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Shape Properties of Irregular Surface Data


Rational cubic function, Triangular patch, Shape parameters, Positivity, Monotonicity


The presented work of this paper addresses the two shape properties, positivity and monotonicity of irregular surface data. The data is initially triangulated and a side-vertex scheme is adopted to interpolate the data over each triangle. Each boundary and radial curve is a rational function with three parameters facilitating 18 parameters in each triangular patch. The presence of these parameters leads to an automotive scheme for shape preservation and shape control. The data dependent constraints are derived on 6 of these parameters for preservation of positive and monotone properties of data, while, remaining 12 are free for shape modification. This scheme is local, does not constrain step length and derivatives, equally applicable to both data and data with derivatives.





Pakistan Journal of Statistics and Operation Research; Vol. 8 No. 4. 2012

Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810