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

Photo editing, Photo Editing Photo-editing programs are paint programs...

Photo Editing Photo-editing programs are paint programs: it just like they comprise several sophisticated functions for altering images and for scheming aspects of the image,

Combined consequence of ambient and diffused reflection, Combined consequen...

Combined consequence of ambient and diffused reflection At this time the resulting intensity I will be the total sum of the intensities in case 8.3.2 and 8.3.3 we find that:

Simulating accelerations - computer animation, Simulating Accelerations - C...

Simulating Accelerations - Computer Animation In previous block, we have seen the dominance and function of mathematics in computer graphics and now, we will undertake the invo

What are the advantages of rendering by patch splitting, What are the advan...

What are the advantages of rendering by patch splitting?  i. It is fast-especially on workstations with a hardware polygon-rendering pipeline.  ii. Its speed can be varied b

Design and label the pattern of the folding carton, Question : You have...

Question : You have been approached to design a ‘tuck top auto-lock bottom' carton package for a high-end cosmetic jar under the brand name ‘Beauty One'. Your client asked you

Distinguish between mono and stereo sound, Problem: (a) Distinguish be...

Problem: (a) Distinguish between mono and stereo sound? (b) Calculate the size of a 5 minutes mono sound file of CD quality and with a 16 -bit rate. (c) With reference

Homogeneous coordinates, What are the uses of homogeneous coordinates? Conv...

What are the uses of homogeneous coordinates? Convert translation rotation and scaling in homogeneous coordinates. In mathematics homogeneous coordinates introduced by August

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