Transformation for isometric projection - transformation, Computer Graphics

Assignment Help:

Transformation for Isometric projection - Transformation

Suppose that P(x,y,z) be any point in a space.  Assume as a given point P(x,y,z) is projected to the P'(x'y',z') on the projection plane as x + y + z = 0. We are involved to determine the projection point P'(x',y',z').

The parametric equation of a line passing via point P(x, y, z) and towards d (1, 1, 1) is:

P + t.d = (x, y, z) + t. (1,1,1) = (x + t, y + t, z + t) is any one point of on the line, here - ∞< t < ∞. The point P' can be acquired, whereas t = t*.

Hence P'=(x',y',z')=(x + t*,y + t*,z + t*), as P' lies on x + y + z = 0 plane.

ð   (x + t*)+(y + t*) + (z + t*)=0

ð  3.t*=-(x + y + z)

ð       t*=-(x + y + z)/3 must be true.

ð     x'= (2.x - y - z)/3 , y'=(-x +2.y - z)/3 , z'=(- x - y +2.z)/3

Hence, P'=(x',y',z')=[(2.x -y-z)/3, (-x +2.y- z)/3, (-x-y+2.z)/3]

In terms of homogeneous coordinates, we acquire:

1635_Transformation for Isometric projection - Transformation.png


Related Discussions:- Transformation for isometric projection - transformation

Important points for key frame systems - computer animation, Important poin...

Important points for Key Frame Systems - Computer Animation In key frame systems the "in-between" "tweening" or frames can be created from the specification of two or more key

What is the minimum amount of video ram, Consider a raster system with the ...

Consider a raster system with the resolution of 1024 x 768 pixels and the color palette calls for 65,536 colors. What is the minimum amount of video RAM that the computer must have

Calculate the entropy of the source, Question 1) Encode the following s...

Question 1) Encode the following string using HUFFMAN ENCODING:                            DO YOU LIKE TINKY WINKY OR EMPTY DUMPTY?     Empty spaces are considered.

Design a graphical user interface, 1. Implement proper exception handling m...

1. Implement proper exception handling mechanism for this application. 2. Display all data a. Search specific data (depending of the user selection, your application should e

Softwares and hardwares for computer animation, Softwares and Hardwares for...

Softwares and Hardwares for Computer Animation The categories of both software as well as hardware needed to work on animation are now to be discussed. Computer animation can b

Discuss the overview of multimedia networks, Question 1 Discuss the overvi...

Question 1 Discuss the overview of multimedia networks Question 2 Discuss the types of synchronization in multimedia system >> Basic synchronization issues Content R

Concept for eliminating hidden lines, Concept for Eliminating Hidden Lines,...

Concept for Eliminating Hidden Lines, Surfaces or Edges To exemplify the concept for eliminating hidden-lines, surfaces or edges, see a classic wire frame model of a cube as i

Hypertext/media and human memory, Hypertext/media and Human Memory Huma...

Hypertext/media and Human Memory Humans associate pieces of information along with other information and make complicated knowledge structures. Thus, this is also said as the h

Definitions of hypermedia, Definitions of Hypermedia It is a term ...

Definitions of Hypermedia It is a term created through Ted Nelson in the year 1970. It utilized as a logical extension of the term hypertext, wherein graphics, video, audi

What is fixed point scaling, What is fixed point scaling?  The location...

What is fixed point scaling?  The location of a scaled object can be controlled by a position known as the fixed point that is to remain unchanged after the scaling transformat

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