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
1. What is the purpose behind the Staircase effect? Ans. The approximation concerned in the calculation for finding of pixel position concerned in the display of lines and th

Types of Animation: -          Procedural Animation    -          Representational Animation -          Stochastic Animation                      -          Behavioura

Question : (a) What do you understand by the term ‘contone'? (b) What are spot colours? (c) You have been asked to prepare an artwork (a magazine) to send to a printer.

QUESTION While the design and printing of a job is of extreme importance, it is what happens to the job after it is printed that can really make it fantastic You have always

What is Multimedia: People only remember 20 percent of what they see and 30 percent of what they hear. But they keep in mind 50 percent of what they see and hear and as much as 80

Determine the perspective transformation matrix upon to z = 5 plane, when the center of projection is at origin. Solution. As z = 5 is parallel to z = 0 plane, the normal is s

what is mean by scan code

Soft Image and Strata Studio - Computer Animation SoftImage It is the one of most well known computer animation software packages. It is used in several top production

Illustration: Find the normalization transformation N that uses the rectangle W (1, 1), X (5, 3), Y (4, 5) and Z (0, 3) as a window and also the normalized device screen like the

Q. Define Advanced Graphics Port? AGP signify Advanced (or Accelerated) Graphics Port. It's a connector standard defining a high speed bus connection between the microprocessor