George Harabin, Amir M. Mirzendehdel, Morad Behandish
{"title":"多轴制造可达性的深度神经隐式表示","authors":"George Harabin, Amir M. Mirzendehdel, Morad Behandish","doi":"10.1016/j.cad.2023.103556","DOIUrl":null,"url":null,"abstract":"<div><p>One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></math></span> sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> via fast Fourier transforms (FFTs) scales as in <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>m</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>log</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> in time and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>m</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing\",\"authors\":\"George Harabin, Amir M. Mirzendehdel, Morad Behandish\",\"doi\":\"10.1016/j.cad.2023.103556\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></math></span> sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> via fast Fourier transforms (FFTs) scales as in <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>m</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>log</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> in time and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>m</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).</p></div>\",\"PeriodicalId\":50632,\"journal\":{\"name\":\"Computer-Aided Design\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer-Aided Design\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S001044852300088X\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer-Aided Design","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S001044852300088X","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing
One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution via fast Fourier transforms (FFTs) scales as in in time and in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).
期刊介绍:
Computer-Aided Design is a leading international journal that provides academia and industry with key papers on research and developments in the application of computers to design.
Computer-Aided Design invites papers reporting new research, as well as novel or particularly significant applications, within a wide range of topics, spanning all stages of design process from concept creation to manufacture and beyond.