Azizan Saaban

Range Restricted C2 Interpolant to Scattered Data

The construction of a range restricted bivariate C2 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. Sufficient conditions are derived on Bezier points in order to ensure that surfaces comprising quintic Bezier triangular patches are always positive and satisfy C2 continuity conditions. The first and second derivatives 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 5. A number of examples are presented.

On piecewise interpolation techniques for estimating solar radiation missing values in Kedah

This paper discusses the use of piecewise interpolation method based on cubic Ball and Bezier curves representation to estimate the missing value of solar radiation in Kedah. An hourly solar radiation dataset is collected at Alor Setar Meteorology Station that is taken from Malaysian Meteorology Deparment. The piecewise cubic Ball and Bezier functions that interpolate the data points are defined on each hourly intervals of solar radiation measurement and is obtained by prescribing first order derivatives at the starts and ends of the intervals. We compare the performance of our proposed method with existing methods using Root Mean Squared Error (RMSE) and Coefficient of Detemination (CoD) which is based on missing values simulation datasets. The results show that our method is outperformed the other previous methods.

G/sup 1/ scattered data interpolation with minimized sum of squares of principal curvatures

One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V = {(x/sub i/, y/sub i/), i=1,...,n} /spl isin/ R/sup 2/ over a polygonal domain and a corresponding set of real numbers {z/sub i/}/sub i=1//sup n/, we wish to construct a surface S which has continuous varying tangent plane everywhere (G/sup 1/) such that S(x/sub i/, y/sub i/) = z/sub i/. Specifically, the polynomial being considered belong to G/sup 1/ quartic Bezier functions over a triangulated domain. In order to construct the surface, we need to construct the triangular mesh spanning over the unorganized set of points, V which will then have to be covered with Bezier patches with coefficients satisfying the G/sup 1/ continuity between patches and the minimized sum of squares of principal curvatures. Examples are also presented to show the effectiveness of our proposed method.

Positivity-Preserving Scattered Data Interpolating Surface using C^1 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 functions

Estimation of missing values in solar radiation data using piecewise interpolation methods: Case study at Penang city

The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools...

Surface interpolation using partial differentiation equation with positivity preserving cubic said-ball curves boundary condition

In this paper, the sufficient condition for the positive preservation of boundary curves for each edges of bicubic rectangular Said-Ball patches will be discussed. With the use of polynomial solution of fourth order linear PDEs, these curves are defined on rectangular grid for the purpose of enhancing the positivity preservation of the interpolating surface. Through an independent adjustment of the lower boundary of edge Said-Ball ordinates, a sufficient condition on boundary curves for individual edge of bicubic rectangular Said-Ball patches is derived. By employing two well recognized test functions, finding reveals that the approach proposed is appropriate with regard to positive preservation of boundary curves and that there is improvement in the positive preservation of the whole interpolating surfaces.

Multidimensional fixed-point theorems and applications

The purpose of this work is to present the applications of multidimensional fixed point theorems. For this, we prove some multidimensional fixed point theorems and then using these theorems we show the existence and uniqueness of solution of a systems of matrix equations.

A necessary condition for the absolute continuity of invariant measure of circle maps with countably infinite number of break points

Let f be a circle homeomorphism with countably many break points that is, differentiable except in countably many points where the derivatives have a jump. Assuming its rotation number ρ to be irrational, we provide a necessary condition for the absolute continuity of invariant measure with respect to the Lebesgue measure.

ON COMPARISON OF ESTIMATION TECHNIQUES FOR SOLAR RADIATION MISSING DATA AT ALOR SETAR AND PENANG AREA IN NORTHERN PENINSULAR MALAYSIA

The radiation data is important for solar data analysis which is significantly for modeling, designing on energy conversion system development and outputting it as a variable that is needed by other related scientific researches.Obtaining the complete data for solar intensity is a tough job when the technical problem is raised either from the sensor’s devices or faulty data transmission. Next, missing values occur accordingly.As a solution, missing value estimation has been introduced to substitute the absent values with imputed values.This article is highlighted to propose cubic Bezier interpolation as potential techniques to generate replacement values. Afterwards, compare the performance capability of few submitted interpolation techniques dealing with difference amount of simulated missing data. Based on our knowledge, curiosity works for replaceable values by applying Bezier interpolation on solar radiation data is limited. The cubic Bezier interpolation performs very well on both areas but the most effective condition is at the lower missing values and higher absent values that come from Alor Setar and Penang cities, respectively, which offer the lowest RMSE value and the r² value nearest to 1

Evaluation of linear interpolation method for missing value on solar radiation dataset in Perlis

This paper intends to reveal the ability of the linear interpolation method to predict missing values in solar radiation time series. Reliable dataset is equally tends to complete time series observed dataset. The absence or presence of radiation data alters long-term variation of solar radiation measurement values. Based on that change, the opportunities to provide bias output result for modelling and the validation process is higher. The completeness of the observed variable dataset has significantly important for data analysis. Occurrence the lack of continual and unreliable time series solar radiation data widely spread and become the main problematic issue. However, the limited number of research quantity that has carried out to emphasize and gives full attention to estimate missing values in the solar radiation dataset.