**Curves and Surfaces - Modeling and Rendering**

We have studied the method of drawing curves in diverse coordinate systems. Also we got the concept that it is the revolution of a curve regarding to some axis which gives rise to an object enclosing several volume and area. For better knowledge, just think how a potter works to produce vessels of various shapes. He just put a lump of wet soil on the disc that is revolving regarding its axis at high speed, then her or his fingers and palm works as a curve, in contact along with the wet soil. Hence, it is the curve that revolves the several axes to produce vessels of the shape s/he desires. In this section let us study a few practical implementations for the ideas that use in the studied of computer graphics. This will assists a lot since in nature God has created everything along with a level of fineness, which if human beings try to achieve such level in their created art (where computer generated or not) here it is quite close to actuality then one has to excessively make utilize of curves and surfaces in a balanced format and the balance is provided via mathematics.

Hence with the edge of mathematics computer graphics we can attain realism. In this section, we will study about the polygon representation techniques: these techniques are quite significant as it's the polygon that constitutes every closed object as tree, clouds, ball and car and so on, to be represented via graphics. Additionally, each polygon has its own mathematical equation that works as the generating function for such polygon. In this topic we will discuss polygon equation of plane and polygon meshes. A study of these topics will help you for a computer oriented approach to know the implementation of mathematical ideas. We are going to discuss one more significant topic in this section, which are Bezier Curves and their properties. It's the Bezier curves that have revolutionized the field of computer graphics and opened a new arena, that is, automobile sector, for designing and analysis of automobiles. Inspired along with this achievement, scientists have attempt and now there is no region i.e. complete without animation and computer graphics.

In this section, we will deal along with fitting curves to the digitized data. Two methods are available for getting these curves cubic spline and parabolicaly blended curves. These are based upon curve fitting methods. They are not an approximate technique but fit the curve point properly. We will also discuss curve fairing methods like Bezier and B spline curves, utilized to approximate the curve when you do not comprise an exact knowledge of the shape of the curve. Well in last but not the least; we will discuss the idea of surface of revolution. It is a significant topic as the products that are designed are actually the surfaces enclosed via the revolution of the curve regarding several axes.