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A graph-based mesh representation for the simulation of fracture and fragmentation for finite element simulations.
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https://www.geofront.eu/demos/lines
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Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges. After obtaining edge representations from the hypergraphs, we then cluster or drop edges to obtain holistic graph-level edge representations. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance, on which our method largely outperforms existing graph representation learning methods. Moreover, our edge representation learning and pooling method also largely outperforms state-of-theart graph pooling methods on graph classification, not only because of its accurate edge representation learning, but also due to its lossless compression of the nodes and removal of irrelevant edges for effective message-passing. Code is available at https://github.com/harryjo97/EHGNN.
TopMesh A Tool for Extracting Topological Information From Non-Manifold Objects
Full paper presentation at the GRAPP2010 international conference.
We present TopMesh, a tool for extracting topological information from non-manifold three-dimensional
objects with parts of non-uniform dimensions. The boundary of such objects is discretized as a mesh of
triangles and of dangling edges, representing one-dimensional parts of the object. The geometrical and
topological information extracted include the number of elements in the mesh, the number of non-manifold
singularities and the Betti numbers, which characterize the topology of an object independently of the discretization of its boundary. TopMesh also computes a decomposition of the mesh into connected parts of uniform dimension, into edge-connected components formed by triangles, and into oriented edge-connected sub-meshes. We describe the functionalities of TopMesh and the algorithms implementing them.
A0280105
This document describes the design and implementation of a 3D graphics rasterizer with texture mapping and shading capabilities on an FPGA. Key aspects include:
1. The rasterizer implements the main components of the 3D graphics pipeline including vertex shader, pixel shader, triangle setup engine, and rasterization engine.
2. Texture mapping and shading are supported through a "slim shader" design that divides triangles into strips and gates unnecessary shading and texturing to improve performance.
3. Address alignment logic is used to reduce power consumption by identifying overlapping texture requests and only fetching unique texels from memory each cycle.
20151130
The document proposes improvements to distributed graph pattern matching algorithms. It introduces a boundary filter technique that aims to shrink large data graphs by removing boundary nodes. These are nodes that only have one relationship in directed graphs. Experiments show the boundary filter approach significantly reduces running time compared to the original distributed tight simulation algorithm, while also improving accuracy by finding more matching subgraphs. The boundary filtering allows independent evaluation of each vertex and scales well to more complex graph patterns.
Wordoku Puzzle Solver - Image Processing Project
This document describes an algorithm to solve Wordoku puzzles by processing image elements. The key steps are: 1) Separating the puzzle grid and keyword, 2) Extracting characters from each, 3) Matching characters using classifiers like cross-correlation and support vector regression, 4) Solving the puzzle by filling values in a matrix, 5) Printing the solved puzzle by pasting characters. The algorithm was tested on various puzzles and fonts, achieving a 90% accuracy rate. Extensions to handle real images and optimize character extraction are proposed for future work.
Verification of Efficacy of Inside-Outside Judgement in Respect of a 3D-Primi...
Verification of Efficacy of Inside-Outside Judgement in Respect of a 3D-Primi...International Journal of Modern Research in Engineering and Technology
For the processing of data such as with 3D printing, Virtual Reality (VR) and
Augmented Reality (AR), there is a need to seek technology which accurately and quickly analyzes the
three-dimensional structures including that of complicated 3D forms. However, unlike in 2D situations
when there are few data points, there is not yet an established method for processing it quickly for 3D
forms due to the fact the objects constructing it are complicated as well as the fact that there is a lot of
data points within the space. Generally, when illustrating a complicated form, a method is used
whereby an object with the complicated form is generated using several primitive shapes. This method
is used in various 3D modelling software because the position of the object can be intuitively and
freely changed and since it can be easily written within DirectX or Java 3D, OpenGL, etc. In this
thesis, it was shown that by using GPGPU (General-Purpose computing on Graphics Processing
Units) in respect of an algorithm with a solid angle, the inside-outside judgement could be conducted
quickly. Specifically, a measurement of inside-outside judgement processing was made for
complicated shapes created from several primitive shapes as well as the measurement of processing
time of several primitive shapes.MATLAB
This document introduces Matlab and how it can be used for computer vision and image processing tasks. Matlab is a useful language for these applications because images can be represented as matrices and many vision algorithms are naturally implemented using matrix operations in Matlab. The document provides examples of reading image files in common formats like PGM and PPM, and demonstrates basic Matlab operations for creating, accessing, and manipulating image matrices.
Geometric modeling111431635 geometric-modeling-glad (1)
This document discusses different types of geometric modeling methods including wireframe, surface, and solid modeling. Wireframe modeling uses points and lines to define objects but does not represent actual surfaces or volumes. Surface modeling defines the outer surfaces of an object. Solid modeling precisely defines the enclosed volume of an object using its faces, edges, and vertices. Constructive solid geometry and boundary representation are two common solid modeling techniques. CSG uses Boolean operations to combine primitive shapes, while boundary representation stores topological information about faces, edges, and vertices. Feature-based modeling allows shapes to be created through operations like extruding, revolving, sweeping, and filling.
LRIEEE-MTT
This document presents two numerical methods for evaluating integrals involving the linear-shape function times the 3D Green's function on a plane triangle. The conventional method splits the integral into an analytical and numerical part, while the alternative method proposed evaluates the integral fully numerically. Numerical results show the alternative method is conceptually simpler, easier to implement, and achieves similar or better accuracy compared to the conventional method.
111431635-geometric-modeling-glad1-150630140219-lva1-app6892 (1).pdf
This document discusses different types of geometric modeling methods including wireframe, surface, and solid modeling. Wireframe modeling uses points and lines to define objects but does not represent actual surfaces or volumes. Surface modeling defines the outer surfaces of an object. Solid modeling precisely defines the enclosed volume of an object using its faces, edges, and vertices. Constructive solid geometry and boundary representation are two common solid modeling techniques. CSG uses Boolean operations to combine primitive shapes, while boundary representation precisely defines the boundaries and topology of a model.
50120130406023
This document summarizes a research paper that proposes using a genetic algorithm to solve the NP-hard graph partitioning problem. The paper aims to partition graphs to minimize the number of cuts between partitions. It describes representing graph partitions as chromosomes that are evolved over generations using genetic operators like crossover and mutation. An algorithm is presented that initially partitions a graph randomly and then applies genetic operators to iteratively improve the partitioning solution by reducing cut size, considered the fitness function. The algorithm was tested on sample graphs and able to find partitioning solutions with a minimum cut size of 10 and average cut size reduced from 14 to 11 over 100 generations.
Ijarcet vol-2-issue-7-2230-2231
This document discusses techniques for representing digital circuit partitioning problems using graph representations. It presents three encoding techniques to map graph partitions to the problem domain: 1) a binary string where each bit represents a cell and its partition, 2) a string with two regions to represent vertices and edge crossings, and 3) a string with regions for vertices and edges. The techniques are evaluated in terms of suitability, with the second approach more suitable for dense circuits. Net cut evaluation is also described to analyze partitioning solutions.
Ijarcet vol-2-issue-7-2230-2231
This document discusses techniques for representing digital circuit partitioning problems using graph representations. It presents three encoding techniques to map graph partitions to the problem domain: 1) a binary string where each bit represents a cell and its partition, 2) a string with two regions to represent vertices and edge crossings, and 3) a string with regions for vertices and edges. The techniques are evaluated in terms of suitability, with the second approach more suitable for dense circuits. Net cut evaluation is also described to analyze partitioning solutions.
Lgm saarbrucken
The document summarizes a method for mining frequent subgraphs from linear graphs. It describes:
1) Representing data like proteins, RNA and texts as linear graphs and the need for algorithms to mine frequent patterns from such graphs.
2) A method called LGM that can efficiently enumerate and mine both connected and disconnected subgraphs from linear graphs using reverse search techniques.
3) Experiments applying LGM to mine motifs from protein structures and phrases from texts, achieving better performance than existing methods.
Design Patterns for Efficient Graph Algorithms in MapReduce__HadoopSummit2010
Design Patterns for Efficient Graph Algorithms in MapReduce__HadoopSummit2010Yahoo Developer Network
Hadoop Summit 2010 - Research Track
Design Patterns for Efficient Graph Algorithms in MapReduce
Jimmy Lin, Michael Schatz, University of Maryland Project Report
The document summarizes a summer internship project to parallelize the TopFitter program, which calculates constraints on deviations from the Standard Model regarding top quarks, in order to speed up computations. The goal of creating a GPU-parallelized version of TopFitter was accomplished, achieving a 3.5x speedup. However, an unidentified bug remains when running on the largest dataset. As a side project, analysis found that interference prevents detection of non-Standard Model effects from events with non-standard color flows, implying a different approach is needed.
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Topology
- 6. Simplices as Graphs Simplices are graphs vertices, and colored edges represent connectivity and orientation. Graphs are directed.
- 8. Local Ordering as Color Maps Triangle 0 sees point 0 as the blue point in segment 0. Triangle 1 sees it as red. color maps
- 9. Cube Mesh as Graph Graphs are quite complex even for meshes with a few elements.
- 10. Plate with Hole Mesh Same graph representation works for 2D. Easy to extract useful features.
- 15. Fracture Algorithm (1) First selected open point is 2, so process open segments 1 and 5 attached to it.
- 16. Fracture Algorithm (2) Extract subgraph for segment 1, which clones open triangle 2, creating triangle 7.
- 17. Fracture Algorithm (3) There are 2 branches in segment 1's subgraph, so the segment is split.
- 18. Fracture Algorithm (4) Next is segment 5, now attached to 0 open triangles. Its subgraph has 2 branches.
- 19. Fracture Algorithm (5) Both open segments for point 2 were split, its subgraph has 2 branches now.
- 20. Fracture Algorithm (6) Next is point 1, with segment 3 the only remaining open segment.
- 21. Fracture Algorithm (7) Segment 3 is split.
- 22. Fracture Algorithm (8) Point 1 is split.
- 23. Fracture Algorithm (9) Finally point 3, with 0 open segments, is split, obtaining 2 separate tetrahedra.
- 24. Two-Tet Mesh and Graphs Before After
- 25. Correctness – Point Cubes Two cubes joined by a point. Fracture all internal triangles. Current algorithm: Graph representation:
- 26. Correctness – Edge Cubes Two cubes joined by an edge. Fracture all internal triangles. Current algorithm: Graph representation:
- 33. Fracture Time