Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast

Given a Cylindrical Algebraic Decomposition of an implicit algebraic curve, visualizing distinct curve arcs is not as easy as it stands because, despite the absence of singularities in the interior, the arcs can pass arbitrary close to each other. We present an algorithm to visualize distinct connected arcs of an algebraic curve efficiently and precise (at a given resolution), irrespective of how close to each other they actually pass. Our hybrid method inherits the ideas of subdivision and curve-tracking methods. With an adaptive mixed-precision model we can render the majority of algebraic curves using floating-point arithmetic without sacrificing the exactness of the final result. The correctness and applicability of our algorithm is borne out by the success of our webdemo1 presented in [10]. Key words: Algebraic curves, geometric computing, curve rendering, visualization, exact computation

• Type: Conference
• Year: 2009
• Where: ISVC
• Authors: Pavel Emeliyanenko, Eric Berberich, Michael Sagraloff
• Keywords: Algebraic Curves, Applied Computing, Distinct Curve Arcs, Implicit Algebraic Curve, ISVC 2009