Acquire a transformation matrix for perspective projection, Computer Graphics

Acquire a transformation matrix for perspective projection for a specified object projected onto x=3 plane as viewed by (5,0,0).

Solution: Plane of projection: x = 3 as given. Here assume that P (x, y, z) be any point in the space. We identify the parametric equation of a line AB, beginning from A and passing   via B is like:

1111_Acquire a transformation matrix for perspective projection 1.png

Figure: (i)

P (t) = A + t. (B - A), o < t < ∞

Consequently parametric equation of a line starting from E (5,0,0) and also passing via P (x, y, z) becomes:

E + t (P - E), o < t < ∞

=  (5, 0, 0) + t [(x, y, z) - (5, 0, 0)]

= (5, 0, 0) + [t (x - 5), t. y, t. z]

= [t. (x - 5) + 5, t. y, t. z].

Suppose here Point P' is obtained, as t = t*

∴ P' = (x', y', z') = [t* (x - 5) + 5, t*y, t*. z]

Because, P' lies on x = 3 plane, consequently

t* (x - 5) + 5 = 3 should be actual;

t* = -2/(x - 5)

P' = (x',y',z') = (3,((-2.z)/(x-5)), ((-2.z)/(x-5)))

= ((3x-15)/(x- 5), (-2y)/(x - 5), (-2z)/(x - 5))

In Homogeneous coordinate system there is:

P' = (x', y', z', 1) = ((3x-15)/(x- 5), (-2y)/(x - 5), (-2z)/(x - 5), 1)

= (3x - 15, - 2.y, - 2.z, x - 5)                  --------------(1)

In Matrix form it will be:

341_Acquire a transformation matrix for perspective projection 2.png

------------------------------(2)

Hence, as in above equation (2) is the needed transformation matrix for perspective view from (5, 0, 0).

Posted Date: 4/4/2013 3:01:21 AM | Location : United States







Related Discussions:- Acquire a transformation matrix for perspective projection, Assignment Help, Ask Question on Acquire a transformation matrix for perspective projection, Get Answer, Expert's Help, Acquire a transformation matrix for perspective projection Discussions

Write discussion on Acquire a transformation matrix for perspective projection
Your posts are moderated
Related Questions
Interlaced GIF: The conventional which is non-interlaced GIF graphic downloads one line of pixels at one time from top to bottom and browsers display all lines of the image as it

Features for good 3-Dimentional modeling software are as: Multiple windows which permit you to view your model in each dimension. Capability to drag and drop primitive

examples and equation of reflection

Categorization of Light resources - Point source This is the easiest model for a light emitter. Currently rays from source obey radically diverging ways from the source positi

Question: Suppose we have a video monitor with a display area measuring 12.8 inches across and 9.6 inches high.  If the resolution is 1024 by 768 and the aspect ratio is 1, what is

Frame animation non- interactive animation rectangular shape (Cartoon movies) It is an "internal" animation method, which is, it is animation within a rectangular frame. This i

Normal 0 false false false EN-US X-NONE X-NONE

2-D and 3-D Transformations Previously, we have presented approaches for the generation of polygonal regions and lines. We identified that once the objects are produced, the v

Types of Graphic Images: Graphic images have been processed through a computer can generally be divided in two distinct categories. That image is either bitmap files or vecto

Question 1) Why are selection tools useful? Describe them based on different categories Question 2) What are the different types of layers? Describe each type Quest