algebra)
Matemáticas
Coordinate system
General Engineering
020207 software engineering
Rational parametrization
02 engineering and technology
Monoid curves and surfaces
Computer Graphics and Computer-Aided Design
μ-basis
Human-Computer Interaction
Singularity
Multiple point
Conic section
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
Algebraic number
Parametrization
Mathematics
Subjects
Details
- ISSN :
- 00978493
- Volume :
- 97
- Database :
- OpenAIRE
- Journal :
- Computers & Graphics
- Accession number :
- edsair.doi.dedup.....1b24e1e44ae6c2ad8d34f19720efa89f