A Resultant Approach to Detect Intersecting Curves In
نویسندگان
چکیده
Given two curves in P 3 , either implicitly or by a param-eterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which vanishes if and only if the two curves intersect. This could be useful in Computer Aided Design, for computing the intersection of algebraic surfaces.
منابع مشابه
A Resultant Approach to Detect Intersecting Curves in P
Given two curves in P 3 , either implicitly or by a param-eterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which vanishes if and only if the two curves intersect. This could be useful in Computer Aided Design, for computing the intersection of algebraic surfaces.
متن کاملTo Appear in ACM Transactions on Graphics Algorithms for Intersecting Parametric and Algebraic Curves I: Simple Intersections
The problem of computing the intersection of parametric and algebraic curves arises in many applications of computer graphics and geometric and solid modeling. Previous algorithms are based on techniques from elimination theory or subdivision and iteration. The former is however, restricted to low degree curves. This is mainly due to issues of e ciency and numerical stability. In this paper we ...
متن کاملAlgorithms for Intersecting Parametric and Algebraic Curves
The problem of computing the intersection of parametric and algebraic curves arises in many applications of computer graphics, geometric and solid modeling. Earlier algorithms are based on techniques from Elimination theory or subdivision and iteration. The former is however, restricted to low degree curves. This is mainly due to issues of efficiency and numerical stability. In this paper we us...
متن کاملAlgorithms for Intersecting Parametric and Algebraic Curves II: Multiple Intersections
The problem of computing the intersection of parametric and algebraic curves arises in many applications of computer graphics, geometric and solid modeling. Previous algorithms are based on techniques from elimination theory or subdivision and iteration and are typically limited to simple intersections of curves. Furthermore, algorithms based on elimination theory are restricted to low degree c...
متن کاملExact Delaunay graph of smooth convex pseudo-circles
We examine the problem of computing exactly the Delaunay graph of a set of possibly intersecting smooth convex pseudo-circles in the Euclidean plane given in parametric form. The diagram is constructed incrementally. We focus on InCircle, under the exact computation paradigm, and express it by a simple polynomial system, which allows for an efficient implementation by means of iterated resultan...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003