Geometric constraint modelling: Boundary planar B-spline curves and control polyhedra for 5-axes response surface graph
This paper introduces a geometric constraint modelling system for 5-axes response surface graph based on free-form boundary planar curves and cross-boundary curves. Both are developed on the basis of nonperiodic B-spline curves. It is evident that ...
An analysis and comparison of parameterization-based computation of differential quantities for discrete surfaces
Normals and curvatures are fundamental for geometric modeling and computer-aided design, but their accurate computations on discrete surfaces are challenging. Two types of methods, namely height-function based and parameterization based polynomial ...
A cyclic basis for closed curve and surface modeling
We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, and that are used by designers in order to control ...
Fast approach for computing roots of polynomials using cubic clipping
This paper presents a new approach, called cubic clipping, for computing all the roots of a given polynomial within an interval. In every iterative computation step, two cubic polynomials are generated to enclose the graph of the polynomial within the ...
Convexity preservation of the interpolating four-point C2 ternary stationary subdivision scheme
Since subdivision schemes can generate curves and surfaces rapidly, they are widely used in the curve and surface modeling. Such topic is one of the important research fields in computer aided geometric design. The convexity preserving properties of the ...
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
We present a novel approach to the problem of multi-degree reduction of Bezier curves with constraints, using the dual constrained Bernstein basis polynomials, associated with the Jacobi scalar product. We give properties of these polynomials, including ...
Quintic space curves with rational rotation-minimizing frames
The existence of polynomial space curves with rational rotation-minimizing frames (RRMF curves) is investigated, using the Hopf map representation for PH space curves in terms of complex polynomials @a(t), @b(t). The known result that all RRMF cubics ...
A torus patch approximation approach for point projection on surfaces
This paper proposes a second order geometric iteration algorithm for point projection and inversion on parametric surfaces. The iteration starts from an initial projection estimation. In each iteration, we construct a second order osculating torus patch ...
Existence conditions for Coons patches interpolating geodesic boundary curves
Given two pairs of regular space curves r"1(u), r"3(u) and r"2(v), r"4(v) that define a curvilinear rectangle, we consider the problem of constructing a C^2 surface patch R(u,v) for which these four boundary curves correspond to geodesics of the ...
