Digital Media

Lecture 5: Vector Graphics

Georgia Gwinnett CollegeSchool of Science and Technology

Dr. Jim Rowan

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

Vector Graphics…

An elegant way to construct digital images that – can have a compact representation – are scalable– provdes access to the objects

And mandatory for 3-D modeling

But first:

Coordinate systems

Coordinate SystemsBitmapped pixel coordinates (integer)4,0 4,1 4,2 4,9

3,0 3,1 3,2 3,9

0,0 0,1 0,2 0,9

x

y

0

1

2

3

4

0 1 2 3 4 9

Coordinate SystemsBitmapped pixel coordinates (integer)

A

E

C D

x

y

0

1

2

3

4

0 1 2 3 4 9

B

5 6

A?= ( , ) B?= ( , ) C?= ( , ) D?= ( , ) E?= ( , )

Coordinate SystemsVector graphics coordinates (real values)

A point is defined by its x and y coordinate

0 1 2 3

1

2

x

y

(1.41, 1.74)(x,y)

They can be fractionalThey can be negative

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

0 1 2 3

1

2

x

y

(1.41, 1.74)point 1

(3.12, 0.95)

displacement from point 1 to point 2?displacement = = [(x2 - x1), (y2 - y1)] = (3.12 - 1.41, 0.95 - 1.74) = (1.71,-0.79)

point 2

Coordinate Systems

Vectors have magnitude (length) and direction This vector goes down 0.79 and to the right 1.71 (1.71 , -0.79)

0 1 2 3

1

2

x

y

(1.41, 1.74)point 1

(3.12, 0.95)point 2

Vectors

Why “vector graphics?”

This is a grandfathered term

It comes from the CRT days when displays could be directly “steered” by their programs

A program passed a vector to the display and the beam would move to the next point drawing a line

Next:

Absolute vs Windowcoordinate systems

Absolute vs Window

Applications render images inside of a window– They know where stuff is in the window– But not where the window is– They deal with relative coordinates

The Operating system– Keeps up with the window– It deals with absolute coordinates

Absolute vs Window

absolute – coordinates: measured 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

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

Bounding boxes; relative and absolute coordinatesx

y

(0,0)

window 1

window 1

desktop screen

bounding box

(210,175)

window

(410,290)

(760,570)

(100,103)

Finally: Vector Graphics

Store shapes economically in the form of formulas or equations of geometric shapes

A line segment can be completely described by its two endpoints…

Let’s look at the line a little closer

Here’s the vector we saw earlier defined by it’s two endpoints

0 1 2 3

1

2

x

(1.41, 1.74)

(3.12, 0.95)

But…

To display a vector graphic you need to convert the vector to a bitmapped graphic…

This presents problems!

Convert Vector to BitmappedVisually...

“completely cover the vector with pixels”

0 1 2 3

1

2

x

Convert Vector to BitmappedVisually...

“completely cover the vector with pixels”

0 1 2 3

1

2

x

Convert Vector to BitmappedResults in an artifact…

a jagged line called an alias that lookslike a series of steps

0 1 2 3

1

2

x

How to mitigate this alias?Anti-aliasing techniques are used but…How does this work?

0 1 2 3

1

2

x

Anti-aliasing

0 1 2 3

1

2

x

our pixellated line to be displayed is in black

Anti-aliasing

0 1 2 3

1

2

x

the original vector graphic stored in the internal model is in red

our pixellated line to be displayed is in black

Anti-aliasing

0 1 2 3

1

2

x

Anti-aliasing

0 1 2 3

1

2

x

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

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 an open curve

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

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

3D vector graphics?

MUCH 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 built inside the computer must be displayed as a 2-D graphic on a computer screen...– This results in the need to specify the

viewpoint