5.
Euclidean Geometry
Greek mathematician – Euclid (300 BC)
Elements – first systematic text on the studies of
geometry. Assuming a small set of axioms
(assumptions), it proves other propositions by logical
deduction.
We focus on the Plane Geometry (2D)
23.
Golden section
The ratio of the golden section is roughly,
1:1.618 or 0.618:1
If we take a look at the Fibonacci sequence,
1, 1, 2, 3, 5, 8, 13, 21, 34, …
When we divide two consecutive numbers …
24.
Fibonacci number
Can you find the relation between the Fibonacci
numbers and this?
25.
Coordinate system
Remember the 2D plane with X and Y axis.
It is a combination of geometry and the number system.
26.
Coordinate geometry
y (+)
sin (θ)
angle θ
x (-)
centre (0, 0)
y (-)
cos (θ)
x (+)
27.
Coordinate geometry
y (+)
x (-)
centre (0, 0)
y (-)
x (+)
28.
Visual Design
Conceptual elements
Point
Line
Plane
Volume
29.
Visual Design
Visual elements
Shape, e.g. SQUARE, TRIANGLE, SQUARE
Size
Colour, e.g. Hue, Saturation, Brightness
Texture
50.
More path command
We start from a simple LINETO with the use of sine and
cosine functions we have learnt in secondary school.
LINETO (cos(?), sin(?))
51.
Coordinate geometry
y (+)
sin (θ)
angle θ
x (-)
centre (0, 0)
y (-)
cos (θ)
x (+)
52.
More path command
Let’s put it together.
MOVETO (1, 0)
LINETO (cos(30), sin(30))
STROKE () []
53.
More path command
We do repetition within a path.
MOVETO (1, 0)
loop 2 [r 30] {
LINETO (cos(30), sin(30))
}
STROKE () []
54.
More path command
We do more repetitions to form a polygon.
MOVETO (1, 0)
loop 12 [r 30] {
LINETO (cos(30), sin(30))
}
CLOSEPOLY ()
STROKE () []
55.
More path command
We add a bit complication.
MOVETO (1, 0)
loop 12 [r (360/13)] {
LINETO (cos(360/13), sin(360/13)}
}
CLOSEPOLY ()
STROKE () []
56.
More path command
We add a bit complication.
MOVETO (1, 0)
loop 12 [r (4*360/13)] {
LINETO (cos(4*360/13), sin(4*360/13))
}
CLOSEPOLY ()
STROKE () []
57.
More path command
We fill it with colour.
MOVETO (1, 0)
loop 12 [r (4*360/13)] {
LINETO (cos(4*360/13), sin(4*360/13))
}
CLOSEPOLY ()
FILL () []
58.
More path command
We modify the fill effect.
MOVETO (1, 0)
loop 12 [r (4*360/13)] {
LINETO (cos(4*360/13), sin(4*360/13))
}
CLOSEPOLY ()
FILL (CF::EvenOdd) []
60.
Randomness
We may from time to time to create something not that
deterministic. That is, we want surprise.
In mathematics, it is randomness and probability we
have learnt in secondary school.
61.
Randomness
Consider throwing a coin, we have Head or Tail. If we
design a coin with one side red and other side blue, we
can draw the coin. It can either be red or blue.
By using Context Free Art, we achieve by using multiple
rules of the same name.
62.
Randomness
First, we define a red coin,
path CoinRed {
MOVETO (0, 0)
ARCTO (1, 0, 0.5)
ARCTO (0, 0, 0.5)
STROKE () []
FILL [h 0 sat 1 b 1]
}
63.
Randomness
Then we define a blue coin,
path CoinBlue {
MOVETO (0, 0)
ARCTO (1, 0, 0.5)
ARCTO (0, 0, 0.5)
STROKE () []
FILL [h 240 sat 1 b 1]
}
64.
Randomness
Then we have two definitions of a shape,
shape MyCoin {
CoinRed []
}
shape MyCoin {
CoinBlue []
}
65.
Randomness
You test by creating a repetition of the MyCoin rule.
66.
Randomness
You can control the ‘randomness’ by specifying a number
for each rule with the same name.
shape myCoin
rule 10% {
…
}
rule 90% {
…
}
67.
Exercise
Using a grid of 3 x 3 to design a few graphical patterns.
68.
Exercise
Using a grid of 3 x 3 to design a few graphical patterns.
69.
Exercise
Create a tile of the basic graphical patterns with the use
of randomness.
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