Minimizing the maximal ratio of weights of rational Bézier curves and surfaces
نویسندگان
چکیده
Article history: Received 21 May 2009 Received in revised form 25 June 2010 Accepted 22 August 2010 Available online 16 September 2010
منابع مشابه
Minimizing the maximal ratio of weights of a rational Bézier curve
This paper presents a solution to the problem of reparameterizing a rational curve by a Möbius transformation such that the maximal ratio of weights in the reparameterized representation is minimized. The problem is reduced to solving a linear programming problem, which can be solved directly and simply. The result can be used to reparameterize rational curves so as to yield tight bounds on der...
متن کاملAn Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves
In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...
متن کاملA New Approach to Design Rational Harmonic Surface over Rectangular or Triangular Domain ⋆
By the degree elevation-based method of approximating rational curves and surfaces using polynomial curves and surfaces, a new effective approach to construct rational Bézier harmonic surfaces over rectangular or triangular domain is presented. First, rational Bézier curves, given as the boundaries, are transferred into some approximate polynomial curves, according to which a polynomial harmoni...
متن کاملMatrix weighted rational curves and surfaces
Rational curves and surfaces are powerful tools for shape representation and geometric modeling. However, the real weights are generally difficult to choose except for a few special cases such as representing conics. This paper presents an extension of rational curves and surfaces by replacing the real weights with matrices. The matrix weighted rational curves and surfaces have the same structu...
متن کاملRational Bézier Formulas with Quaternion and Clifford Algebra Weights
We consider Bézier-like formulas with weights in quaternion and geometric (Clifford) algebra for parametrizing rational curves and surfaces. The simplest non-trivial quaternionic case of bilinear formulas for surface patches is studied in detail. Such formulas reproduce well known biquadratic parametrizations of principal Dupin cyclide patches, and are characterized in general as special Darbou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computer Aided Geometric Design
دوره 27 شماره
صفحات -
تاریخ انتشار 2010