Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space
| Autor: | Bernard Mourrain, Yi-King Choi, Changhe Tu, Xiaohong Jia, Wenping Wang |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Algebraic properties
Discrete mathematics Algebra and Number Theory Intersection curve Mathematical analysis 020207 software engineering 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Computational Mathematics Quadratic equation 0202 electrical engineering electronic engineering information engineering Partition (number theory) Projective space 0101 mathematics Invariant (mathematics) Symbolic algorithm Mathematics |
| Zdroj: | Journal of Symbolic Computation. 73:221-243 |
| ISSN: | 0747-7171 |
| Popis: | We propose a symbolic algorithm for detecting the variations in the topological and algebraic properties of the intersection curve of two quadratic surfaces (QSIC) that are moving or deforming in PR 3 (real projective 3-space). The core of our algorithm computes all the critical instants when the QSIC changes type using resultants and Jordan forms. These critical instants partition the time axis into intervals within which the QSIC is invariant. The QSIC at the computed critical instants and within the time intervals can both be exactly determined using symbolic technique. Examples are provided to illustrate our algorithm. |
| Databáze: | OpenAIRE |
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