Coordinate-based neural networks parameterizing implicit surfaces have emerged
as efficient representations of geometry. They effectively act as parametric
level sets with the zero-level set defining the surface of interest. We present
a framework that allows applying deformation operations defined for
triangle meshes onto such implicit surfaces. Several of these operations can be
viewed as energy-minimization problems that induce an instantaneous flow field
on the explicit surface. Our method uses the flow field to deform parametric
implicit surfaces by extending the classical theory of level sets. We also
derive a consolidated view for existing methods on differentiable surface
extraction and rendering, by formalizing connections to the level-set theory. We
show that these methods drift from the theory and that our approach exhibits
improvements for applications like surface smoothing, mean-curvature
flow, inverse rendering and user-defined editing on implicit geometry.
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