Construction of smooth closed surfaces by ball functions on a cube

In Computer Aided Geometric Design (CAGD), surface constructions are basically formed from collections of surface patches, by placing a certain continuity condition between adjacent patches. Even though tensor product BŽzier patches are currently used extensively in most CAGD systems to model free-form surfaces, this method can only be used to generate closed surface of genus one, i.e. a surface which is equivalent to a torus. A surface with tangent plane continuity is known as a first order geometrically smooth surface or a G1 surface. This paper presents a simple G1 surface construction method, i.e. a surface of genus zero, by defining Ball bicubic functions on faces of a cube. The constructed basis functions have small support and sum to one. The functions are useful for designing, approximating and interpolating a simple closed surface of genus zero. This construction method was first introduced by Goodman in 1991 who defined biquadratic generalised B-spline functions on faces of a simple quadrilateral mesh. Several examples of surfaces/objects which are constructed by the proposed method are presented in this paper

Keindahan matematik Dalam Penyelesaian Faraid.

Kertas kerja ini akan membincangkan kaedah matematik moden dalam penyelesaian faraid khususnya keindahan matematik dalam masalah aul

Performance of the triangulation-based methods Of positivity-preserving scattered data interpolation

We present the result and accuracy comparison of generalized positivity-preserving schemes for triangular Bézier patches of 1C and 2C scattered data interpolants that have been c on structed. We compare three methods of 1C schemes using cubic triangular Bézier patches and one 2C scheme using quintic triangular Bézier patches.Our test case consists of four sets of node/test function pairs, with node-count ranging from 26 to 100 data points. The absolute maximum and mean errors are computed using 33×33 evaluation points on a uniform rectangular grid

Positivity-preserving scattered data interpolating surface using C1 piecewise cubic triangular patches

The construction of a bivariate C1 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bezier points in order to ensure that surfaces comprising cubic Bezier triangular patches are always positive and satisfy C1 continuity conditions. Initial gradients at the data sites are estimated and then modified if necessary to ensure that these conditions are satisfied. The construction is local and easy to implement. Graphical examples are presented using two test function

Convexity-preserving scattered data interpolation

This study deals with constructing a convexity-preserving bivariate C1 interpolants to scattered data whenever the original data are convex. Sufficient conditions on lower bound of Bezier points are derived in order to ensure that surfaces comprising cubic Bezier triangular patches are always convex and satisfy C1 continuity conditions. Initial gradients at the data sites are estimated and then modified if necessary to ensure that these conditions are satisfied. The construction is local and easy to be implemented. Graphical examples are presented using several test functions

Range restricted positivity-preserving G1 scattered data interpolation

The construction of a range restricted bivariate G1 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bézier points in order to ensure that surfaces comprising quartic Bézier triangular patches are always positive and satisfy G1 continuity conditions. The gradients at the data sites are then calculated (and modified if necessary) to ensure that these conditions are satisfied. Its construction is local and easily extended to include as upper and lower constraints to the interpolating surfaces of the form z = C(x,y) where C is a polynomial of degree less or equal to 4. Moreover, G1 piecewise polynomial surfaces consisting of polynomial pieces of the form z = C(x,y) on the triangulation of the data sites are also admissible constraints. A number of examples are presented

Functional Scattered DataG1 Interpolation With Sum Of Squares Of Principal Curvatures.

Scattered Data interpolation deals with fitting of a smooth surface to set of non-uniformly distributed data points which extends to all positions in a domain

Spatial estimation of average daily precipitation using multiple linear regression by using topographic and wind speed variables in tropical climate

Complex topography and wind characteristics play important roles in rising air masses and in daily spatial distribution of the precipitations in complex region. As a result, its spatial discontinuity and behaviour in complex areas can affect the spatial distribution of precipitation. In this work, a two-fold concept was used to consider both spatial discontinuity and topographic and wind speed in average daily spatial precipitation estimation using Inverse Distance Weighting (IDW) and Multiple Linear Regression (MLR) in tropical climates. First, wet and dry days were identified by the two methods. Then the two models based on MLR (Model 1 and Model 2) were applied on wet days to estimate the precipitation using selected predictor variables. The models were applied for month wise, season wise and year wise daily averages separately during the study period. The study reveals that, Model 1 has been found to be the best in terms of categorical statistics, R2 values, bias and special distribution patterns. However, it was found that sets of different predictor variables dominates in different months, seasons and years. Furthermore, necessities of other data for further enhancement of the results were suggested

Improved sufficient conditions for monotonic piecewise rational quartic interpolation

In 2004, Wang and Tan described a rational Bernstein-Bézier curve interpolation scheme using a quartic numerator and linear denominator. The scheme has a unique representation, with parameters that can be used either to change the shape of the curve or to increase its smoothness. Sufficient conditions are derived by Wang and Tan for preserving monotonicity, and for achieving either C1 or C2 continuity. In this paper, improved sufficient conditions are given and some numerical results presented