Rational bi-cubic G2 splines for design with basic shapes
نویسندگان
چکیده
The paper develops a rational bi-cubic G2 (curvature continuous) analogue of the non-uniform polynomial C2 cubic B-spline paradigm. These rational splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, in one by default smoothly-connected structure. The versatility of this new tool for processing exact geometry is illustrated by conceptual design from basic shapes.
منابع مشابه
Free-form splines combining NURBS and basic shapes
We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...
متن کاملRational G Splines
We develop a class of rational, G2-connected splines of degree 3 that allow modeling multiple basic shapes, such as segments of conics and circle arcs in particular, in one structure. This can be used, for example, to have portions of a control polygon exactly reproduce segments of the shapes while other portions blend between these primary shapes. We also show how to reparameterize the splines...
متن کاملModeling with rational biquadratic splines
We develop a rational biquadratic G analogue of the non-uniform C B-spline paradigm. These G splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, and combine them into one smoothly-connected structure. This enables a design process that starts with basic shapes, re-pepresents them in spline form and uses the spline form to provide shape handles for locali...
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 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 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:
- Comput. Graph. Forum
دوره 30 شماره
صفحات -
تاریخ انتشار 2011