-- <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