Digital Media

Dr. Jim Rowan

ITEC 2110

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 – have a compact representation – are scalable– are easy to edit

• And mandatory for 3-D modeling

First…

Coordinate systems

Coordinate systems

• Bitmapped 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

A

E

C D

x

y

0

1

2

3

4

0 1 2 3 4 9

B

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

Coordinate systems• Vector 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)

Can be fractionalCan 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

Coordinate systems

0 1 2 3

1

2

x

y

(1.41, 1.74)

point 1

(3.12, 0.95)

displacement frompoint 1 to point 2...

= [(x2 - x1), (y2 - y1)](3.12 - 1.41, 0.95 - 1.74)(1.71,-0.79)

point 2

• 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)

AKA vector

0 1 2 3

1

2

x

y

(1.41, 1.74)

(3.12, 0.95)

• 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)

Vector graphics?

Absolute vs Window coordinates

• rendering software renders images in a window

• windows can be moved at will so...• the rendering program only knows where the

object is relative to the window it is in• rendering software does not know where the

window is on the screen• a coordinate transformation must be

performed

Absolute & Relative Coordinates

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 Boxx

y

(0,0)

window 1

window 1

desktop screen

bounding box

(150,200)

window

(410,290)

(760,570)

(100,103)

Vector graphics

• Store shapes (like the line) very economically in the form of formulas or equations

• But which formula?• A line is defined by

y = mx + b (but that is for an infinitely long line)

• In computer graphics we want a line segment, i.e. it has endpoints

• Since a line segment can also be completely described by its endpoints…

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)

To display a vector graphic you need to convert the

vector graphic line to a

bitmapped graphic

Convert Vector to BitmappedVisually... “completely cover

the vector with pixels”

0 1 2 3

1

2

x

Vector to Bitmapped

0 1 2 3

1

2

x

The artifact created:A jagged line…This is “aliasing”

0 1 2 3

1

2

x

Aliasing

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

Aliasing

• Even 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. • http://en.wikipedia.org/wiki/Aliasing

To combat aliasing:anti-aliasing

• Techniques to mitigate the affect of aliases

• Smoothes the edges of jagged lines

Using anti-aliasing techniqueson our original line

0 1 2 3

1

2

x

our pixellated line to be displayed (the external model) is in black

combating aliases:anti-aliasing techniques

0 1 2 3

1

2

x

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

combating aliases:anti-aliasing techniques

0 1 2 3

1

2

x

combating aliases:anti-aliasing techniques“average the grayness”

0 1 2 3

1

2

x

• So far we have just looked at a line– The line was stored as its endpoints

• What about other shapes?

vector graphics:shapes

• connected lines are stored as a polyline– internally the polyline is stored as a series of

points

• closed polylines form a shape• open polyline is a jagged line

vector graphics:rectangles and squares

• rectangles can be described by two corners• squares are special cases of the rectangle

vector graphics:ellipses and circles

• ellipses can be described by two points• circles are special cases of the ellipses

– they are stored as a single point

http://en.wikipedia.org/wiki/Ellipse

vector graphics: 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– This is how drawn shapes become objects like the

cowboy on Toy Story (except that the characters in toy story were created in 3D, not 2D)

– solid color, pattern or gradient (linear or radial)

• Lines have ends– ends can be messy when joined so…– mitre, rounded, square, bevel

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

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

Questions?