3-d transformation, Computer Graphics

Assignment Help:

3-D Transformation

The capability to represent or display a three-dimensional object is basically to the knowing of the shape of that object. Moreover, the capability to rotate, translate and also project views of such object is also, in various cases, basically to the understanding of its shape. Manipulation, construction and viewing of 3-dimensional graphic images need the utilization of coordinate transformations and 3-dimensional geometric. Within geometric transformation, the coordinate system is set and the desired transformation of the object is finished w.r.t. the coordinate system. During coordinate transformation, the object is fixed and the preferred transformation of the object is complete on the coordinate system itself. Such transformations are formed via composing the essential transformations of translation, rotation and scaling. All of these transformations can be demonstrated as a matrix transformation. It permits more complex transformations to be constructed by utilization of matrix concatenation or multiplication. We can make the complicated objects/pictures, via immediate transformations. In order to demonstrate all these transformations, we require utilizing homogeneous coordinates.

Thus, if P(x,y,z) be any point in 3-dimensional space then in Homogeneous coordinate system, we add a fourth-coordinate to a point. It is in place of (x,y,z), all points can be represented via a Quadruple (x,y,z,H), where H≠0; along with the condition is x1/H1=x2/H2; y1/H1=y2/H2; z1/H1=z2/H2. For two points (x1, y1, z1, H1) = (x2, y2, z2, H2) ; such that H1 ≠ 0, H2 ≠ 0. Hence any point (x,y,z) in Cartesian system can be illustrated by a four-dimensional vector like (x,y,z,1) in HCS. Similarly, if (x,y,z,H) be any point in Homogeneous coordinate system then (x/H,y/H,z/H) be the equivalent point in Cartesian system. Hence, a point in 3-dimensional space (x,y,z) can be demonstrated by a four-dimensional point as: (x',y',z',1)=(x,y,z,1).[T], here [T] is several transformation matrix and (x',y'z',1) is a new coordinate of a specified point (x,y,z,1), so after the transformation.

The completed 4x4 transformation matrix for 3-dimensional homogeneous coordinates as:

2350_3-D Transformation.png

The upper left (3x3) sub matrix generates scaling, reflection, rotation and shearing transformation. The lower left (1x3) sub-matrix generates translation and the upper right (3x1) sub-matrix produces a perspective transformation that we will study in the subsequent section. The final lower right-hand (1x1) sub-matrix generates overall scaling.


Related Discussions:- 3-d transformation

Polygon filling algorithm - raster graphics and clipping, Polygon Filling A...

Polygon Filling Algorithm - Raster Graphics and Clipping In several graphics displays, this becomes essential to differentiate between different regions by filling them along

Video controller, Video controller : A Fixed area of the system memory co...

Video controller : A Fixed area of the system memory controller for the frame buffer, and the video controller is given direct access to the frame – buffer memory, frame – buffer

Interpolation of surface - polygon rendering, Interpolation of surface - Po...

Interpolation of surface - Polygon Rendering Interpolation of surface normals beside the polygonedge between two vertices is demonstrated above in the figure 15. Here the norm

Introduction to computer graphics, Introduction To Computer Graphics ...

Introduction To Computer Graphics Early man employed drawings to communicate even before he learnt to communicate, write or count. Incidentally, these earliest hierogly

Specular reflection - polygon rendering & ray tracing method, Specular Refl...

Specular Reflection - Polygon Rendering & Ray Tracing Methods Specular reflection is while the reflection is stronger in one viewing direction that is a bright spot, termed

What are the important properties of bezier curve, What are the important p...

What are the important properties of Bezier Curve?  It requires only four control points It always passes by the first and last control points The curve lies enti

Applications-introduction to computer graphics, Applications Research ...

Applications Research in computer graphics has a wide range of application as well as both photorealistic and non-photorealistic image synthesis, image-based rendering and mod

Bresenham line generation algorithm for positive slope, Bresenham Line Gene...

Bresenham Line Generation Algorithm for Positive Slope (BLD algorithm for positive slope (0 - If slope is negative then utilize reflection transformation to transform the

Z-buffer algorithm, How to implement z-buffer algorithm using C programming...

How to implement z-buffer algorithm using C programming

Need for video compression, Need for Video Compression: T he high bit ...

Need for Video Compression: T he high bit rates that result from the various types of digital video make their transmission through their intended channels very difficult. Eve

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