.. status: ok 21.4 images5.input ------------------ The parameterization of the Etruscan Venus is due to George Frances. Etruscan Venus .. spadVerbatim :: venus(a,r,steps) ==   surf := (u:DFLOAT, v:DFLOAT): Point DFLOAT +->     cv := cos(v)     sv := sin(v)     cu := cos(u)     su := sin(u)     x := r * cos(2*u) * cv + sv * cu     y := r * sin(2*u) * cv - sv * su     z := a * cv     point [x,y,z]   draw(surf, 0..%pi, -%pi..%pi, var1Steps==steps,        var2Steps==steps, title == "Etruscan Venus") venus(5/2, 13/10, 50)                                  The Etruscan Venus The Figure-8 Klein Bottle Klein bottle parameterization is from Differential Geometry and Computer Graphics by Thomas Banchoff, in Perspectives in Mathematics, Anniversary of Oberwolfasch 1984, Birkh\\"{a}user-Verlag, Basel, pp. 43-60. .. spadVerbatim :: klein(x,y) ==   cx := cos(x)   cy := cos(y)   sx := sin(x)   sy := sin(y)   sx2 := sin(x/2)   cx2 := cos(x/2)   sq2 := sqrt(2.0@DFLOAT)   point [cx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), _          sx * (cx2 * (sq2 + cy) + (sx2 * sy * cy)), _          -sx2 * (sq2 + cy) + cx2 * sy * cy] draw(klein, 0..4*%pi, 0..2*%pi, var1Steps==50,             Figure-8 Klein bottle      var2Steps==50,title=="Figure Eight Klein Bottle") The next two images are examples of generalized tubes. .. spadVerbatim :: )read ntube rotateBy(p, theta) ==                                      Rotate a point p by   c := cos(theta)                                          θ around the origin   s := sin(theta)   point [p.1*c - p.2*s, p.1*s + p.2*c] bcircle t ==                                               A circle in three-space   point [3*cos t, 3*sin t, 0] twist(u, t) ==                                             An ellipse that twists   theta := 4*t                                             around four times as   p := point [sin u, cos(u)/2]                             t revolves once   rotateBy(p, theta) ntubeDrawOpt(bcircle, twist, 0..2*%pi, 0..2*%pi,           Twisted Torus              var1Steps == 70, var2Steps == 250) twist2(u, t) ==                                            Create a twisting circle   theta := t   p := point [sin u, cos(u)]   rotateBy(p, theta) cf(u,v) == sin(21*u)                                       Color function with 21 stripes ntubeDrawOpt(bcircle, twist2, 0..2*%pi, 0..2*%pi,          Striped Torus   colorFunction == cf, var1Steps == 168,   var2Steps == 126)