1. Digital Media
Dr. Jim Rowan
ITEC 2110

2. So far… We have compared bitmapped graphics and vector graphics
We have discussed bitmapped images, some file formats and some file compression techniques
Today we are going to talk in a bit more detail about vector graphics
Later we will cover Color
Then 3D vector graphics

3. Vector Graphics… An elegant way to construct digital images that
can have a compact representation
are scalable
have access to the objects
And mandatory for 3-D modeling

4. First…
Coordinate systems

5. Coordinate systems Bitmapped pixel coordinates (integer) x y 4,0 4,1
4,2
4,9
3,0
3,1
3,2
3,9
0,0
0,1
0,2
0,9 4 3 x 2 1 1 2 3 4 9 y

6. Coordinate systems bitmapped4 3 x 2 1 1 2 3 4 9 y
A= ( , ) B= ( , ) C= ( , ) D= ( , ) E= ( , )

7. Coordinate systems Vector graphics coordinates (real values)
A point is defined by its x and y coordinate y
(x,y)
Can be fractional
Can be negative 2
(1.41, 1.74) 1 1 2 3 x

8. Coordinate systems Vector graphics coordinates (real values)
A displacement (distance between points or movement from one point to another) can be defined by a pair of points y
displacement from
point 1 to point 2...
displacement =
[(x2 - x1), (y2 - y1)]
= ( , )
(1.71,-0.79)
point 1 2
(1.41, 1.74) 1
point 2
(3.12, 0.95) 1 2 3 x

9. AKA vector Vectors have magnitude (length) and direction
This vector goes down 0.79 and to the right 1.71
It is a two dimensional (x&y) vector that goes down and to the right (1.71,-0.79) y 2
(1.41, 1.74) 1
(3.12, 0.95) 1 2 3 x

10. Why is it called vector graphics?
Another grandfathered term
From the time when displays were directly “steered” by their programs
Give the display two points and it would move the beam from one point to the other drawing a line...
This movement could be described as a vector since it has magnitude (length) and direction (from one point to the other)

11. Absolute vs Window coordinates
rendering software renders images in a window
windows can be moved around and...
the rendering program only knows where the object is relative to the window it is in and…
rendering software does not know where the window is on the screen so…
a coordinate transformation must be performed

12. Absolute vs Window coordinates
coordinates: measurement back to the upper left hand corner of the screen
relative (to the window)
coordinates measurement back to the upper left hand corner of the window
to convert relative to absolute, add the relative coordinates to the absolute coordinate of the upper left hand corner of that window

13. Absolute & Relative Coordinates

14. The Bounding Box It’s a way to locate an object in space
what point is used to place an object?
the center of the object’s mass?
the upper left corner?
the lower right corner?
images can be contained inside a “bounding box” which is the smallest box that contains all the points found in an object

15. Bounding Box x (0,0) desktop screen window bounding box y (100,103)
(410,290)
window 1
(210,175)
(760,570)

16. Vector graphics
Stores shapes (like a rectangle) very economically in the form of formulas or equations of geometric shapes
Since a line segment can also be completely described by its endpoints…
In computer graphics a line is defined by a line segment (i.e. it has endpoints)

17. Here’s the vector we saw earlier defined by it’s two endpoints2
(1.41, 1.74)
(3.12, 0.95) 1 1 2 3 x

18. To display a vector graphic you need to convert the vector graphic line to a bitmapped graphic… which presents problems!

19. Convert Vector to Bitmapped Visually
Convert Vector to Bitmapped Visually... “completely cover the vector with pixels” 2 1 1 2 3 x

20. Vector to Bitmapped 2 1 1 2 3 x

21. The artifact created: A jagged line… This is “aliasing”2 1 1 2 3 x

22. Aliasing(vector)
When converting a vector graphic to a bitmapped graphic we can’t create a perfect representation
What we end up with is a bitmapped version of the vector
It’s not really the original but rather an alias of the original version
Can have negative effects

23. Aliasing (bitmapped)
When we view a bitmapped digital photograph on a display, the reconstruction is performed by a display device, and by our eyes and by our brain.
If the reconstructed image differs from the original image, we are seeing an alias.
Can have negative effects

24. To combat negative effects of aliasing? anti-aliasing
These are techniques to mitigate the affect of aliases
“Smoothes” the edges of jagged lines
How does this work?

25. Using anti-aliasing techniques on our original line
our pixellated line to be displayed (the external model) is in black 2 1 1 2 3 x

26. combating aliases: anti-aliasing techniques
the original vector graphic line
stored in the internal model is in red
our pixellated line to be displayed (the external model) is in black 2 1 1 2 3 x

27. combating aliases: anti-aliasing techniques2 1 1 2 3 x

28. combating aliases: anti-aliasing techniques “average the grayness”2 1 1 2 3 x

29. So far we have just looked at a line
The line was stored as its endpoints
What about other shapes?

30. Shapes made from connected lines
connected lines are stored as a polyline
internally the polyline is stored as a series of points
closed polylines form a shape
an open polyline is just a jagged line

31. rectangles and squares
rectangles can be described by two corners
squares are special cases of the rectangle

32. ellipses and circles ellipses can be described by two points
circles are special cases of the ellipses
they are stored as a single point

33. vector graphics: drawing smooth curves
Question: How would you draw a curve using a computer with a mouse?
You can’t draw smooth lines very easily
A line tool with handles (based on the Bezier curve) can be manipulated by those handles

34. Lines and curves Bezier curves can be smoothly joined together
An anchor point is the point where one joins the other
When a curve closes on itself it is considered a closed curve
When it doesn’t it’s just an open curve

35. Lines and curves Closed (and open for that matter) lines can be filled
solid color, pattern or gradient (linear or radial)
Lines can have different ends
mitre, rounded, square, bevel

36. The language of Manipulating objects…
Translation: is a simple up/down side-to-side movement
Scaling: make bigger or smaller
Rotation: about a point
Reflection: about a line

37. 3-D? Way more complex than 2-D
3-D shapes (objects) are defined by their surfaces
Made even more complicated by the fact that a 3-D object inside the computer must be translated into 2-D to be rendered on a computer screen...
This results in the need to specify the viewpoint

38. Questions?