40,955 research outputs found
Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian
Neural implicit representation is a promising approach for reconstructing
surfaces from point clouds. Existing methods combine various regularization
terms, such as the Eikonal and Laplacian energy terms, to enforce the learned
neural function to possess the properties of a Signed Distance Function (SDF).
However, inferring the actual topology and geometry of the underlying surface
from poor-quality unoriented point clouds remains challenging. In accordance
with Differential Geometry, the Hessian of the SDF is singular for points
within the differential thin-shell space surrounding the surface. Our approach
enforces the Hessian of the neural implicit function to have a zero determinant
for points near the surface. This technique aligns the gradients for a
near-surface point and its on-surface projection point, producing a rough but
faithful shape within just a few iterations. By annealing the weight of the
singular-Hessian term, our approach ultimately produces a high-fidelity
reconstruction result. Extensive experimental results demonstrate that our
approach effectively suppresses ghost geometry and recovers details from
unoriented point clouds with better expressiveness than existing fitting-based
methods
A survey of partial differential equations in geometric design
YesComputer aided geometric design is an area
where the improvement of surface generation techniques
is an everlasting demand since faster and more accurate
geometric models are required. Traditional methods
for generating surfaces were initially mainly based
upon interpolation algorithms. Recently, partial differential
equations (PDE) were introduced as a valuable
tool for geometric modelling since they offer a number
of features from which these areas can benefit. This work
summarises the uses given to PDE surfaces as a surface
generation technique togethe
Ray casting implicit fractal surfaces with reduced affine arithmetic
A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store
Digitally interpreting traditional folk crafts
The cultural heritage preservation requires that objects persist throughout time to continue to communicate an intended meaning. The necessity of computer-based preservation and interpretation of traditional folk crafts is validated by the decreasing number of masters, fading technologies, and crafts losing economic ground. We present a long-term applied research project on the development of a mathematical basis, software tools, and technology for application of desktop or personal fabrication using compact, cheap, and environmentally friendly fabrication devices, including '3D printers', in traditional crafts. We illustrate the properties of this new modeling and fabrication system using several case studies involving the digital capture of traditional objects and craft patterns, which we also reuse in modern designs. The test application areas for the development are traditional crafts from different cultural backgrounds, namely Japanese lacquer ware and Norwegian carvings. Our project includes modeling existing artifacts, Web presentations of the models, automation of the models fabrication, and the experimental manufacturing of new designs and forms
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