شرعی نقطہ نظر سے عقل اور اس كی حدود كار تحقیقی جائزہ

The meaning of word "Din" are it applied to all the faith, worship and also cov ers that complete code of life which the Holy Prophet (S. A. VV) gave to ultima. Almighty, Allah has given a special and superior status to the human beings and has bestowed upon the human beings the quest for knowledge. Of course, knowledge is the power which enables the human beings to distinguish clearly between what is good or bad. But other words this is the human wisdom which the creator of this world has bestowed upon the human beings. So it is quite clear that the entire system of faith and worship which Almighty Allah has sent to the human beings through the revelation over the Holy Prophet is exactly according to the common mind and intellect. Since there are certain limitations to the common mind and it cannot go beyond these limitations. This research paper present on investigation of these limits form Sharia point of view.

Shape Preserving Trigonometric Spline Curves and Surfaces for Computer Graphics

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.