Created
August 30, 2024 15:17
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Tensegrity twisted prism in 3D, using SageMath
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| # Tensegrity twisted prism. PM 2Ring 2024.08.31 | |
| def ball(radius, **kwargs): | |
| var('u,v') | |
| kw = dict(plot_points=40) | kwargs | |
| return spherical_plot3d(radius, (u, 0, 2*pi), (v, 0, pi), **kw) | |
| def axis_matrix(W): | |
| a, b, c = W | |
| if abs(c) == 1: | |
| return identity_matrix(3) * sgn(c) | |
| U = vector([b, -a, 0]).normalized() | |
| V = W.cross_product(U) | |
| return matrix([U, V, W]).T | |
| def cyl(V0, V1, radius=1, **kwargs): | |
| W = V1 - V0 | |
| wnorm = W.norm() | |
| M = axis_matrix(W / wnorm) | |
| func = V0 + M * vector([radius * cos(u), radius * sin(u), v]) | |
| kw = dict(plot_points=(40, 2)) | kwargs | |
| return parametric_plot3d(func, (u, 0, 2*pi), (v, 0, wnorm), **kw) | |
| def circ(q): | |
| sn, cs = n(2 * pi * q).sincos() | |
| return vector((cs, sn, 0)) | |
| @interact | |
| def main(num=3, twist=1/3, | |
| height=3.0r, c_rad=0.10r, t_rad=0.05r, | |
| c_color="#0a0", t_color="#b00", | |
| dark=True, perspective=True, auto_update=False): | |
| Z = vector((0, 0, height)) | |
| pos_lo = [circ(i / num) for i in range(num)] | |
| pos_hi = [circ((i + twist) / num) + Z for i in range(num)] | |
| P = Graphics() | |
| b = ball(radius=c_rad, color=c_color) | |
| P += sum(b.translate(p) for p in pos_lo + pos_hi) | |
| P += sum(cyl(*pq, radius=t_rad, color=t_color) | |
| for pq in zip(pos_lo, pos_lo[1:]+pos_lo[:1])) | |
| P += sum(cyl(*pq, radius=t_rad, color=t_color) | |
| for pq in zip(pos_hi, pos_hi[1:]+pos_hi[:1])) | |
| P += sum(cyl(*pq, radius=t_rad, color=t_color) | |
| for pq in zip(pos_lo, pos_hi)) | |
| P += sum(cyl(*pq, radius=c_rad, color=c_color) | |
| for pq in zip(pos_lo, pos_hi[1:]+pos_hi[:1])) | |
| theme = "dark" if dark else "light" | |
| projection = "perspective" if perspective else "orthographic" | |
| kw = dict(frame=False, theme=theme, projection=projection, online=True) | |
| P.show(**kw) | |
| P.save("tensegrity.html", **kw) |
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