Experiments in Mathematical Web Animation

Transcription

1 Experiments in Mathematical Web Animation Steven Bellenot Mathematics Florida State University bellenot/class/f0/web/anim.pdf Mathematics and the Web Sep, 00

2 Outline

3 Outline Why animate? There is too much eye candy.

4 Outline Why animate? There is too much eye candy. Graphics formats and conversions

5 Outline Why animate? There is too much eye candy. Graphics formats and conversions Applications that can produce animations

6 Outline Why animate? There is too much eye candy. Graphics formats and conversions Applications that can produce animations Programming that can produce animations

7 Why Animate I: Sometimes time is part of the problem

8 Why Animate I: Sometimes time is part of the problem Parametric equations, time dependent DE s

9 Why Animate I: Sometimes time is part of the problem Parametric equations, time dependent DE s Data visualization of time dependent data

10 Why Animate I: Sometimes time is part of the problem Parametric equations, time dependent DE s Data visualization of time dependent data Time series

11 Why Animate I: Sometimes time is part of the problem Parametric equations, time dependent DE s Data visualization of time dependent data Time series Are weather animations eye candy?

12 Why Animate II: Time as a dimension

13 Why Animate II: Time as a dimension Using time as the th dimension

14 Why Animate II: Time as a dimension Using time as the th dimension PDE solutions u(x, t)

15 Why Animate II: Time as a dimension Using time as the th dimension PDE solutions u(x, t) x y + z = C, evolution on C

16 Why Animate II: Time as a dimension Using time as the th dimension PDE solutions u(x, t) x y + z = C, evolution on C Should we bring back family of curves?

17 Why Animate III: Time is the metaphor

18 Why Animate III: Time is the metaphor limits

19 Why Animate III: Time is the metaphor limits homotopy

20 Why Animate III: Time is the metaphor limits homotopy algorithms

21 Why Animate III: Time is the metaphor limits homotopy algorithms Is zooming in on a numerical root eye candy?

22 Still Graphics Formats Raster

23 Still Graphics Formats Raster color for each pixel

24 Still Graphics Formats Raster color for each pixel SIZE: height x width x color can be huge

25 Still Graphics Formats Raster color for each pixel SIZE: height x width x color can be huge Compression lossless vs lossy

26 Still Graphics Formats Raster color for each pixel SIZE: height x width x color can be huge Compression lossless vs lossy Gif, Png (lossless): best for geometric figures

27 Still Graphics Formats Raster color for each pixel SIZE: height x width x color can be huge Compression lossless vs lossy Gif, Png (lossless): best for geometric figures Jpg (lossy): best for photos.

28 Still Graphics Formats Vector

29 Still Graphics Formats Vector list of geometric primitives

30 Still Graphics Formats Vector list of geometric primitives ps (Adobe) pagelayout text

31 Still Graphics Formats Vector list of geometric primitives ps (Adobe) pagelayout text pdf (Adobe) pagelayout compressed text

32 Still Graphics Formats Vector list of geometric primitives ps (Adobe) pagelayout text pdf (Adobe) pagelayout compressed text dvi TEX pagelayout binary

33 Still Graphics Formats Vector list of geometric primitives ps (Adobe) pagelayout text pdf (Adobe) pagelayout compressed text dvi TEX pagelayout binary SVG web(xml)based text/binary

34 Animation Graphics Formats

35 Animation Graphics Formats Animation a sequence of still graphics (frames)

36 Animation Graphics Formats Animation a sequence of still graphics (frames) Speed fps (frames/second), normal

37 Animation Graphics Formats Animation a sequence of still graphics (frames) Speed fps (frames/second), normal Animated gifs Raster

38 Animation Graphics Formats Animation a sequence of still graphics (frames) Speed fps (frames/second), normal Animated gifs Raster Mpeg, Quicktime: Film need helpers Raster

39 Animation Graphics Formats Animation a sequence of still graphics (frames) Speed fps (frames/second), normal Animated gifs Raster Mpeg, Quicktime: Film need helpers Raster Swf (Flash Swift file) Vector

40 Maple to create an animation

41 Maple to create an animation Parametric equations

42 Maple to create an animation Parametric equations Can export to html (with animated gifs)

43 Maple to create an animation Parametric equations Can export to html (with animated gifs) Maple animation controls are lost

44 Maple to create an animation Parametric equations Can export to html (with animated gifs) Maple animation controls are lost Worst of both worlds, vector description but raster format

45 Bits n pieces to create 0000.gif

46 Bits n pieces to create 0000.gif Binary data converted to ascii

47 Bits n pieces to create 0000.gif Binary data converted to ascii Ascii data use by gnuplot yielding a xpm file

48 Bits n pieces to create 0000.gif Binary data converted to ascii Ascii data use by gnuplot yielding a xpm file Converted xpm to gif (pbm, now convert)

49 Bits n pieces to create 0000.gif Binary data converted to ascii Ascii data use by gnuplot yielding a xpm file Converted xpm to gif (pbm, now convert) glued gif s to animated gif

50 Programming animation

51 Programming animation Java program that cycles through frame files

52 Programming animation Java program that cycles through frame files Java/Javascript program that draws the frames

53 Programming animation Java program that cycles through frame files Java/Javascript program that draws the frames Flash (program)

54 Programming animation Java program that cycles through frame files Java/Javascript program that draws the frames Flash (program) Helper applications

55 Orbit

56 Orbit Illustration for a calculus project

57 Orbit Illustration for a calculus project A moon whose velocity is sometimes zero

58 Orbit Illustration for a calculus project A moon whose velocity is sometimes zero First attempt Maple

59 Orbit Illustration for a calculus project A moon whose velocity is sometimes zero First attempt Maple Second attempt Java SWF (Flash format)