Evolutionary Graphics - Class 02 2014

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Evolutionary Graphics - Class 02 2014

  1. 1. VART3227 Evolutionary Graphics Class 02: Coordinates & geometry
  2. 2. VART3227 Remember in last week. We described our patterns. Horizontal lines distributed evenly… Four squares, symmetric…
  3. 3. VART3227 Any systematic way to describe, notate, analyze visual forms in everyday life?
  4. 4. Euclid
  5. 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)
  6. 6. Straight line
  7. 7. Circle
  8. 8. Parallel lines
  9. 9. Numbers We also learn numbers in primary school. Integer Rational number Real number
  10. 10. Integer We are familiar with Integers, 1, 2, 3, 4, 5, …
  11. 11. Integer Some number sequences are geometric in nature. For example, 1, 4, 9, 16, 25, 36, …
  12. 12. Square number
  13. 13. Square number In Context Free Art, we can have nested repetitions, startshapemyShape shape myShape { loop 5 [y 1] { loop 5 [x 1] CIRCLE [] } }
  14. 14. Integer Another number sequence is, 1, 3, 6, 10, 15, 21, … Guess what shape it is?
  15. 15. Integer Another number sequence is, 1, 4, 9, 16, 25, 36, … Can it be something else other than a square?
  16. 16. Integer Hex numbers are, 1, 7, 19, 37, 61, … It arranges like a hexagon.
  17. 17. Integer
  18. 18. Fibonacci numbers One of the most interesting number sequence is the Fibonacci number. 1, 1, 2, 3, 5, 8, 13, 21, 34, …
  19. 19. Golden section
  20. 20. Golden section
  21. 21. Typography
  22. 22. Golden section
  23. 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. 24. Fibonacci number Can you find the relation between the Fibonacci numbers and this?
  25. 25. Coordinate system Remember the 2D plane with X and Y axis. It is a combination of geometry and the number system.
  26. 26. Coordinate geometry y (+) sin (θ) angle θ x (-) centre (0, 0) y (-) cos (θ) x (+)
  27. 27. Coordinate geometry y (+) x (-) centre (0, 0) y (-) x (+)
  28. 28. Visual Design Conceptual elements Point Line Plane Volume
  29. 29. Visual Design Visual elements Shape, e.g. SQUARE, TRIANGLE, SQUARE Size Colour, e.g. Hue, Saturation, Brightness Texture
  30. 30. Visual Design Repetition
  31. 31. Visual Design Structure
  32. 32. Visual Design Gradation
  33. 33. Visual Design Radiation
  34. 34. CFA Implementation in Context Free Art
  35. 35. Lines Two points give you a straight line. MOVETO (0, 0) LINETO (1, 1)
  36. 36. Multiple lines When you have multiple lines, MOVETO (0, 0) LINETO (1, 2) LINETO (2, 0) LINETO (0, 0)
  37. 37. Multiple lines You expect a triangular shape?
  38. 38. Multiple lines Take this one again, MOVETO (0, 0) LINETO (1, 2) LINETO (2, 0) LINETO (0, 0) CLOSEPOLY ()
  39. 39. Shape It looks better.
  40. 40. Circular path Try the following circular path with ARCTO, MOVETO (0, 0) ARCTO (1, 0, 0.5)
  41. 41. Circular path
  42. 42. Circular path Try the following circular path with ARCTO, MOVETO (0, 0) ARCTO (1, 0, 0.5, CF::ArcCW) CF::ArcCW means clockwise.
  43. 43. Circular path
  44. 44. Circular path To complete the path as a circle, MOVETO (0, 0) ARCTO (1, 0, 0.5) ARCTO (0, 0, 0.5) CLOSEPOLY () STROKE () [] FILL [h 60 sat 1 b 1]
  45. 45. Circular path
  46. 46. Circular path To draw an ellipse, MOVETO (0, 0) ARCTO (1, 0, 0.5, 0.3, 180) ARCTO (0, 0, 0.5, 0.3, 180) CLOSEPOLY () STROKE () [] FILL [h 60 sat 1 b 1]
  47. 47. Circular path
  48. 48. Colour wheel – hue
  49. 49. Example photo
  50. 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. 51. Coordinate geometry y (+) sin (θ) angle θ x (-) centre (0, 0) y (-) cos (θ) x (+)
  52. 52. More path command Let’s put it together. MOVETO (1, 0) LINETO (cos(30), sin(30)) STROKE () []
  53. 53. More path command We do repetition within a path. MOVETO (1, 0) loop 2 [r 30] { LINETO (cos(30), sin(30)) } STROKE () []
  54. 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. 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. 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. 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. 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) []
  59. 59. Sample image
  60. 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. 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. 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. 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. 64. Randomness Then we have two definitions of a shape, shape MyCoin { CoinRed [] } shape MyCoin { CoinBlue [] }
  65. 65. Randomness You test by creating a repetition of the MyCoin rule.
  66. 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. 67. Exercise Using a grid of 3 x 3 to design a few graphical patterns.
  68. 68. Exercise Using a grid of 3 x 3 to design a few graphical patterns.
  69. 69. Exercise Create a tile of the basic graphical patterns with the use of randomness.

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