HOME | DD
MathMod — Bended Schwarz Torus
#3d #mathmod #mathematics
Published: 2015-11-23 00:19:10 +0000 UTC; Views: 273; Favourites: 2; Downloads: 1
Redirect to original
Description
Bended Schwarz CubeThis mathematical model is a bended cube, filled with "thick" Schwarz minimal surfaces.
The fourth image show the steps it took to model this object, starting with the Schwarz minimal surface.
MathMod script:
{
"Iso3D": {
"Description": ["Schwarz Cube Torus-1.0 by Abderrahman Taha 22/11/2015"],
"Name": ["Schwarz Cube Torus"],
"Component": ["SchwarzCubeTorus_1",
"SchwarzCubeTorus_2",
"SchwarzCubeTorus_3",
"SchwarzCubeTorus_4"],
"Const": ["k=6"],
"Funct": ["Iso=cos(x)+cos(y)+cos(z)",
"Iso4= (Iso(x+sin(x)*.4/sqrt(sin(x)*sin(x)+sin(y)*sin(y)+sin(z)*sin(z)),y+sin(y)*.4/sqrt(sin(x)*sin(x)+sin(y)*sin(y)+sin(z)*sin(z)),z+sin(z)*.4/sqrt(sin(x)*sin(x)+sin(y)*sin(y)+sin(z)*sin(z)),t))",
"Iso5= (Iso(x-sin(x)*.4/sqrt(sin(x)*sin(x)+sin(y)*sin(y)+sin(z)*sin(z)),y-sin(y)*.4/sqrt(sin(x)*sin(x)+sin(y)*sin(y)+sin(z)*sin(z)),z-sin(z)*.4/sqrt(sin(x)*sin(x)+sin(y)*sin(y)+sin(z)*sin(z)),t))",
"TickIso2= (Iso4(x,y,z,t)*Iso5(x,y,z,t))",
"isoCondition= (x^20+(y/4)^20+z^20-3.23^20)",
"isoTransform_2=if(isoCondition(x,y,z,t)<0,TickIso2(k*x,k*y,k*z,t),1)",
"isoTransform_3=isoTransform_2(x*cos(pi*y/(k*pi))-z*sin(pi*y/(k*pi)),y,x*sin(pi*y/(k*pi))+z*cos(pi*y/(k*pi)),t)"],
"Fxyz": ["-isoTransform_3(sqrt(x*x+y*y)-6.5,3*atan2(y,x),z,t)",
"-isoTransform_3(sqrt(x*x+y*y)-6.5,3*atan2(y,x),z,t)",
"-isoTransform_3(sqrt(x*x+y*y)-6.5,3*atan2(y,x),z,t)",
"-isoTransform_3(sqrt(x*x+y*y)-6.5,3*atan2(y,x),z,t)"],
"Xmax": ["0",
"0",
"11",
"11"],
"Xmin": ["-11",
"-11",
"0",
"0"],
"Ymax": ["0",
"11",
"0",
"11"],
"Ymin": ["-11",
"0",
"-11",
"0"],
"Zmax": ["5",
"5",
"5",
"5"],
"Zmin": ["-5",
"-5",
"-5",
"-5"]
},
"Texture": {
"Colors": ["R=.8",
"G=0.6",
"B=0.1",
"T=1"],
"Name": "Gold",
"Noise": "1"
}
}
