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notebooks/04.12-Three-Dimensional-Plotting.ipynb

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"\n",
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"Analogous to the contour plots we explored in [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb), ``mplot3d`` contains tools to create three-dimensional relief plots using the same inputs.\n",
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"Like two-dimensional ``ax.contour`` plots, ``ax.contour3D`` requires all the input data to be in the form of two-dimensional regular grids, with the Z data evaluated at each point.\n",
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"Here we'll show a three-dimensional contour diagram of a three-dimenisonal sinusoidal function:"
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"Here we'll show a three-dimensional contour diagram of a three-dimensional sinusoidal function:"
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"Now from this parametrization, we must determine the *(x, y, z)* positions of the embedded strip.\n",
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"Thinking about it, we might realize that there are two rotations happening: one is the position of the loop about its center (what we've called $\\theta$), while the other is the twisting of the strip about its axis (we'll call this $\\phi$). For a Mobuis strip, we must have the strip makes half a twist during a full loop, or $\\Delta\\phi = \\Delta\\theta/2$."
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"Thinking about it, we might realize that there are two rotations happening: one is the position of the loop about its center (what we've called $\\theta$), while the other is the twisting of the strip about its axis (we'll call this $\\phi$). For a Möbius strip, we must have the strip makes half a twist during a full loop, or $\\Delta\\phi = \\Delta\\theta/2$."
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