Projections - viewing transformation, Computer Graphics

Assignment Help:

Projections - Viewing Transformation

Specified 3-D object in a space, Projection can be explained as a mapping of 3-D object into 2-D viewing screen. Now, 2-D screen is termed as Plane of projection or view plane that constitutes the display surface. The mapping is resolved by projection rays termed as the projectors. Geometric projections of objects are formed via the intersection of lines termed as projectors with a plane termed as plane of projection or view plane. Projectors are lines from an arbitrary point, termed as the centre of projection i.e. COP, by each point in an object. Following figure 1 demonstrates a mapping of point P(x,y,z) on its image P′(x',y',z') in the view plane.

1676_Projections - Viewing Transformation.png

Figure: 1

If the COP that is center of projection is located at finite point in the 3-space, the effect is a perspective projection. If the COP i.e. center of projection is located at infinity, all the projectors are parallel and the consequence is a parallel projection. Following figure 2(a)-(b) demonstrates the diversity between perspective and parallel projections. In following figure 2(a): ABCD is projected to A'B'C'D' on the plane of projection and O is a COP. In the condition of parallel projection the rays by an object converge at infinity, the rays from the object turn into parallel and will have a direction termed as "direction of projection".

621_Projections - Viewing Transformation 1.png

Figure 2(b): Parallel projection


Related Discussions:- Projections - viewing transformation

Fixed point scaling, what is fixed point scaling? how composit transformati...

what is fixed point scaling? how composit transformation techniques works on it

Mathematical description of oblique projection onto xy-plane, Mathematical ...

Mathematical description of an Oblique projection onto xy-plane  In order to expand the transformation for the oblique projection, identify the Figure. This figure explains a

What is the theory of gestalt, Question: (a) After having worked for s...

Question: (a) After having worked for several years as a graphic designer you decide to start a company of your own; MediaDesign ltd. The most valuable asset of a company is i

Properties of bezier curves - modeling and rendering, Properties of Bezier ...

Properties of Bezier Curves - modeling and rendering A very helpful property of a Bezier curve is that it always passes via the first and last control points. Such the bounda

Line drawing display - random scan display device, Line Drawing Display - R...

Line Drawing Display - Random Scan Display Device The display through this system is termed as Line Drawing Display. The sequence controls the subsequent stages, demonstrated

What is graphics, What is Graphics It is a term that refers to any com...

What is Graphics It is a term that refers to any computer device or program which makes a computer able of displaying and manipulating pictures. The name also refers to the im

What is scaling and shearing, What is scaling and shearing? The scaling...

What is scaling and shearing? The scaling transformations alters the shape of an object and can be carried out  by multiplying every vertex (x,y) by scaling factor Sx, Sy where

What is a spline, What is a spline?  To produce a smooth curve by a des...

What is a spline?  To produce a smooth curve by a designed set of points, a flexible strip called spline is used. Like spline curve can be mathematically explained with a piece

General perspective transformation, General Perspective transformation w.r....

General Perspective transformation w.r.t. an arbitrary center of projection Suppose here that the COP is at C(a,b,c), as demonstrated in Figure. By Figure, the vectors CP

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