Posts tagged: cubes

Mathematica code:

Rot60 = 
Table[
Table[
RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],
{v, 1, 8, 1}],
{a, 0, 2 Pi, 2 Pi/60}]

Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}

CubeProjections[color_, pr_, b_, s_, h_, w_, m_, a_] :=
Graphics[
Table[
Translate[
{AbsoluteThickness[h], If[color == 0, Black, White],
Line[
Table[
Table[
Rot60[[1 + Mod[w (y + m*x) + a, 60]]][[Edge[[k]]]][[c]],
{c, 1, 2, 1}],
{k, 1, 16, 1}]]},
{s*x, s*y}],
{x, -6, 6, 1}, {y, -b, b, 1}],
PlotRange -> {{-pr/3, pr/3}, {-pr+1, pr-1}}, ImageSize -> 500,
Background -> If[color == 0, White, Black]
]

Manipulate[
PM = {color, pr, b, s, h, w, m, a};
CubeProjections[color, pr, b, s, h, w, m, a],
{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 20, 1},
{{s, 3}, 0, 5}, {{h, 1}, .01, 10},
{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},
{a, 1, 60, 1}]

P = {0, 29, 20, 1.3, 2.5, 1, 0, 0}

Manipulate[
CubeProjections30[P[[1]], P[[2]], P[[3]], P[[4]], P[[5]], P[[6]],
P[[7]], a],
{a, 1, 30, 1}]
Mathematica code:Rot80 =  Table[  Table[   RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],  {v, 1, 8, 1}],{a, 0, 2 Pi,  Pi/80}]Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}CubeTrail[h_, op_, N_, s_, r_, z_, t_, PR_, IS_, C_] := Graphics[  Table[   Scale[    Translate[     {AbsoluteThickness[h], Opacity[op],       If[C == 1, Black, White],      Line[       Table[        {Rot80[[1 + Mod[t, 80]]][[Edge[[e]]]][[1]],         Rot80[[1 + Mod[t, 80]]][[Edge[[e]]]][[2]]},        {e, 1, 16, 1}]]},     r{Cos[2 Pi*(n*t/80 + k)/N], Sin[2 Pi*(n*t/80 + k)/N]}],    z^n, r{Cos[2 Pi*(n*t/80 + k)/N], Sin[2 Pi*(n*t/80 + k)/N]}],   {k, 1, N, 1},   {n, 1, s, 1}],  PlotRange -> PR, ImageSize -> 500,   Background -> If[C == 0, Black, White]]Manipulate[P = {h, op, N, s, r, z, t, PR, IS, C}; CubeTrail[h, op, N, s, r, z, t, PR, 500, 0],{{h, 1}, 0, 20}, {op, 1, 0}, {{N, 4}, 1, 16, 1}, {s, 1, 100, 1}, {{r, 3.5}, 0, 10}, {z, 1, 0},{{PR, 5}, 1, 5}, {C, 0, 1, 1},{t, 0, 100, 1}]P ={1.5, 1, 4, 8, 3.8, 0.75, 0, 5, 500, 0}Manipulate[CubeTrail[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],t,P[[8]],500,0],{t, 1, 80, 1}]

Mathematica
code:
Rot80 = 
Table[
Table[
RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],
{v, 1, 8, 1}],
{a, 0, 2 Pi, Pi/80}]

Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}

CubeTrail[h_, op_, N_, s_, r_, z_, t_, PR_, IS_, C_] :=
Graphics[
Table[
Scale[
Translate[
{AbsoluteThickness[h], Opacity[op],
If[C == 1, Black, White],
Line[
Table[
{Rot80[[1 + Mod[t, 80]]][[Edge[[e]]]][[1]],
Rot80[[1 + Mod[t, 80]]][[Edge[[e]]]][[2]]},
{e, 1, 16, 1}]]},
r{Cos[2 Pi*(n*t/80 + k)/N], Sin[2 Pi*(n*t/80 + k)/N]}],
z^n, r{Cos[2 Pi*(n*t/80 + k)/N], Sin[2 Pi*(n*t/80 + k)/N]}],
{k, 1, N, 1},
{n, 1, s, 1}],
PlotRange -> PR, ImageSize -> 500,
Background -> If[C == 0, Black, White]]

Manipulate[P = {h, op, N, s, r, z, t, PR, IS, C};
CubeTrail[h, op, N, s, r, z, t, PR, 500, 0],
{{h, 1}, 0, 20}, {op, 1, 0},
{{N, 4}, 1, 16, 1}, {s, 1, 100, 1},
{{r, 3.5}, 0, 10}, {z, 1, 0},
{{PR, 5}, 1, 5}, {C, 0, 1, 1},
{t, 0, 100, 1}]

P ={1.5, 1, 4, 8, 3.8, 0.75, 0, 5, 500, 0}

Manipulate[
CubeTrail[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],t,P[[8]],500,0],
{t, 1, 80, 1}]

Mathematica code:

Rot = 
Table[
Table[
RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],
{v, 1, 8, 1}],
{a, 0, 2 Pi, 2 Pi/100}]

Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}

CubeProjections[color_, pr_, b_, s_, h_, w_, m_, a_] :=
Graphics[
Table[
Translate[
{AbsoluteThickness[h], If[color == 0, Black, White],
Line[
Table[
Table[
Rot[[1 + Mod[w (y + m*x) + a, 100]]][[Edge[[k]]]][[c]],
{c, 1, 2, 1}],
{k, 1, 16, 1}]]},
{s*x, s*y}],
{x, -b, b, 1}, {y, -b, b, 1}],
PlotRange -> {{-5*pr/14, 5*pr/14}, {-pr, pr}}, ImageSize -> 500,
Background -> If[color == 0, White, Black]
]

Manipulate[
PM = {color, pr, b, s, h, w, m, a};
CubeProjections[color, pr, b, s, h, w, m, a],
{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 20, 1},
{{s, 3}, 0, 5}, {{h, 1}, .01, 10},
{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},
{a, 1, 100, 1}]

P = {0, 27.7, 20, 1.3, 2.75, 1, 0, 18}


Show@
CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],P[[8]]]


Mathematica code:
RotAxis = Table[Table[  Table[    R[o, {.01 + x, .01 + y, 0}, {0, 0, 0}],    {o, 0, 2 Pi, 2 Pi/80}], {x, -10, 10, 1}], {y, -10, 10, 1}]Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}CubeProjections[color_, pr_, b_, s_, h_, w_, m_, o_] :=Graphics[ Table[  Translate[   {AbsoluteThickness[h], If[color == 0, Black, White],    Line[     Table[      Table[      RotAxis[[11 + y]][[11 + x]]      [[1 + Mod[Round[ (Pi + ArcTan[.01 + x, .01 + y])/2Pi] + o, 80]]]      [[Edge[[k]]]][[c]],       {c, 1, 2, 1}],      {k, 1, 16, 1}]]},   {s*x, s*y}],  {x, -b, b, 1}, {y, -b, b, 1}], PlotRange -> {{-pr, pr}, {-pr, pr}}, ImageSize -> 500,  Background -> If[color == 0, White, Black] ]Manipulate[PM = {color, pr, b, s, h, w, m, a};CubeProjections[color, pr, b, s, h, w, m, a],{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 10, 1},{{s, 3}, 0, 5}, {{h, 1}, .01, 10},{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},{a, 1, 80, 1}]P = {0, 20, 5, 3.6, 1.5, 1, 1, 1}Manipulate[CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],a],{a, 1, 79, 2}]

Mathematica code:

RotAxis =
 Table[Table[
Table[
R[o, {.01 + x, .01 + y, 0}, {0, 0, 0}],
{o, 0, 2 Pi, 2 Pi/80}],
 {x, -10, 10, 1}], {y, -10, 10, 1}]

Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}

CubeProjections[color_, pr_, b_, s_, h_, w_, m_, o_] :=
Graphics[
Table[
Translate[
{AbsoluteThickness[h], If[color == 0, Black, White],
Line[
Table[
Table[
RotAxis[[11 + y]][[11 + x]]
[[1 + Mod[Round[ (Pi + ArcTan[.01 + x, .01 + y])/2Pi] + o, 80]]]
[[Edge[[k]]]][[c]],
{c, 1, 2, 1}],
{k, 1, 16, 1}]]},
{s*x, s*y}],
{x, -b, b, 1}, {y, -b, b, 1}],
PlotRange -> {{-pr, pr}, {-pr, pr}}, ImageSize -> 500,
Background -> If[color == 0, White, Black]
]

Manipulate[
PM = {color, pr, b, s, h, w, m, a};
CubeProjections[color, pr, b, s, h, w, m, a],
{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 10, 1},
{{s, 3}, 0, 5}, {{h, 1}, .01, 10},
{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},
{a, 1, 80, 1}]

P = {0, 20, 5, 3.6, 1.5, 1, 1, 1}

Manipulate[
CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],a],
{a, 1, 79, 2}]
Mathematica code:
RotAxis = Table[Table[  Table[    R[o, {.01 + x, .01 + y, 0}, {0, 0, 0}],    {o, 0, 2 Pi, 2 Pi/80}], {x, -10, 10, 1}], {y, -10, 10, 1}]Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}CubeProjections[color_, pr_, b_, s_, h_, w_, m_, o_] :=Graphics[ Table[  Translate[   {AbsoluteThickness[h], If[color == 0, Black, White],    Line[     Table[      Table[      RotAxis[[11 + y]][[11 + x]][[o]][[Edge[[k]]]][[c]],       {c, 1, 2, 1}],      {k, 1, 16, 1}]]},   {s*x, s*y}],  {x, -b, b, 1}, {y, -b, b, 1}], PlotRange -> {{-pr, pr}, {-pr, pr}}, ImageSize -> 500,  Background -> If[color == 0, White, Black] ]Manipulate[PM = {color, pr, b, s, h, w, m, a};CubeProjections[color, pr, b, s, h, w, m, a],{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 10, 1},{{s, 3}, 0, 5}, {{h, 1}, .01, 10},{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},{a, 1, 80, 1}]P = {0, 20, 5, 3.6, 1.5, 1, 1, 1}Manipulate[CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],a],{a, 1, 79, 2}]

Mathematica code:

RotAxis =
 Table[Table[
Table[
R[o, {.01 + x, .01 + y, 0}, {0, 0, 0}],
{o, 0, 2 Pi, 2 Pi/80}],
 {x, -10, 10, 1}], {y, -10, 10, 1}]

Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}

CubeProjections[color_, pr_, b_, s_, h_, w_, m_, o_] :=
Graphics[
Table[
Translate[
{AbsoluteThickness[h], If[color == 0, Black, White],
Line[
Table[
Table[
RotAxis[[11 + y]][[11 + x]][[o]][[Edge[[k]]]][[c]],
{c, 1, 2, 1}],
{k, 1, 16, 1}]]},
{s*x, s*y}],
{x, -b, b, 1}, {y, -b, b, 1}],
PlotRange -> {{-pr, pr}, {-pr, pr}}, ImageSize -> 500,
Background -> If[color == 0, White, Black]
]

Manipulate[
PM = {color, pr, b, s, h, w, m, a};
CubeProjections[color, pr, b, s, h, w, m, a],
{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 10, 1},
{{s, 3}, 0, 5}, {{h, 1}, .01, 10},
{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},
{a, 1, 80, 1}]

P = {0, 20, 5, 3.6, 1.5, 1, 1, 1}

Manipulate[
CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],a],
{a, 1, 79, 2}]

Mathematica code:
Rot =  Table[  Table[   RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],  {v, 1, 8, 1}],{a, 0, 2 Pi, 2 Pi/100}]Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}CubeProjections[color_, pr_, b_, s_, h_, w_, m_, o_] :=Graphics[ Table[  Translate[   {AbsoluteThickness[h], If[color == 0, Black, White],    Line[     Table[      Table[       Rot[[1 + Mod[w (y + m*x) + a, 100]]][[Edge[[k]]]][[c]],       {c, 1, 2, 1}],      {k, 1, 16, 1}]]},   {s*x, s*y}],  {x, -b, b, 1}, {y, -b, b, 1}], PlotRange -> {{-pr, pr}, {-pr, pr}}, ImageSize -> 500,  Background -> If[color == 0, White, Black] ]Manipulate[PM = {color, pr, b, s, h, w, m, a};CubeProjections[color, pr, b, s, h, w, m, a],{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 10, 1},{{s, 3}, 0, 5}, {{h, 1}, .01, 10},{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},{a, 1, 100, 1}]P = {1, 28, 9, 3, 1.4, 1, 1, 30}Manipulate[CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],a],{a, 48, 0, -2}]



Mathematica code:

Rot = 
Table[
Table[
RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],
{v, 1, 8, 1}],
{a, 0, 2 Pi, 2 Pi/100}]

Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}

CubeProjections[color_, pr_, b_, s_, h_, w_, m_, o_] :=
Graphics[
Table[
Translate[
{AbsoluteThickness[h], If[color == 0, Black, White],
Line[
Table[
Table[
Rot[[1 + Mod[w (y + m*x) + a, 100]]][[Edge[[k]]]][[c]],
{c, 1, 2, 1}],
{k, 1, 16, 1}]]},
{s*x, s*y}],
{x, -b, b, 1}, {y, -b, b, 1}],
PlotRange -> {{-pr, pr}, {-pr, pr}}, ImageSize -> 500,
Background -> If[color == 0, White, Black]
]

Manipulate[
PM = {color, pr, b, s, h, w, m, a};
CubeProjections[color, pr, b, s, h, w, m, a],
{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 10, 1},
{{s, 3}, 0, 5}, {{h, 1}, .01, 10},
{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},
{a, 1, 100, 1}]

P = {1, 28, 9, 3, 1.4, 1, 1, 30}

Manipulate[
CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],a],
{a, 48, 0, -2}]
2-D projections of rotating cubes
Mathematica code:
Rot =  Table[  Table[   RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],  {v, 1, 8, 1}],{a, 0, 2 Pi, 2 Pi/100}]Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}CubeProjections[color_, pr_, b_, s_, h_, w_, m_, o_] :=Graphics[ Table[  Translate[   {AbsoluteThickness[h], If[color == 0, Black, White],    Line[     Table[      Table[       Rot[[1 + Mod[w (y + m*x) + a, 100]]][[Edge[[k]]]][[c]],       {c, 1, 2, 1}],      {k, 1, 16, 1}]]},   {s*x, s*y}],  {x, -b, b, 1}, {y, -b, b, 1}], PlotRange -> {{-pr, pr}, {-pr, pr}}, ImageSize -> 500,  Background -> If[color == 0, White, Black] ]Manipulate[PM = {color, pr, b, s, h, w, m, a};CubeProjections[color, pr, b, s, h, w, m, a],{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 10, 1},{{s, 3}, 0, 5}, {{h, 1}, .01, 10},{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},{a, 1, 100, 1}]P = {0, 26.7, 7, 3.5, 1.3, 5, 1, 0}Manipulate[CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],a],{a, 48, 0, -2}]


2-D projections of rotating cubes

Mathematica code:

Rot = 
Table[
Table[
RotationTransform[a, {1, 1, 0}, {0, 0, 0}][Tuples[{-1, 1}, 3][[v]]],
{v, 1, 8, 1}],
{a, 0, 2 Pi, 2 Pi/100}]

Edge := {1, 2, 4, 3, 7, 8, 6, 5, 1, 3, 4, 8, 7, 5, 6, 2}

CubeProjections[color_, pr_, b_, s_, h_, w_, m_, o_] :=
Graphics[
Table[
Translate[
{AbsoluteThickness[h], If[color == 0, Black, White],
Line[
Table[
Table[
Rot[[1 + Mod[w (y + m*x) + a, 100]]][[Edge[[k]]]][[c]],
{c, 1, 2, 1}],
{k, 1, 16, 1}]]},
{s*x, s*y}],
{x, -b, b, 1}, {y, -b, b, 1}],
PlotRange -> {{-pr, pr}, {-pr, pr}}, ImageSize -> 500,
Background -> If[color == 0, White, Black]
]

Manipulate[
PM = {color, pr, b, s, h, w, m, a};
CubeProjections[color, pr, b, s, h, w, m, a],
{color, 0, 1, 1}, {{pr, 17}, 1, 52}, {{b, 5}, 1, 10, 1},
{{s, 3}, 0, 5}, {{h, 1}, .01, 10},
{{w, 1}, 0, 20, 1},{{m, 1}, 0, 20, 1},
{a, 1, 100, 1}]

P = {0, 26.7, 7, 3.5, 1.3, 5, 1, 0}

Manipulate[
CubeProjections[P[[1]],P[[2]],P[[3]],P[[4]],P[[5]],P[[6]],P[[7]],a],
{a, 48, 0, -2}]