Arm-Root Curve Fitting Based on Body Surface Feature Points for Young Male

This paper is aiming to obtain an arm-root curve function performing the human arm-root size and shape realistically. A gypsum replica of upper arm for young male was made and scanned for extracting the 3D coordinates of 4 feature points of shoulder point, the anterior/posterior armpit point and the axillary point describing the real arm-root shape under the normalized definitions, and the 5 landmarks were confirmed additionally for improving the fitting precision. Then, the wholly and piecewise fitting of arm-root curve with 9 feature points and mark points in total were generated respectively based on least square polynomial fitting method. Comparing to the wholly fitting, the piecewise fitted function segmented by the line between anterior and posterior axillary points showed a high fitting degree of arm-root morphology with R-square of 1, the length difference between fitted curve and gypsum curve is 0.003 cm within error range. And it provided a basic curve model with standard feature points to simulate arm-root morphology realistically by curve fitting for accurate body measurement extraction.

Cubic Algebraic Spline Curves Design

In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves.

PIECEWISE RATIONAL APPROXIMATIONS OF REAL ALGEBRAIC CURVES

We use a combination of both algebraic and numerical techniques to construct a C-1-continuous, piecewise (m, n) rational epsilon-approximation of a real algebraic plane curve of degree d. At singular points we use the classical Weierstrass Preparation Theorem and Newton power series factorizations, based on the technique of Hensel lifting. These, together with modified rational Pade approximations, are used to efficiently construct locally approximate, rational parametric representations for all real branches of an algebraic plane curve. Besides singular points we obtain an adaptive selection of simple points about which the curve approximations yield a small number of pieces yet achieve C-1 continuity between pieces. The simpler cases of C-1 and C-0 continuity are also handled in a similar manner. The computation of singularity, the approximation error bounds and details of the implementation of these algorithms are also provided.

Nother-type theorem of piecewise algebraic curves on triangulation

The piecewise algebraic curve is a kind generalization of the classical algebraic curve. Nther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space.In this paper,using the properties of bivariate splines,the Nther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.

The Cayley-Bacharach Theorem for Continuous Piecewise Algebraic Curves over Cross-cut Triangulations

A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, we propose the Cayley-Bacharach theorem for continuous piecewise algebraic curves over cross-cut triangulations. We show that, if two continuous piecewise algebraic curves of degrees m and n respectively meet at ranT distinct points over a cross-cut triangulation, where T denotes the number of cells of the triangulation, then any continuous piecewise algebraic curve of degree m ＋ n - 2 containing all but one point of them also contains the last point.

The Bezout Number of Piecewise Algebraic Curves

Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves, a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found. Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper.

Some Researches on Real Piecewise Algebraic Curves

The piecewise algebraic curve,defined by a bivariate spline,is a generalization of the classical algebraic curve.In this paper,we present some researches on real piecewise algebraic curves using elementary algebra.A real piecewise algebraic curve is studied according to the fact that a real spline for the curve is indefinite,definite or semidefinite(nondefinite).Moreover, the isolated points of a real piecewise algebraic curve is also discussed.

Upper Bound and Lower Bound Estimate of Monotone Increasing Fractal Function

Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure. In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f（x）（it is a monotone increasing fractal function） and its some applications.