Symbolic manipulation in geometric modeling
BASTL, B. Symbolic manipulation in geometric modeling. ZČU, FAV, KMA, Plzeň : 2004, 120 s.
|Anglický název:||Symbolic manipulation in geometric modeling|
|Místo konání:||ZČU, FAV, KMA, Plzeň|
|Abstrakt EN:||The thesis is devoted to applications of variable elimination methods in geometric modeling and focuses on two issues - self-intersection of curves and surfaces and implicitization of NURBS curves and surfaces. Research into surface self-intersection is motivated by the need to solve problems caused by it, especially in mechanical engineering. The thesis presents a symbolic-numeric algorithm for finding a self-intersection of an surface with rational parametrization. The need to have implicit and parametric representation of algebraic variety depends on operations one wants to perform with the variety. Several implicitization methods are reviewed and compared with respect to computation times. The thesis presents a method which provides an interval on some coordinate axis or a domain in some coordinate plane to determine the part of the implicit representation corresponding to the original curve or surface given by parametrization.|