3-d transformation, Computer Graphics

3-D Transformation

The capability to represent or display a three-dimensional object is basically to the knowing of the shape of that object. Moreover, the capability to rotate, translate and also project views of such object is also, in various cases, basically to the understanding of its shape. Manipulation, construction and viewing of 3-dimensional graphic images need the utilization of coordinate transformations and 3-dimensional geometric. Within geometric transformation, the coordinate system is set and the desired transformation of the object is finished w.r.t. the coordinate system. During coordinate transformation, the object is fixed and the preferred transformation of the object is complete on the coordinate system itself. Such transformations are formed via composing the essential transformations of translation, rotation and scaling. All of these transformations can be demonstrated as a matrix transformation. It permits more complex transformations to be constructed by utilization of matrix concatenation or multiplication. We can make the complicated objects/pictures, via immediate transformations. In order to demonstrate all these transformations, we require utilizing homogeneous coordinates.

Thus, if P(x,y,z) be any point in 3-dimensional space then in Homogeneous coordinate system, we add a fourth-coordinate to a point. It is in place of (x,y,z), all points can be represented via a Quadruple (x,y,z,H), where H≠0; along with the condition is x1/H1=x2/H2; y1/H1=y2/H2; z1/H1=z2/H2. For two points (x1, y1, z1, H1) = (x2, y2, z2, H2) ; such that H1 ≠ 0, H2 ≠ 0. Hence any point (x,y,z) in Cartesian system can be illustrated by a four-dimensional vector like (x,y,z,1) in HCS. Similarly, if (x,y,z,H) be any point in Homogeneous coordinate system then (x/H,y/H,z/H) be the equivalent point in Cartesian system. Hence, a point in 3-dimensional space (x,y,z) can be demonstrated by a four-dimensional point as: (x',y',z',1)=(x,y,z,1).[T], here [T] is several transformation matrix and (x',y'z',1) is a new coordinate of a specified point (x,y,z,1), so after the transformation.

The completed 4x4 transformation matrix for 3-dimensional homogeneous coordinates as:

2350_3-D Transformation.png

The upper left (3x3) sub matrix generates scaling, reflection, rotation and shearing transformation. The lower left (1x3) sub-matrix generates translation and the upper right (3x1) sub-matrix produces a perspective transformation that we will study in the subsequent section. The final lower right-hand (1x1) sub-matrix generates overall scaling.

Posted Date: 4/3/2013 5:59:52 AM | Location : United States

Related Discussions:- 3-d transformation, Assignment Help, Ask Question on 3-d transformation, Get Answer, Expert's Help, 3-d transformation Discussions

Write discussion on 3-d transformation
Your posts are moderated
Related Questions
Authoring Tools Authoring tools generally refers to computer software that assists multimedia developers produce products. Authoring tools are various from computer programmi

Question 1 Write a note on digitizers Question 2 Discuss on line drawing algorithm Question 3 Explain 3D viewing Question 4 Explain different types of cohe

what is normalization transformation?why is it needed and important?give simple example also.

Performing rotation about an Axis For performing rotation about an axis parallel to one of the coordinate axes (say z-axis), you first need to translate the axis (and hence the

Passive Computer Animations: That has no option for users to utilize computer graphics today is mostly interactive for example: movies. Frame animation is non-interactive anim

Define Random Scan/Raster Scan displays. Ans. Random scan is a process in which the display is made by the electronic beam, which is directed, only to the points or division of

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

what is physx.?

QUESTION (a) Draw and explain the block diagram of a Digital Signal Processing System for an analog signal. (b) Draw the pictorial representation of the signals at each leve

a__________of a scene is apart of a scene by which relate one part of the scene with the other parts of the scene