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MathMod — Pretty Ball
#implicit #mathematics #surface #mathmod
Published: 2015-08-25 01:55:09 +0000 UTC; Views: 438; Favourites: 1; Downloads: 1
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Description
This mathematical object was generated using the "Thickness generator" script and MathMod-3.1.This script is an implementation of the formula I made some time ago, to generate thickness for implicit surface:
G[x, y, z] = F[x, y, z] * F[x - (T/R)*dF()/dx, y - (T/R)*dF()/dy, z - (T/R)*df()/dz]
R = sqrt[(dF()/dx)^2 + (dF()/dy)^2 + (dF()/dz)^2]
T = Thickness value
I'll show how to generate other cool mathematical object by simply changing some of this script parameters.
The attached script is a modified version of the "Thickness generator" script in order to generate the mathematical object "PrettyBall"
{
"Iso3D": {
"Description": ["TicknessGenerator-1.0 by Abderrahman Taha 24/08/2015"],
"Name": [
"TicknessGenerator"
],
"Component": [
"PrettyBall_1",
"PrettyBall_2",
"PrettyBall_3"
],
"Const": [
"cx=0.0000000000001",
"cy=0.0000000000001",
"cz=0.0000000000001",
"xmax=8",
"xmin=-8",
"ymax=8",
"ymin=-8",
"zmax=8",
"zmin=-8"
],
"Funct": [
"Iso=cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x)",
"Tickness
.9)","Tickness2
.4)","DFx
(Iso(x,y,z,t)-Iso(x+cx,y,z,t))/cx)","DFy
(Iso(x,y,z,t)-Iso(x,y+cy,z,t))/cy)","DFz
(Iso(x,y,z,t)-Iso(x,y,z+cz,t))/cz)","Rapport
sqrt(DFx(x,y,z,t)*DFx(x,y,z,t)+DFy(x,y,z,t)*DFy(x,y,z,t)+DFz(x,y,z,t)*DFz(x,y,z,t)))","Iso3
Iso(x-DFx(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),y-DFy(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),z-DFz(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),t))","Iso2
Iso(x+DFx(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),y+DFy(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),z+DFz(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),t))","Iso4
Iso(x-DFx(x,y,z,t)*Tickness2(x,y,z,t)/Rapport(x,y,z,t),y-DFy(x,y,z,t)*Tickness2(x,y,z,t)/Rapport(x,y,z,t),z-DFz(x,y,z,t)*Tickness2(x,y,z,t)/Rapport(x,y,z,t),t))","Iso5
Iso(x+DFx(x,y,z,t)*Tickness2(x,y,z,t)/Rapport(x,y,z,t),y+DFy(x,y,z,t)*Tickness2(x,y,z,t)/Rapport(x,y,z,t),z+DFz(x,y,z,t)*Tickness2(x,y,z,t)/Rapport(x,y,z,t),t))","TickIso2
Iso4(x,y,z,t)*Iso5(x,y,z,t))","isoCondition
x*x + y*y + z*z - 64)"],
"Fxyz": [
"if(isoCondition(x,y,z,t)<0, TickIso2(x,y,z,t),1) + exp(isoCondition(x,y,z,t)/3)",
"if(isoCondition(x,y,z,t)<0, Iso3(x,y,z,t),1) + exp(isoCondition(x,y,z,t)/3)",
"if(isoCondition(x,y,z,t)<0,-Iso2(x,y,z,t),1) + exp(isoCondition(x,y,z,t)/3)"
],
"Xmax": [
"8",
"8",
"8"
],
"Xmin": [
"-8",
"-8",
"-8"
],
"Ymax": [
"8",
"8",
"8"
],
"Ymin": [
"-8",
"-8",
"-8"
],
"Zmax": [
"8",
"8",
"8"
],
"Zmin": [
"-8",
"-8",
"-8"
]
}
}
