Top Gadgets in 2011

In my choice, the top gadgets in 2011 are:

Apple iPhone 4s
With 8 megapixels and all-new optics, this just might be the best camera ever on a mobile phone. It just might be the only camera you’ll ever need. And if you think that’s amazing, wait until you see your photos.


Samsung Galaxy S2
8 MP camera with flash, Android OS, Sensors, High Screen Resolution


Amazon Kindle
Review and remember more of what you read.
Follow people of interest to you to see their Public Notes.
Manage your books, highlights, and notes.


MOTOROLA-XOOM
A super smart phone


Panasonic Smart VIERA
Experience the very best in 2D / 3D picture quality and design with the What Hi-FI? Television of the year 2011. Introducing the Smart Viera, the Smart TV from Panasonic – available in a range of 32”-42” LED and 42”-65” Neo Plasma screens.

3D Transformation: Introduction

3D-Transformation

Manipulation, viewing, and construction of three-dimensional graphic images require the use of three-dimensional geometric and coordinate transformations. In geometric transformation, the coordinate system is fixed, and the desired transformation of the object is done with respect to the coordinate system. In coordinate transformation, the object is fixed and the desired transformation of the object is done on the coordinate system itself. These transformations are formed by composing the basic transformations of translation, scaling, and rotation. Each of these transformations can be represented as a matrix transformation. This permits more complex transformations to be built up by use of matrix multiplication or concatenation. We can construct the complex objects/pictures, by instant transformations. In order to represent all these transformations, we need to use homogeneous coordinates.

Hence, if P(x,y,z) be any point in 3-D space, then in Homogeneous Coordinate System, we add a fourth-coordinate to a point. That is instead of (x,y,z), each point can be represented by a Quadruple (x,y,z,H) such that H≠0; with the condition that x1/H1=x2/H2; y1/H1=y2/H2; z1/H1=z2/H2. For two points (x₁, y₁, z₁, H₁) = (x₂, y₂, z₂, H₂) where H₁ ≠ 0, H₂ ≠ 0. Thus any point (x,y,z) in Cartesian system can be represented by a four-dimensional vector as (x,y,z,1) in HCS. Similarly, if (x,y,z,H) be any point in HCS then (x/H,y/H,z/H) be the corresponding point in Cartesian system. Thus, a point in three-dimensional space (x,y,z) can be represented by a four-dimensional point as: (x’,y’,z’,1)=(x,y,z,1).[T], where [T] is some transformation matrix and (x’,y’z’,1) is a new coordinate of a given point (x,y,z,1), after the transformation.

3D Transformation

Methods for geometric transformations and object modeling in 3D are extended from 2D methods by including the considerations for the z coordinate.

Basic Transformations

Translation

We translate a 3D point by adding translation distances, tx, ty, and tz, to the original coordinate position (x,y,z):

x' = x + tx, y' = y + ty, z' = z + tz

Scaling

Scaling With Respect to the Origin

We scale a 3D object with respect to the origin by setting the scaling factors sx, sy and sz, which are multiplied to the original vertex coordinate positions (x,y,z):

x' = x * sx, y' = y * sy, z' = z * sz

Coordinate-Axes Rotations

A 3D rotation can be specified around any line in space. The easiest rotation axes to handle are the coordinate axes.

3D Rotations about an Axis which is parallel to an Axis

1. Step 1. Translate the object so that the rotation axis coincides with the parallel coordinate axis.
2. Step 2. Perform the specified rotation about that axis.
3. Step 3. Translate the object so that the rotation axis is moved back to its original position.

General 3D Rotations

1. Step 1. Translate the object so that the rotation axis passes through the coordinate origin.
2. Step 2. Rotate the object so that the axis of rotation coincides with one of the coordinate axes.
3. Step 3. Perform the specified rotation about that coordinate axis.
4. Step 4. Rotate the object so that the rotation axis is brought back to its original orientation.
5. Step 5. Translate the object so that the rotation axis is brought back to its original position.