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,

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
QUESTION 1. Create a COMPLETE storyboard for a movie of 2 minutes duration on ONE of the following subject: a. Poverty b. Global Warming c. Smoking d. Drugs e. D

Buffer Areas Required For Z-Buffer Algorithm For applying z-buffer algorithm, we need two buffer areas or two 2-Dimentional arrays: 1) Depth-buffer [i,j], to sa

Ray Tracing - Polygon Rendering & Ray Tracing Methods Ray tracing obeys all rays from the eye of the viewer back to the light sources. The method Ray tracing is very good at

Horizontal retrace - Display Devices In a refresh CRT monitor, the time it takes for an electron beam to return to the left most point on the next horizontal line after refresh

What is the use of Projection reference point?  In Perspective projection, the object positions are transformed to the view plane with these converged projection line and the p

Parallel Projection In parallel projection, objects in scene are projected onto the 2D view plane along rays parallel to a projection vector. Parallel projection is orthogra

Consider a Shiny Surface Along With Diffused Reflection coefficient Consider a shiny surface along with diffused reflection coefficient of 0.8 and ambient reflection coeffici

Animation, Video and Digital Movies : These are sequences of bitmapped graphic scenes or frames, quickly played back. But animations can also be made inside the authoring system t

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