Incorporating Sharp Features in the General Solid Sweep Framework

This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family h of rigid motions. Our extension allows the input solid to have sharp features, and thus it is a...

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Veröffentlicht in:	Computer graphics forum Jg. 35; H. 5; S. 21 - 31
Hauptverfasser:	Adsul, Bharat, Machchhar, Jinesh, Sohoni, Milind
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Oxford Blackwell Publishing Ltd 01.08.2016
Schlagworte:	and object representations Boundary representation Categories and Subject Descriptors (according to ACM CCS) Computer graphics Digital video Hoisting I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations Mathematical analysis Orientation Parameter robustness Pilots Singularities solid Studies surface Trimming
ISSN:	0167-7055, 1467-8659
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Abstract	This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family h of rigid motions. Our extension allows the input solid to have sharp features, and thus it is a significant and useful generalization of that work. This naturally requires a precise description of the geometry of the surface generated by the sweep of a sharp edge supported by two intersecting smooth faces. We uncover the geometry along with the related issues like parametrization and singularities via a novel mathematical analysis. Correct trimming of such a surface is achieved by an analysis of the interplay between the cone of normals at a sharp point and its trajectory under h. The overall topology is explained by a key lifting theorem which allows us to compute the adjacency relations amongst entities in the swept volume by relating them to corresponding adjacencies in the input solid. Moreover, global issues related to body‐check such as orientation, singularities and self‐intersections are efficiently resolved. Examples from a pilot implementation illustrate the efficiency and effectiveness of our framework.
AbstractList	This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family h of rigid motions. Our extension allows the input solid to have sharp features, and thus it is a significant and useful generalization of that work. This naturally requires a precise description of the geometry of the surface generated by the sweep of a sharp edge supported by two intersecting smooth faces. We uncover the geometry along with the related issues like parametrization and singularities via a novel mathematical analysis. Correct trimming of such a surface is achieved by an analysis of the interplay between the cone of normals at a sharp point and its trajectory under h. The overall topology is explained by a key lifting theorem which allows us to compute the adjacency relations amongst entities in the swept volume by relating them to corresponding adjacencies in the input solid. Moreover, global issues related to body-check such as orientation, singularities and self-intersections are efficiently resolved. Examples from a pilot implementation illustrate the efficiency and effectiveness of our framework. This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family h of rigid motions. Our extension allows the input solid to have sharp features, and thus it is a significant and useful generalization of that work. This naturally requires a precise description of the geometry of the surface generated by the sweep of a sharp edge supported by two intersecting smooth faces. We uncover the geometry along with the related issues like parametrization and singularities via a novel mathematical analysis. Correct trimming of such a surface is achieved by an analysis of the interplay between the cone of normals at a sharp point and its trajectory under h. The overall topology is explained by a key lifting theorem which allows us to compute the adjacency relations amongst entities in the swept volume by relating them to corresponding adjacencies in the input solid. Moreover, global issues related to body‐check such as orientation, singularities and self‐intersections are efficiently resolved. Examples from a pilot implementation illustrate the efficiency and effectiveness of our framework.
Author	Machchhar, Jinesh Adsul, Bharat Sohoni, Milind
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References	Rossignac J., Kim J., Song S., Suh K., Joung C.: Boundary of the volume swept by a free-form solid in screw motion. Computer-Aided Design 39 (2007), 745-755. 2 Abdel-Malek K., Blackmore O., Joy K.: Swept volumes: Foundations, perspectives and applications. International Journal of Shape Modeling 12, 1 (2006), 87-127. 1 Kim Y.J., Vardhan G., Lin M.C., Manocha D.: Fast swept volume approximation of complex polyhedral models. Computer-Aided Design 36 (2004), 1013-1027. 2 Xu Z.-Q., Ye X.-Z., Chen Z.-Y., Zhang Y., Zhang S.-Y.: Trimming self-intersections in swept volume solid modelling. Journal of Zhejiang University Science 9, 4 (2008), 470-480. 9 Elber G.: Global error bounds and amelioration of sweep surfaces. Computer-Aided Design 29, 6 (1997), 441-447. 2 Abdel-Malek K., Yeh H.-J.: Geometric representation of the swept volume using jacobian rank-deficiency conditions. Computer-Aided Design 29, 6 (1997), 457-468. 2 Lane J.M., Riesenfeld R.F.: Bounds on a polynomial. BIT Numerical Mathematics 21, 1 (1981), 112-117. 7 Blackmore D., Samulyak R., Leu M.C.: Trimming swept volumes. Computer-Aided Design 31, 3 (1999), 215-223. 9, 10 Erdim H., Ilies H.T.: Classifying points for sweeping solids. Computer-Aided Design 40, 9 (2008), 987-998. 2, 10 Blackmore D., Leu M.C., Wang L.P.: Sweep-envelope differential equation algorithm and its application to nc machining verification. Computer-Aided Design 29, 9 (1997), 629-637. 2, 3 Ilies H., Shapiro V.: The dual of sweep. Computer-Aided Design 31, 3 (1999), 185-201. 2 Adsul B., Machchhar J., Sohoni M.: A computational framework for boundary representation of solid sweeps. Computer-Aided Design and Applications 12, 2 (2015), 181-191. 1, 2, 3, 4, 5, 6, 10 Lee S.W., Nestler A.: Complete swept volume generation, part ii: Nc simulation of self-penetration via comprehensive analysis of envelope profiles. Computer-Aided Design 43, 4 (2011), 442-456. 1 Adsul B., Machchhar J., Sohoni M.: Local and global analysis of parametric solid sweeps. Computer Aided Geometric Design 31, 6 (2014), 294-316. 1, 2, 4, 6, 9, 10 Lee S.W., Nestler A.: Complete swept volume generation, part i: Swept volume of a piecewise c1-continuous cutter at five-axis milling via gauss map. Computer-Aided Design 43, 4 (2011), 427-441. 1, 2, 3, 4 Peternell M., Pottmann H., Steiner T., Zhao h.: Swept volumes. Computer-Aided Design and Applications 2 (2005), 599-608. 2, 4 2007; 39 2015; 12 2006; 12 2004; 36 2008; 9 2009 1997; 29 2011; 43 1999; 31 2005; 2 2008; 40 1981; 21 2014; 31 e_1_2_10_9_2 e_1_2_10_11_2 e_1_2_10_8_2 e_1_2_10_12_2 e_1_2_10_20_2 e_1_2_10_10_2 e_1_2_10_19_2 e_1_2_10_3_2 e_1_2_10_17_2 e_1_2_10_2_2 e_1_2_10_18_2 e_1_2_10_5_2 e_1_2_10_15_2 e_1_2_10_4_2 e_1_2_10_16_2 e_1_2_10_7_2 e_1_2_10_13_2 e_1_2_10_6_2 e_1_2_10_14_2
References_xml	– reference: Xu Z.-Q., Ye X.-Z., Chen Z.-Y., Zhang Y., Zhang S.-Y.: Trimming self-intersections in swept volume solid modelling. Journal of Zhejiang University Science 9, 4 (2008), 470-480. 9 – reference: Ilies H., Shapiro V.: The dual of sweep. Computer-Aided Design 31, 3 (1999), 185-201. 2 – reference: Lee S.W., Nestler A.: Complete swept volume generation, part i: Swept volume of a piecewise c1-continuous cutter at five-axis milling via gauss map. Computer-Aided Design 43, 4 (2011), 427-441. 1, 2, 3, 4 – reference: Lee S.W., Nestler A.: Complete swept volume generation, part ii: Nc simulation of self-penetration via comprehensive analysis of envelope profiles. Computer-Aided Design 43, 4 (2011), 442-456. 1 – reference: Abdel-Malek K., Blackmore O., Joy K.: Swept volumes: Foundations, perspectives and applications. International Journal of Shape Modeling 12, 1 (2006), 87-127. 1 – reference: Abdel-Malek K., Yeh H.-J.: Geometric representation of the swept volume using jacobian rank-deficiency conditions. Computer-Aided Design 29, 6 (1997), 457-468. 2 – reference: Adsul B., Machchhar J., Sohoni M.: A computational framework for boundary representation of solid sweeps. Computer-Aided Design and Applications 12, 2 (2015), 181-191. 1, 2, 3, 4, 5, 6, 10 – reference: Blackmore D., Leu M.C., Wang L.P.: Sweep-envelope differential equation algorithm and its application to nc machining verification. Computer-Aided Design 29, 9 (1997), 629-637. 2, 3 – reference: Adsul B., Machchhar J., Sohoni M.: Local and global analysis of parametric solid sweeps. Computer Aided Geometric Design 31, 6 (2014), 294-316. 1, 2, 4, 6, 9, 10 – reference: Peternell M., Pottmann H., Steiner T., Zhao h.: Swept volumes. Computer-Aided Design and Applications 2 (2005), 599-608. 2, 4 – reference: Blackmore D., Samulyak R., Leu M.C.: Trimming swept volumes. Computer-Aided Design 31, 3 (1999), 215-223. 9, 10 – reference: Erdim H., Ilies H.T.: Classifying points for sweeping solids. Computer-Aided Design 40, 9 (2008), 987-998. 2, 10 – reference: Rossignac J., Kim J., Song S., Suh K., Joung C.: Boundary of the volume swept by a free-form solid in screw motion. Computer-Aided Design 39 (2007), 745-755. 2 – reference: Kim Y.J., Vardhan G., Lin M.C., Manocha D.: Fast swept volume approximation of complex polyhedral models. Computer-Aided Design 36 (2004), 1013-1027. 2 – reference: Lane J.M., Riesenfeld R.F.: Bounds on a polynomial. BIT Numerical Mathematics 21, 1 (1981), 112-117. 7 – reference: Elber G.: Global error bounds and amelioration of sweep surfaces. Computer-Aided Design 29, 6 (1997), 441-447. 2 – volume: 12 start-page: 87 issue: 1 year: 2006 end-page: 127 article-title: Swept volumes: Foundations, perspectives and applications publication-title: International Journal of Shape Modeling – volume: 29 start-page: 457 issue: 6 year: 1997 end-page: 468 article-title: Geometric representation of the swept volume using jacobian rank‐deficiency conditions publication-title: Computer‐Aided Design – volume: 12 start-page: 181 issue: 2 year: 2015 end-page: 191 article-title: A computational framework for boundary representation of solid sweeps publication-title: Computer‐Aided Design and Applications – volume: 29 start-page: 629 issue: 9 year: 1997 end-page: 637 article-title: Sweep‐envelope differential equation algorithm and its application to nc machining verification publication-title: Computer‐Aided Design – volume: 29 start-page: 441 issue: 6 year: 1997 end-page: 447 article-title: Global error bounds and amelioration of sweep surfaces publication-title: Computer‐Aided Design – volume: 2 start-page: 599 year: 2005 end-page: 608 article-title: Swept volumes publication-title: Computer‐Aided Design and Applications – volume: 31 start-page: 294 issue: 6 year: 2014 end-page: 316 article-title: Local and global analysis of parametric solid sweeps publication-title: Computer Aided Geometric Design – volume: 43 start-page: 442 issue: 4 year: 2011 end-page: 456 article-title: Complete swept volume generation, part ii: Nc simulation of self‐penetration via comprehensive analysis of envelope profiles publication-title: Computer‐Aided Design – volume: 9 start-page: 470 issue: 4 year: 2008 end-page: 480 article-title: Trimming self‐intersections in swept volume solid modelling publication-title: Journal of Zhejiang University Science – volume: 31 start-page: 215 issue: 3 year: 1999 end-page: 223 article-title: Trimming swept volumes publication-title: Computer‐Aided Design – start-page: 373 year: 2009 end-page: 378 article-title: Reliable sweeps – volume: 39 start-page: 745 year: 2007 end-page: 755 article-title: Boundary of the volume swept by a free‐form solid in screw motion publication-title: Computer‐Aided Design – volume: 40 start-page: 987 issue: 9 year: 2008 end-page: 998 article-title: Classifying points for sweeping solids publication-title: Computer‐Aided Design – volume: 43 start-page: 427 issue: 4 year: 2011 end-page: 441 article-title: Complete swept volume generation, part i: Swept volume of a piecewise c1‐continuous cutter at five‐axis milling via gauss map publication-title: Computer‐Aided Design – volume: 31 start-page: 185 issue: 3 year: 1999 end-page: 201 article-title: The dual of sweep publication-title: Computer‐Aided Design – volume: 36 start-page: 1013 year: 2004 end-page: 1027 article-title: Fast swept volume approximation of complex polyhedral models publication-title: Computer‐Aided Design – volume: 21 start-page: 112 issue: 1 year: 1981 end-page: 117 article-title: Bounds on a polynomial publication-title: BIT Numerical Mathematics – ident: e_1_2_10_9_2 doi: 10.1016/S0010-4485(96)00085-1 – ident: e_1_2_10_19_2 doi: 10.1631/jzus.A071357 – ident: e_1_2_10_5_2 doi: 10.1016/S0010-4485(96)00097-8 – ident: e_1_2_10_20_2 doi: 10.1145/1629255.1629306 – ident: e_1_2_10_13_2 doi: 10.1016/j.cad.2010.12.010 – ident: e_1_2_10_18_2 – ident: e_1_2_10_15_2 doi: 10.1007/BF01934076 – ident: e_1_2_10_2_2 doi: 10.1142/S0218654306000858 – ident: e_1_2_10_7_2 doi: 10.1016/S0010-4485(99)00017-2 – ident: e_1_2_10_3_2 doi: 10.1016/j.cagd.2014.05.009 – ident: e_1_2_10_11_2 – ident: e_1_2_10_12_2 doi: 10.1016/j.cad.2004.01.004 – ident: e_1_2_10_17_2 doi: 10.1016/j.cad.2007.02.016 – ident: e_1_2_10_14_2 doi: 10.1016/j.cad.2010.12.012 – ident: e_1_2_10_8_2 doi: 10.1016/j.cad.2008.07.005 – ident: e_1_2_10_6_2 doi: 10.1016/S0010-4485(96)00101-7 – ident: e_1_2_10_16_2 doi: 10.1080/16864360.2005.10738324 – ident: e_1_2_10_10_2 doi: 10.1016/S0010-4485(99)00015-9 – ident: e_1_2_10_4_2 doi: 10.1080/16864360.2014.962430
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SubjectTerms	and object representations Boundary representation Categories and Subject Descriptors (according to ACM CCS) Computer graphics Digital video Hoisting I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations Mathematical analysis Orientation Parameter robustness Pilots Singularities solid Studies surface Trimming
Title	Incorporating Sharp Features in the General Solid Sweep Framework
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