Computer Science Workbench

1 Outline of CAD/CAM/CAE.- 1.1 Introduction.- 1.2 CAD System.- 1.3 CAM System.- 1.4 CAE System.- 1.5 3D CAD Systems.- 2 3D CAD Systems and Solid Models.- 2.1 Introduction.- 2.2 How to Represent Solids.- 2.3 Advantages of a Solid Modeler.- 2.4 Representation of Objects in a Solid Modeler.- 2.4.1 CSG and boundary representations.- 2.4.2 Hybrid systems.- 2.4.3 Other representation methods.- 2.5 Comparison of CSG and Boundary Representations.- 3 Solid Modeler DESIGNBASE.- 3.1 Introduction.- 3.2 Features of DESIGNBASE.- 3.3 Software Structure of DESIGNBASE.- 3.4 Data Structure of Boundary Representations.- 3.4.1 Solid models with boundary representations.- 3.4.2 Data structures of boundary representations.- 3.4.3 Data structure of topological elements in DESIGNBASE.- 3.4.4 Data structure of geometric elements in DESIGNBASE.- 3.5 Primitive Operations.- 3.5.1 Topological elements and Euler formula.- 3.5.2 Euler operations.- 3.5.3 Primitive operations in DESIGNBASE.- 3.6 An Example of Primitive Operations.- 4 Free-Form Curves.- 4.1 Introduction.- 4.2 Parametric Curves.- 4.2.1 Algebraic representation.- 4.2.2 Parametric representation.- 4.3 Bezier Curves.- 4.3.1 How to represent Bezier curves.- 4.3.2 Division and connection of Bezier curves.- 4.3.3 Degree elevation of Bezier curves.- 4.4 Rational Bezier Curves.- 4.4.1 How to represent rational Bezier curves.- 4.4.2 Weights and their effects.- 4.4.3 Creation of conic sections.- 4.5 B-Spline Curves.- 4.5.1 How to represent B-spline curves.- 4.5.2 Knot vectors and curves.- 4.5.3 Connection and division of curves.- 4.6 NURBS.- 4.6.1 How to represent NURBS.- 4.6.2 How to represent conic sections with NURBS.- 4.6.3 Connection of curves.- 4.7 Programs.- 4.7.1 Program to obtain coordinates on a curve.- 4.7.2 Program to obtain a derivative vector on a curve.- 4.7.3 Program to divide a curve.- 5 Free-Form Surfaces.- 5.1 Introduction.- 5.2 Quadric Surfaces.- 5.3 Parametric Patches.- 5.4 Coons Surfaces.- 5.5 Bezier Surfaces.- 5.6 Rational Bezier Surfaces.- 5.7 NURBS.- 5.8 Gregory Patches.- 5.9 Rational Boundary Gregory Patches.- 5.10 Connection of Patches.- 5.10.1 Conditions on connectivity.- 5.10.2 Connection of Gregory patches.- 5.10.3 Connection of rational boundary Gregory patches.- 5.11 Interpolation of Patches.- 5.11.1 Irregular meshes.- 5.11.2 Interpolation of curve meshes.- 5.11.3 Interpolation of triangular surfaces.- 5.11.4 Interpolation of surfaces containing an odd number of sides.- 5.11.5 Interpolation of surfaces containing an even number of sides.- 5.11.6 Interpolation of curve meshes containing T-nodes.- 5.12 Transformation of Patches.- 5.12.1 Transformation between Bezier surface and Coons surface.- 5.12.2 Transformation of rational boundary Gregory patch into rational Bezier surface.- 5.13 Programs.- 5.13.1 Program to obtain coordinates on a surface.- 5.13.2 Program to obtain a partial derivative vector of a surface.- 6 Intersection Calculations.- 6.1 Introduction.- 6.2 Intersection Calculations Between Curves.- 6.2.1 Algebraic calculation method.- 6.2.2 Geometric calculation method.- 6.3 Intersection Calculations Between a Curve and a Surface.- 6.3.1 Algebraic calculation method.- 6.3.2 Geometric calculation method.- 6.4 Intersection Calculations Between Surfaces.- 6.4.1 Intersection calculations between quadratic surfaces.- 6.4.2 Intersection calculations between free-form surfaces.- 6.4.3 Recursive subdivision method.- 6.4.4 Marching method.- 6.5 Intersection Calculation in DESIGNBASE.- 7 Local Operations.- 7.1 Introduction.- 7.2 Creation and Modification of Solids with Surfaces.- 7.2.1 Defining surfaces by skinning.- 7.2.2 Defining surfaces by translating control points.- 7.2.3 Defining surface by interpolation.- 7.2.4 Defining surfaces by Boolean operations.- 7.3 Primitive Solid Generation.- 7.3.1 Creation of a parallelepiped and a cylinder.- 7.3.2 Creation of a rotational model.- 7.3.3 Creation of a mirror-image model.- 7.3.4 Creation of a skinning model.- 7.3.5 Creation of a sweep model.- 7.4 Local Modification Operations.- 7.4.1 Creation and modification of edges.- 7.4.2 Lifting operation.- 7.4.3 Model cutting.- 7.4.4 Model gluing.- 7.5 Programs of Local Operations.- 8 Boolean Operations.- 8.1 Introduction.- 8.2 Boolean Operations of Solids with Free-Form Surfaces and Their Problems.- 8.2.1 Intersection calculations.- 8.2.2 How to deal with intersection curves.- 8.3 Boolean Operation Algorithm in DESIGNBASE.- 8.3.1. Intersection calculations between edges and surfaces.- 8.3.2 Intersection calculations between surfaces.- 8.3.3 Creation of intersection vertices.- 8.3.4 Creation of intersection edges.- 8.3.5 Classification of boundaries and deletion of unnecessaryparts.- 8.3.6 Gluing of two solids.- 8.3.7 Examples of execution.- 9 Rounding Operation.- 9.1 Introduction.- 9.2 Problems with the Rounding Operation.- 9.3 Rounding Operation in DESIGNBASE.- 9.4 Example of Rounding Operation Execution.- 9.5 Algorithm of Rounding Operation.- 9.6 How to Calculate Trajectories Drawn by Tangent Points.- 10 Functions in Aiding Design.- 10.1 Introduction.- 10.2 Parametric Design.- 10.3 UNDO * REDO Operations.- 10.3.1 Interactive system.- 10.3.2 UNDO * REDO operations in DESIGNBASE.- 10.3.3 Representation of the solid creation process.- 10.3.4 UNDO * REDO with Boolean operations.- 10.4 Creation of Similar Shapes.- 10.4.1 Limits of the UNDO * REDO operations.- 10.4.2 Reexecution function.- 10.4.3 Limits of reexecution function.- 11 Rendering.- 11.1 Introduction.- 11.2 Color Components and Shading Model.- 11.2.1 Color representation.- 11.2.2 Ambient light.- 11.2.3 Diffuse reflection light.- 11.2.4 Specular reflection light.- 11.2.5 Transmission light.- 11.3 Z-Buffer Method.- 11.4 Scan Line Method.- 11.4.1 Characteristics of scan line method.- 11.4.2 Actual processing in the scan line method.- 11.4.3 Coherence in the scan line method.- 11.4.4 Antialiasing - A-buffer method.- 11.5 Ray Tracing Method.- 11.5.1 Antialiasing in the ray tracing method.- 11.6 Mapping Method.- 11.6.1 Significance of mapping.- 11.6.2 Texture mapping.- 11.6.3 Reflection mapping.- 11.6.4 Refraction mapping.- 11.6.5 Bump mapping.- 11.6.6 Solid texture.- 12 Mass Properties.- 12.1 Introduction.- 12.2 How to Obtain Surface Area.- 12.2.1 Monte Carlo method.- 12.2.2 Element subdivision method.- 12.2.3 Polygonization.- 12.2.4 Numerical integration.- 12.3 How to Obtain Volume, Center of Gravity, and Moment of Inertia.- 12.3.1 Monte Carlo method.- 12.3.2 Element subdivision method.- 12.3.3 Method using integration theorem.- 12.4 Mass Property Calculation in DESIGNBASE.- 13 3-Dimensional Modeling Method.- 13.1 Introduction.- 13.2 Resin Model Creation System.- 13.2.1 Fundamental principles.- 13.2.2 UV curing resin.- 13.2.3 Laser control.- 13.2.4 Data processing.- 13.3 Link with Modeler.- 13.3.1 Link with surface modeler.- 13.3.2 Link with solid modeler.- 13.4 DESIGNBASE and Resin Model Creation System.- 14 Solid Models and Structure Analysis.- 14.1 Introduction.- 14.2 History of Finite Element Method.- 14.3 Finite Element Method and Solid Models.- 14.4 3-Dimensional Mesh Generation.- 14.5 KSWAD - Integrated CAE System.- 14.5.1 How to apply data of solid modeler.- 14.5.2 Genuine automatic meshing.- 14.5.3 Mapped meshing.- 14.5.4 Examples of analyses by KSWAD.- References.