Application of Spline Curves in Geometric Presentation

This work is completed under through Minor Research Project sanctioned by UGC, New DELHI, INDIA. This is original work. this gives a new dimension for geometrical modelling through spline curves and surfaces. Brief objectives of the work are as follows: (1) Construction of some spline bases with shape parameter. (2) All the geometric properties of spline curves like positivity, small support, symmetry, normality, convex hull, variation diminishing will be analyzed. (3) Strong convex hull property will be studied. (4) To increase the curve and surface modeling flexibility, multiple and local shape parameters will be introduced. (5) Approximation of spline functions will be studied and compared with other existing results. (6) To find out the significant range of shape parameters so that curves can approximate the control polygon. (7) To design sculpt example and analyze the effect of shape parameters on curve shape. (8) To design surface modeling arithmetic and to develop a Space Freedom Surface Modeling System based on the Computer Graphics theories and using C++ programming language and MATLAB.