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Description
The beautiful "Richmond Polar" parametric surface...
MathMod script:
{
"Param3D": {
"Name": [
"Richmondpolar"
],
"Component": [
"richmondpolar"
],
"Description ": [
"richmondpolar(n)[t](u,v):={-cos(t + v)/(2*u) -u^(2*n + 1)*cos(t - (2*n + 1)*v)/(4*n + 2),-sin(t + v)/(2*u) +u^(2*n + 1)*sin(t - (2*n + 1)*v)/(4*n + 2),u^n*cos(t - n*v)/n}is the polar parametrization of a 1-parameter family of minimal surfaces such that {r,theta}->richmondpolar[n][0][r,theta] is a minimal surface with one planar end of degree n."
],
"Fx": [
"-cos(t + v)/(2*u) - u^3*cos(t - 3*v)/6"
],
"Fy": [
"-sin(t + v)/(2*u) + u^3*sin(t - 3*v)/6"
],
"Fz": [
"u*cos(t - v)"
],
"Umax": [
"1.3"
],
"Umin": [
"0.3"
],
"Vmax": [
"2*pi"
],
"Vmin": [
"0"
]
},
"Texture": {
"Colors": [
"R=1.5*.41",
"G=2*0.81*abs(cos((x*x+y*y+z*z)/2)*sin((x*x+y*y+z*z)/2))",
"B=2*0.8601*abs(cos((x*x+y*y+z*z)/2)*cos((x*x+y*y+z*z)/2)*sin((x*x+y*y+z*z)/2))",
"T=1"
],
"Name": "WorleyNoise",
"Noise": "NoiseW(4*x,4*y,4*z,4,2,0)+NoiseW(4*x,4*y,4*z,4,12,0.1)"
}
}
MathMod script:
{
"Param3D": {
"Name": [
"Richmondpolar"
],
"Component": [
"richmondpolar"
],
"Description ": [
"richmondpolar(n)[t](u,v):={-cos(t + v)/(2*u) -u^(2*n + 1)*cos(t - (2*n + 1)*v)/(4*n + 2),-sin(t + v)/(2*u) +u^(2*n + 1)*sin(t - (2*n + 1)*v)/(4*n + 2),u^n*cos(t - n*v)/n}is the polar parametrization of a 1-parameter family of minimal surfaces such that {r,theta}->richmondpolar[n][0][r,theta] is a minimal surface with one planar end of degree n."
],
"Fx": [
"-cos(t + v)/(2*u) - u^3*cos(t - 3*v)/6"
],
"Fy": [
"-sin(t + v)/(2*u) + u^3*sin(t - 3*v)/6"
],
"Fz": [
"u*cos(t - v)"
],
"Umax": [
"1.3"
],
"Umin": [
"0.3"
],
"Vmax": [
"2*pi"
],
"Vmin": [
"0"
]
},
"Texture": {
"Colors": [
"R=1.5*.41",
"G=2*0.81*abs(cos((x*x+y*y+z*z)/2)*sin((x*x+y*y+z*z)/2))",
"B=2*0.8601*abs(cos((x*x+y*y+z*z)/2)*cos((x*x+y*y+z*z)/2)*sin((x*x+y*y+z*z)/2))",
"T=1"
],
"Name": "WorleyNoise",
"Noise": "NoiseW(4*x,4*y,4*z,4,2,0)+NoiseW(4*x,4*y,4*z,4,12,0.1)"
}
}
Image size
1918x1700px 1.04 MB
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Comments2
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Elegant shape and a great texture too! 