Bezier surfaces - modeling and rendering, Computer Graphics

Assignment Help:

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.


Related Discussions:- Bezier surfaces - modeling and rendering

Briefly describe the variants of the interaction model, Question: a) Th...

Question: a) The implications of transparency are a major influence on the design of system software. There are eight forms of transparency. Name and give a small description o

Multimedia tools, MULTIMEDIA TOOLS : In this sense, we will emphasize on v...

MULTIMEDIA TOOLS : In this sense, we will emphasize on various tools utilized in the field of multimedia. Basic Tools: The fundamental toolset for building multimedia p

Differentiate among interpolation and approximation spline, Differentiate a...

Differentiate among interpolation spline and approximation spline?  When the spline curve passes by all the control points then it is known as interpolate. When the curve is

What are the important applications of computer graphics, Can you list at l...

Can you list at least three important applications of computer graphics? There are lots of interesting applications of computer graphics. Three common applications are compute

Explain the bresenham line generation algorithm, 1. Explain the Bresenham ...

1. Explain the Bresenham line generation algorithm via digitizing the line with end  points as (15, 5) and also (25,13). Ans. Now we are utilizing the Bresenham line generati

Bezier surfaces - modeling and rendering, Bezier Surfaces - Modeling and Re...

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 su

Area filling algorithms - output primitives, Area Filling Algorithms Be...

Area Filling Algorithms Before we go ahead with area filling algorithms, a word about pixel addressing and object geometry. You know that line segments are discretized into fin

Reflection, determine the tranformation matrix for reflection,computer grap...

determine the tranformation matrix for reflection,computer graphics

Merits -phong shading or normal vector interpolation shading, Merits -Phong...

Merits -Phong shading or Normal Vector Interpolation Shading Hence by finding intensities at various points across the edge we determine the intensity that is varying across t

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