What is homogeneous coordinate, Computer Graphics

Assignment Help:

What is homogeneous coordinate? Discuss the composite transformation matrix for two successive translations and scaling.

In design and picture formation process, many times we may require to perform translation rotation and scaling to fit the picture components into their proper positions. In the previous section we have seen that each of the basic transformation can be expressed in the general matrix form. To produce a sequence of transformations with above equations, such as translation followed by rotation and then scaling, we must calculate the transformed coordinate’s one step at a time. First coordinates are translates then these translated coordinates are scaled and finally the scaled coordinates are rotated. But this sequence of transformation process is not efficient. A more efficient approach is to combine sequence of transformation into one transformation so that the final coordinate position is obtained directly from initial coordinate. This eliminates the calculation of intermediate coordinate values. In order to combine sequence of transformation terms in M2. To achieve this we have to represent matrix M as 3 * 3 matrixes instead of 2 * 2 introducing an additional dummy coordinate W. Here points are specified by three numbers instead of two. This coordinate system and it allows us to express all transformation equations as matrix multiplication. For two dimensional transformation we can have =1. 


Related Discussions:- What is homogeneous coordinate

Explain about the computer animation, Explain about the Computer animation ...

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

Drawing program with object- oriented design, For this assignment, you will...

For this assignment, you will add to the drawing program new features that are similar to features that you already have. Apply object-oriented design concepts such as inheritance

Matrix for orthographic projection, Matrix for Orthographic Projection ...

Matrix for Orthographic Projection Orthographic projections are projections into one of the coordinate planes x=0, y=0or z=0. The matrix for orthographic projection on the z=0

Projections - viewing transformation, Projections - Viewing Transformation ...

Projections - Viewing Transformation Specified 3-D object in a space, Projection can be explained as a mapping of 3-D object into 2-D viewing screen. Now, 2-D screen is termed

What is the need of homogeneous coordinates, What is the need of homogeneou...

What is the need of homogeneous coordinates?  To perform more than one transformation at a time, use homogeneous coordinates or matrixes. They decrease unwanted calculations in

Dda program to plot line segments, Use DDA algorithm to get the output of y...

Use DDA algorithm to get the output of your program as shown in Figure ANs: Use DDA( ) function to plot line segments that have end points on diametrically opposite points

General perspective transformation, General Perspective transformation w.r....

General Perspective transformation w.r.t. an arbitrary center of projection Suppose here that the COP is at C(a,b,c), as demonstrated in Figure. By Figure, the vectors CP

How avar values generate to get realistic movement, How avar values generat...

How avar values generate to get realistic movement There are numerous ways of generating avar values to get realistic movement. One way is to use markers on a real person (or w

Explain briefly ancillary operations, Problem: a. Explain briefly six A...

Problem: a. Explain briefly six Ancillary Operations? b. When do ancillary operations take place? c. (i) What is flexography? (ii) Provide examples of finished produ

Cel animation - computer animation, Cel Animation - Computer Animation ...

Cel Animation - Computer Animation Making an animation by using this method, all characters are drawn on a separate piece of transparent paper. Also a background is drawn on a

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