Important points about the bezier curves, Computer Graphics

Important points about the bezier curves - modeling and rendering

1) Generalizing the idea of Bezier curve of degree at n based upon n+1 control point p0,.....pn

P(0)= P0

P(1) =pn

Values of parametric initial derivates of Bezier curve at the ending points can be computed from control point Coordinates are:

P'(0) = -nP0 +n P1

P'(1) = -nPn-1 +  nPn

Hence, the slope at the starting of the curve is beside the line joining two control points and the slope on the end of the curve is beside the line connecting the last two endpoints.

2) Convex hull: For 0≤ t ≤ 1, the Bezier curve lies completely in the convex hull of its control points. This property for a Bezier curve ensures about polynomial will not contain erratic oscillation.

3) Bezier curves are invariant about affine transformations, although they are not invariant about projective transformations.

4) To the Bezier curve, the vector tangent at the beginning or stop is parallel to the line connecting the first two or last two control points.

5) Bezier curves appear a symmetry property: The similar Bezier curve shape is acquired if the control points are considered in the opposite order. The merely difference will be the parametric way of the curve. The direction of rising parameter reverses while the control points are considered in the reverse sequence.

6) Adjusting the location of a control point changes the shape of the curve in a "predictable manner". Spontaneously, the curve "follows" the control point.

Posted Date: 4/4/2013 5:29:01 AM | Location : United States







Related Discussions:- Important points about the bezier curves, Assignment Help, Ask Question on Important points about the bezier curves, Get Answer, Expert's Help, Important points about the bezier curves Discussions

Write discussion on Important points about the bezier curves
Your posts are moderated
Related Questions
LCD - Liquid Crystal Display A liquid crystal display consists of two glass plates each containing a light polarizer. One glass plate contains vertical polarizer and the ot

Single Point Perspective Transformation - Viewing Transformations In order to derive the particular point perspective transformations beside the x and y-axes, we construct fi

Explain the concept of t he frame buffer

Question 1: (a) Once a selection is made, what area of the image can be edited? (b) What is the purpose of saving selections? (c) How can you move a selection while you a

What is an axonometric orthographic projection and cabinet projection? The orthographic projection can show more than one face of an object.  Such an orthographic projection i

Quicktime Quicktime is the video format devised through and used through Apple and can be utilized at varying quality and file sizes. This is quite broadly used and has affecte

difference between vecgen and breshnam algorithm

explain the working procedure of crt digram

Explain Three Dimensional Transformations A 3D geometric transformation is utilized extensively in object modelling and rendering. 2D transformations are naturally extended to