-
Notifications
You must be signed in to change notification settings - Fork 41
/
loxodrome_concat.scad
137 lines (116 loc) · 4.41 KB
/
loxodrome_concat.scad
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
// loxodrome
// uses open tube code
// orginal endless tube code by nop head
// requires openscad development snapshot 2014-01-14 e
// http://www.openscad.org/downloads.html
// with concat enabled in edit/preferences/features
function m_translate(v) = [ [1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[v.x, v.y, v.z, 1 ] ];
function m_rotate(v) = [ [1, 0, 0, 0],
[0, cos(v.x), sin(v.x), 0],
[0, -sin(v.x), cos(v.x), 0],
[0, 0, 0, 1] ]
* [ [ cos(v.y), 0, -sin(v.y), 0],
[0, 1, 0, 0],
[ sin(v.y), 0, cos(v.y), 0],
[0, 0, 0, 1] ]
* [ [ cos(v.z), sin(v.z), 0, 0],
[-sin(v.z), cos(v.z), 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1] ];
function vec3(v) = [v.x, v.y, v.z];
function transform(v, m) = vec3([v.x, v.y, v.z, 1] * m);
function orientate(p0, p) =
m_rotate([0, atan2(sqrt(pow(p[0], 2) + pow(p[1], 2)), p[2]), 0])
* m_rotate([0, 0, atan2(p[1], p[0])])
* m_translate(p0);
function circle_points(r = 1, a = 0) =
a < 360
? concat([[r * sin(a), r * cos(a),0]], circle_points(r, a + 360 / $fn))
: [] ;
function loop_points(step, end , t = 0) =
t <= end
? concat([f(t)], loop_points(step, end, t + step))
: [] ;
function transform_points(list, matrix, i = 0) =
i < len(list)
? concat([ transform(list[i], matrix) ], transform_points(list, matrix, i + 1))
: [];
function tube_points(loop_points, section_points, i=0) =
i < len(loop_points)-1
? concat(
transform_points(
section_points,
orientate(loop_points[i],(loop_points[i + 1]- loop_points[i])/2)),
tube_points(loop_points,section_points, i + 1))
: []
;
function tube_faces(facets, s, i = 0) =
i < facets
? concat([[s * facets + i,
s * facets + (i + 1) % facets,
(s + 1) * facets + (i + 1) % facets,
(s + 1) * facets + i]
],
tube_faces(facets, s, i + 1))
: [];
function tube_end(facets, s, i = 0) =
i < facets
? concat( [s * facets + i], tube_end(facets, s, i+1))
: [];
function loop_faces(segs,facets, j = 0) =
j < segs
? concat(tube_faces(facets, j), loop_faces(segs, facets, j + 1))
: [];
function loop_all_faces(segs,facets) =
concat (
[reverse(tube_end(facets,0))], // reverse direction for this face
loop_faces(segs,facets),
[tube_end(facets,segs)]);
function reverse_r(v,n) =
n == 0
? [v[0]]
: concat([v[n]],reverse_r(v,n-1))
;
function reverse(v) = reverse_r(v, len(v)-1);
pi = 3.14159;
rad = 2 * pi / 360;
function sinh(x) = (1 - exp( -2 * x) )/ (2 * exp(-x));
function cosh(x) = (1 + exp( -2 * x)) / (2 * exp(-x));
function tanh(x) = sinh(x) / cosh(x);
function cot(x) = 1 / tan(x);
/*
for ( x = [ -e: 0.1: e])
echo (x, sinh(x), cosh(x), tanh(x));
*/
function m(beta,long,long0) = cot(beta) * ( long - long0) * rad;
function lox (t,beta,long0) =
[ cos(t) / cosh(m(beta,t,long0)),
sin(t) / cosh(m(beta,t,long0)),
tanh(m(beta,t,long0))
];
function f(t) = [0,r *sin(t), r * cos(t) ];
function loop_points(step, end, t = 0, beta,long0, r ) =
t <= end
? concat(r*[lox(t,beta,long0)], loop_points(step, end, t + step, beta,long0, r ))
: [] ;
step=10;
r=10;
thickness=0.5;
long0 = 0;
beta = 70;
section_points = circle_points(thickness, $fn=20); // some values will break the polyhedron
// echo(section_points);
translate([0,0,r + thickness])
for (a= [0:90:270]) {
rotate([0,0,a])
assign(loop_points = loop_points(step, 500, -500, beta ,long0, r))
// echo(loop_points);
assign(tube_points = tube_points(loop_points,section_points),
// echo(tube_points);
faces = loop_all_faces(len(loop_points)-2, len(section_points)))
// echo(faces);
polyhedron(points = tube_points, faces = faces);
}