Computer Graphics has a great impact on the existent world in a variety of ways. A variety of applications exist to demonstrate the power of Computer Graphics. Data Visualization is one of them. There is a wide range of applications that are grounded on certain underlying data which is to be exhibited on digital displays. This underlying data has three noteworthy shape patterns named as positive, monotone and convex. This thesis is concerned with the construction of new and effective shape preserving schemes to draw the smooth trigonometric spline curves and surfaces for positive, constrained, monotone and convex shapes of the data. For this persistence, firstly, a quadratic trigonometric spline function with three parameters is developed and it is extended to bi-quadratic trigonometric spline function including six parameters in its description. Two parameters of quadratic trigonometric spline function and four parameters of bi-quadratic trigonometric spline function are constrained to draw the shape preserving trigonometric spline curves and surfaces for positive, constrained, monotone and convex 2D and 3D regular data patterns respectively. Rest of the parameters, one parameter in quadratic trigonometric spline function and two parameters in bi-quadratic trigonometric spline function, are kept free for the shape refinement of shape preserving trigonometric spline curves and surfaces respectively. Furthermore, a cubic trigonometric spline function with two parameters is also developed. One parameter included in its description is constrained to draw the shape preserving trigonometric spline curves for positive, constrained, monotone and convex 2D regular data patterns whereas remaining one parameter is left free for further shape amendment as per requirements. The trigonometric cubic spline function is also extended to bi-cubic trigonometric spline functions which include four parameters in its construction. Two of them are constrained to draw the shape preserving trigonometric spline surfaces for positive, constrained, monotone and convex 3D regular data patterns while the remaining two parameters are left free for further shape modification whenever needed. The proposed and developed schemes are illustrated with examples of 2D and 3D regular data of positive, constrained, monotone and convex shapes. These illustrations help and guide to validate and demonstrate the proposed schemes. The error bounds of developed quadratic trigonometric spline functions and cubic trigonometric spline functions are also estimated which are of order three.