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
Resolution Graphic demonstrations are utilized in presentations to assist convey a concept or express a mood, two kinds of demonstrations graphics are: Vector, and B

what is the opengl code for tcp connection?


Implement displacement mapping and bump mapping on a sphere. The displacement can be whatever your choice. The bump map can be whatever your choice as well.

Transformation for 3-D Shearing 2-dimensional xy-shearing transformation, as explained in equation, can also be simply extended to 3-dimensional case. All coordinates are tran

Event Driven Devices - Polling Polling: The status of all devices is periodically checked in a repetitive manner through a polling loop. While an event happens, the loop is

What do you mean by parabolic splines?  For parabolic splines a parabola is fitted by the first three points p1, p2,p3 of the data array of kot points. Then a second parabolic

Introduction of Polygon Rendering and Ray Tracing Method Different type of sources of light and the reflections generated by the object in exposure of these sources. As an obje

Write a C program which takes points as input from mouse clicks (left button) and then performs an action.  Apply your program to generate a closed polygon as follows: Every time a