I cannot understand why the same transformations in 2D and 3D do not give the similar results (flat join segment line). In 3D the segments are not joined. Please help!
H = 0.5;
seg = {Line[{{0, 0}, {0, 2 H}}], Disk[{0, H}, 0.1]};
alpha[n_] := (1 + n /10) Pi/20;
Table[Translate[
Rotate[seg, -
Sum[alpha[j], {j, 0, n}]], {H (Sin[ Sum[alpha[j], {j, 0, n}]] +
2 Sum[Sin[Sum[ alpha[j], {j, 0, i}]], {i, 1, n - 1}]),
H (1 + Cos[ Sum[alpha[j], {j, 0, n}]] +
2 Sum[Cos[Sum[alpha[j], {j, 0, i}]], {i, 1, n - 1}])}], {n,30}];
Graphics[%]
H = 0.5;
seg = {Line[{{0, 0, 0}, {0, 0, 2 H}}], Sphere[{0, 0, H}, 0.1]};
alpha[n_] := (1 + n /10) Pi/20;
Table[Translate[
Rotate[seg,
Sum[ alpha[j], {j, 0, n}], {0, 1,
0}], {H (Sin[ Sum[alpha[j], {j, 0, n}]] +
2 Sum[Sin[Sum[ alpha[j], {j, 0, i}]], {i, 1, n - 1}]), 0,
H (1 + Cos[ Sum[alpha[j], {j, 0, n}]] +
2 Sum[Cos[Sum[alpha[j], {j, 0, i}]], {i, 1, n - 1}])}], {n, 30}];
Graphics3D[%, Boxed -> False]