Code:
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, <fD> equals the thickness, and <fE> is zero.
function makeCuboid (a, b, c, d, e)
local t = random()
local l = random3(-a, a)
local w = random3(-b, b)
local h = random3(-c, c)
local L = random3(a - d, a)
local W = random3(b - d, b)
local H = random3(c - d, c)
local p = randomSign()
if (t < 1/3) then
l = L * p
elseif (t < 2/3) then
w = W * p
elseif (t <= 1) then
h = H * p
end
return
{
l,
h,
w,
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, <fD> equals the thickness, and <fE> is zero.
function makeEllipsoid (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local H = random3(c - d, c)
local u = random3(180)
local v = random3(360)
return
{
L * cos(v) * sin(u),
H * sin(v) * sin(u),
W * cos(u),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, <fD> equals the thickness, and <fE> is zero.
function makeCylinder (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local h = random3(-c, c)
local u = random3(180)
local v = random3(360)
return
{
L * cos(v),
h,
W * sin(v),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, <fD> equals the thickness, and <fE> is zero.
function makeCone (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local h = random3(-c, c)
local v = random3(360)
return
{
(1 - h / c) * L * cos(v) / 2,
h,
(1 - h / c) * W * sin(v) / 2,
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the width of the tube, <fD> equals the thickness, and <fE> equals the height of the tube.
function makeToroid (a, b, c, d, e)
local H = random3(c - d, c)
local M = random3(e - d, e)
local v = random3(360)
local o = random3(360)
return
{
(a + M * cos(v)) * cos(o),
H * sin(v),
(b + M * cos(v)) * sin(o),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, and <fD> equals the width (thickness is not supported), <fE> is the number of revolutions.
function makeHelicoid (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local t = random()
return
{
L * cos(t * e * 360),
c * (2 * t - 1),
W * sin(t * e * 360),
}
end
-- <fA> equals the length of axis 1 at a height of 1000 units, <fB> equals the length of axis 2 at a height of 1000 units, <fC> equals the length of axis 3, <fD> equals the thickness, and <fE> is zero.
function makeParaboloid (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local h = random3(-c, c)
local v = random3(360)
return
{
L * sqrt(h / 1000) * cos(v),
h,
W * sqrt(h / 1000) * sin(v),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, <fD> equals the thickness, and <fE> is zero.
function makeHyperboloid (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local H = random3(c - d, c)
local t = random()
local v = random3(360)
local p = randomSign()
return
{
L * sqrt(1 + (t * p)^2) * cos(v),
H * (t * p),
W * sqrt(1 + (t * p)^2) * sin(v),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, <fD> equals the thickness, and <fE> is zero.
function makeAstroid (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local H = random3(c - d, c)
local v = random3(360)
local o = random3(360)
return
{
L * (cos(o) * cos(v))^3,
H * (sin(v))^3,
W * (sin(o) * cos(v))^3,
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals roughly the inverse of the length of axis 3 for large numbers of objects, <fD> equals the thickness, and <fE> is zero.
function makeFunnel (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local H = random3(c - d, c)
local t = random()
local v = random3(360)
return
{
L * t * cos(v),
H * log(t) / 10,
W * t * sin(v),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the distance between each twist, <fD> is zero, and <fE> is the number of twists.
function makeDini (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local H = random3(c - d, c)
local v = random3(360)
local u = random3(180)
return
{
L * (cos(e * v) * sin(u/2)),
H * (cos(u/2) + log(tan(u/4)) + rad(e * v) / (2 * PI)),
W * (sin(e * v) * sin(u/2)),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the height of the screw, <fD> is zero, and <fE> is zero.
function makeCorkscrew (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local H = random3(c - d, c)
local v = random3(360)
local u = random3(180)
return
{
L * cos(v) * cos(u),
H * rad(v) / (2 * PI),
W * sin(v) * cos(u),
}
end
-- <fA> equals the length of axis 1 of the tube, <fB> equals the length of axis 2 of the tube, <fC> equals the vertical separation between revolutions, <fD> equals the radius of the center gap, and <fE> equals the number of revolutions.
function makeSeashell (a, b, c, d, e)
local t = random()
local o = random3(360)
return
{
(d / e + (1 - t) * (1 + cos(o))) * a * cos(e * t * 360),
c * t^(1/2) * (2 * e - 1) + b * sin(o) * (1 - t),
(d / e + (1 - t) * (1 + cos(o))) * a * sin(e * t * 360),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the maximum height of the wave, <fD> zero, and <fE> equals the frequency of the wave pattern.
function makeSineDisc (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local H = random3(c - d, c)
local t = random()
local v = random3(360)
return
{
L * t * cos(v),
H * sin(t * 360 * e),
W * t * sin(v),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the maximum height of the wave, <fD> zero, and <fE> equals the frequency of the wave pattern.
function makeSinePlane (a, b, c, d, e)
local s = random()
local t = random()
return
{
a * s * 2 - a,
c * (sin(s * 360 * e) + sin(t * 360 * e)) / 2,
b * t * 2 - b,
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals half the width of the strip, <fD> is zero, and <fE> is zero.
function makeMoebius (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local h = random3(-c, c)
local v = random3(360)
return
{
L * cos(v) + h * cos(v/2) * cos(v),
h * sin(v/2),
W * sin(v) + h * cos(v/2) * sin(v),
}
end
-- <fA> equals the length of the bounding cube, <fB> equals the thickenss of the curve, <fD> equals the speed of the second arc relative to the first, <fD> equals the speed of the third arc relative to the first, and <fE> equals the number of revolutions.
function makeLissajous3D (a, b, c, d, e)
local v = random3(360)
local o = random3(360)
local u = random3(180)
return
{
a * sin(v * e) + b * sin(u) * cos(o),
a * sin(v * e * c) + b * sin(u) * sin(o),
a * sin(v * e * d) + b * cos(u),
}
end
-- <fA> equals the scaling along the x-axis, <fB> equals the scaling along the z-axis, <fC> equals the scaling along the y-axis, <fD> is zero, and <fE> is zero.
function makeKlein (a, b, c, d, e)
local u = random3(360)
local v = random3(180)
local X = cos(u) * (cos(u/2) * (sqrt(2) + cos(v)) + sin(u/2) * sin(v) * cos(v))
local Y = -1 * sin(u/2) * (sqrt(2) + cos(v)) + cos(u/2) * sin(v) * cos(v)
local Z = sin(u) * (cos(u/2) * (sqrt(2) + cos(v)) + sin(u/2) * sin(v) * cos(v))
return
{
X * a,
Y * c,
Z * b,
}
end
-- <fA> equals the scaling along the x-axis, <fB> equals the scaling along the z-axis, <fC> equals the scaling along the y-axis, <fD> is zero, and <fE> is zero.
function makeKlein8 (a, b, c, d, e)
local u = random3(360)
local v = random3(360)
local X = (e + cos(u/2) * sin(v) - sin(u/2) * sin(v*2)) * cos(u)
local Y = sin(u/2) * sin(v) + cos(u/2) * sin(v*2)
local Z = (e + cos(u/2) * sin(v) - sin(u/2) * sin(v*2)) * sin(u)
return
{
X * a,
Y * c,
Z * b,
}
end
-- description missing
function makeKuen (a, b, c, d, e)
local u = random3(180)
local v = random3(360)
local X = 2 * (cos(v) + rad(v) * sin(v)) * sin(u) / (1 + rad(v)^2 * sin(u)^2)
local Y = log(tan(u/2)) + 2 * cos(u) / (1 + rad(v)^2 * sin(u)^2)
local Z = 2 * (sin(v) - rad(v) * cos(v)) * sin(u) / (1 + rad(v)^2 * sin(u)^2)
return
{
X * a,
Y * c,
Z * b,
}
end
-- <fA> equals the scaling along the x-axis, <fB> equals the scaling along the z-axis, <fC> equals the scaling along the y-axis, <fD> is zero, and <fE> is an integer greater than 2.
function makeBoy (a, b, c, d, e)
local u = random3(360)
local v = random3(180)
local X = (2/3) * (cos(u) * cos(2 * v) + sqrt(2) * sin(u) * cos(v)) * cos(u) / (sqrt(2) - sin(2 * u) * sin(3 * v))
local Y = sqrt(2) * cos(u)^2 / (sqrt(2) - sin(2 * u) * sin(2 * v))
local Z = (2/3) * (cos(u) * sin(2 * v) - sqrt(2) * sin(u) * sin(v)) * cos(u) / (sqrt(2) - sin(2 * u) * sin(3 * v))
return
{
X * a,
Y * c,
Z * b,
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, and <fD> equals the thickness.
function makeRectangle (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local l = random3(-a, a)
local w = random3(-b, b)
local h = random3(-c, c)
local p = randomSign()
if (t <= 1/2) then
l = L * p
elseif (t <= 1) then
w = W * p
end
return
{
l,
h,
w,
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the length of axis 3, and <fD> equals the thickness.
function makeEllipse (a, b, c, d, e)
local L = random3(a - d, a)
local W = random3(b - d, b)
local h = random3(-c, c)
local v = random3(360)
return
{
L * cos(v),
h,
W * sin(v),
}
end
-- <fA> equals the distance between the vertex and the focus, <fB> equals the length, <fC> equals the height, and <fD> equals the thickness.
function makeParabola (a, b, c, d, e)
local w = random3(-b, b)
local h = random3(-c, c)
local p = randomSign()
return
{
sqrt(4 * w * a) * p + random3(-d/2, d/2),
h,
w + random3(-d/2, d/2),
}
end
-- <fA> equals the length of axis 1, <fB> equals the length of axis 2, <fC> equals the distance from the origin to one of the foci, <fD> equals the thickness.
function makeHyperbola (a, b, c, d, e)
local h = random3(-c, c)
local v = random3(360)
return
{
a / cos(v) + random3(-d/2, d/2),
h,
b * tan(v) + random3(-d/2, d/2),
}
end
-- <fA> equals the radius of the greater circle, <fB> equals the radius of the lesser circle, <fC> equals the height above or below the plane, <fD> equals the distance from the center of the lesser circle, and <fE> equals the number of revolutions.
function makeHypotrochoid (a, b, c, d, e)
local h = random3(-c, c)
local v = random3(360)
return
{
(a - b) * cos(v * e) + d * cos((a - b) / b * v * e),
h,
(a - b) * sin(v * e) - d * sin((a - b) / b * v * e),
}
end
-- <fA> equals the radius of the greater circle, <fB> equals the radius of the lesser circle, <fC> equals the height above or below the plane, <fD> equals the distance from the center of the lesser circle, and <fE> equals the number of revolutions.
function makeEpitrochoid (a, b, c, d, e)
local h = random3(-c, c)
local v = random3(360)
return
{
(a + b) * cos(v * e) - d * cos((a + b) / b * v * e),
h,
(a + b) * sin(v * e) - d * sin((a + b) / b * v * e),
}
end
-- <fA> equals the length of the bounding square, <fB> equals the phase shift, <fC> equals the height of the curve, <fD> equals the speed of the second arc relative to the first, and <fE> equals the number of revolutions.
function makeLissajous2D (a, b, c, d, e)
local h = random3(-c, c)
local v = random3(360)
return
{
a * sin(v * e + b),
h,
a * sin(v * e * d),
}
end
