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

Differentiate between raster and vector images, QUESTION a) Differentia...

QUESTION a) Differentiate between raster and vector images. b) Explain the concept of bit depth. What is the minimum number if bits required for a one-colour digital image t

Draw line segment - digital differential analyzer algorithm, Example 1: Dr...

Example 1: Draw line segment from point (2, 4) to (9, 9) by using Digital Differential Analyzer algorithm. Solution: We know usual equation of line is specified via y = mx

What is 2d, Question 1 What is 2D? Explain method of converting 2D pattern...

Question 1 What is 2D? Explain method of converting 2D patterns into 3D images Question 2 Write about the following tools to create dart Create dart Multiply dar

3d studio max -softwares for computer animation, 3DStudio Max -Softwares fo...

3DStudio Max -Softwares for computer animation The successor to 3-DStudio 3.0, 3-DStudio Max runs in WindowsNT. This is completely object-oriented, featuring new enhancements a

Define addressability, What is meant by Addressability?  The Addressabi...

What is meant by Addressability?  The Addressability is the number of individual dots per inch (d.p.i) that can be formed. If the address of the current dot is (x, y) then the

Find the normalization transformation, Illustration: Find the normalizatio...

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

X-shear regarding the origin - 2-d and 3-d transformations, X-shear Regardi...

X-shear Regarding the Origin - 2-d and 3-d transformations Suppose an object point P(x,y) be moved to P'(x',y') in the x-direction, via the given scale parameter 'a',that is,

Number system, Perform the indicated base conversions 548 to base 5

Perform the indicated base conversions 548 to base 5

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