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

What is shearing, What is shearing?  The shearing transformation actua...

What is shearing?  The shearing transformation actually slants the object with the X direction or the Y direction as needed.ie; this transformation slants the shape of an obje

Computer simulation - computer aided design, Computer simulation - Computer...

Computer simulation - Computer Aided Design Computer simulation is the manner of designing a model of a real or theoretical physical system, not including the model on a digit

Given two triangles p along with vertices as p1(100, Given two triangles P ...

Given two triangles P along with vertices as P1(100,100,50), P2(50,50,50), P3(150,50,50) and q along with vertices as Q1(40,80,60), q2(70,70,50), Q3( 10,75,70), determine that tria

Area subdivision method-obscures the continuing two surface, Assume here ar...

Assume here are three polygon surfaces P,Q, R along with vertices specified by as: P: P1(1,1,1), P2(4,5,2), P3(5,2,5) And as Q: Q1(2,2,0.5), Q2(3,3,1.75), Q3(6,1,0.5) R: R1(0.5,

Functions available in animation packages, Functions Available in Animation...

Functions Available in Animation Packages Some broad functions available in animation packages are as: Object Function to manage and store the object database , where

Z- buffer algorithm, Q.   Describe the z- Buffer algorithm for hidden surfa...

Q.   Describe the z- Buffer algorithm for hidden surface removal. Ans. Z- buffer method: This method compares surface depths at each pixel position on the projection plane. T

Transformation for 3-d scaling, As we already seen that the scaling proces...

As we already seen that the scaling process is mainly utilized to change the size of an object. The scale factors find out whether the scaling is a magnification as s>1 or a red

Cathode ray tube - graphics hardware, Cathode Ray Tube - Graphics Hardware ...

Cathode Ray Tube - Graphics Hardware Cathode Ray Tube: this is a refreshing display device. The idea of a refreshing display is depicted pictorially is given as: In fact

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