Investigation of Practical Representation and Parameterization of the Rational Cubic Conic Sections
نویسندگان
چکیده
This paper presents a practical representation containing a parameter of rational cubic conic sections and research’s deeply the inner properties. Firstly, the parameter how to affect the control points, inner weights and shoulder point is discussed. Secondly, the inner relation between the parameter and the weights of the nonstandard-form quadratic rational conic sections is analyzed in detail. Change in the parameter value actually corresponds to a rational linear parameter transformation. Finally, we discuss the inverse calculation of the cubic rational conic sections and obtain the inverse calculation methods suitable for engineering applications.
منابع مشابه
Necessary and sufficient conditions for rational quartic representation of conic sections
Conic section is one of the geometric elements most commonly used for shape expression and mechanical accessory cartography. A rational quadratic Bézier curve is just a conic section. It cannot represent an elliptic segment whose center angle is not less than . However, conics represented in rational quartic format when compared to rational quadratic format, enjoy better properties such as bein...
متن کاملRational Cubic Implicitization
An explicit expression for the unique implicitization of any planar rational cubic Bézier curve is presented, the only exception being when the tangents at the ends of the curve are parallel. The representation is in the form of a cubic Bernstein-Bézier triangle and is invariant under affine transformations of the curve. The implicitization degenerates to zero if and only if the curve degenerat...
متن کاملA Generalization of Rational Bernstein Bézier Curves
This paper is concerned with a generalization of BernsteinBézier curves. A one parameter family of rational BernsteinBézier curves is introduced based on a de Casteljau type algorithm. A subdivision procedure is discussed , and matrix representation and degree elevation formulas are obtained. We also represent conic sections using rational q-BernsteinBézier curves.
متن کاملConvex Surface Visualization Using Rational Bi- cubic Function
The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...
متن کاملWEAK AND STRONG DUALITY THEOREMS FOR FUZZY CONIC OPTIMIZATION PROBLEMS
The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...
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 2013