Boundary Representation Modelling Techniques

By: Ian Stroud

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Hardcover | 8 September 2006

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Hardcover
808 Pages

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22.86 x 15.24 x 3.81

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Boundary representation is the principal solid modelling method used in modern CAD/CAM systems. There have been a long series of developments on which currently available systems are based, full details of which are only partially known. Ian Stroud's thorough coverage of these developments puts this technology in perspective. It includes:

data structures
algorithms and other related techniques including non-manifold modelling
product modelling
graphics
disc files and data exchange
some applications related topics.

A basic knowledge of the technique will make it easier to use kernel modelling packages for application developments.

Ian Stroud started working with boundary representation solid modelling in 1977. Since then he has researched and is researching a wide variety of topics in and around this field. The information in the book comes from the results of this research.

Industry Reviews

From the reviews: "This is a comprehensive and serious work on solid modeling using boundary representation (B-reps). ! This text distinguishes itself in that the author concentrates on boundary representation as the one approach for solid modeling to focus on, instead of broadly introducing various theories of the field. ! The author has made an important contribution to the solid modeling literature that will be welcomed by academia and industry alike." (Minette Carl and R. Goldberg, ACM Computing Reviews, January, 2008)

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Non-Fiction Mathematics Calculus & Mathematical Analysis Numerical Analysis Computing & I.T.Graphical & Digital Media Applications Computer-Aided Design CAD Computer Science Artificial Intelligence Computer Vision Arts & Entertainment Architecture

Architectural Structure & Design

Introduction	p. 1
Background	p. 1
Representations for solid modelling	p. 3
Cell decomposition	p. 3
General sweeping	p. 3
Set theoretic	p. 5
Boundary representation	p. 5
Implications for commercialisation	p. 6
Product modelling	p. 7
Modelling Background	p. 11
The BUILD system	p. 13
Baumgart and the winged-edge representation	p. 14
BUILD system: Developments and extensions	p. 16
The GPM project	p. 19
Feature recognition and features in modelling	p. 22
Non-manifold modelling	p. 23
Modelling system implementation	p. 24
Research directions	p. 25
Datastructures and tools	p. 29
Modelling datastructures	p. 29
Open questions	p. 32
Elements of the datastructure	p. 34
Geometry	p. 39
Arbitrary representations	p. 41
Topological connections	p. 42
Modelling facilities	p. 47
Traversing all related elements in a structure	p. 57
Single entity traversals	p. 67
Topological utilities	p. 68
Geometric interrogations	p. 70
General utilities	p. 73
Assembly structures	p. 74
Determining the assembly structure	p. 75
Handling instances	p. 80
Constraints or connections	p. 80
Mechanism libraries	p. 81
Euler operators	p. 83
Spanning sets and decompositions	p. 84
Restrictions	p. 91
Special representations	p. 93
Conversions between representations	p. 97
Modelling operations on special models	p. 103
Setting a wireframe model in a surface	p. 103
Blending and chamfering	p. 106
Sweeping	p. 108
Joining and splitting along edges	p. 110
Planar sectioning	p. 112
Boolean operations	p. 114
Shelling objects	p. 115
Unfolding models	p. 115
Compound models	p. 119
Conclusions	p. 122
Stepwise modelling algorithms	p. 125
Boolean operations	p. 126
Finding the Boolean interactions	p. 127
Special cases in intersection boundary creation	p. 132
Creating the intersection boundary	p. 133
Merging the objects (creating new shells)	p. 135
Boolean operations with assemblies	p. 139
Local Boolean operations	p. 141
Sweeping/Swinging	p. 142
Improved sweep/swing algorithm	p. 145
Sweeping along a path	p. 151
Sweeping wireframe models	p. 153
First algorithm	p. 155
Non-Eulerian edge sweeping	p. 155
Eulerian edge sweeping	p. 157
Second algorithm	p. 158
Swinging flat	p. 164
Gluing coincident identical topology	p. 167
Gluing identical faces	p. 167
Gluing coincident identical edges	p. 173
Gluing coincident identical vertices	p. 177
Reflect	p. 178
Bend	p. 179
The basic algorithm	p. 179
Giving sheet objects thickness	p. 183
The basic algorithm	p. 183
Planar sectioning	p. 185
The basic algorithm	p. 185
Imprinting	p. 192
The basic algorithm	p. 192
Creating the dual of an object	p. 195
Constructing the topology of the dual	p. 196
Creating the geometry of the dual	p. 198
Setting a surface in a face (SETSURF)	p. 199
The basic algorithm	p. 199
Special cases	p. 203
Extensions to the algorithm	p. 203
Drafting	p. 207
Gluing non-matching faces	p. 208
The basic algorithm	p. 211
Special cases	p. 213
Modelling operator definition	p. 215
Definition of requirements	p. 216
Finishing and manufacturing operations	p. 217
Converting degenerate models and parts of models	p. 218
Other operations	p. 221
Task decomposition	p. 222
Finishing operation task decomposition	p. 223
Model conversion task decomposition	p. 226
Complex operation task decomposition	p. 227
Pathological conditions	p. 229
Examples	p. 231
Add a slot or pocket to a face	p. 231
Rebate an edge	p. 243
Product modelling	p. 253
Product modelling	p. 254
Design information	p. 255
Customer-based order information	p. 257
Production planning information	p. 258
Information classes	p. 259
Category 1 - shape	p. 259
Category 2 - shape modifiers	p. 260
Category 3 - features	p. 260
Category 4 - attributes	p. 260
Category 5 - constraints	p. 260
Category 6 - free-standing geometry	p. 261
Category 7 - connections	p. 261
Handling information during modelling	p. 262
Category 1 - The basic shape of the model	p. 263
Category 2 - Shape modifiers	p. 263
Category 3 - Features	p. 264
Category 4 - Passive information	p. 269
Category 5 - Constraints	p. 269
Category 6 - Geometric frameworks	p. 270
Category 7 - Mechanisms and linkages	p. 270
Feature modelling	p. 273
Feature datastructures	p. 276
Feature facesets	p. 277
Feature frames	p. 278
Manual feature acquisition	p. 280
Design by features	p. 281
Adding features to a shape	p. 281
Building objects from isolated features	p. 284
Feature recognition	p. 285
Classic feature recognition	p. 285
Features and applications	p. 293
Volumetric decomposition	p. 296
Feature verification	p. 296
Structuring features	p. 297
Graphics	p. 299
Model-space graphics	p. 301
Drawing styles	p. 303
Viewing coordinate system and model transformations	p. 306
Drawing all edges in a body	p. 307
Drawing edges and silhouettes	p. 311
Exact hidden line algorithms	p. 312
Bread slicing	p. 313
Ray tracing	p. 314
Device-space graphics	p. 314
Facetting an object	p. 317
Drawing free-standing geometry	p. 319
Drawing non-geometric information	p. 321
Inputting and outputting	p. 325
Writing to disc	p. 325
Reading from disc	p. 329
Reading old discfiles	p. 331
Examples	p. 331
Supplementary information	p. 338
Communication with other modellers	p. 339
STEP	p. 346
Printing models	p. 356
Modeller access	p. 365
Command interpreter architecture	p. 366
Working stacks	p. 366
Command structures (sub-interpreters)	p. 367
Syntax handling	p. 373
Model element identification	p. 375
Multi-user modelling	p. 379
Splitting up the command interpreter	p. 379
Blocking access to sensitive model parts	p. 383
Command files and macro-languages	p. 383
Application programming interfaces	p. 383
Classic programming interfaces	p. 384
DJINN	p. 384
Free-form geometry	p. 387
Basics	p. 387
Bezier geometry	p. 388
B-spline geometry	p. 393
Rational forms	p. 398
NURBS geometry	p. 399
Curves with multiple pieces	p. 400
Surfaces	p. 402
Interpolation	p. 406
Interpolation for a single curve	p. 406
Interpolation with a point and a tangent vector	p. 413
Interpolation with compound curves	p. 415
Lofting	p. 417
Adding free-form surfaces to a face	p. 425
SETSURF	p. 425
Multi-patch SETSURF	p. 425
Embossing a free-form surface	p. 427
Miscellaneous comments	p. 429
Building a model from surface patches	p. 431
Creating surface topology	p. 432
Sewing together partial objects	p. 432
Handling problems	p. 432
Model 'sculpting' methods	p. 433
Implemented operations	p. 434
Smoothing	p. 443
Conclusions	p. 451
Applications	p. 453
Model verification	p. 453
Justification	p. 454
Verifications	p. 455
Model verification in ACIS	p. 459
Final remarks	p. 470
Model 'healing'	p. 471
Assembly healing	p. 472
Topological healing	p. 472
Geometric healing	p. 475
Combined healing	p. 479
Making things nice	p. 479
Self-intersection repair	p. 481
Information repair	p. 481
Generating an octree model from a B-rep	p. 482
Recreating a B-rep from an STL file	p. 483
Reading non-connected facet formats	p. 485
Reading a shared vertex file	p. 488
Rapid prototyping	p. 491
Slice approximation	p. 494
Layer approximation	p. 496
Reverse engineering	p. 496
Measurement	p. 499
Pointset merging	p. 505
Segmentation of surfaces and surface fitting	p. 509
Model recreation	p. 511
Volume calculation	p. 515
Tetrahedral element decomposition	p. 518
Patterns	p. 523
The Medial Axis Transform	p. 535
The medial axis transform	p. 535
MAT of a solid object	p. 537
MAT terminology	p. 537
Calculating critical points	p. 539
Dual space	p. 542
The multiple start point algorithm	p. 542
The divide-and-conquer algorithm	p. 552
Creating the modified dual	p. 576
Extracting nodes	p. 577
The negative MAT	p. 589
Subdividing and offsetting	p. 592
MAT with real geometry?	p. 601
Miscellaneous aspects of modelling	p. 603
Geometric tolerances	p. 603
Debugging	p. 605
Error handling	p. 605
Error messages	p. 605
Return codes and tracebacks	p. 606
Acknowledgements	p. 607
Data definitions	p. 609
Datastructure definitions	p. 609
VERTEX	p. 609
EDGE	p. 611
LOOP-EDGE LINK	p. 615
VERTEX-EDGE LINK	p. 616
BUNDLE	p. 616
WEDGE	p. 616
FACE	p. 617
LOOP	p. 617
FACEGROUP	p. 619
SHELL	p. 619
WIREFRAME_OBJECT	p. 620
SHEET_OBJECT	p. 620
VOLUME_OBJECT	p. 621
POINT	p. 622
CURVE	p. 623
CURVETYPE	p. 623
SURFACE	p. 623
SURFACETYPE	p. 624
INSTANCE	p. 624
GROUP-OF-OBJECTS	p. 625
FEATURE	p. 625
FRAMETYPE	p. 627
FEATURE-LINK	p. 627
MECHANISM_CONSTRAINT	p. 627
SHAPE_MODIFIER	p. 628
CONSTRAINT_DATA	p. 629
SUPPLEMENTARY_GEOMETRY	p. 629
PASSIVE_DATA	p. 629
NAME	p. 630
INFORMATION_ELEMENT	p. 630
TRANSFORMATION	p. 630
GENERAL_GROUP	p. 630
GENERAL_GROUP LINK	p. 631
SPACE	p. 631
ACCESS	p. 632
Geometry formats	p. 632
PLANE	p. 633
PLANE (alternative)	p. 633
SPHERE	p. 634
CYLINDER	p. 634
CONE	p. 634
GENERAL QUADRIC	p. 634
TOROID	p. 635
FREE-FORM SURFACE	p. 635
STRAIGHT LINE	p. 635
STRAIGHT LINE - short form	p. 636
CIRCLE	p. 636
CIRCULAR ARC - short form	p. 636
ELLIPSE	p. 637
PARABOLA	p. 637
HYPERBOLA	p. 637
FREE-FORM CURVE	p. 639
Feature frames	p. 639
Boss	p. 639
Pocket	p. 639
Slot	p. 640
Partial slot	p. 640
Bridge	p. 640
Reentrant	p. 640
Rail	p. 640
Through hole	p. 641
Unclassified	p. 641
Datastructure traversals	p. 643
Multiple element traversals	p. 643
Owner to single level structure following	p. 645
Shared entity traversal	p. 645
Tree-structure traversal	p. 646
Topological set traversal	p. 647
Manifold datastructure traversals	p. 649
Non-manifold datastructure traversals	p. 650
Edge element traversals	p. 650
rloop	p. 651
lloop	p. 652
svert	p. 652
evert	p. 653
rcwe	p. 653
rcce	p. 654
lcwe	p. 655
lcce	p. 656
Single element traversals	p. 657
vopev	p. 657
lopel	p. 658
ecwel	p. 658
eccel	p. 658
vcwel	p. 659
vccel	p. 659
ecwev	p. 660
eccev	p. 660
lcwev	p. 661
lccev	p. 661
ecwlv	p. 661
ecclv	p. 662
eclev	p. 662
vve	p. 663
Topological utilities	p. 665
Creating and deleting entities	p. 665
Moving entities to new owners	p. 666
Separate sequence of edges into new loop	p. 667
Separate a sequence of edges belonging to a new vertex	p. 668
Separate a set of adjacent faces, edges, and vertices into a new shell	p. 668
Check whether an edge is a wire edge	p. 669
Check whether an edge or vertex is a spur	p. 669
Check whether a loop is a hole-loop	p. 670
Checks for special object types	p. 670
Copy an object	p. 670
Modify an object with a transformation	p. 671
Geometrical utilities	p. 673
Geometric intersection package	p. 673
Planar intersections	p. 678
Cylinder intersections	p. 684
Cone intersections	p. 688
Sphere intersections	p. 690
Torus intersections	p. 690
Numeric patch intersections	p. 690
Curve tangent	p. 691
Surface normal	p. 693
Parameter value of point on curve	p. 694
Parameter values of a point on a surface	p. 698
Curve coordinates from parameter value	p. 701
Surface coordinates from parameter values	p. 703
Create a surface by sweeping an edge	p. 704
Modify geometry	p. 705
Reparametrise a curve	p. 706
Offset curve from a given curve	p. 706
Offset surface from a given surface	p. 707
General utilities	p. 709
Marker bits	p. 709
Matrix and vector packages	p. 709
Point in body	p. 709
Point in face	p. 711
Loop in face	p. 713
Intersect a face with a curve	p. 713
Curve-edge orientation	p. 715
Convex, concave, smooth edge	p. 715
Loop area and orientation	p. 716
Euler operators	p. 719
Make edge vertex (spur vertex and edge)	p. 723
Make an edge and vertex (split an edge)	p. 725
Make an edge and vertex (split a vertex)	p. 729
Make an edge and a face	p. 733
Make an edge and a face (slicing an edge)	p. 735
Make an edge and kill a hole-loop	p. 736
Make an edge and kill a face and body (shell)	p. 736
Make a vertex, a face, and a new object	p. 737
Make a hole-loop and kill a face	p. 739
Make a vertex and a hole-loop	p. 741
Kill an edge and vertex	p. 741
Kill an edge	p. 743
Kill a hole-loop and make a face	p. 746
Kill a vertex and a hole-loop	p. 747
Merge coincident vertices	p. 748
The null operator	p. 748
Modelling implementation notes	p. 751
Boolean operations	p. 751
Sweeping/Swinging	p. 753
Sweeping wireframe models	p. 759
Gluing coincident identical topology	p. 760
Face joining	p. 760
Edge joining	p. 760
Reflect	p. 761
Bend	p. 761
Giving sheet objects thickness	p. 762
Planar sectioning	p. 763
Imprinting	p. 764
Creating the dual of an object	p. 764
Bibliography	p. 765
Index	p. 777
Table of Contents provided by Ingram. All Rights Reserved.

Boundary Representation Modelling Techniques

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