Topic
MicroTiles
About: MicroTiles is a research topic. Over the lifetime, 9 publications have been published within this topic receiving 52 citations.
Papers
TL;DR: A new representation for structuring partial symmetries (partial self‐correspondences), which is called “microtiles”, is introduced, which can build all objects that are (r+ε)‐similar to S for any ε >0.
Abstract: In this paper, we develop a theoretical framework for characterizing shapes by building blocks. We address two questions: First, how do shape correspondences induce building blocks? For this, we introduce a new representation for structuring partial symmetries (partial self-correspondences), which we call “microtiles”. Starting from input correspondences that form point-wise equivalence relations, microtiles are obtained by grouping connected components of points that share the same set of symmetry transformations. The decomposition is unique, requires no parameters beyond the input correspondences, and encodes the partial symmetries of all subsets of the input. The second question is: What is the class of shapes that can be assembled from these building blocks? Here, we specifically consider r-similarity as correspondence model, i.e., matching of local r-neighborhoods. Our main result is that the microtiles of the partial r-symmetries of an object S can build all objects that are (r+e)-similar to S for any e >0. Again, the construction is unique. Furthermore, we give necessary conditions for a set of assembly rules for the pairwise connection of tiles. We describe a practical algorithm for computing microtile decompositions under rigid motions, a corresponding prototype implementation, and conduct a number of experiments to visualize the structural properties in practice. © 2012 Wiley Periodicals, Inc.
22 citations
TL;DR: The rapid self-assembly of photolithographic microTiles into large crystalline monolayers is achieved and has the potential to assemble different shapes and sizes of microtiles into complex architectures.
Abstract: The rapid self-assembly of photolithographic microtiles into large crystalline monolayers is achieved. Crystalline monolayers get trapped at the liquid-liquid interface and re-emerge at the air-liquid interface by mixing a cosolvent, which then deposits on the solid surface in seconds. This method has the potential to assemble different shapes and sizes of microtiles into complex architectures.
18 citations
1 Jan 2006
TL;DR: In this paper, the authors present a method in which regular, micro-scaled units are made to self-assemble into arbitrary, reconfigurable structures by controlling the local flow conditions in a microchannel array.
Abstract: In this paper we present a novel microfabrication method in which regular, micro-scaled units are made to self-assemble into arbitrary, reconfigurable structures. We describe a series of experiments that involve the assembly of silicon microtiles in a multilayer PDMS microchamber. By controlling the local flow conditions in a microchannel array, the attraction, bonding, migration, and rejection of individual and paired microtiles are demonstrated.
9 citations
TL;DR: In this article, three-dimensional polymeric microtiles are fabricated out of the superposition of two structural SU-8 layers featuring chiral copies of the same centro-symmetric pattern to investigate the dynamics of fluidic self-assembly at sub-millimeter scale.
4 citations
4 Mar 2015
TL;DR: This work addresses the problem of computing a microtile decomposition and shows how to efficiently detect r-symmetric of points on triangle meshes and introduces an efficient method for computing microtiles, which permits such involved analysis to be used in variety of geometry processing applications.
Abstract: In their paper [2012], Kalojanov et al. introduce a theoretical model for shape decomposition into microtiles - building blocks derived by a set of correspondences that define an equivalence relation on the surface points of a given model. The authors also showed that for a specific correspondence functions (rigid r-neighborhood matching) the set of microtiles characterizes all shapes r-similar to a given exemplar. Here, we address the problem of computing a microtile decomposition and show how to efficiently detect r-symmetric of points on triangle meshes. We first demonstrate that a microtile decomposition w.r.t. rigid r-symmetry is computable. Afterwards, we introduce an efficient method for computing microtiles, which permits such involved analysis to be used in variety of geometry processing applications.
1 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2016 | 1 |
| 2015 | 1 |
| 2014 | 2 |
| 2013 | 1 |
| 2012 | 1 |
| 2011 | 1 |