Bezier cubic curves, Computer Graphics

Assignment Help:

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.  

 

 


Related Discussions:- Bezier cubic curves

2-d and 3-d transformations, 2-D and 3-D Transformations Previously, w...

2-D and 3-D Transformations Previously, we have presented approaches for the generation of polygonal regions and lines. We identified that once the objects are produced, the v

Crt, working of crt

working of crt

Determine about the liquid crystal display, Determine about the Liquid Crys...

Determine about the Liquid Crystal Display LCDs are organic molecules, naturally in crystalline state, and they get liquified when excited by heat or E field. Crystalline state

Briefly explain how the median filter works, QUESTION 1 (a) Write a run...

QUESTION 1 (a) Write a run method in Image J environment for the following cases Contrast and Brightness Histogram Generation Histogram Equalisation   (b)

2d clipping, What is 2d clipping in computer graphics

What is 2d clipping in computer graphics

Methods for drawing thick lines, Describe any two methods for drawing thick...

Describe any two methods for drawing thick lines. Two method for drawing thick lines are: (1) Using the line- width command: "setline width scale factor (iw)" Line width param

Constant intensity shading or flat shading, Constant intensity shading OR F...

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

Graphics, GRAPHICS: It is one of the core elements of any multimedia ...

GRAPHICS: It is one of the core elements of any multimedia application. We all have heard a well-known saying as "one picture conveys a message of 1000 words", hence without

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd