HOME | DD

Description
Superformula, from Johan Gielis who was the first to propose a new geometrical approach for modelling and understanding various abstract, natural, and man-made shapes.
The Superformula :
x = R1(θ)cos(θ)* R2(phi)cos(phi),
y = R1(θ)sin(θ) * R2(phi)cos(phi),
z = R2(phi)sin(phi),
where phi (latitude) varies between −π/2 and π/2, θ (longitude) between −π and π, R1 and R2 are superformulas equations in polar coordinates.
Johan Gielis's article: www.amjbot.org/content/90/3/33…
Wikipedia: en.wikipedia.org/wiki/Superfor…
MathMod script:
{
"Param3D": {
"Name": [
"Star_7"
],
"Component": [
"Star_7"
],
"Fx": [
"cos(u)*cos(v)*(abs(cos(7*v/4))^1.7+abs(sin(7*v/4))^1.7)^(-1/0.2)*(abs(cos(7*u/4))^1.7+abs(sin(7*u/4))^1.7)^(-1/0.2)"
],
"Fy": [
"cos(u)*sin(v)*(abs(cos(7*v/4))^1.7+abs(sin(7*v/4))^1.7)^(-1/0.2)*(abs(cos(7*u/4))^1.7+abs(sin(7*u/4))^1.7)^(-1/0.2)"
],
"Fz": [
"sin(u)*(abs(cos(7*u/4))^1.7+abs(sin(7*u/4))^1.7)^(-1/0.2)"
],
"Umax": [
"pi/2"
],
"Umin": [
"-pi/2"
],
"Vmax": [
"2*pi"
],
"Vmin": [
"0"
]
},
"Texture": {
"Colors": [
"R=1.5*cos(x*pi)*sin(z*pi)",
"G=1.5*sin(x*pi)*cos(y*pi)",
"B=1.5*sin(y*pi)*cos(z*pi)",
"T=1"
],
"Name": "Lines3",
"Noise": "NoiseW(10*x,10*y,10*z,1,2,0)"
}
}

Description
Superformula, from Johan Gielis who was the first to propose a new geometrical approach for modelling and understanding various abstract, natural, and man-made shapes.
The Superformula :
x = R1(θ)cos(θ)* R2(phi)cos(phi),
y = R1(θ)sin(θ) * R2(phi)cos(phi),
z = R2(phi)sin(phi),
where phi (latitude) varies between −π/2 and π/2, θ (longitude) between −π and π, R1 and R2 are superformulas equations in polar coordinates.
Johan Gielis's article: www.amjbot.org/content/90/3/33…
Wikipedia: en.wikipedia.org/wiki/Superfor…
MathMod script:
{
"Param3D": {
"Name": [
"Star_7"
],
"Component": [
"Star_7"
],
"Fx": [
"cos(u)*cos(v)*(abs(cos(7*v/4))^1.7+abs(sin(7*v/4))^1.7)^(-1/0.2)*(abs(cos(7*u/4))^1.7+abs(sin(7*u/4))^1.7)^(-1/0.2)"
],
"Fy": [
"cos(u)*sin(v)*(abs(cos(7*v/4))^1.7+abs(sin(7*v/4))^1.7)^(-1/0.2)*(abs(cos(7*u/4))^1.7+abs(sin(7*u/4))^1.7)^(-1/0.2)"
],
"Fz": [
"sin(u)*(abs(cos(7*u/4))^1.7+abs(sin(7*u/4))^1.7)^(-1/0.2)"
],
"Umax": [
"pi/2"
],
"Umin": [
"-pi/2"
],
"Vmax": [
"2*pi"
],
"Vmin": [
"0"
]
},
"Texture": {
"Colors": [
"R=1.5*cos(x*pi)*sin(z*pi)",
"G=1.5*sin(x*pi)*cos(y*pi)",
"B=1.5*sin(y*pi)*cos(z*pi)",
"T=1"
],
"Name": "Lines3",
"Noise": "NoiseW(10*x,10*y,10*z,1,2,0)"
}
}