Project Overview.- 1 CAD/CAM data exchange in the industrial environment - methodology and tools.- 1.0 Introduction.- 1.1 Experiences with CAD data transfer.- 1.2 Problems caused by the specification.- 1.3 Problems regarding the processor quality.- 1.4 Problems caused by differences between CAD/CAM systems.- 1.5 Usage of CAD data exchange software in the industrial environment.- 1.6 Basis of neutral file adaption.- 1.6.1 Overcoming system differences.- 1.6.2 Overcoming differences in applications.- 1.7 Usage of neutral file adapting system NFAS.- 1.7.1 Presuppositions.- 1.7.2 Exchanging data between CATIA and CADCPL via NFAS.- 1.8 Summary.- 2 Exchange of curve and surface data.- 2.0 Introduction.- 2.1 Forms of representation.- 2.2 Exchange mechanisms.- 2.2.1 Parametric evaluators.- 3 Neutral file interface requirements.- 3.0 Introduction.- 3.1 Design objectives.- 3.2 Neutral file entities.- 3.3 General parametric curve and surface representations.- 3.3.1 Stability experiments.- 3.3.2 Analysis.- 3.3.3 Results.- 3.3.4 Conclusions.- 4 Conversions between representations.- 4.0 Introduction.- 4.1 Parametrisation.- 4.2 Degree elevation.- 4.3 Bezier ? explicit polynomial.- 4.3.1 Bezier to explicit polynomial: curves.- 4.3.2 Bezier to explicit polynomial: surfaces.- 4.3.3 Explicit polynomial to Bezier: curves.- 4.3.4 Explicit polynomial to Bezier: surfaces.- 4.3.5 Summary.- 4.4 B-spline ? Bezier.- 4.4.1 B-spline (uniform) to Bezier: curves.- 4.4.2 B-spline (uniform) to Bezier: surfaces.- 4.4.3 B-spline (non-uniform) to Bezier: curves.- 4.4.4 Single knot insertion.- 4.4.5 Multiple knot insertion.- 4.4.6 The Cox-de Boor recursion formula.- 4.4.7 The B-spline to Bezier algorithm.- 4.4.8 The linear transformation method.- 4.4.9 B-spline (non-uniform) to Bezier: surfaces.- 4.4.10 The matrix method.- 4.4.11 Summary.- 4.4.12 Bezier to B-spline: curves.- 4.4.13 Bezier to B-spline: surfaces.- 4.5 B-spline ? explicit polynomial.- 4.5.1 B-spline (uniform) to explicit polynomial: curves.- 4.5.2 B-spline (uniform) to explicit polynomial: surfaces.- 4.5.3 B-spline (non-uniform) to explicit polynomial: curves.- 4.5.4 B-spline (non-uniform) to explicit polynomial: surfaces.- 4.5.5 Explicit polynomial to B-spline: curves.- 4.5.6 de Boor-Fix algorithm.- 4.5.7 Explicit polynomial to B-spline: surfaces.- Appendix 1 to Chapter 4.- Appendix 2 to Chapter 4.- 5 Degree reduction approximations.- 5.0 Introduction.- 5.1 Constrained Chebyshev polynomials.- 5.2 Parametric curve approximation using constrained Chebyshev polynomials.- 5.3 Surface approximation using constrained Chebyshev polynomials.- 6 More general curve and surface approximations.- 6.1 Parametric curve and surface approximation using orthogonal functions.- 6.2 Orthogonal polynomials and the least squares criterion.- 6.3 Constrained orthogonal polynomials.- 6.4 Curve approximation.- 6.4.1 Curve approximation example.- 6.5 Surface approximation.- 6.5.1 Simple surface approximation example.- 6.6 More general curve approximation problems.- 6.7 More general surface approximation problems.- References.- Appendix A: The neutral file check system.- A.1 The necessity of data exchange software.- A.2 The IGES tools.- A.2.1 The SYNTAX analysis program.- A.2.2 The POINTER analysis program.- A.2.3 The IGES check program.- A.2.4 The STATISTIC program.- A.2.5 The IGES statistic comparator program ISCOMP.- A.3 The VDAFS ANALYZER.- Appendix B: The neutral file adapting system NFAS.- B.0 Introduction.- B.1 System design.- B.1.1 NFAS control program.- B.1.2 Neutral file call interface.- B.1.3 Programming language and operating systems.- B.2 The performance of NFAS.- B.2.1 The NFAS command language.- B.2.2 The functionality of NFAS.- B.3 Implementation of NFAS.- List of Illustrations.- List of Tables.
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