18,372 research outputs found
Multi-scale space-variant FRep cellular structures
Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures
on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular
structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic
space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due
to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or
along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel
representations
Attracting and repelling Lagrangian coherent structures from a single computation
Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling
or most attracting material surfaces in a finite-time dynamical system. To
identify both types of hyperbolic LCSs at the same time instance, the standard
practice has been to compute repelling LCSs from future data and attracting
LCSs from past data. This approach tacitly assumes that coherent structures in
the flow are fundamentally recurrent, and hence gives inconsistent results for
temporally aperiodic systems. Here we resolve this inconsistency by showing how
both repelling and attracting LCSs are computable at the same time instance
from a single forward or a single backward run. These LCSs are obtained as
surfaces normal to the weakest and strongest eigenvectors of the Cauchy-Green
strain tensor.Comment: Under consideration for publication in Chaos/AI
The existence of thick triangulations -- an "elementary" proof
We provide an alternative, simpler proof of the existence of thick
triangulations for noncompact manifolds. Moreover, this proof
is simpler than the original one given in \cite{pe}, since it mainly uses tools
of elementary differential topology. The role played by curvatures in this
construction is also emphasized.Comment: 7 pages Short not
Parametric Surfaces for Augmented Architecture representation
Augmented Reality (AR) represents a growing communication channel, responding to the need to expand reality with additional information, offering easy and engaging access to digital data. AR for architectural representation allows a simple interaction with 3D models, facilitating spatial understanding of complex volumes and topological relationships between parts, overcoming some limitations related to Virtual Reality. In the last decade different developments in the pipeline process have seen a significant advancement in technological and algorithmic aspects, paying less attention to 3D modeling generation. For this, the article explores the construction of basic geometries for 3D model’s generation, highlighting the relationship between geometry and topology, basic for a consistent normal distribution. Moreover, a critical evaluation about corrective paths of existing 3D models is presented, analysing a complex architectural case study, the virtual model of Villa del Verginese, an emblematic example for topological emerged problems. The final aim of the paper is to refocus attention on 3D model construction, suggesting some "good practices" useful for preventing, minimizing or correcting topological problems, extending the accessibility of AR to people engaged in architectural representation
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