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

Scan-line method, In contrast to depth-buffer method, here we identify one ...

In contrast to depth-buffer method, here we identify one surface at one time, scan-line method deals along with multiple surfaces. Since it processes each scan-line at one time, al

Why Video Game Characters Look Better Today, what is the control for Why Vi...

what is the control for Why Video Game Characters Look Better Today

Historical method – oral tradition, Historical method - Oral tradition: ...

Historical method - Oral tradition: Only the teacher was the source of information The teacher treated as a role model. The teacher was the main resource to meet indiv

Sound editing programs, Sound Editing Programs; Sound editing tools for bo...

Sound Editing Programs; Sound editing tools for both digitized and MIDI sound; by that you see music and also hear it. Through drawing a representation of a sound in fine growths,

What is jpeg, Question 1 What is JPEG? How do you change the quality of a ...

Question 1 What is JPEG? How do you change the quality of a JPEG image? Question 2 What are the advantages and challenges of virtual classroom? Question 3 What do

Design a bitmap for the english vowels, 1. Design a bitmap for the English ...

1. Design a bitmap for the English vowels A, E, I, O, U for two different sizes and then implement the bitmaps to plot these vowels on the display. Keep in mind that baseline of al

Card or page based tools, Card or Page Based Tools : In these authoring sy...

Card or Page Based Tools : In these authoring systems, components are organized as pages of a book or a stack of cards. Thousands of pages or cards may be obtainable in the stack

Traditional animation techniques , Traditional Animation techniques as: ...

Traditional Animation techniques as: 1) Key Frames                        2) Cel Animation Formula: Required Key frames for a film = {[Time(in seconds)]

Chain of responsibility and the iterator patterns, QUESTION (a) Conside...

QUESTION (a) Consider the observer, façade, chain of responsibility and the iterator patterns. i) Give detailed descriptions and draw their structures. ii) Explain the in

Important notes for negative accelerations, Important Notes for Negative Ac...

Important Notes for Negative Accelerations Note : Having projections of points on curve, above Y axis we will obtain a pattern similar to figure 8 that is needed to produce ne

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