/usr/share/axiom-20120501/input/antoine.input is in axiom-test 20120501-8.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | )set break resume
)spool antoine.output
)set message test on
)set message auto off
)clear all
--S 1 of 11
)set expose add con DenavitHartenbergMatrix
--R
--I DenavitHartenbergMatrix is now explicitly exposed in frame frame0
--E 1
--S 2 of 11
tri2tri(t1: List Point DoubleFloat, t2: List Point DoubleFloat): _
DHMATRIX(DoubleFloat) ==
n1 := triangleNormal(t1)
n2 := triangleNormal(t2)
tet2tet(concat(t1, n1), concat(t2, n2))
--R
--R Function declaration tri2tri : (List(Point(DoubleFloat)),List(Point(
--R DoubleFloat))) -> DenavitHartenbergMatrix(DoubleFloat) has been
--R added to workspace.
--R Type: Void
--E 2
--S 3 of 11
tet2tet(t1: List Point DoubleFloat, t2: List Point DoubleFloat): _
DHMATRIX(DoubleFloat) ==
m1 := makeColumnMatrix t1
m2 := makeColumnMatrix t2
m2 * inverse(m1)
--R
--R Function declaration tet2tet : (List(Point(DoubleFloat)),List(Point(
--R DoubleFloat))) -> DenavitHartenbergMatrix(DoubleFloat) has been
--R added to workspace.
--R Type: Void
--E 3
--S 4 of 11
makeColumnMatrix(t) ==
m := new(4,4,0)$DHMATRIX(DoubleFloat)
for x in t for i in 1..repeat
for j in 1..3 repeat
m(j,i) := x.j
m(4,i) := 1
m
--R
--R Type: Void
--E 4
--S 5 of 11
triangleNormal(t) ==
a := triangleArea t
p1 := t.2 - t.1
p2 := t.3 - t.2
c := cross(p1, p2)
len := length(c)
len = 0 => error "degenerate triangle!"
c := (1/len)*c
t.1 + sqrt(a) * c
--R
--R Type: Void
--E 5
--S 6 of 11
triangleArea t ==
a := length(t.2 - t.1)
b := length(t.3 - t.2)
c := length(t.1 - t.3)
s := (a+b+c)/2
sqrt(s*(s-a)*(s-b)*(s-c))
--R
--R Type: Void
--E 6
--S 7 of 11
torusRot: DHMATRIX(DoubleFloat)
--R
--R Type: Void
--E 7
--S 8 of 11
drawRings(n) ==
s := create3Space()$ThreeSpace DoubleFloat
-- create an identity transformation
dh:DHMATRIX(DoubleFloat) := identity()
drawRingsInner(s, n, dh)
makeViewport3D(s, "Antoine's Necklace")
--R
--R Type: Void
--E 8
--S 9 of 11
drawRingsInner(s, n, dh) ==
n = 0 =>
drawRing(s, dh)
void()
t := 0.0@DoubleFloat -- the current angle around the ring
p := 0.0@DoubleFloat -- the angle of the subring from the plane
tr := 1.0@DoubleFloat -- the amount to translate the subring
inc := 0.1@DoubleFloat -- translation increment
-- subdivide the ring into 10 linked rings
for i in 1..10 repeat
tr := tr + inc
inc := -inc
dh' := dh * rotatez(t) * translate(tr, 0.0@DoubleFloat, 0.0@DoubleFloat) *
rotatey(p) * scale(0.35@DoubleFloat, 0.48@DoubleFloat, 0.4@DoubleFloat)
drawRingsInner(s, n-1, dh')
t := t + 36.0@DoubleFloat
p := p + 90.0@DoubleFloat
void()
--R
--R Type: Void
--E 9
--S 10 of 11
drawRing(s, dh) ==
free torusRot
torusRot := dh
makeObject(torus, 0..2*%pi, 0..2*%pi, var1Steps == 6, space == s,
var2Steps == 15)
--R
--R Type: Void
--E 10
--S 11 of 11
torus(u ,v) ==
cu := cos(u)/6
torusRot * point [(1+cu)*cos(v), (1+cu)*sin(v), (sin u)/6]
--R
--R Type: Void
--E 11
)spool
)lisp (bye)
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