Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space
نویسندگان
چکیده
We propose a symbolic algorithm for detecting the variations in the topological and algebraic properties of the intersection curve of two moving quadrics in PR(real projective 3-space). The core of our algorithm computes all the instants when the intersection curve of two moving quadrics changes type using resultants and Jordan forms. These instants partition the time axis into intervals within which the type of the intersection curve of the two moving quadrics can be determined by the method proposed in [Tu et al. (2009)]. Examples are provided to illustrate our algorithm.
منابع مشابه
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
Computing the intersection curve of two quadric surfaces is an important problem in geometric computation, ranging from shape modeling in computer graphics and CAD/CAM, collision detection in robotics and computational physics, to arrangement computation in computational geometry. We present the solution to the fundamental problem of complete classification of morphologies of the intersection c...
متن کاملClassifying the Nonsingular Intersection Curve of Two Quadric Surfaces
We present new results on classifying the morphology of the nonsingular intersection curve of two quadrics by studying the roots of the characteristic equation, or the discriminant, of the pencil spanned by the two quadrics. The morphology of a nonsingular algebraic curve means the structural (or topological) information about the curve, such as the number of disjoint connected components of th...
متن کاملA characterization of quadrics by intersection numbers
This work is inspired by a paper of Hertel and Pott on maximum non-linear functions [8]. Geometrically, these functions correspond with quasi-quadrics; objects introduced in [5]. Hertel and Pott obtain a characterization of some binary quasi-quadrics in a ne spaces by their intersection numbers with hyperplanes and spaces of codimension 2. We obtain a similar characterization for quadrics in pr...
متن کاملParameterizing Intersections of Time-Varying Quadrics
This report addresses the problem of computing the parametrization of the intersection of deformable quadratic algebraic surfaces (quadrics) in projective space. It also presents an automatic method for describing the evolution in time of the topology of the intersection. The work is based on the results from [3, 4], which offer an exact parametrization of the intersection of two quadrics with ...
متن کاملNear-optimal parameterization of the intersection of quadrics: I. The generic algorithm
We present the first exact and efficient algorithm for computing a proper parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational coefficients. The output functions parameterizing the intersection in projective space are polynomial, whenever it is possible, which is the case when the intersection is not a smooth qua...
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:
- J. Symb. Comput.
دوره 73 شماره
صفحات -
تاریخ انتشار 2016