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
BlackJack is a popular card game played in many casinos. The player plays against the dealer aiming to reach 21 points, or a score higher than the dealer without exceeding 21. The

List out the merits and demerits of DVST?  The merits and demerits of direct view storage tubes [DVST] are as follows  It has a flat screen Refreshing of screen is


Important points for Bresenham Line Generation Algorithm Note: Bresenhams algorithm is generalised to lines along with arbitrary slopes with identifying the symmetry

how can I draw a flower.

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

Basic Tests - Producing Polygon Surface A few basic tests that must be performed before producing a polygon surface through any graphic package as: 1) All vertexes are list

What is Computer Graphics. Computer graphics remains most existing and rapidly growing computer fields. Computer graphics may be explained as a pictorial representation or gra

Explain application areas of computer graphics in different areas.    Early computer graphics has only certain special capabilities such as straight lines circles and ellipses

Explain about the Computer animation Computer animation is the art of creating moving images by computer software and hardware. For 3D animation, objects are designed on a