Journal of Prime Research in Mathematics

# A Novel Approach for the Visualization of Constrained Data using GC1 Bi-Cubic Functions

Farheen Ibraheem$$^{a,*}$$, Ayesha Shakeel$$^b$$, Muhammad Bilal Riaz$$^c$$

$$^a$$ Department of Mathematics, Forman Christian College-A Chartered University-FCCU, Lahore, Pakistan

$$^b$$ Department of Mathematics, University of Wah, Wah Cantt, Pakistan.

$$^c$$ Department of Mathematics, University of the Management and Technology- UMT, Lahore, Pakistan.

Correspondence should be addressed to: : farheenibraheem@fccollege.edu.pk

### Abstract

One of the fundamental issues in engineering, computer graphics, data visualization, interpolation and many more areas is to create a shape preserving surface from supplied data points. Data can be characterized as convex, monotone and positive. This research focuses on developing new smooth and efficient shape preserving schemes for convex, monotone and positive 3D data set positioned on a rectangular mesh. For this purpose, a GC1 continuous cubic function with two free parameters have been advanced to GC1 bicubic coons surface patches. There are eight free shape parameters in each rectangular patch which are constrained to ascertain these intrinsic data attributes that is convexity, positivity and monotonicity. The proposed interpolant governs the shape of data locally and data dependent constraints on shape parameters manage the shape preservation. Moreover, proposed scheme is verified and demonstrated graphically

#### Keywords:

Shape preservation, rational function, convex curve and surface, GC1continuity .