Post has attachment
Post has attachment
This is a hexacosihedron (600 faces). It was constructed with 3 kinds of different tetrahedra: 1,260-a + 912-b + 288-c [I constructed it on 15 Feb, 2012 at 19:40, the last in a long afternoon...] (lol)
Symmetry is Th (tetrahedral complete w. horiz. reflection)
Post has attachment
Post has attachment
Seashell 02 (parametric surface)
It's unlikely to find such seashell in nature but...who cares? :-)
The attached script shows a way to fine-tune the protuberances distribution over each different shell shape (see the "th" function definition)
MathMod script:
{
"Param3D": {
"Description ": ["Seashell by Abderrahman Taha 19/04/2017"],
"Name": ["Sea Shells_003"],
"Component": ["Sea Shell"],
"Const": ["cu=0.001",
"cv=0.001",
"N=14",
"M=4",
"MaxU=pi",
"MinU=0",
"MaxV=5*pi/2",
"MinV=0",
"a=0.2",
"b=1",
"c=0.1",
"n=2"],
"Funct": [" th = 0.1* ( ( 1 - abs ( u-pi/2 ) / MaxU )
( v / MaxV + 0.05 ) * abs ( cos ( N * (u ) ) ^ 3 - sin ( N * ( v)) ^2 ) ) ^ 3",
" Fx = if ( M=1,2(1-exp(u/(6*pi)))cos(u)*cos(v/2)^2,if(M=2,((a(1-v/(2*pi))(1+cos(u))+c)*cos(n*v))*6+4,if(M=3,2^v(sin(u)cos(u))/35,if( M=4,1.2^v(sin(u)^2*sin(v))+2,2*(1-exp(u/(6*pi)))cos(u)*cos(v/2)^2))))",
" Fy = if ( M=1,2(-1+exp(u/(6*pi)))sin(u)*cos(v/2)^2,if(M=2,((a(1-v/(2*pi))(1+cos(u))+c)*sin(n*v))*6+4,if(M=3,2^v(sin(u)^2*sin(v))/35-4,if(M=4,1.2^v*(sin(u)cos(u))+5,2(-1+exp(u/(6*pi)))sin(u)*cos(v/2)^2))))",
" Fz = if ( M=1,1-exp(u/(3*pi))-sin(v)+exp(u/(6*pi))*sin(v),if(M=2,(b*v/(2*pi)+a(1-v/(2*pi))sin(u))*6-6,if(M=3,2^v(sin(u)^2*cos(v))/35-12,if(M=4,1.2^v*(sin(u)^2*cos(v)) -12,1-exp(u/(3*pi))-sin(v)+exp(u/(6*pi))*sin(v)))))",
"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))",
"Rapp=u/sqrt(u*u+v*v+t*t)",
"Fx=Fx(u,v,t)+th(u,v-3*t,t)*Rapp(n1(u,v,t),n2(u,v,t),n3(u,v,t))",
"Fy=Fy(u,v,t)+th(u,v-3*t,t)*Rapp(n2(u,v,t),n1(u,v,t),n3(u,v,t))",
"Fz=Fz(u,v,t)+th(u,v-3*t,t)*Rapp(n3(u,v,t),n1(u,v,t),n2(u,v,t))"],
"Fx": ["Fx(u,v,t)"],
"Fy": ["Fy(u,v,t)"],
"Fz": ["Fz(u,v,t)"],
"Umax": ["MaxU"],
"Umin": ["MinU"],
"Vmax": ["MaxV"],
"Vmin": ["MinV"]
}
}ï»¿
19/04/2017
4 Photos - View album
Post has attachment
This little solid (fig 1) is a space-filler: it is formed of 12 tetrakaidecahedra plus 8 non regular dodecahedra (in red), both the h14 & the h12 appearing in the celebrated Weaire-Phelan structure which I posted here some time ago.
Please compare this with this other solid (fig. 2) composed of 24 tetrakaidecahedra & 9 non regular dodecahedra (the dodecs are in red & there is one at the center). This is the celebrated Clathrate type I (that I also posted in this bunch some time ago)
The symmetry of both solids is Th (tetrahedral complete w. horiz reflection)
4/18/17
2 Photos - View album
Post has attachment
Fly through a cubic fractal (the "Menger sponge") and watch it split apart.ï»¿
Post has attachment
Post has attachment
Post has attachment
Seashell (parametric surface)
Looking for a more realistic Seashell model by using trigonometric expressions for the protuberance.
MathMod script:
{
"Param3D": {
"Description ": ["SeaShell by Abderrahman Taha 16/04/2017"],
"Name": ["SeaShell_001"],
"Component": ["SeaShell"],
"Const": ["cu=0.001",
"cv=0.001",
"N=5",
"M=3",
"MaxU=6*pi",
"MinU=0",
"MaxV=2*pi",
"MinV=0",
"a=0.2",
"b=1",
"c=0.1",
"n=2"],
"Funct": ["th=-(((u)/MaxU+0.05 ) * 0.4*abs(cos(7*(u))^3 - sin(7*(v))^2 ))^3",
"Fx=2*(1-exp(u/(6*pi))) * cos(u) * cos(v/2)^2",
"Fy=2*(-1+exp(u/(6*pi))) * sin(u) * cos(v/2)^2",
"Fz=1-exp(u/(3*pi))-sin(v)+exp(u/(6*pi)) *sin(v)",
"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))",
"Rapp=u/sqrt(u*u+v*v+t*t)",
"Fx=Fx(u,v,t)+th(u,v-3*t,t)*Rapp(n1(u,v,t),n2(u,v,t),n3(u,v,t))",
"Fy=Fy(u,v,t)+th(u,v-3*t,t)*Rapp(n2(u,v,t),n1(u,v,t),n3(u,v,t))",
"Fz=Fz(u,v,t)+th(u,v-3*t,t)*Rapp(n3(u,v,t),n1(u,v,t),n2(u,v,t))"],
"Fx": ["-Fx(u,v,t)"],
"Fy": ["Fy(u,v,t)"],
"Fz": ["Fz(u,v,t)"],
"Umax": ["MaxU"],
"Umin": ["MinU"],
"Vmax": ["MaxV"],
"Vmin": ["MinV"]
}
}ï»¿
16/04/2017
3 Photos - View album
Post has attachment