1. Drawing Issues Drawing Coordinate Systems Drawing with Pixels CS-321
11/28/2018
Drawing Issues
Drawing Coordinate Systems
Drawing with Pixels
Dr. Mark L. Hornick

2. Part 1: Coordinate Systems
We have some choices to make when drawing
CS-321 Dr. Mark L. Hornick

3. Which coordinate system should we use?
CS-321
11/28/2018
Which coordinate system should we use?
Modeling/local coordinates
World coordinates
Normalized device coordinates
Device coordinates
Dr. Mark L. Hornick

4. Modeling/Local Coordinates
Convenient for object to be drawn
Typical units: meters, feet, etc.
Might not be Cartesian (.e.g. polar)
floats and doubles are common
10.0m
(0,0)
7.5m
CS-321 Dr. Mark L. Hornick

5. World Coordinates Groups of objects are combined Form a complete image
Allows prototype objects
Drawn in local coordinates
Copied, resized and moved into world coordinates
Units still feet, meters, etc.
Local/Modeling Coordinates
75m
100m
World
CS-321 Dr. Mark L. Hornick

6. World coordinates
CS-321 Dr. Mark L. Hornick

7. World coordinates
CS-321 Dr. Mark L. Hornick

8. World coordinates
CS-321 Dr. Mark L. Hornick

9. Normalized Device Coordinates
Device-independent
Horizontal and vertical ranges of 0 to 1
“Independence” layer between world and various devices
Screen (windows of various sizes)
Printer
Viewport (ch 6 in text)
zooming 1
NDC
CS-321 Dr. Mark L. Hornick

10. Device Coordinates DC Actual pixels to draw
Allows for movable drawing windows
Usually handled by the window system
Pixel size (pixels/inch) is relevant
Typical processing
(xmc,ymc)(xwc,ywc) (xndc,yndc) (xdc,ydc)
1280 1 DC
1024
CS-321 Dr. Mark L. Hornick

11. How do we go from one coordinate system to another?
Transformation of coordinates
2nd half of course
Pay attention in MA-383!
CS-321 Dr. Mark L. Hornick

12. Part 2: Drawing with Pixels
CS-321
11/28/2018
Part 2: Drawing with Pixels
Drawing algorithms we’ve looked at:
Point, line, circle, etc.
Assume pixel centers as reference
Real pixels have finite size
Affects graphic primitive rendering
Inter-pixel distances are fixed
Limited precision
CS-321 Dr. Mark L. Hornick
Dr. Mark L. Hornick

13. Pixel Addressing Addressing a pixel by its center leads to problems
A pixel occupies a finite space
It is not a true “point”
Consider a line from (2,1) to (5,1)
Actual length = 3
Drawn length = 4 longer than theoretical length 4
CS-321 Dr. Mark L. Hornick 3

14. Boundary Addressing Address pixels by their “boundaries” 3 2 1
This “removes” the last pixel
CS-321 Dr. Mark L. Hornick

15. Boundary Addressing We attempt to plot the interior of objects
draw pixel if center is inside boundary
Still not ideal
Pixels are not exactly adjacent –> result too small
6543 2 1
CS-321 Dr. Mark L. Hornick

16. Compensating for Pixel Size
CS-321
11/28/2018
Compensating for Pixel Size
Ignore the problem?
May make little difference
On 12” screen with 1280 pixels, 1 pixel ~.01”
On rectangle 200x300 (60000 pixels)
Dropping 1 pixel > (199x299) = 499 pixels (<1% area diff)
“Quantization” is most apparent on small elements
CS-321 Dr. Mark L. Hornick
Dr. Mark L. Hornick