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Skeletal Sphere

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Description

"Skeletal Sphere" (parametric & implicit ) versions
The top two images are for the parametric version. The others are for the implicit version.
This model is to show a very interesting fact:I had only to work the "Thickness" definition from the implicit version of the "Skeletal Sphere" to get this new parametric model!
Mainly the work was done when I did this conversion:
"Tickness= (.1*cos(10*atan2(x,y))*sin(10*atan2(z,sqrt(x*x+y*y))))",
converted to :
"Tickness=abs(.1*cos(10*u)*sin(10*v))"


"Skeletal Sphere" (parametric version)

MathMod script:
{
"Param3D": {
"Description ": ["Skeletal Sphere (parametric version) by Abderrahman Taha 05/10/2015"],
"Name": ["Skeletal Sphere (parametric version)"],
"Component": ["SkeletalSphere"],
"Const": ["cu=0.0000000000001",
"cv=0.0000000000001"],
"Funct":  ["Fx=cos(u)*cos(v)",
"Fy=cos(u)*sin(v)",
"Fz=sin(u)",
"DFxu= ((Fx(u,v,t)-Fx(u+cu,v,t))/cu)",
"DFxv= ((Fx(u,v,t)-Fx(u,v+cv,t))/cv)",
"DFyu= ((Fy(u,v,t)-Fy(u+cu,v,t))/cu)",
"DFyv= ((Fy(u,v,t)-Fy(u,v+cv,t))/cv)",
"DFzu= ((Fz(u,v,t)-Fz(u+cu,v,t))/cu)",
"DFzv= ((Fz(u,v,t)-Fz(u,v+cv,t))/cv)",
"n1= (DFyu(u,v,t)*DFzv(u,v,t)-DFzu(u,v,t)*DFyv(u,v,t))",
"n2= (DFzu(u,v,t)*DFxv(u,v,t)-DFxu(u,v,t)*DFzv(u,v,t))",
"n3= (DFxu(u,v,t)*DFyv(u,v,t)-DFyu(u,v,t)*DFxv(u,v,t))",
"R=sqrt (n1(u,v,t)^2+n2(u,v,t)^2+n3(u,v,t)^2)",
"Tickness=abs(.1*cos(10*u)*sin(10*v))",
"Gx=Fx(u,v,t)+Tickness(u,v,t)*n1(u,v,t)/R(u,v,t)",
"Gy=Fy(u,v,t)+Tickness(u,v,t)*n2(u,v,t)/R(u,v,t)",
"Gz=Fz(u,v,t)+Tickness(u,v,t)*n3(u,v,t)/R(u,v,t)"],
"Fx":  ["Gx(u,v,t)"],
"Fy":  ["Gy(u,v,t)"],
"Fz":  ["Gz(u,v,t)"],
"Umax":  ["pi/2"],
"Umin":  ["-pi/2"],
"Vmax":  ["2*pi"],
"Vmin":  ["0"]
}
}


"Skeletal Sphere" (implicit version)
MathMod script:
{
"Iso3D": {
"Description": ["Skeletal Sphere (implicit version) by Abderrahman Taha 06/10/2015"],
"Name": ["Skeletal Sphere (implicit version)"],
"Component": ["SkeletalSphere"],
"Const": ["cx=0.0000000000001",
"cy=0.0000000000001",
"cz=0.0000000000001"],
"Funct": ["Iso=x*x+y*y+z*z-1",
"Tickness= (.1*cos(10*atan2(x,y))*sin(10*atan2(z,sqrt(x*x+y*y))))",
"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)))",
"Iso2= (Iso(x+t*DFx(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),y+t*DFy(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),z+t*DFz(x,y,z,t)*Tickness(x,y,z,t)/Rapport(x,y,z,t),t))",
"TickIso=max(Iso2(x,y,z,1), Iso2(x,y,z,-1))"],
"Fxyz": ["TickIso(x,y,z,t)"],
"Xmax": ["1.2"],
"Xmin": ["-1.2"],
"Ymax": ["1.2"],
"Ymin": ["-1.2"],
"Zmax": ["1.2"],
"Zmin": ["-1.2"]
}
}

Image size
1728x1629px 2.97 MB
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