Bezier cubic curves, Computer Graphics

Q. What are Bezier cubic curves? Derive their properties. OR  What are Bezier cubic curves? Derive these properties. Also show that the sum of the blending functions is identical to 1 for all values of t. Why is it important?

Ans. A Bezier curve section can be fitted to any no. of control points. The no. of control points to be approximated and their relative position determines the degree of the Bezier polynomial. These coordinates can be blended to produce the following position vector P (u), which describes the path of an approximating Bezier polynomial function between P0 and Pn. Thus the slope at the beginning of the curve is along the line joining the first two control points and the slope at the end of the curve is along the line joining the last two endpoints. Bezier curves are widely available in various CAD systems in graphics packages in painting packages since they are easy to implement and they are reasonably powerful in curve design. Many graphic packages provide only cubic spleen functions. This gives reasonable design flexibility while avoiding the increased calculation needed with higher order polynomials.  



Posted Date: 7/12/2012 6:50:39 AM | Location : United States

Related Discussions:- Bezier cubic curves, Assignment Help, Ask Question on Bezier cubic curves, Get Answer, Expert's Help, Bezier cubic curves Discussions

Write discussion on Bezier cubic curves
Your posts are moderated
Related Questions
Cohen Sutherland algorithm Point clipping is very simple.  All you need to check is whether a point is inside the window extremes in x- and y-directions.  For line clipping sev

Suppose P be the point object along with the coordinate (x,y,z). We want to translate such object point to the new position as, P'(x',y',z') through the translation Vector as V=t x

Question 1 What is Multimedia? Explain sound multimedia element Question 2 Explain any three elements of drawings Question 3 Explain any three types of drawing Quest

Constant intensity shading OR Flat shading  In this technique particular intensity is calculated for each polygon surface that is all points that lie upon the surface of the

Overview of Hardware Primitives With the advancement of computer technology, computer graphics has become a practical tool used in real life applications in diverse areas such

what is normalization transformation?why is it needed and important?give simple example also.

Bresenham Line Generation Algorithm for Positive Slope (BLD algorithm for positive slope (0 - If slope is negative then utilize reflection transformation to transform the

Referential Links: A third type of link is a referential link. It is associated to the associative link. Quite than representing a relationship among two related ideas, a referent

Graphic Interchange Format (GIF): The Graphic Interchange Format is an efficient implies to transmit images across data networks. In the early 1990 year the original designers of

What is Resolution, how to adjust it.  Resolution: The maximum number of points that can be displayed without overlap on a CRT is referred to as the resolution . A more prec