Bezier surfaces - modeling and rendering, Computer Graphics

Bezier Surfaces - Modeling and Rendering

Two sets of Bezier curve can be utilized to design an object surface by identifying by an input mesh of control points. The Bézier surface is termed as the cartesian product of the blending functions of 2 Bézier curves.

1123_Bezier Surfaces - Modeling and Rendering.png

Here with p j,k identifying the location of the (m + 1) with (n + 1) control points.

The consequent properties of the Bézier curve implemented to the Bézier surface.

The surface doesn't in common pass via the control points except for the corners of the control point grid.

The surface is contained inside the convex hull of the control points.

225_Bezier Surfaces - Modeling and Rendering 2.png

The control points are linked via a dashed line, and solid lenes demonstrates curves of constant u and v. All curves is plotted by varying v over the interval by 0 to 1, along with u fixed at one of the values in this sections interval curves of constant v are then plotted.

Here figures (a), (b), (c) demonstrate Bezier surface plots. The control points are linked by dashed lines and the solid lines demonstrate curves of constant u and v also. All the curve of constant u is plotted via varying v over the interval start 0 to 1, along with u fixed at one of the values in this single interval. Curves of constant v are plotted likewise.

 

1126_Bezier Surfaces - Modeling and Rendering 3.png

In above figure (c) first-order continuity is established via making the ratio of length L1 to length L2 constant for all collinear line of control points after the boundary in between the surface sections. As in figure (c) demonstrates also a surface formed along with two Bezier sections. Since with curves, a smooth transition from one part to another is assured via establishing both zero-order and first-order continuity on the boundary line. Zero-order continuity is acquired by matching control points at the boundary. So first-order continuity is acquired by choosing control points along a straight line across the boundary and via keeping a constant ration of collinear line segments for every set of identified control points across section boundaries.

Posted Date: 4/4/2013 6:07:57 AM | Location : United States







Related Discussions:- Bezier surfaces - modeling and rendering, Assignment Help, Ask Question on Bezier surfaces - modeling and rendering, Get Answer, Expert's Help, Bezier surfaces - modeling and rendering Discussions

Write discussion on Bezier surfaces - modeling and rendering
Your posts are moderated
Related Questions
Question: a) Datagram packet delivery and Virtual circuit packet delivery are two approaches to the delivery of packets by the network layer. Explain. b) What is the meaning

#BLA for slope greater and equal to 1

JPEG Graphics: Another graphic file format usually utilized on the Web to minimize graphics file sizes is the Joint Photographic Experts Group that is JPEG compression scheme. Not

Cyrus Beck Algorithm - Line Clipping Algorithm Cyrus Beck Line clipping algorithm is actually, a parametric line-clipping algorithm. The term parametric means that we requi

Phong Model or Phong Specular Reflection Model It is an empirical model that is not based on physics, although physical observation. Phong observed here for extremely shiny su

Question 1: (a) Describe the term Mask Path and give brief steps how you could change a rectangle into a triangle with respect to time in AE CS3. (b) Expressions are ve

Question 1: (a) Explain in detail what you understand by the term image compositing and where it is more often used? (b) You are given 3-5 images to make a photo montage/ima

Audio File Formats: It is a container format for storing audio data in a computer system. Many file formats are there for storing audio files. The common approach towards

Implement the Scan line polygon fill algorithm for any arbitrary polygon in C-language and then use your code to fill each of the following type of polygon. i)  Convex polygon

self test exercise 17 asked you to overload the operator >> and the operator Overload biinary operator + to add pairs according to the rule (a, b) + (c, d) = (a + c, b, + d) overl