MAE 455 Computer-Aided Design and DraftingGeometric ModelingCreating 3D solid geometry in a computer!MAE 455 Computer-Aided Design and Drafting2Partial History of Geometric Modeling1963 Wireframe Computer Graphics “Invented” (Ivan Sutherland, MIT)MAE 455 Computer-Aided Design and Drafting3Partial HistoryDAC-1, General Motors, early 1960’sMAE 455 Computer-Aided Design and Drafting4Partial History of Geometric Modeling1967 Surface Modeling (S.A. Coons)1973 Solid Modeling – Constructive Solid Geometry(Laning et al., Draper Lab. )1973 Solid Modeling – Boundary Representation (Ian Braid, Cambridge U.)1985 Feature Modeling (Pratt & Wilson)1990 Parametric Modeling (PTC)MAE 455 Computer-Aided Design and Drafting5Wireframe Modeling• Stores positions of lines (in 2D or 3D)• Helpful for drafting (easy multiple views and easy editing)• Ambiguous surfaces limit the automation possibilities (e.g. no volume calculation, no NC tool path generation)?MAE 455 Computer-Aided Design and Drafting6Surface Modeling• Stores equations of surfaces• Most 3D graphics libraries use surface modeling• Good for visualizing complex surfaces and automated NC path generation of complex surfaces• Material volume information is ambiguous or hard to determine (therefore can’t calculate volume)From K., Lee “Principles of CAD/CAM/CAE Systems,” Addison-WesleyMAE 455 Computer-Aided Design and Drafting7• Various mathematical representations exist that each allow point-set classification:“Is a given point inside or outside the solid region?”• Solid models can be used for:– volume calculations– Automatic FE mesh generation– Collision determination in robotics or NC path generationSolid ModelingMAE 455 Computer-Aided Design and Drafting8Solid Modeling FunctionsDifferent ways that a user can create solid shapes:• Primitive creation• Boolean operations• Sweep operations• Surface operations• Engineering Feature-Based modeling• Parametric modelingMAE 455 Computer-Aided Design and Drafting9Primitive Creation• Primitives are simple solid shapes with simple mathematical surfaces• Can be controlled by a small number of dimension and position parametersFrom K. Lee “Principles of CAD/CAM/CAE Systems,” Addison-WesleyMAE 455 Computer-Aided Design and Drafting10Boolean Operations• Boolean operations are used to make more complicated shapes by combining simpler shapes• 3 types of operations are possible:– union (‘∪’) or “join”– intersection (‘∩’)– difference (‘-’) or “subtract”• Be careful:From K. Lee “Principles of CAD/CAM/CAE Systems,” Addison-WesleyMAE 455 Computer-Aided Design and Drafting11Sweeping Operations• Use 2D wireframe section(s) to generate a 3D solid.• This includes operations such as:– extrude– revolve– sweep– loft From K. Lee “Principles of CAD/CAM/CAE Systems,” Addison-WesleyMAE 455 Computer-Aided Design and Drafting12Surface Operations• These operate directly on the solid model faces, edges and vertices to create a desired modification.• Examples:– chamfering– rounding/filleting– drafting– shellingFrom K. Lee “Principles of CAD/CAM/CAE Systems,” Addison-WesleyMAE 455 Computer-Aided Design and Drafting13Feature-Based Modeling• Features are shapes having engin-eering significance. They usually are the geometric embodiment of machining operations or the function of a component.• Examples:– hole - pocket– slot - boss• Many systems provide for user-defined features.• Many people use the term “Feature” to refer to any kind of solid modeling operation.From K. Lee “Principles of CAD/CAM/CAE Systems,” Addison-WesleyMAE 455 Computer-Aided Design and Drafting14Parametric Modeling• Parameters are found in a CAD model as:– dimensions in 2D sketches– dimensions on 3D geometry (advanced systems only)– modeling operation parameters– variables in user-equations• Entire part geometry can be controlled by a small number of key
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