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Daniel Mejia Parra

Daniel Mejia Parra
Vicomtech · Industry and Advanced Manufacturing

Ph.D.

About

24
Publications
6,220
Reads
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82
Citations
Additional affiliations
July 2020 - present
Vicomtech
Position
  • Researcher
Description
  • Computational Geometry Applications in Industry and Medicine. Thermal Simulation of Machining Processes. Dimensional Inspection. Computer Graphics.
July 2019 - December 2020
Universidad EAFIT
Position
  • PostDoc Position
Description
  • Researcher. Computational Geometry, Computer Graphics, Applied Mathematics.
August 2015 - June 2020
Vicomtech
Position
  • Intern
Description
  • Computational Geometry Applications in Industry and Medicine. Heat Transfer Simulation for Laser Cutting. Dimensional Inspection. Computer Graphics.
Education
July 2016 - June 2020
Universidad EAFIT
Field of study
  • Computational Geometry, Computer Graphics, Applied Mathematics
January 2014 - June 2016
Universidad EAFIT
Field of study
  • Computational Geometry
January 2009 - December 2013
Universidad EAFIT
Field of study
  • Engineering Mathematics

Publications

Publications (24)
Article
Full-text available
Given a 2-manifold triangular mesh \(M \subset {\mathbb {R}}^3\), with border, a parameterization of \(M\) is a FACE or trimmed surface \(F=\{S,L_0,\ldots ,L_m\}\). \(F\) is a connected subset or region of a parametric surface \(S\), bounded by a set of LOOPs \(L_0,\ldots ,L_m\) such that each \(L_i \subset S\) is a closed 1-manifold having no inte...
Article
Full-text available
In the context of smart manufacturing, the concept of Visual Computing is a key enabling technology for Industry 4.0. Visual Computing and Physically-based simulation enables the implementation of interactive, visual and (in most cases) non-disruptive solutions within the context of (a) the production process (off-line or in-line) the shop floor, (...
Article
Full-text available
In the context of shape processing, the estimation of the medial axis is relevant for the simplification and re-parameterization of 3D bodies. The currently used methods are based on (1) General fields, (2) Geometric methods and (3) voxel-based thinning. They present shortcomings such as (1) overrepresentation and non-smoothness of the medial axis...
Conference Paper
Full-text available
This short abstract is based in a Conference Keynote about use cases of Computer Graphics and Visual Computing for Industry 4.0 and Operator 4.0. An extended version of this article was published by invitation of the Conference Organizers in the International Journal for Simulation and Multidisciplinary Design Optimization.
Article
Full-text available
In the context of CAD CAM CAE (Computer-Aided Design, Manufacturing and Engineering) and Additive Manufacturing, the computation of level sets of closed 2-manifold triangular meshes (mesh slicing) is relevant for the generation of 3D printing patterns. Current slicing methods rely on the assumption that the function used to compute the level sets s...
Conference Paper
In the context of numerical methods, the problem of frequency-domain (spectral) simulations is crucial for the solution of Partial Differential Equations. Fast Fourier Transform (FFT) algorithms significantly reduce the computational cost of such simulations and enable parallelization using Graphics Processing Units (GPUs). In the particular subdom...
Thesis
Full-text available
This Doctoral Thesis develops novel articulations of Differential Operators on Manifolds for applications on Computer Aided Design, Manufacture and Computer Graphics, as follows: (1) Mesh Parameterization and Segmentation. Development and application of Laplace-Beltrami, Hessian, Geodesic and Curvature operators for topology and geometry – driven s...
Article
Full-text available
In flexible manufacturing systems, fast feedback from simulation solutions is required for effective tool path planning and parameter optimization. In the particular sub-domain of laser heating/cutting of thin rectangular plates, current state-of-the-art methods include frequency-domain (spectral) analytic solutions that greatly reduce the required...
Article
Full-text available
In the context of CAD, CAM, CAE, and reverse engineering, the problem of mesh parameterization is a central process. Mesh parameterization implies the computation of a bijective map ϕ from the original mesh M ∈ R 3 to the planar domain ϕ ( M ) ∈ R 2 . The mapping may preserve angles, areas, or distances. Distance-preserving parameterizations (i.e.,...
Conference Paper
Full-text available
Point-cloud-to-mesh registration estimates a rigid transformation that minimizes the distance between a point sample of a surface and a reference mesh of such a surface, both lying in different coordinate systems. Point-cloud-to-mesh-registration is an ubiquitous problem in medical imaging, CAD CAM CAE, reverse engineering, virtual reality and many...
Article
In the context of Computer Simulation, the problem of heat transfer analysis of thin plate laser heating is relevant for downstream simulations of machining processes. Alternatives to address the problem include (i) numerical methods, which require unaffordable time and storage computing resources even for very small domains, (ii) analytical method...
Article
Full-text available
Industrial dimensional assessment presents instances in which early control is exerted among "warm" (approx. 600 • C) pieces. Early control saves resources, as defective processes are timely stopped and corrected. Existing literature is devoid of dimensional assessment on warm workpieces. In response to this absence, this manuscript presents the im...
Article
Full-text available
Interactive multi-beam laser machining simulation is crucial in the context of tool path planning and optimization of laser machining parameters. Current simulation approaches for heat transfer analysis (1) rely on numerical Finite Element methods (or any of its variants), non-suitable for interactive applications; and (2) require the multiple lase...
Conference Paper
Full-text available
In Reverse Engineering (RE), mesh segmentation is usually followed by mesh parameterization. A segmentation of a mesh M is not acceptable if the parameterization of its sub-mesh Mi fails. A defined parameterization failure criterion is given by the non-bijective nature of the parameterization ψi: Mi → R2. Current mesh segmentation algorithms produc...
Article
Mesh segmentation and parameterization are crucial for Reverse Engineering (RE). Bijective parameterizations of the sub-meshes are a sine-qua-non test for segmentation. Current segmentation methods use either (1) topologic or (2) geometric criteria to partition the mesh. Reported topology-based segmentations produce large sub-meshes which reject pa...
Article
In the context of computer numeric control (CNC)-based sheet metal laser cutting, the problem of heat transfer simulation is relevant for the optimization of CNC programs. Current physically based simulation tools use numeric or analytic algorithms which provide accurate but slow solutions due to the underlying mathematical description of the model...
Article
Full-text available
In design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (B-Rep), which in turn is central for feature-based design, machining, parametric CAD and reverse engineering, among others. Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (grap...
Article
Full-text available
FEA simulation of thermal metal cutting is central to interactive design and manufacturing. It is therefore relevant to assess the applicability of FEA open software to simulate 2D heat transfer in metal sheet laser cuts. Application of open source code (e.g. FreeFem++, FEniCS, MOOSE) makes possible additional scenarios (e.g. parallel, CUDA, etc.),...
Article
Purpose Mesh Parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus area distortion. This study aims to present an assessment of the sensitivity of the minimized distortion with respect to weighed area and angle distortions. Design...
Conference Paper
Traditionally, the data generated by industrial metrology software is stored as static reports that metrology experts produce for engineering and production departments. Nevertheless, industry demands new approaches that provide ubiquitous and real time access to overall geometry, manufacturing and other data. Web3D technologies can help to improve...
Conference Paper
Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional H for Dimensionality Reduction (DR) of a sampled manifold M. This article presents a variation of classic HLLE for parameterization of 3D triangular meshes. Contrary to classic HLLE which estimates local Hessian nullspaces, the proposed appro...
Conference Paper
Finite Element Methods (FEM) have been used to simulate a variety of physical phenomena in the industrial manufacturing sector. This paper addresses the simulation of the thermal properties in the metal sheet laser cutting. A comparison of very well known FEM software is presented. The results present small differences between the temperature distr...
Conference Paper
Mesh segmentation can be achieved by considering (a) geometric, (b) topologic or (c) a combination of geometric and topologic features on the surface. Although considering geometric characteristics would be relatively easy, our main intention is to keep the discussion on the topological aspect given that topology-based methods are foggy in their ba...
Conference Paper
En este trabajo se representa el comportamiento de una parcela de seis a treinta hectáreas, destinada a la agricultura extensiva y a la ganadería de doble propósito, en piso térmico frío, a altitudes entre los 2000 y 3000 metros sobre el nivel del mar. En estas regiones se tiene el 7.9% del territorio nacional y corresponde generalmente a geografía...

Questions

Question (1)
Question
I'm currently running a 2D Steady Linear Heat Transfer Analysis on a squared shell (DS4 elements) in ABAQUS. I'm able to run the simulation without the Remeshing Rule. However, introducing a Remeshing Rule I always get "Error in job: PROGRAM IS ASKED TO INVERT A SINGULAR MATRIX". I have tried several different default as well as user-defined remeshing parameters (initial mesh, sizing method, constraints). What am I doing wrong?

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