tour.xtl

1⍝!/usr/bin/env xetal
2⍝ Manifold, the spaces drawn: a point of each kind from its map, and
3⍝ one distance measured along each space against the straight line
4⍝ through it. Run with "just demo Manifold tour".
5"mf:" u̲se< "Manifold"
6
7Pi ← p̲i @
8
9⍝ Two points of the sphere a tenth of a radian apart along the
10⍝ equator, and two a quarter turn apart: the straight line and the
11⍝ great circle, nearly equal near, not far.
12near ← ᵐᶠs̲pherePoints 2 2 r̲eshape 0.0 0.0 0.1 0.0
13far ← ᵐᶠs̲pherePoints (Pi ÷ 2.0) × 2 2 r̲eshape 0.0 0.0 1.0 0.0
14(s̲qrt '+ r̲/ ((1 s̲elect near) − 2 s̲elect near) ^ 2.0) c̲at (1 s̲elect near) ᵐᶠs̲phereDistance 2 s̲elect near
15(s̲qrt '+ r̲/ ((1 s̲elect far) − 2 s̲elect far) ^ 2.0) c̲at (1 s̲elect far) ᵐᶠs̲phereDistance 2 s̲elect far
16
17⍝ Five points along the great circle between the two far points.
18(1 s̲elect far, 2 s̲elect far) ᵐᶠs̲phereArc 4
19
20⍝ The torus of radii 3 and 1: its outer rim, its inner rim, and how
21⍝ far off it the middle of the hole is.
223.0 1.0 ᵐᶠt̲orusPoints Pi × 2 2 r̲eshape 0.0 0.0 0.0 1.0
233.0 1.0 ᵐᶠt̲orusOff 0.0 0.0 0.0
24
25⍝ Two points of the Swiss roll one turn apart at the same height: 2 pi
26⍝ apart through the air, and along the sheet much farther.
27a ← 6.0 0.0
28b ← (6.0 + 2.0 × Pi) c̲at 0.0
29W ← ᵐᶠr̲ollPoints 2 2 r̲eshape a c̲at b
30W
31(s̲qrt '+ r̲/ ((1 s̲elect W) − 2 s̲elect W) ^ 2.0) c̲at a ᵐᶠr̲ollDistance b
32
33⍝ Two points of the Poincare disk 0.2 apart in the plane, near the
34⍝ middle and near the rim: the disk's distance between them.
35(0.0 0.0 ᵐᶠb̲allDistance 0.2 0.0) c̲at 0.78 0.0 ᵐᶠb̲allDistance 0.98 0.0
36(0.78 0.0, 0.98 0.0) ᵐᶠb̲allGeodesic 2