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 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.