Outlines the development of a three-dimensional computer-aided design (CAD) system and its range of applications. The contributors also describe the concept of solid models and the theory of curves and surfaces. Concepts are illustrated through a number of "real world" applications.
3D CAD is one of the most important technologies of the 90sfor the engineering and manufacturing world. 3D CAD systemscan provide a competitive edge in the development of newproducts. This book presents the development of athree-dimensional CAD system and its wide range ofapplications. It describes the concepts of solid models, andthe theory of curves and surfaces and it illustrates theseconcepts through "reals world" applications.
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.
