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
Photo Editing Photo-editing programs are paint programs: it just like they comprise several sophisticated functions for altering images and for scheming aspects of the image,

Military: In order to enter the military, one has to go by various training. Depending upon whether you want to be in the army, navy or the marines, you may be working along with

Important point about the De casteljeau algorithm 1)      Bezier Curve: P (u) =    ................     (1) Here B n,i (u) = n c i u i (1 - u) n-i        ..

Basics of Animation - Computer animation Historical and traditional methods for production of animation: As we have studied the transformations linked in computer graphics

Character Generation You know that graphics displays often contain components which are text based.  For example graph labels, annotations, descriptions on data flow diagrams,

Video Conferencing and Virtual Reality Virtual reality is a truly fascinating multimedia application. In such, the computer creates an artificial environment using hardware an

Role in Education and Training:- A multimedia presentation is an important way to introduce new concepts or described a new technology. Individuals determine it easy to understand


explainapplication of coherence in visible surface detection method

Question 1: Name at least four file formats and explain in detail what they mean and how they are use? Question 2: What are "Process Colours"? Answer in a single para