Acquire a transformation matrix for perspective projection, Computer Graphics

Assignment Help:

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).


Related Discussions:- Acquire a transformation matrix for perspective projection

De casteljau algorithm - 2d clipping algorithms, De Casteljau Algorithm ...

De Casteljau Algorithm For computation of Bézier curves an iterative algorithm known as de Casteljau algorithm is used.  The algorithm uses repeated linear interpolation.

Assumptions for area subdivision method, Assumptions for Area Subdivision M...

Assumptions for Area Subdivision Method a) ¾   Plane of projection is z=0 plane b) ¾ Orthographic parallel projections c) ¾   Direction of projection as d= (0,0,-1) d

Registers, explain the registers used in video controller

explain the registers used in video controller

What are the advantages of the boundary representation, Advantages of the B...

Advantages of the Boundary Representation (i) This format gives efficient picture generation and easy access to other geometric information. (ii) The changes produced by mos

Drawing program with object- oriented design, For this assignment, you will...

For this assignment, you will add to the drawing program new features that are similar to features that you already have. Apply object-oriented design concepts such as inheritance

Physx, what is physx.?

what is physx.?

Lcd - liquid crystal display, LCD - Liquid Crystal Display A liquid...

LCD - Liquid Crystal Display A liquid crystal display consists of two glass plates each containing a light polarizer. One glass plate contains vertical polarizer and the ot

Briefly describe what you understand by smoothing, Question: (a) List a...

Question: (a) List and explain different types of lights that can be used in After Effects. (b) How is the density of dots between the boxes in a motion path related to th

Important points for key frame systems - computer animation, Important poin...

Important points for Key Frame Systems - Computer Animation In key frame systems the "in-between" "tweening" or frames can be created from the specification of two or more key

Define advanced graphics port, Q. Define Advanced Graphics Port? AGP si...

Q. Define Advanced Graphics Port? AGP signify Advanced (or Accelerated) Graphics Port. It's a connector standard defining a high speed bus connection between the microprocessor

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