[PDF][PDF] Neural implicit surfaces in higher dimension
arXiv preprint arXiv:2201.09636, 2022•academia.edu
This work investigates the use of neural networks admitting high-order derivatives for
modeling dynamic variations of smooth implicit surfaces. For this purpose, it extends the
representation of differentiable neural implicit surfaces to higher dimensions, which opens
up mechanisms that allow to exploit geometric transformations in many settings, from
animation and surface evolution to shape morphing and design galleries. The problem is
modeled by a k-parameter family of surfaces Sc, specified as a neural network function f …
modeling dynamic variations of smooth implicit surfaces. For this purpose, it extends the
representation of differentiable neural implicit surfaces to higher dimensions, which opens
up mechanisms that allow to exploit geometric transformations in many settings, from
animation and surface evolution to shape morphing and design galleries. The problem is
modeled by a k-parameter family of surfaces Sc, specified as a neural network function f …
Abstract
This work investigates the use of neural networks admitting high-order derivatives for modeling dynamic variations of smooth implicit surfaces. For this purpose, it extends the representation of differentiable neural implicit surfaces to higher dimensions, which opens up mechanisms that allow to exploit geometric transformations in many settings, from animation and surface evolution to shape morphing and design galleries.
The problem is modeled by a k-parameter family of surfaces Sc, specified as a neural network function f: R3× R k→ R, where Sc is the zero-level set of the implicit function f (·, c): R3→ R, with c∈ Rk, with variations induced by the control variable c. In that context, restricted to each coordinate of Rk, the underlying representation is a neural homotopy which is the solution of a general partial differential equation.
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