Repositorio Institucional Universidad EAFIT ::Examinando por Autor "Acosta D.A."

Examinando por Autor "Acosta D.A."

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Approximation of the mechanical response of large lattice domains using homogenization and design of experiments
(Universitatea Politehnica Bucuresti, 2020-01-01) Montoya-Zapata D.; Acosta D.A.; Cortés C.; Pareja-Corcho J.; Moreno A.; Posada J.; Ruiz-Salguero O.; Montoya-Zapata D.; Acosta D.A.; Cortés C.; Pareja-Corcho J.; Moreno A.; Posada J.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Procesos Ambientales (GIPAB)
Lattice-based workpieces contain patterned repetition of individuals of a basic topology (Schwarz, ortho-walls, gyroid, etc.) with each individual having distinct geometric grading. In the context of the design, analysis and manufacturing of lattice workpieces, the problem of rapidly assessing the mechanical behavior of large domains is relevant for pre-evaluation of designs. In this realm, two approaches can be identified: (1) numerical simulations which usually bring accuracy but limit the size of the domains that can be studied due to intractable data sizes, and (2) material homogenization strategies that sacrifice precision to favor efficiency and allow for simulations of large domains. Material homogenization synthesizes diluted material properties in a lattice, according to the volume occupancy factor of such a lattice. Preliminary publications show that material homogenization is reasonable in predicting displacements, but is not in predicting stresses (highly sensitive to local geometry). As a response to such shortcomings, this paper presents a methodology that systematically uses design of experiments (DOE) to produce simple mathematical expressions (meta-models) that relate the stress-strain behavior of the lattice domain and the displacements of the homogeneous domain. The implementation in this paper estimates the von Mises stress in large Schwarz primitive lattice domains under compressive loads. The results of our experiments show that (1) material homogenization can efficiently and accurately approximate the displacements field, even in complex lattice domains, and (2) material homogenization and DOE can produce rough estimations of the von Mises stress in large domains (more than 100 cells). The errors in the von Mises stress estimations reach 42% for domains of up to 24 cells. This result means that coarse stress-strain estimations may be possible in lattice domains by combining DOE and homogenized material properties. This option is not suitable for precise stress prediction in sensitive contexts wherein high accuracy is needed. Future work is required to refine the meta-models to improve the accuracies of the estimations. © 2020 by the authors.
Approximation of the mechanical response of large lattice domains using homogenization and design of experiments
(Universitatea Politehnica Bucuresti, 2020-01-01) Montoya-Zapata D.; Acosta D.A.; Cortés C.; Pareja-Corcho J.; Moreno A.; Posada J.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
Lattice-based workpieces contain patterned repetition of individuals of a basic topology (Schwarz, ortho-walls, gyroid, etc.) with each individual having distinct geometric grading. In the context of the design, analysis and manufacturing of lattice workpieces, the problem of rapidly assessing the mechanical behavior of large domains is relevant for pre-evaluation of designs. In this realm, two approaches can be identified: (1) numerical simulations which usually bring accuracy but limit the size of the domains that can be studied due to intractable data sizes, and (2) material homogenization strategies that sacrifice precision to favor efficiency and allow for simulations of large domains. Material homogenization synthesizes diluted material properties in a lattice, according to the volume occupancy factor of such a lattice. Preliminary publications show that material homogenization is reasonable in predicting displacements, but is not in predicting stresses (highly sensitive to local geometry). As a response to such shortcomings, this paper presents a methodology that systematically uses design of experiments (DOE) to produce simple mathematical expressions (meta-models) that relate the stress-strain behavior of the lattice domain and the displacements of the homogeneous domain. The implementation in this paper estimates the von Mises stress in large Schwarz primitive lattice domains under compressive loads. The results of our experiments show that (1) material homogenization can efficiently and accurately approximate the displacements field, even in complex lattice domains, and (2) material homogenization and DOE can produce rough estimations of the von Mises stress in large domains (more than 100 cells). The errors in the von Mises stress estimations reach 42% for domains of up to 24 cells. This result means that coarse stress-strain estimations may be possible in lattice domains by combining DOE and homogenized material properties. This option is not suitable for precise stress prediction in sensitive contexts wherein high accuracy is needed. Future work is required to refine the meta-models to improve the accuracies of the estimations. © 2020 by the authors.
Approximation of the mechanical response of large lattice domains using homogenization and design of experiments
(Universitatea Politehnica Bucuresti, 2020-01-01) Montoya-Zapata D.; Acosta D.A.; Cortés C.; Pareja-Corcho J.; Moreno A.; Posada J.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Lattice-based workpieces contain patterned repetition of individuals of a basic topology (Schwarz, ortho-walls, gyroid, etc.) with each individual having distinct geometric grading. In the context of the design, analysis and manufacturing of lattice workpieces, the problem of rapidly assessing the mechanical behavior of large domains is relevant for pre-evaluation of designs. In this realm, two approaches can be identified: (1) numerical simulations which usually bring accuracy but limit the size of the domains that can be studied due to intractable data sizes, and (2) material homogenization strategies that sacrifice precision to favor efficiency and allow for simulations of large domains. Material homogenization synthesizes diluted material properties in a lattice, according to the volume occupancy factor of such a lattice. Preliminary publications show that material homogenization is reasonable in predicting displacements, but is not in predicting stresses (highly sensitive to local geometry). As a response to such shortcomings, this paper presents a methodology that systematically uses design of experiments (DOE) to produce simple mathematical expressions (meta-models) that relate the stress-strain behavior of the lattice domain and the displacements of the homogeneous domain. The implementation in this paper estimates the von Mises stress in large Schwarz primitive lattice domains under compressive loads. The results of our experiments show that (1) material homogenization can efficiently and accurately approximate the displacements field, even in complex lattice domains, and (2) material homogenization and DOE can produce rough estimations of the von Mises stress in large domains (more than 100 cells). The errors in the von Mises stress estimations reach 42% for domains of up to 24 cells. This result means that coarse stress-strain estimations may be possible in lattice domains by combining DOE and homogenized material properties. This option is not suitable for precise stress prediction in sensitive contexts wherein high accuracy is needed. Future work is required to refine the meta-models to improve the accuracies of the estimations. © 2020 by the authors.
FEA Structural Optimization Based on Metagraphs
(Springer Verlag, 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Sanchez-Londono D.; Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Procesos Ambientales (GIPAB)
Evolutionary Structural Optimization (ESO) seeks to mimic the form in which nature designs shapes. This paper focuses on shape carving triggered by environmental stimuli. In this realm, existing algorithms delete under - stressed parts of a basic shape, until a reasonably efficient (under some criterion) shape emerges. In the present article, we state a generalization of such approaches in two forms: (1) We use a formalism that enables stimuli from different sources, in addition to stress ones (e.g. kinematic constraints, friction, abrasion). (2) We use metagraphs built on the Finite Element constraint graphs to eliminate the dependency of the evolution on the particular neighborhood chosen to be deleted in a given iteration. The proposed methodology emulates 2D landmark cases of ESO. Future work addresses the implementation of such stimuli type, the integration of our algorithm with evolutionary based techniques and the extension of the method to 3D shapes. © 2019, Springer International Publishing AG, part of Springer Nature.
FEA Structural Optimization Based on Metagraphs
(Springer Verlag, 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Evolutionary Structural Optimization (ESO) seeks to mimic the form in which nature designs shapes. This paper focuses on shape carving triggered by environmental stimuli. In this realm, existing algorithms delete under - stressed parts of a basic shape, until a reasonably efficient (under some criterion) shape emerges. In the present article, we state a generalization of such approaches in two forms: (1) We use a formalism that enables stimuli from different sources, in addition to stress ones (e.g. kinematic constraints, friction, abrasion). (2) We use metagraphs built on the Finite Element constraint graphs to eliminate the dependency of the evolution on the particular neighborhood chosen to be deleted in a given iteration. The proposed methodology emulates 2D landmark cases of ESO. Future work addresses the implementation of such stimuli type, the integration of our algorithm with evolutionary based techniques and the extension of the method to 3D shapes. © 2019, Springer International Publishing AG, part of Springer Nature.
FEA Structural Optimization Based on Metagraphs
(Springer Verlag, 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
Evolutionary Structural Optimization (ESO) seeks to mimic the form in which nature designs shapes. This paper focuses on shape carving triggered by environmental stimuli. In this realm, existing algorithms delete under - stressed parts of a basic shape, until a reasonably efficient (under some criterion) shape emerges. In the present article, we state a generalization of such approaches in two forms: (1) We use a formalism that enables stimuli from different sources, in addition to stress ones (e.g. kinematic constraints, friction, abrasion). (2) We use metagraphs built on the Finite Element constraint graphs to eliminate the dependency of the evolution on the particular neighborhood chosen to be deleted in a given iteration. The proposed methodology emulates 2D landmark cases of ESO. Future work addresses the implementation of such stimuli type, the integration of our algorithm with evolutionary based techniques and the extension of the method to 3D shapes. © 2019, Springer International Publishing AG, part of Springer Nature.
A General Meta-graph Strategy for Shape Evolution under Mechanical Stress
(Taylor and Francis Inc., 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Posada J.; Sanchez-Londono D.; Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Posada J.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Procesos Ambientales (GIPAB)
The challenges that a shape or design stands are central in its evolution. In the particular domain of stress/strain challenges, existing approaches eliminate under-demanded neighborhoods from the shape, thus producing the evolution. This strategy alone incorrectly (a) conserves disconnected parts of the shape and (b) eliminates neighborhoods which are essential to maintain the boundary conditions (supports, loads). The existing analyses preventing (a) and (b) are conducted in an ad-hoc manner, by using graph connectivity. This manuscript presents the implementation of a meta-graph methodology, which systematically lumps together finite element subsets of the current shape. By considering this meta-graph connectivity, the method impedes situations (a) and (b), while maintaining the pruning of under-demanded neighborhoods. Research opportunities are open in the application of this methodology with other types of demand on the shape (e.g., friction, temperature, drag, and abrasion). © 2019, © 2019 Taylor & Francis Group, LLC.
A General Meta-graph Strategy for Shape Evolution under Mechanical Stress
(Taylor and Francis Inc., 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Posada J.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
The challenges that a shape or design stands are central in its evolution. In the particular domain of stress/strain challenges, existing approaches eliminate under-demanded neighborhoods from the shape, thus producing the evolution. This strategy alone incorrectly (a) conserves disconnected parts of the shape and (b) eliminates neighborhoods which are essential to maintain the boundary conditions (supports, loads). The existing analyses preventing (a) and (b) are conducted in an ad-hoc manner, by using graph connectivity. This manuscript presents the implementation of a meta-graph methodology, which systematically lumps together finite element subsets of the current shape. By considering this meta-graph connectivity, the method impedes situations (a) and (b), while maintaining the pruning of under-demanded neighborhoods. Research opportunities are open in the application of this methodology with other types of demand on the shape (e.g., friction, temperature, drag, and abrasion). © 2019, © 2019 Taylor & Francis Group, LLC.
A General Meta-graph Strategy for Shape Evolution under Mechanical Stress
(Taylor and Francis Inc., 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Posada J.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
The challenges that a shape or design stands are central in its evolution. In the particular domain of stress/strain challenges, existing approaches eliminate under-demanded neighborhoods from the shape, thus producing the evolution. This strategy alone incorrectly (a) conserves disconnected parts of the shape and (b) eliminates neighborhoods which are essential to maintain the boundary conditions (supports, loads). The existing analyses preventing (a) and (b) are conducted in an ad-hoc manner, by using graph connectivity. This manuscript presents the implementation of a meta-graph methodology, which systematically lumps together finite element subsets of the current shape. By considering this meta-graph connectivity, the method impedes situations (a) and (b), while maintaining the pruning of under-demanded neighborhoods. Research opportunities are open in the application of this methodology with other types of demand on the shape (e.g., friction, temperature, drag, and abrasion). © 2019, © 2019 Taylor & Francis Group, LLC.
Meta-modeling of Lattice Mechanical Responses via Design of Experiments
(Institute of Electrical and Electronics Engineers Inc., 2020-01-01) Montoya-Zapata D.; Acosta D.A.; Cortes C.; Pareja-Corcho J.; Moreno A.; Posada J.; Ruiz-Salguero O.; Montoya-Zapata D.; Acosta D.A.; Cortes C.; Pareja-Corcho J.; Moreno A.; Posada J.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Procesos Ambientales (GIPAB)
In the context of lattice manufacturing, the problem of mechanical and structural characterization of large lattice domains is relevant. Lattice materials are used in engineering (e.g. in energy absorption and heat conduction) and biomedical (e.g. bone implants and artificial tissues) applications. However, the numerical simulation of large lattice domains is limited by its complicated geometry, which hinders the meshing stage and produces intractable finite element meshes. The existing efforts to simulate large lattice domains are based on the generation of simplified homogeneous domains equipped with material properties that approximate the behavior of the lattice domain equipped with the bulk material. Using this approach, one can estimate the displacements field over the lattice domain using a lighter mesh and a cheaper simulation. However, since stresses are influenced by geometrical conditions, the stresses of the simplified domain do not match the stresses of the lattice domain. As a response to this limitation, this article proposes a methodology based on the systematic use of design of experiments to devise meta-models to estimate the mechanical response of lattice domains. The devised meta-models can be integrated with material homogenization to allow the mechanical characterization of large lattice domains. In this paper, we apply the proposed methodology to develop meta-models for the estimation of the von Mises stress in Schwarz Primitive lattice domains. Results show that the proposed methodology is able to generate efficient and accurate meta-models whose inputs are based on the displacements on the boundary of the Schwarz cell. Therefore, numerical simulations with the homogeneous simplified domain can be used to feed the meta-models. Additional work is still required to integrate the developed meta-models with material homogenization to test large Schwarz Primitive lattice domains under working loads. © 2020 IEEE.
Meta-modeling of Lattice Mechanical Responses via Design of Experiments
(Institute of Electrical and Electronics Engineers Inc., 2020-01-01) Montoya-Zapata D.; Acosta D.A.; Cortes C.; Pareja-Corcho J.; Moreno A.; Posada J.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In the context of lattice manufacturing, the problem of mechanical and structural characterization of large lattice domains is relevant. Lattice materials are used in engineering (e.g. in energy absorption and heat conduction) and biomedical (e.g. bone implants and artificial tissues) applications. However, the numerical simulation of large lattice domains is limited by its complicated geometry, which hinders the meshing stage and produces intractable finite element meshes. The existing efforts to simulate large lattice domains are based on the generation of simplified homogeneous domains equipped with material properties that approximate the behavior of the lattice domain equipped with the bulk material. Using this approach, one can estimate the displacements field over the lattice domain using a lighter mesh and a cheaper simulation. However, since stresses are influenced by geometrical conditions, the stresses of the simplified domain do not match the stresses of the lattice domain. As a response to this limitation, this article proposes a methodology based on the systematic use of design of experiments to devise meta-models to estimate the mechanical response of lattice domains. The devised meta-models can be integrated with material homogenization to allow the mechanical characterization of large lattice domains. In this paper, we apply the proposed methodology to develop meta-models for the estimation of the von Mises stress in Schwarz Primitive lattice domains. Results show that the proposed methodology is able to generate efficient and accurate meta-models whose inputs are based on the displacements on the boundary of the Schwarz cell. Therefore, numerical simulations with the homogeneous simplified domain can be used to feed the meta-models. Additional work is still required to integrate the developed meta-models with material homogenization to test large Schwarz Primitive lattice domains under working loads. © 2020 IEEE.
Meta-modeling of Lattice Mechanical Responses via Design of Experiments
(Institute of Electrical and Electronics Engineers Inc., 2020-01-01) Montoya-Zapata D.; Acosta D.A.; Cortes C.; Pareja-Corcho J.; Moreno A.; Posada J.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
In the context of lattice manufacturing, the problem of mechanical and structural characterization of large lattice domains is relevant. Lattice materials are used in engineering (e.g. in energy absorption and heat conduction) and biomedical (e.g. bone implants and artificial tissues) applications. However, the numerical simulation of large lattice domains is limited by its complicated geometry, which hinders the meshing stage and produces intractable finite element meshes. The existing efforts to simulate large lattice domains are based on the generation of simplified homogeneous domains equipped with material properties that approximate the behavior of the lattice domain equipped with the bulk material. Using this approach, one can estimate the displacements field over the lattice domain using a lighter mesh and a cheaper simulation. However, since stresses are influenced by geometrical conditions, the stresses of the simplified domain do not match the stresses of the lattice domain. As a response to this limitation, this article proposes a methodology based on the systematic use of design of experiments to devise meta-models to estimate the mechanical response of lattice domains. The devised meta-models can be integrated with material homogenization to allow the mechanical characterization of large lattice domains. In this paper, we apply the proposed methodology to develop meta-models for the estimation of the von Mises stress in Schwarz Primitive lattice domains. Results show that the proposed methodology is able to generate efficient and accurate meta-models whose inputs are based on the displacements on the boundary of the Schwarz cell. Therefore, numerical simulations with the homogeneous simplified domain can be used to feed the meta-models. Additional work is still required to integrate the developed meta-models with material homogenization to test large Schwarz Primitive lattice domains under working loads. © 2020 IEEE.
Pixel-based Wake Interaction and Power Estimation for a Wind Farm with Irregular Boundary
(2018-10-18) Ohlsen,, G; Ruiz-Salguero O.; Full,, T.; Acosta D.A.; Ohlsen,, G; Ruiz-Salguero O.; Full,, T.; Acosta D.A.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Procesos Ambientales (GIPAB)
In the domain of generation of wind turbine energy, it is central to correctly estimate the interactions among the various turbines in a wind turbine farm.
Pixel-based Wake Interaction and Power Estimation for a Wind Farm with Irregular Boundary
(2018-10-18) Ohlsen,, G; Ruiz-Salguero O.; Full,, T.; Acosta D.A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In the domain of generation of wind turbine energy, it is central to correctly estimate the interactions among the various turbines in a wind turbine farm.
Pixel-based Wake Interaction and Power Estimation for a Wind Farm with Irregular Boundary
(2018-10-18) Ohlsen,, G; Ruiz-Salguero O.; Full,, T.; Acosta D.A.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
In the domain of generation of wind turbine energy, it is central to correctly estimate the interactions among thevarious turbines in a wind turbine farm.
Weighted area/angle distortion minimization for Mesh Parameterization
(EMERALD GROUP PUBLISHING LIMITED, 2017-01-01) Mejia D.; Acosta D.A.; Ruiz-Salguero O.; Mejia D.; Acosta D.A.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Procesos Ambientales (GIPAB)
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/methodology/approach: A Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg-Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: a with 0 = a = 1) and angle distortion (weight: 1 - a). Findings: The present study parameterization algorithm has linear complexity [O(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets. Originality/value: The devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones. © Emerald Publishing Limited.
Weighted area/angle distortion minimization for Mesh Parameterization
(EMERALD GROUP PUBLISHING LIMITED, 2017-01-01) Mejia D.; Acosta D.A.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
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/methodology/approach: A Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg-Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: a with 0 = a = 1) and angle distortion (weight: 1 - a). Findings: The present study parameterization algorithm has linear complexity [O(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets. Originality/value: The devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones. © Emerald Publishing Limited.
Weighted area/angle distortion minimization for Mesh Parameterization
(EMERALD GROUP PUBLISHING LIMITED, 2017-01-01) Mejia D.; Acosta D.A.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
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/methodology/approach: A Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg-Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: a with 0 = a = 1) and angle distortion (weight: 1 - a). Findings: The present study parameterization algorithm has linear complexity [O(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets. Originality/value: The devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones. © Emerald Publishing Limited.

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