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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/14/11/304 |
| _version_ | 1797511579551399936 |
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| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:47:16Z |
| format | Article |
| id | doaj.art-9935e7a3f8a2439b89f30dc5dd774ba8 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T05:47:16Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-9935e7a3f8a2439b89f30dc5dd774ba82023-11-22T22:04:35ZengMDPI AGAlgorithms1999-48932021-10-01141130410.3390/a14110304Analytic Form Fitting in Poor Triangular MeshesCristian Rendon-Cardona0Jorge Correa1Diego A. Acosta2Oscar Ruiz-Salguero3Laboratory of CAD CAM CAE, Universidad EAFIT, Cra 49 no 7-sur-50, Medellín 050022, ColombiaManufactura Cohesiva SAS, Cra 32B #10-30, Medellín 050021, ColombiaGrupo de Desarrollo y Diseno de Procesos (DDP), Universidad EAFIT, Cra 49 no 7-sur-50, Medellín 050022, ColombiaLaboratory of CAD CAM CAE, Universidad EAFIT, Cra 49 no 7-sur-50, Medellín 050022, ColombiaFitting 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.https://www.mdpi.com/1999-4893/14/11/304analytic form fittingpoor triangular meshesspatial hashingreal time |
| spellingShingle | Cristian Rendon-Cardona Jorge Correa Diego A. Acosta Oscar Ruiz-Salguero Analytic Form Fitting in Poor Triangular Meshes Algorithms analytic form fitting poor triangular meshes spatial hashing real time |
| title | 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_short | Analytic Form Fitting in Poor Triangular Meshes |
| title_sort | analytic form fitting in poor triangular meshes |
| topic | analytic form fitting poor triangular meshes spatial hashing real time |
| url | https://www.mdpi.com/1999-4893/14/11/304 |
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