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mathmodcollection.js
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mathmodcollection.js
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{
"MathModels": [
{
"Param3D": {
"Description": ["Basket by Abderrahman Taha 11/10/2018"
],
"Name": ["Basket"
],
"Component": ["Basket"
],
"Const": ["d=(33/1000)","k=33","umin=0","umax=2*pi","vmin=0","vmax=2*pi","du=1/10000","dv=1/10000"
],
"Funct": ["Fx=(u/4)*sin(k*u)+v","Fy=(u/4)*cos(k*u)+v","Fz=exp((u^(185/100))/55)+v","Rapp=u/sqrt(u*u+v*v+t*t)","DFxu=((Fx(u+du,v,t)-Fx(u,v,t))/du)","DFxv=((Fx(u,v+dv,t)-Fx(u,v,t))/dv)","DFyu=((Fy(u+du,v,t)-Fy(u,v,t))/du)","DFyv=((Fy(u,v+dv,t)-Fy(u,v,t))/dv)","DFzu=((Fz(u+du,v,t)-Fz(u,v,t))/du)","DFzv=((Fz(u,v+dv,t)-Fz(u,v,t))/dv)","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))","F2x=Fx(u,0,t)","F2y=Fy(u,0,t)","F2z=Fz(u,0,t)","DF2xu=DFxu(u,0,t)","DF2yu=DFyu(u,0,t)","DF2zu=DFzu(u,0,t)","DF2xu2=n1(u,0,t)","DF2yu2=n2(u,0,t)","DF2zu2=n3(u,0,t)","Nxu=Rapp(DF2xu2(u,v,t),DF2yu2(u,v,t),DF2zu2(u,v,t))","Nyu=Rapp(DF2yu2(u,v,t),DF2xu2(u,v,t),DF2zu2(u,v,t))","Nzu=Rapp(DF2zu2(u,v,t),DF2yu2(u,v,t),DF2xu2(u,v,t))","Binxu=(DF2yu(u,v,t)*Nzu(u,v,t)-DF2zu(u,v,t)*Nyu(u,v,t))/sqrt(DF2xu(u,v,t)^2+DF2yu(u,v,t)^2+DF2zu(u,v,t)^2)","Binyu=(DF2zu(u,v,t)*Nxu(u,v,t)-DF2xu(u,v,t)*Nzu(u,v,t))/sqrt(DF2xu(u,v,t)^2+DF2yu(u,v,t)^2+DF2zu(u,v,t)^2)","Binzu=(DF2xu(u,v,t)*Nyu(u,v,t)-DF2yu(u,v,t)*Nxu(u,v,t))/sqrt(DF2xu(u,v,t)^2+DF2yu(u,v,t)^2+DF2zu(u,v,t)^2)","Tx=F2x(u,v,t)+d*(Nxu(u,v,t)*cos(v)+Binxu(u,v,t)*sin(v))","Ty=F2y(u,v,t)+d*(Nyu(u,v,t)*cos(v)+Binyu(u,v,t)*sin(v))","Tz=F2z(u,v,t)+d*(Nzu(u,v,t)*cos(v)+Binzu(u,v,t)*sin(v))"
],
"Fx": ["Tx(u,v,t)"
],
"Fy": ["Ty(u,v,t)"
],
"Fz": ["Tz(u,v,t)"
],
"Grid": ["40000","20"
],
"Umax": ["umax"
],
"Umin": ["umin"
],
"Vmax": ["vmax"
],
"Vmin": ["vmin"]
},
"Texture": {
"Colors": ["R=(20000*(3*(x^2+y^2)^4-6*x*x*y*y))%(4/10) +(46/100)","G=(100000*((x^2+y^2)-7*x*x*y*y))%(65/100)","B= (20000*((x^2+y^2)^3-10*x*x*y*y))%(2/10)+(1/10)","T=1"
],
"Name": "Trefoil",
"Noise": ""
}
},
{
"Param3D": {
"Description ": ["Spiky Klein by Abderrahman Taha 19/08/2018"],
"Name": ["Spiky Klein"],
"Component": ["SpikyKlein"],
"Const": ["c=1/1000",
"N=5",
"A=3.5",
"B=2",
"C=3",
"D=3"],
"Funct": ["th = (3/10)* ((abs(sin(11*u) * cos(11*v)))^19+(1/10)*((sin(2*N*u))))",
"Fx= if(v<2*pi, (A-(A-1) * cos(v)) * cos(u), if(v<3*pi, - B + ( B+cos(u))*cos(v),- B + B *cos(v)-cos(u)))",
"Fy= if(v<2*pi,(A - (A-1)*cos(v))*sin(u), sin(u))",
"Fz= if(v<pi, -C*sin(v), if(v<2*pi, D*v-D*pi, if(v<3*pi,(( D -1)+cos(u))*sin(v)+D*pi,-D*v+D*4*pi)))",
"DFxu=((Fx(u,v,t)-Fx(u+c,v,t))/c)",
"DFxv=((Fx(u,v,t)-Fx(u,v+c,t))/c)",
"DFyu=((Fy(u,v,t)-Fy(u+c,v,t))/c)",
"DFyv=((Fy(u,v,t)-Fy(u,v+c,t))/c)",
"DFzu=((Fz(u,v,t)-Fz(u+c,v,t))/c)",
"DFzv=((Fz(u,v,t)-Fz(u,v+c,t))/c)",
"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)",
"Gx= Fx(u,v,t)+th(u,v-3*t,t)*Rapp(n1(u,v,t),n2(u,v,t),n3(u,v,t))",
"Gy= Fy(u,v,t)+th(u,v-3*t,t)*Rapp(n2(u,v,t),n1(u,v,t),n3(u,v,t))",
"Gz= Fz(u,v,t)+th(u,v-3*t,t)*Rapp(n3(u,v,t),n1(u,v,t),n2(u,v,t))"],
"Fx": ["Gx(u,v,t)"],
"Fy": ["Gy(u,v,t)"],
"Fz": ["Gz(u,v,t)"],
"Umax": ["2*pi"],
"Umin": ["0"],
"Vmax": ["4*pi"],
"Vmin": ["0"]
}
},
{
"Iso3D": {
"Description ": ["Geode by Abderrahman Taha 20/08/2018"
],
"Component": ["Geode1","Geode2"
],
"Const": ["A=4","B=3"
],
"Fxyz": ["-((((x/(101/100))^2+y^2+(z/(105/100))^2-1)+((4/10)*NoiseW(A*x,A*y,A*z,(4),(1),(0)))/3))*(atan2(x,y)<pi/2)*(x^2+y^2+z^2-2/10)","-(((x^2+y^2+z^2-(21/100))*(atan2(x,y)<pi/2)*((x^2+y^2+z^2-2/10)+(NoiseW(B*x,B*y,B*z,(4),(2),(1))+NoiseW(B*x,B*y,B*z,(4),(2),(1)))/5)))"
],
"Name": ["Geode_02"
],
"Xmax": ["(15/10)","(15/10)"
],
"Xmin": ["-1","-1"
],
"Ymax": ["1","1"
],
"Ymin": ["-1","-1"
],
"Zmax": ["(15/10)","(15/10)"
],
"Zmin": ["-1","-1"
]
},
"Texture": {
"Colors": ["R=if((x*x+y*y+z*z)>(81/100),(95/100)*cos((x*x+y*y+z*z)/(17/10)), (2/10))+(2/10)","G=if((x*x+y*y+z*z)>(8/10), (8/10)*(cos((x*x+y*y+z*z)/5)*sin((x*x+y*y+z*z)))*sin((x*x+y*y+z*z)/(3/10)), (5/10)*sin((x*x+y*y+z*z)*9))+(2/10)","B=if((x*x+y*y+z*z)<(8/10),(cos((x*x+y*y+z*z))*cos((x*x+y*y+z*z))*sin((x*x+y*y+z*z)))+(4/10), (1/10))+(5/10)","T=1"
],
"Name": "WorleyNoise",
"Noise": "-((35/100)*NoiseW(2*x,2*y,2*z,(4),(1),(0))+(178/100)*NoiseW(2*x,2*y,2*z,(4),(0),(0)))"
}
},
{
"Param3D": {
"Description": ["Helix Zome by Abderrahman Taha 01/09/2018"
],
"Name": ["Helix Zome"
],
"Funct": ["Fx=(d/4)*(sin((u)+v)+sin(v))","Fy=(d/4)*(cos((u)+v)+cos(v))","Fz=K*if(u<pi , (d/(2*pi))*(u), (d/(2*pi))*(2*pi-u))","Rapp=u/sqrt(u*u+v*v+t*t)","DFxu=((Fx(u+du,v,t)-Fx(u,v,t))/du)","DFxv=((Fx(u,v+dv,t)-Fx(u,v,t))/dv)","DFyu=((Fy(u+du,v,t)-Fy(u,v,t))/du)","DFyv=((Fy(u,v+dv,t)-Fy(u,v,t))/dv)","DFzu=((Fz(u+du,v,t)-Fz(u,v,t))/du)","DFzv=((Fz(u,v+dv,t)-Fz(u,v,t))/dv)","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))","F2x=Fx(u,v1min + CmpId(0)*Gv,t)","F2y=Fy(u,v1min + CmpId(0)*Gv,t)","F2z=Fz(u,v1min + CmpId(0)*Gv,t)","DF2xu=DFxu(u,v1min + CmpId(0)*Gv,t)","DF2yu=DFyu(u,v1min + CmpId(0)*Gv,t)","DF2zu=DFzu(u,v1min + CmpId(0)*Gv,t)","DF2xu2=n1(u,v1min + CmpId(0)*Gv,t)","DF2yu2=n2(u,v1min + CmpId(0)*Gv,t)","DF2zu2=n3(u,v1min + CmpId(0)*Gv,t)","Nxu=Rapp(DF2xu2(u,v,t),DF2yu2(u,v,t),DF2zu2(u,v,t))","Nyu=Rapp(DF2yu2(u,v,t),DF2xu2(u,v,t),DF2zu2(u,v,t))","Nzu=Rapp(DF2zu2(u,v,t),DF2yu2(u,v,t),DF2xu2(u,v,t))","Binxu=(DF2yu(u,v,t)*Nzu(u,v,t)-DF2zu(u,v,t)*Nyu(u,v,t))/sqrt(DF2xu(u,v,t)^2+DF2yu(u,v,t)^2+DF2zu(u,v,t)^2)","Binyu=(DF2zu(u,v,t)*Nxu(u,v,t)-DF2xu(u,v,t)*Nzu(u,v,t))/sqrt(DF2xu(u,v,t)^2+DF2yu(u,v,t)^2+DF2zu(u,v,t)^2)","Binzu=(DF2xu(u,v,t)*Nyu(u,v,t)-DF2yu(u,v,t)*Nxu(u,v,t))/sqrt(DF2xu(u,v,t)^2+DF2yu(u,v,t)^2+DF2zu(u,v,t)^2)","Tx=F2x(u,v,t)+(Nxu(u,v,t)*cos(v)+Binxu(u,v,t)*sin(v))","Ty=F2y(u,v,t)+(Nyu(u,v,t)*cos(v)+Binyu(u,v,t)*sin(v))","Tz=F2z(u,v,t)+(Nzu(u,v,t)*cos(v)+Binzu(u,v,t)*sin(v))"
],
"Component": ["Helix_Zome_00","Helix_Zome_01","Helix_Zome_02","Helix_Zome_03","Helix_Zome_04","Helix_Zome_05","Helix_Zome_06","Helix_Zome_07","Helix_Zome_08","Helix_Zome_09","Helix_Zome_10","Helix_Zome_11","Helix_Zome_12","Helix_Zome_13","Helix_Zome_14","Helix_Zome_15","Helix_Zome_16","Helix_Zome_17","Helix_Zome_18","Helix_Zome_19"
],
"Const": ["v1min=0","v1max=2*pi","M=20","du=1/10000","dv=1/10000","umin=0","umax=2*pi","vmin=0","vmax=2*pi","Gv=(v1max-v1min)/M","d=100","K=3/2"
],
"Grid": ["100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60","100","60"
],
"Fx": ["Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)","Tx(u,v,t)"
],
"Fy": ["Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)","Ty(u,v,t)"
],
"Fz": ["Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)","Tz(u,v,t)"
],
"Umax": ["umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax","umax"
],
"Umin": ["umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin","umin"
],
"Vmax": ["vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax","vmax"
],
"Vmin": ["vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin","vmin"
]
}, "Texture": {
"Colors": ["R=7/10","G=7/10","B=7/10","T=1"
],
"Name": "Lines",
"Noise": ""
}
},
{
"Iso3D": {
"Description": ["(2,5)-Torusknoten by Stephan Klaus 03/09/2018"],
"Component": ["Torusknoten"],
"Const": ["a=.22","b=.2","N=10"],
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"A = ((abs(u-2/3) <1/81)+ (abs(u-20/27) <1/81)+ (abs(u-16/27) <1/81)+(abs(u-8/9) <1/81) + (abs(u-26/27) <1/81) + (abs(u-22/27) <1/81) +(abs(u-4/9) <1/81) +(abs(u-14/27) <1/81) +(abs(u-10/27) <1/81) +(abs(u+2/3) <1/81) +(abs(u+16/27) <1/81) +(abs(u+20/27) <1/81) +(abs(u+4/9) <1/81) +(abs(u+10/27) <1/81) +(abs(u+14/27) <1/81) +(abs(u+8/9) <1/81) +(abs(u+22/27) <1/81) +(abs(u+26/27) <1/81) +(abs(u) <1/81) + (abs(u-2/27) <1/81) +(abs(u+2/27) <1/81) +(abs(u-2/9) <1/81) + (abs(u-8/27) <1/81) + (abs(u-4/27) <1/81) +(abs(u+2/9) <1/81)+(abs(u+4/27) <1/81)+(abs(u+8/27) <1/81))",
"B = ((abs(u-2/3) <1/27)+(abs(u-8/9) <1/27) + (abs(u-4/9) <1/27) +(abs(u+2/3) <1/27) +(abs(u+4/9) <1/27) + (abs(u+8/9) <1/27) +(abs(u) <1/27) + (abs(u-2/9) <1/27) + (abs(u+2/9) <1/27))",
"C = ((abs(u-2/3) <1/9) + (abs(u+2/3) <1/9) + (abs(u) <1/9))",
"D = u^100"
],
"Fxyz": [
"-(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*((Cx*(Cy+Cz) + Cz*Cy) =0)*((Bx*(By+Bz)+Bz*By) =0)*((Ax*(Ay+Az)+Az*Ay)=0))"
],
"Xmin": [
"-1DOTSYMBOL001"
],
"Xmax": [
" 1DOTSYMBOL001"
],
"Ymin": [
"-1DOTSYMBOL001"
],
"Ymax": [
" 1DOTSYMBOL001"
],
"Zmin": [
"-1DOTSYMBOL001"
],
"Zmax": [
" 1DOTSYMBOL001"
]
}
},
{
"Iso3D": {
"Name": [
"MengerSpongeSubdivision"
],
"Varu": [
"A = ((abs(u-2/3) <1/81)+ (abs(u-20/27) <1/81)+ (abs(u-16/27) <1/81)+(abs(u-8/9) <1/81) + (abs(u-26/27) <1/81) + (abs(u-22/27) <1/81) +(abs(u-4/9) <1/81) +(abs(u-14/27) <1/81) +(abs(u-10/27) <1/81) +(abs(u+2/3) <1/81) +(abs(u+16/27) <1/81) +(abs(u+20/27) <1/81) +(abs(u+4/9) <1/81) +(abs(u+10/27) <1/81) +(abs(u+14/27) <1/81) +(abs(u+8/9) <1/81) +(abs(u+22/27) <1/81) +(abs(u+26/27) <1/81) +(abs(u) <1/81) + (abs(u-2/27) <1/81) +(abs(u+2/27) <1/81) +(abs(u-2/9) <1/81) + (abs(u-8/27) <1/81) + (abs(u-4/27) <1/81) +(abs(u+2/9) <1/81)+(abs(u+4/27) <1/81)+(abs(u+8/27) <1/81))",
" B = ((abs(u-2/3) <1/27)+(abs(u-8/9) <1/27) + (abs(u-4/9) <1/27) +(abs(u+2/3) <1/27) +(abs(u+4/9) <1/27) + (abs(u+8/9) <1/27) +(abs(u) <1/27) + (abs(u-2/9) <1/27) + (abs(u+2/9) <1/27))",
"C = ((abs(u-2/3) <1/9) + (abs(u+2/3) <1/9) + (abs(u) <1/9))",
"D = u^100"
],
"Component": [
" MengerSponge1",
" MengerSponge2",
" MengerSponge3",
" MengerSponge4",
" MengerSponge5",
" MengerSponge6",
" MengerSponge7",
" MengerSponge8"
],
"Fxyz": [
" -(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) ) ",
"-(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) ) ",
"-(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) ) ",
"-(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) )",
"-(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) ) ",
"-(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) ) ",
"-(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) ) ",
"-(Dx + Dy + Dz -1)*(((abs(x) >1/3 | abs(y) > 1/3)*(abs(z) >1/3 | abs(y) > 1/3)*(abs(x) >1/3 | abs(z) > 1/3))*( (Cx*(Cy+Cz) + Cz*Cy) =0)*( (Bx*(By+Bz) + Bz*By) =0)*( (Ax*(Ay+Az) + Az*Ay) =0) )"
],
"Xmin": [
"-1DOTSYMBOL001",
" -1DOTSYMBOL001",
" -1DOTSYMBOL001",
" -1DOTSYMBOL001",
" 0DOTSYMBOL000",
" 0DOTSYMBOL000",
" 0DOTSYMBOL000",
" 0DOTSYMBOL000"
],
"Xmax": [
" 0DOTSYMBOL000 ",
" 0DOTSYMBOL000",
" 0DOTSYMBOL000",
" 0DOTSYMBOL000",
" 1DOTSYMBOL001",
" 1DOTSYMBOL001",
" 1DOTSYMBOL001",
" 1DOTSYMBOL001"
],
"Ymin": [
"-1DOTSYMBOL001",
" -1DOTSYMBOL001",
" 0DOTSYMBOL000",
" 0DOTSYMBOL000",
" -1DOTSYMBOL001",
" -1DOTSYMBOL001",
" 0DOTSYMBOL000",
" 0DOTSYMBOL000 "
],
"Ymax": [
" 0DOTSYMBOL000 ",
" 0DOTSYMBOL000",
" 1DOTSYMBOL001",
" 1DOTSYMBOL001",
" 0DOTSYMBOL000 ",
" 0DOTSYMBOL000",
" 1DOTSYMBOL001",
" 1DOTSYMBOL001"
],
"Zmin": [
"-1DOTSYMBOL001",
" 0DOTSYMBOL000 ",
" -1DOTSYMBOL001",
" 0DOTSYMBOL000",
" -1DOTSYMBOL001",
" 0DOTSYMBOL000 ",
" -1DOTSYMBOL001",
" 0DOTSYMBOL000 "
],
"Zmax": [
" 0DOTSYMBOL000 ",
" 1DOTSYMBOL001",
" 0DOTSYMBOL000",
" 1DOTSYMBOL001",
" 0DOTSYMBOL000 ",
" 1DOTSYMBOL001",
" 0DOTSYMBOL000",
" 1DOTSYMBOL001"
]
}
},
{
"Iso3D": {
"Name": [
"Cayley_1"
],
"Component": [
"Cayley_1"
],
"Fxyz": [
"(x^2 + y ^2 - x^2 *z + y ^2 *z + z ^2 -1)"
],
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 4"
],
"Xmin": [
"-4 "
],
"Xmax": [
" 4"
],
"Ymin": [
"-4 "
],
"Ymax": [
" 4"
],
"Zmin": [
"-4 "
],
"Zmax": [
" 4"
]
}
},
{
"Iso3D": {
"Name": [
"Cayley_2"
],
"Component": [
"Cayley_2"
],
"Fxyz": [
"-5*(x*x*y + x*x*z + y*y*x + y*y*z + z*z*y + z*z*x) +2*(x*y + x*z + y*z)"
],
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 1"
],
"Xmin": [
"-1 "
],
"Xmax": [
" 1"
],
"Ymin": [
"-1 "
],
"Ymax": [
" 1"
],
"Zmin": [
"-1 "
],
"Zmax": [
" 1"
]
}
},
{
"Iso3D": {
"Name": [
"Nordstrand"
],
"Cnd": [
"((x-0DOTSYMBOL1)^2+(y-0DOTSYMBOL1)^2+(z-0DOTSYMBOL1)^2)>1"
],
"Component": [
" Nordstrand"
],
"Fxyz": [
" 25*(x^3*(y+z)+y^3*(x+z)+z^3*(x+y))+50*(x^2*y^2+x^2*z^2+y^2*z^2)-125*(x^2*y*z+y^2*x*z+z^2*x*y)+60*x*y*z-4*(x*y+x*z+y*z)"
],
"Xmax": [
" 1DOTSYMBOL1"
],
"Xmin": [
"-1DOTSYMBOL1"
],
"Ymax": [
" 1DOTSYMBOL1"
],
"Ymin": [
"-1DOTSYMBOL1"
],
"Zmax": [
" 1DOTSYMBOL1"
],
"Zmin": [
"-1DOTSYMBOL1"
]
}
},
{
"Iso3D": {
"Name": [
"Togliatti"
],
"Cnd": [
"(x^2 + y^2 + z^2) > 100"
],
"Component": [
"Togliatti"
],
"Const": [
" w=1DOTSYMBOL3"
],
"Fxyz": [
"64*(x -w)*(x^4 - 4*w*x^3 -10*x^2*y^2 - 4*x^2*w^2 + 16*w^3*x - 20*w*x*y^2 + 5*y^4 + 16*w^4 - 20*y^2*w^2) -5*sqrt(5 - sqrt(5))*(2*z - sqrt(5 - sqrt(5))*w)*(4*(x^2 + y^2 - z^2) + (1 + 3*sqrt(5))*w^2)^2"
],
"Xmax": [
"10"
],
"Xmin": [
"-10"
],
"Ymax": [
"10"
],
"Ymin": [
"-10"
],
"Zmax": [
"10"
],
"Zmin": [
"-10"
]
}
},
{
"Iso3D": {
"Name": [
"Dervish"
],
"Component": [
" Dervish"
],
"Cnd": [
"(x^2+y^2+z^2)>15"
],
"Const": [
"r = (1/4)*(1+3*sqrt(5))",
"a = -(8/5)*(1+1/(sqrt(5)))*sqrt(5-sqrt(5))",
"c = (1/2)*sqrt(5-sqrt(5))"
],
"Fxyz": [
" a*(x-z)*(cos((2*pi)/5)*x-sin((2*pi)/5)*y-z) *(cos((4*pi)/5)*x-sin((4*pi)/5)*y-z) *(cos((6*pi)/5)*x-sin((6*pi)/5)*y-z) *(cos((8*pi)/5)*x-sin((8*pi)/5)*y-z) + (1-c*z)*(x^2+y^2-1+r*z^2)^2"
],
"Xmin": [
"-4"
],
"Xmax": [
" 4"
],
"Ymin": [
"-4"
],
"Ymax": [
" 4"
],
"Zmin": [
"-4"
],
"Zmax": [
" 4"
]
}
},
{
"Iso3D": {
"Name": [
"Barth-sextic"
],
"Component": [
"Barth-sextic"
],
"Cnd": [
"(x^2+y^2+z^2)>9"
],
"Const": [
" w=1DOTSYMBOL0",
" phi=(1/2)*(1+sqrt(5))"
],
"Fxyz": [
"4*(phi^2*x^2-y^2)*(phi^2*y^2-z^2)*(phi^2*z^2-x^2)-(1+2*phi)*(x^2+y^2+z^2-w^2)^2*w^2"
],
"Xmax": [
"3"
],
"Xmin": [
"-3"
],
"Ymax": [
"3"
],
"Ymin": [
"-3"
],
"Zmax": [
"3"
],
"Zmin": [
"-3"
]
}
},
{
"Iso3D": {
"Name": [
"Labs-Septic"
],
"Component": [
"Labs-Septic"
],
"Cnd": [
"(x^2+y^2+z^2)>25"
],
"Const": [
" w = 1DOTSYMBOL0",
"a1 = -(12/7)*(-0DOTSYMBOL14010685)^2 -(384/49)*(-0DOTSYMBOL14010685) -(8/7)",
"a2 = -(32/7)*(-0DOTSYMBOL14010685)^2 +(24/49)*(-0DOTSYMBOL14010685) -4",
"a3 = -4*(-0DOTSYMBOL14010685)^2 +(24/49)*(-0DOTSYMBOL14010685) -4",
"a4 = -(8/7)*(-0DOTSYMBOL14010685)^2 +(8/49)*(-0DOTSYMBOL14010685) -8/7",
"a5 = 49*(-0DOTSYMBOL14010685)^2 -7*(-0DOTSYMBOL14010685) +50"
],
"Fxyz": [
"(x*(x^6-3*7*x^4*y^2+5*7*x^2*y^4-7*y^6)+7*z*((x^2+y^2)^3-2^3*z^2*(x^2+y^2)^2+2^4*z^4*(x^2+y^2))-2^6*z^7)-((z+a5*w)*((z+w)*(x^2+y^2)+a1*z^3+a2*z^2*w+a3*z*w^2+a4*w^3)^2)"
],
"Xmax": [
"5"
],
"Xmin": [
"-5"
],
"Ymax": [
"5"
],
"Ymin": [
"-5"
],
"Zmax": [
"5"
],
"Zmin": [
"-5"
]
}
},
{
"Iso3D": {
"Name": [
"Endraß-Octic"
],
"Component": [
"Endraß-Octic"
],
"Cnd": [
"(x^2+y^2+z^2)>25"
],
"Const": [
" w = 1DOTSYMBOL0",
"a1 = 1DOTSYMBOL0",
"a2 = 1DOTSYMBOL0",
"a3 = 1DOTSYMBOL0",
"a4 = -1DOTSYMBOL0"
],
"Fxyz": [
"64 * (x^2 - w^2)*(y^2 - w^2)*((x + y)^2 -2*w^2)*((x - y)^2 -2*w^2) - (-4*(1 + a1*2^(1/2))*(x^2 + y^2)^2 + (8*(2 + a2*2^(1/2))*z^2 + 2*(2 + a3*7*2^(1/2))*w^2 )* (x^2 + y^2) - 16*z^4+ 8*(1 + a4*2*2^(1/2))*z^2*w^2 - (1 + 12*2^(1/2))*w^4)^2"
],
"Xmax": [
"5"
],
"Xmin": [
"-5"
],
"Ymax": [
"5"
],
"Ymin": [
"-5"
],
"Zmax": [
"5"
],
"Zmin": [
"-5"
]