Local Convexity Shape-Preserving Surface Data Visualization by Spline Function
Muhammad Abbas *
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia.
Ahmad Abd Majid
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia.
Mohd Nain Hj Awang
School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia.
Jamaludin Md Ali
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia.
*Author to whom correspondence should be addressed.
Abstract
The main purpose of this paper is the visualization of convex surface data to present a smooth, visually pleasing and interactive convexity preserving surfaces. The rational cubic function with three free parameters is extended to rational bi-cubic partially blended function to preserve the shape of convex surface data. The function involves twelve free parameters in each rectangular patch. Data dependent constraints are derived for four of these parameters to preserve the shape of convex surface data while other eight are left free to user for the refinement of convexity preserving surface of data. Moreover, the scheme under discussion is , flexible, simple, local and economical as compared to existing schemes
Keywords: Shape-preserving interpolation, rational bi-cubic partially blended function, convex surface, convex surface data, free parameters.