Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the to...

We present efficient algorithms to construct both C1 and C 2 smooth meshes of cubic and quintic A-patches to approximate a given polyhedron P in three dimensions. The A~patch is a smooth and single-sheeted zero-contour patch of a trivariate polynomial in Bernstein-Bezier (BB) form defined within a tetrahedron. The smooth mesh constructions rely on a novel scheme to build an inner simplicial hul...

We present a sufficient criterion for the Bernstein-Bezier (BB) form of a trivariate polynomial within a tetrahedron, such that the real zero contour of the polynomial defines a smooth and single sheeted algebraic surface patch. We call this an A-patch. We present algorithms to build a mesh of cubic A-patches to interpolate a given set of scattered point data in three dimensions, respecting the...

Toric surface patches have two significant geometric properties: they are multi-sided and they are generalizations of both the triangular and rectangular Bezier surface patches. They also have a very nice algebraic property: their implicit equations are closely related to the Dixon determinant. In particular, for bi-cubic toric patches without base points, their implicit equation can always be ...

In this paper, several principles of popular routing algorithms and models of Auto-Guided-Vehicles are presented. Tests were conducted and it was found that the Bezier Curve solution is the most unsteady algorithm because it is highly relative to the complexity of maps, particle density, curve dimension, numbers of AGVs, etc. Fuzzy logic is one of the easiest algorithms in programming, but the ...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...

This paper presents a scale method for developing high dimensional scale functions to blend implicitly defined objects. Scale functions are differentiable on the entire domain except the origin, provide blending range control, and behave like Min/Max operators everywhere, so even a successive composition of blending operations containing overlapped blending regions can be generated smoothly. Be...

In this paper we approximate a cylindrical helix by biconic and bi-quadratic Bezier curves. Each approximation method is G end-points interpolation of the helix. We present a sharp upper bound of the Hausdorff distance between the helix and each approximation curve. We also show that the error bound has the approximation order three and monotone increases as the length of the helix increases. A...

We give a piecewise cubic curve fitting algorithm which preserves monotonicity of the data. The algorithm has a higher order of convergence than the Fritsch-Carlson algorithm and is simpler than the Eisenstat-Jackson-Lewis algorithm.