Abstract
A class of planar rational polynomial curves is discussed for which it is possible, under certain conditions, to convert between the parametric and implicit equations with no computation. It is shown that rational cubic curves belong to this class. This insight leads to an efficient method for computing the implicit equation of a parametric cubic curve. Also, the inversion equation (which computes the parameter of a point on the curve given the coordinates) is found to be the ratio of two linear expressions in x and y. The implicit representation of rational cubic curves described in this paper is shown to lend itself to geometric transformations such as rotation, translation, and scaling. Application of these techniques to computing the intersection of two rational cubic curves is also discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
