Purdue University Purdue e-Pubs Department of Computer Science Technical Reports Department of Computer Science 1990 Conversion Methods Between Parametric and Implicit Curves and Surfaces Christoph M. Hoffmann Purdue University,
[email protected] Report Number: 90-975 Hoffmann, Christoph M., "Conversion Methods Between Parametric and Implicit Curves and Surfaces" (1990). Department of Computer Science Technical Reports. Paper 828. https://docs.lib.purdue.edu/cstech/828 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact
[email protected] for additional information. CONVERSION METHODS BETWEEN PARAME1RIC AND IMPLICIT CURVES AND SURFACES ChriSloph M. Hoffmann CSD-1R-975 April 1990 COllyersioll lI.Iethods Between Parametric and Implicit. Curves and Surfaces' Christoph i\1. Hoffmannt ('l)mpmN SriPIICP Department PnrdulO' Flliver~ity West Lafa,vetlf'. Ind. ·17907 Abstract W.. prr.seHL methods for parameterizin!!; implicit curves and surfaces and for implicit. izing parametric curves and surfaces. hased Oil computational techniques from algebraic gl?onwf.ry, Aft.er reviewing the basic mat.lu·matical facts of relevance. WP, describe and i!lustral,e state-of-the-art algorithms and illsights for the conversion problem. lI'eywords: Parametric and inlplicit curves and surfaces. parameterization. implicitizatioll, elimi nation, birational maps, projection. Algebraic geomet.ry. symbolic computation, Grabller bases. 11101l0i05. resultallts. ":"ioles {or the course UlIiflJillg P(ll"IJmell'lc (11111 {m/lhcil. Sllr/ace Repr·cJenlatlOm. a.l SIGGRAPH '90. ISupported in part by NSF Granl CCR 86-1981, O1.lld ONR Contract N00014-90-J-1599. 1 Introduction These 110f,Pi'i contain the slides of t.he course (:"llif.'li1l9 Pnmmf'lric and [ml,li('it Sllrface Re}Jre .~, H/n/.j()II.~ /01' CmlllHJ1.er Gmphics.