I understand how implicit representation eases certain computations. But I guess there are only limited standard geometries/surfaces which we can express implicitly. For most general cases, discretized geometries or explicit representation would be greatly useful. How often are implicit geometries used in graphics algorithm and applications?

keenan

@sbhilare We can easily represent any shape implicitly, as long as we're willing to use a sampled representation, such as distance values sampled onto a regular grid---see especially this slide. Another common possibility is to sample distance values onto the vertices of a tetrahedral mesh, and linearly interpolate these values over the interior of each tetrahedron using barycentric coordinates. The zero set of this interpolated function then defines the surface itself.

I understand how implicit representation eases certain computations. But I guess there are only limited standard geometries/surfaces which we can express implicitly. For most general cases, discretized geometries or explicit representation would be greatly useful. How often are implicit geometries used in graphics algorithm and applications?

@sbhilare We can easily represent any shape implicitly, as long as we're willing to use a

sampledrepresentation, such as distance values sampled onto a regular grid---see especially this slide. Another common possibility is to sample distance values onto the vertices of a tetrahedral mesh, and linearly interpolate these values over the interior of each tetrahedron using barycentric coordinates. The zero set of this interpolated function then defines the surface itself.