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Markov Chains || Step-By-Step || ~xRay Pixy

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Learn Markov Chains step-by-step using real-life examples. Video Chapters: Markov Chains 00:00 Introduction 00:19 Topics Covered 01:49 Markov Chains Applications 02:04 Markov Property 03:18 Example 1 03:54 States, State Space, Transition Probabilities 06:17 Transition Matrix 08:17 Example 02 09:17 Example 03 10:26 Example 04 12:25 Example 05 14:16 Example 06 16:49 Example 07 18:11 Example 08 24:56 Conclusion
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Viewing Pipeline - 2 Dimensional Viewing in Computer Graphics

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 Viewing Pipeline: Viewing Transformation in several steps:

1. Modeling Coordinates

2. World Coordinate System

3. Clipping Window

4. Normalize - Normalized Coordinates 

5. Device Coordinate 

6. ViewPort

7. Clipping

First, we construct the scene in the world coordinates using the output primitives. Next, obtain a particular orientation for the window, we can set up a 2D viewing coordinate plane and define windows in the viewing coordinate system.

The viewing coordinate reference frame is used to provide a method for setting up arbitrary orientations for a rectangular window. 

Once the viewing reference frame is established. we can transform description in the world coordinate to viewing coordinates.

After that define a viewport in normalized coordinates ( in the range from 0 to 1).

2D Viewing Pipeline can be achieved by the following steps: 

1. Construct world coordinate scene using modeling coordinate transformation. 

2. convert world coordinates to viewing coordinates.

3. Transform viewing coordinate to normalized coordinates (i.e., Between 0 and 1, or between -1 and 1)

4. MAP normalized coordinates to device coordinates. 

WINDOW TO VIEWPORT COORDINATE TRANSFORMATION

This is also known as window viewport transform or windowing transformation.

MAPPING of a part of a world coordinate scene to device coordinates is referenced as viewing transformation.

VIEWPORT COORDINATE TRANSFORMATION - 3 MAIN STEPS

1. Object with its window is translated until the lower-left corner of the window is at the origin.

ORIGINAL 
AFTER Translation 

2. Object and window are now scaled until the window has the dimension the same as the viewport. We are converting the object into the image and window in the viewport. 

AFTER Scaling

3. Another Translation to move the viewport to its correct position on the screen.




Viewing Transformation performed in 3 Steps: Translation, Scaling and again Translation. 


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