For non-uniform control polygons, a parameterized four-point interpolation curve ternary subdivision scheme is proposed, and its convergence continuity are demonstrated. Following subdivision, surface on regular quadrilateral meshes proposed by applying the tensor product method. Analyses were conducted updating rules of parameters, proving that limit continuous. In this paper, we present novel...

We present two related algorithms for flattening (generating polyline approximations for) curves associated with planar cubic Bézier segments. One flattens the path curve, and the other flattens the left and right offset curves. The algorithm for flattening path curves yields an average of 67% of the vertices generated by recursive subdivision, while maintaining flatness to within 4% of the spe...

Popular subdivision algorithms like Catmull-Clark and Loop are C almost everywhere, but suffer from shape artifacts and reduced smoothness exactly near the so-called “extraordinary vertices” that motivate their use. Subdivision theory explains that inherently, for standard stationary subdivision algorithms, curvature-continuity and the ability to model all quadratic shapes requires a degree of ...

Subdivision is a convenient tool to construct objective curves and surfaces directly from given scattered points. Stationary p-subdivision schemes are highly efficient in the acquisitions of curve/surface points in shape modeling. The features of supported set of nonnegative mask of uniform convergent stationary subdivision schemes are important to their theoretic researches and applications. A...

In this paper we present a method of circular arc approximation by quartic Bézier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvaturecontinuous quartic spline under the su...

Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke. We apply this mas...

A five-point binary subdivision scheme with a parameter u is presented. The generating polynomial method and the Hölder exponent are used to investigate the uniform convergence and C continuity of this subdivision scheme, where k depends on the choice of the parameter u. Moreover, the conditions on the initial points are discussed for the given limit curve to be convexity preserving and an exam...

We introduce a new method to approximate algebraic space curves. The algorithm combines a subdivision technique with local approximation of piecewise regular algebraic curve segments. The local technique computes pairs of polynomials with modified Taylor expansions and generates approximating circular arcs. We analyze the connection between the generated approximating arcs and the osculating ci...

Bézier curve flattening by recursive subdivision requires that the maximum excursion of the subdivided curve segment be known so that recursion can be terminated once this value drops below the specified flatness criterion. A much more accurate method than the most commonly used techniques to evaluate this distance is presented. This method stops recursion sooner, significantly reducing the num...

Wepresent ternary six-point interpolating subdivision schemewith one shape parameter for curve design. The behavior of the limit curve defined by the scheme is analyzed in terms of the Laurent polynomial and attains C degree of smoothness. 2000 Mathematics Subject Classification: 65D17, 65D07, 65D05 DOI: 10.1134/S1995080208030062