غیر مسلموں سے تعلقات اور بقائے باہمی کی اساس: سیرت النبیﷺ کے تناظر میں

Islam is universal Religion which not only clear with issues related to Muslims but also clarify the rules and regulations to have intinary with Non-Muslims. Islam emphasizes on primary/ basic rules about relationship of Muslims and Non- Muslims Communities; justice, peace, mutual harmony and co-operation. No force conversion and freedom of thought, Non compulsion Of impartiality convenant. Islam forces on mutual existence in according of these rules. So, clash of civilizations can be avoided in the present age.

Approximation of Planar Curves for Computer Aided Designs

Computer Aided Design (CAD) is used for the manufacture and analysis of designs in industry. The transcendental planar curves such as spirals and conics are inconsistent with the Computer Aided Design system. In CAD planar curves, which provide free-form mathematical description of shapes, are approximated to parametric curves and used as the basic building block. The planar curves such as circle, parabola, ellipse, hyperbola are employed in the research work presented here for shape expression, designing of mechanical accessories (tube benders, cutters, wrenches, clamp systems, inspection gauges), designing of railway and highway routes, construction of roller coaster and outline of the fonts in Computer Aided Design system. The cubic C-Bézier curve, cubic H-Bézier curve and parametric rational cubic curve are practiced to approximate these planar curves. These curves are in control point form and satisfy the properties of famous ordinary Bézier and spline curves. We establish that these curves, which are generalization of cubic Fergusons curves, cubic Bézier curves and cubic uniform B-spline curves are more efficient and closer to the control polygon than the ordinary Bézier and spline curves. The proposed approximation schemes are designed to control the geometric features of planar curves with the geometric constraints. The control points of the cubic C-Bézier curve, cubic H-Bézier curve and parametric rational cubic curve are evaluated by geometric approximation constraints. We use a number of optimization techniques to control the error of the proposed schemes and to provide a unique approximating curve for a given planar curve. The schemes in practice at present approximate planar curves in terms of control points and weights of rational quadratic Bézier curve. The main contribution of this thesis is that the proposed geometric approximation schemes are based on end tangents and curvatures of planar curves. Therefore, these approximation schemes do not need the rational quadratic Bézier representation of planar curves. Numerical experiments suggest that the presented approximation schemes of this thesis are simple, effective and feasible. The absolute errors for developed approximation schemes are less than the prevailing schemes. The smaller absolute error confirms the applicability and efficiency of the proposed methods.