1. Chapter 10:
Coordinate Systems
Chapter 10

2. This Chapter: we will learn
the w2n transform
World and Normalized Device Coordinate Systems
World Coordinate Window
Coordinate Transformation
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3. Transformation of Tut 3.1 (10.1)
In all tutorials, we …
Initialize MW MV MP to identity
Compute world2ndc and load into MV
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4. The world2ndc transform
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5. All vertices are transformed!
D3D transforms all vertices (Vi) by If
Then
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6. Tutorial 3.1: re-visit
Transformed to …
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7. Tut 10.2: Drawing without w2n
Observation: ≤ x/y ≤ +1
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8. Tut 10.3: Verify ±1 Range Window Dimension Draw a unit circle
200 pixels x 200 pixels
Draw a unit circle
Center at (0,0)
Radius = 1.0
Observe indeed:
NDC – Normalized Device Coordinate
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9. Tut 10.4/10.5: Experiment with NDC
Tutorial 10.4:
Same Unit circle
100x200 pixel area
Tutorial 10.5:
Same Unit circle
200x100 pixel area
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10. Observations: Remember: In this case: All vertices are in NDC (±1)
MV MW MP: are initialized to Identity
All vertices are in NDC (±1)
Output always forced into entire device drawing area!
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11. Conclusion: NDC to Device!!
NDC to Device Space automatically
Where:
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12. NDC to Device Transform
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13. Device Coordinate (DC) System
Defined on the device
Lower left as origin
For “Windows”
Units are in pixels
Compare to Hardware Coordinate
Origin at upper left
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14. Normalized Device Coordinate (NDC) System
X/Y ranges between -1 to +1
2x2 square area
All Graphics API
Expects NDC!
Automatically transforms from NDC to drawing area
Mn2d is automatic!!
True for ALL Graphics APIs!!
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15. Advantage of NDC Consistency and Flexibility Convenience:
Programmer does not need to aware of display dimension
Program will run on any display size
Convenience:
±1 convenient for scaling
Problem with NDC:
±1 are not intuitive to humans/programmers!
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16. Drawing a face …
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17. Transformation involve (Tut 9.9)
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18. World Coordinate System (WC)
Convenient system for design!
We have to
compute and apply
in our program
World Coordinate System (WC)
Graphics API
computes and applies
automatically
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19. Tut 10.6: DC independence! Mn2d Can draw to any DC space!
Scale to Device Coordinate (DC) automatically by Graphics API
Can draw to any DC space!
Tut 10.6: draws 300x300 face to
500x500 pixels DC space!
Looks Identical to Tut 9.9!
Tut 9.9: 300x300 pixels DC
Graphics API
computes and applies
automatically
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20. Tut 10.7: Same face in different WC
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21. Tut 10.7: WC Window WC Window The X/Y bounds that enclose the face
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22. Tut 10.7: Required Mw2n
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23. Tut 10.7: Implementation Appears identical to Tut: 10.6 and 9.9
Completely different Mw2n
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24. Tut 10.8: Location of WC Window
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25. Tut 10.8: Implementation Define the entire geometric human
Draws with defined WC Window
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26. The WC Window and Mw2n All vertices (Vi) goes through:
In our implementation:
Mw2n is stored in MV
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27. Vertex in Different Coordinate Spaces
Vwc – vetex in WC Space
Vndc – vetex in NDC Space
Vdc – vetex in DC Space
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28. Same Vertex in WC, NDC, DC …
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29. WC to DC transform (Mw2d)
Given: Or
Let
Then
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30. More about
Recall: Or
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31. WC to DC 3 Important Pieces
Center (cxwc, cywc) – pan: what/where is visible
Dimension (Wwc, Hwc) – Zoom: size of visible objects
Ratio : WC to DC height/width ratio
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32. Lib 10: WC Window Support
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33. Lib10: DC  WC Xform
To cover
later
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34. Lib10: LoadW2NDCXform() (to MV)
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35. Tut 10.9: Work with WC Window
Set WC Window
Must be done during initialization
Before each draw of model
Call LoadW2NDCXform() to define Mw2n
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36. Tut 10.10: Moving WC Window
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37. Tut 10.10: WindowHandler details
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38. Tut 10.10: Implementation Detail
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39. Tut 10.10: Handler::DrawGraphics()
Our App has two instances of WindowHandler
m_main_view instance of CMainHandler
m_small_view instance CDrawOnlyHandler
Both instances will invoke this DrawGraphics()
Each instance has an unique WC Window
Each invocation loads a different Mw2n
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40. Tut 10.11: Scaling WC Window
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41. Tut 10.11: Zooming … Mw2n is computed and loaded into MV Intuition …
Larger (WWC, HWC) corresponds to
Smaller scaling factors (in numerators)
Large (WWC, HWC) is zooming out
You see more in the given device space
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42. Width to Height ratios:
From WC to DC:
Translate: by World Center
Scale: from WC window to DC displace size
Translate: to position the drawing area
When:
Objects will be scaled differently in X and Y
Circles will not be round!!
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43. Aspect Ratio … Define: To maintain circle square …
Aspect ratio of WC Window must be the same as aspect ratio of DC display area
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44. Inverse Trasnform Given vertex in WC: Vwc
We know ..
Now, mouse clicks are in DC space!
Given Vdc
How can we compute
what is
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45. Computing …
Recall:
Let:
Then:
Or:
Finally:
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46. DC to WC:
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