Visualisation of Implicit Algebraic Curves

We describe a new algorithm for the visualisation of implicit algebraic curves, which isolates the singular points, compute the topological degree around these points in order to check that the topology of the curve can be deduced from the points on the boundary of these singular regions. The other regions are divided into x or y regular regions, in which the branches of the curve are also determined from information on the boundary. Combined with enveloping techniques of the polynomial represented in the Bernstein basis, it is shown on examples that this algorithm is able to render curves defined by high degree polynomials with large coefficients, to identify regions of interest and to zoom safely on these regions. The problem of analysing and visualisation of implicit curve appears in many applications of Geometric Modeling. Fundamental operations, such as computing the intersection curve of two parametric surfaces lead to the analysis of implicit curves in the parameter domain. In...

• Type: Conference
• Year: 2007
• Where: PG
• Authors: Lionel Alberti, Bernard Mourrain
• Keywords: Computer Graphics, Curve, Implicit Algebraic Curves, Implicit Curves, PG 2007