The Taper Modifier is designed to smooth the edges of the density in a mesh as exemplified by the renderings below. It is a scaling as a function of inwards distance from the inner and outer surface of the mesh.
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The first image on the left shows a bipolar structure with a constant density. Here the emission goes right up the mesh and make evident the coarse mesh structure. In the second image a Taper Modifier was applied with the Taper function as shown below the render. As configured it generates a gentle glow around the surface.
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The render on the right has a different Taper function. It shows how it can be used to generate more complete multi-shell structures. Note that each hump in the Taper function generates two shells, one from the outside surface and a second from the inside surface. If the mesh has no inner surface, only one shell is generated.
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Note that for complex high resolution meshes the Taper Modifier is computationally expensive. So, balance between the computing time and the need for it. Much testing can be sped up by temporarily disabling the Taper Modifier while it is not needed.
Name: Provide a name for the modifier that closely describes its function.
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Taper: Opens a graph to set the Taper function. The Taper function is most conveniently set up as a Point function. To smooth the edges, set the value to zero at position zero and transition to a value of 1 at the desired distance from the surface. Note that this transition scale does not change with position in an object. It may therefore not get to 1, if there is a shell that is thinner than the transition scale. This is the case in the example below, where the shell becomes thin towards the center and therefore the emission very low. This can be compensated for partially by adjusting the Magnitude graph.
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Magnitude: A graph that allows one to compensate for "lost" emission, from the taper in regions of these shells.