1--Copyright The Numerical Algorithms Group Limited 1994.
2
3-- Color gallery page 5
4
5
6-- Etruscan Venus
7-- Parameterization by George Frances
8
9venus(a,r,steps) ==
10  surf := (u:DoubleFloat, v:DoubleFloat): Point DoubleFloat +->
11    cv := cos(v)
12    sv := sin(v)
13    cu := cos(u)
14    su := sin(u)
15    x := r * cos(2*u) * cv + sv * cu
16    y := r * sin(2*u) * cv - sv * su
17    z := a * cv
18    point [x,y,z]
19  draw(surf, 0..%pi, -%pi..%pi, var1Steps==steps,var2Steps==steps,
20       title == "Etruscan Venus")
21
22venus(5/2, 13/10, 50)
23
24-- Figure Eight Klein Bottle
25-- Parameterization from:
26-- "Differential Geometry and Computer Graphics" by Thomas Banchoff
27-- in Perspectives in Mathemtaics, Anneversry of Oberwolfasch 1984.
28-- Beirkhauser-Verlag, Basel, pp 43-60.
29
30klein(x,y) ==
31  cx := cos(x)
32  cy := cos(y)
33  sx := sin(x)
34  sy := sin(y)
35  sx2 := sin(x/2)
36  cx2 := cos(x/2)
37  sq2 := sqrt(2.0@DoubleFloat)
38  point [cx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), _
39         sx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), _
40         -sx2 * (sq2 + cy) + cx2 * sy * cy]
41
42draw(klein, 0..4*%pi, 0..2*%pi, var1Steps==50, var2Steps==50, _
43     title=="Figure Eight Klein Bottle")
44
45-- Twisted torus
46
47)read ntube
48
49-- rotate a 2-d point by theta round the origin
50rotateBy(p, theta) ==
51  c := cos(theta)
52  s := sin(theta)
53  point [p.1*c - p.2*s, p.1*s + p.2*c]
54
55-- a circle in 3-space
56bcircle t ==
57  point [3*cos t, 3*sin t, 0]
58
59-- an ellipse which twists around 4 times as t revolves once.
60twist(u, t) ==
61  theta := 4*t
62  p := point [sin u, cos(u)/2]
63  rotateBy(p, theta)
64
65ntubeDrawOpt(bcircle, twist, 0..2*%pi, 0..2*%pi, _
66             var1Steps == 70, var2Steps == 250)
67
68-- Striped torus
69
70-- a twisting circle
71twist2(u, t) ==
72  theta := t
73  p := point [sin u, cos(u)]
74  rotateBy(p, theta)
75
76-- color function producing 21 stripes
77cf(u,v) == sin(21*u)
78
79ntubeDrawOpt(bcircle, twist2, 0..2*%pi, 0..2*%pi, _
80              colorFunction == cf, var1Steps == 168, var2Steps == 126)
81