Derive the common transformation of parallel projection, Computer Graphics

Derive the common transformation of parallel projection into the xy-plane in the direction of projection d=aI+bJ+cK.

Solution: The common transformation of parallel projection into the xy-plane towards the projection d=aI+bJ+cK, is derived as follows in the figure a:

Assume here that P(x,y,z) be an object point, projected to P'(x',y',z') into the z'=0 plane. By figure (a) we observe that the vectors d and PP' have the similar direction. It implies that:

PP'=k.d , comparing part, we find that:

x'-x=k.a

y'-y=k.b

z'-z=k.c

As like z'=0 on the projection plane, we obtain k=-z/c. As,

x'=x-a.z/c

y'=y-b.z/c

 z'=0    

2279_Derive the common transformation of parallel projection 1.png

Figure: (a)

 

In terms of coordinates of homogeneous, so this equation can be become as:

1961_Derive the common transformation of parallel projection.png

 

It is,  P'h =Ph.Ppar,z , here Ppar,z  is the parallel projection along with the direction of projection d along the unit vector k.

Posted Date: 4/3/2013 6:30:26 AM | Location : United States







Related Discussions:- Derive the common transformation of parallel projection, Assignment Help, Ask Question on Derive the common transformation of parallel projection, Get Answer, Expert's Help, Derive the common transformation of parallel projection Discussions

Write discussion on Derive the common transformation of parallel projection
Your posts are moderated
Related Questions
Acquire the perspective transformation onto z = - 2 Plane, where (0, 0, 18) is the center of projection. Solution: Now centre of projection, C (a, b, c) = (0, 0, 18) ∴ (n 1

What is run length encoding?   Run length encoding is a compression method used to store the intensity values in the frame buffer, which keeps each scan line as a set of intege

QUESTION You are employed as a graphics designer in an advertising agency and recently completed a brochure artwork for a client. You need to send the file for printing before

Touch Panels - Input and output devices It allows displayed screen or object positions to be selected along with the touch of the finger and is also termed as Touch Sensitive

What is Computer Graphics. Computer graphics remains most existing and rapidly growing computer fields. Computer graphics may be explained as a pictorial representation or gra

CRT - Cathode Ray Tube Electron gun is used to send an electron beam aimed at a particular point on the screen. Deflection system is used to make the beam strike the screen

Orientation Dependence - Modeling and Rendering The outcomes of interpolated-shading models are dependent of the projected polygon's orientation. Because values are interpolat

2. Describe how the Bresenham rasterisation algorithm is advantageous when compared to any other existing method.

Silicon Graphics - Hardware for computer animation The SGI platform is one of the most broadly used hardware platforms in professional or broadcast feature computer animation

What is reflection and clipping? The reflection is actually the transformation that makes a mirror image of an object. For this use some angles and lines of reflection.  Cli