Analytic Form Fitting in Poor Triangular Meshes

Fitting of analytic forms to point or triangle sets is central to computer-aided design, manufacturing, reverse engineering, dimensional control, etc. The existing approaches for this fitting assume an input of statistically strong point or triangle sets. In contrast, this manuscript reports the des...

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Autores principales:	Cristian Rendon-Cardona, Jorge Correa, Diego A. Acosta, Oscar Ruiz-Salguero
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	analytic form fitting poor triangular meshes spatial hashing real time Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/9935e7a3f8a2439b89f30dc5dd774ba8
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id	oai:doaj.org-article:9935e7a3f8a2439b89f30dc5dd774ba8
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spelling	oai:doaj.org-article:9935e7a3f8a2439b89f30dc5dd774ba82021-11-25T16:12:53ZAnalytic Form Fitting in Poor Triangular Meshes10.3390/a141103041999-4893https://doaj.org/article/9935e7a3f8a2439b89f30dc5dd774ba82021-10-01T00:00:00Zhttps://www.mdpi.com/1999-4893/14/11/304https://doaj.org/toc/1999-4893Fitting of analytic forms to point or triangle sets is central to computer-aided design, manufacturing, reverse engineering, dimensional control, etc. The existing approaches for this fitting assume an input of statistically strong point or triangle sets. In contrast, this manuscript reports the design (and industrial application) of fitting algorithms whose inputs are specifically poor triangular meshes. The analytic forms currently addressed are planes, cones, cylinders and spheres. Our algorithm also extracts the support submesh responsible for the analytic primitive. We implement spatial hashing and boundary representation for a preprocessing sequence. When the submesh supporting the analytic form holds strict <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mn>0</mn></msup></semantics></math></inline-formula>-continuity at its border, submesh extraction is independent of fitting, and our algorithm is a real-time one. Otherwise, segmentation and fitting are codependent and our algorithm, albeit correct in the analytic form identification, cannot perform in real-time.Cristian Rendon-CardonaJorge CorreaDiego A. AcostaOscar Ruiz-SalgueroMDPI AGarticleanalytic form fittingpoor triangular meshesspatial hashingreal timeIndustrial engineering. Management engineeringT55.4-60.8Electronic computers. Computer scienceQA75.5-76.95ENAlgorithms, Vol 14, Iss 304, p 304 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	analytic form fitting poor triangular meshes spatial hashing real time Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
spellingShingle	analytic form fitting poor triangular meshes spatial hashing real time Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 Cristian Rendon-Cardona Jorge Correa Diego A. Acosta Oscar Ruiz-Salguero Analytic Form Fitting in Poor Triangular Meshes
description	Fitting of analytic forms to point or triangle sets is central to computer-aided design, manufacturing, reverse engineering, dimensional control, etc. The existing approaches for this fitting assume an input of statistically strong point or triangle sets. In contrast, this manuscript reports the design (and industrial application) of fitting algorithms whose inputs are specifically poor triangular meshes. The analytic forms currently addressed are planes, cones, cylinders and spheres. Our algorithm also extracts the support submesh responsible for the analytic primitive. We implement spatial hashing and boundary representation for a preprocessing sequence. When the submesh supporting the analytic form holds strict <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mn>0</mn></msup></semantics></math></inline-formula>-continuity at its border, submesh extraction is independent of fitting, and our algorithm is a real-time one. Otherwise, segmentation and fitting are codependent and our algorithm, albeit correct in the analytic form identification, cannot perform in real-time.
format	article
author	Cristian Rendon-Cardona Jorge Correa Diego A. Acosta Oscar Ruiz-Salguero
author_facet	Cristian Rendon-Cardona Jorge Correa Diego A. Acosta Oscar Ruiz-Salguero
author_sort	Cristian Rendon-Cardona
title	Analytic Form Fitting in Poor Triangular Meshes
title_short	Analytic Form Fitting in Poor Triangular Meshes
title_full	Analytic Form Fitting in Poor Triangular Meshes
title_fullStr	Analytic Form Fitting in Poor Triangular Meshes
title_full_unstemmed	Analytic Form Fitting in Poor Triangular Meshes
title_sort	analytic form fitting in poor triangular meshes
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/9935e7a3f8a2439b89f30dc5dd774ba8
work_keys_str_mv	AT cristianrendoncardona analyticformfittinginpoortriangularmeshes AT jorgecorrea analyticformfittinginpoortriangularmeshes AT diegoaacosta analyticformfittinginpoortriangularmeshes AT oscarruizsalguero analyticformfittinginpoortriangularmeshes
_version_	1718413271015358464

Analytic Form Fitting in Poor Triangular Meshes

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