GEOMETRIC AND SOLID MODELING

By G. FIZAY

TOPOLOGICAL ASPECTS EDGE ORIENTATION SINGULARITIES ON EDGES EDGE-IDENTI?CATION INFORMATION NOTES AND REFERENCES SURFACE INTERSECTIONS CHAPTER OVERVIEW INTERSECTING TWO IMPLICIT SURFACES NUMERICALLY CONSTRUCTION OF THE APPROXIMANT SELECTION OF STEP SIZE NEWTON ITERATION SINGULAR VALUE DECOMPOSITION TRACING IN HIGHER DIMENSIONS THE METHOD NUMERICALLY INTERSECTING TWO PARAMETRIC SURFACES SURFACE OPERATIONS IN HIGHER DIMENSIONS MAPPING SURFACE INTERSECTIONS TO PLANE CURVES SUBSTITUTION MAPS PROJECTION METHODS PLANE ALGEBRAIC CURVES PLACE OF A CURVE QUADRATIC TRANSFORMATIONS BRANCH AND CURVE DESINGULARIZATION TRACING WITH DESINGULARIZATION LOCATING SINGULARITIES BRINGING THE SINGULARITY TO THE ORIGIN PRESERVING THE DIRECTION OF TRACING REMARKS ON SURFACE INTERSECTION GR¨OBNER BASES TECHNIQUES ALGEBRAIC CONCEPTS FIELDS, RINGS, AND POLYNOMIALS FIELD EXTENSIONS AND RATIONAL FUNCTIONS MULTIVARIATE POLYNOMIALS AND IDEALS THE RESIDUE CLASS RING OF AN IDEAL ALGEBRAIC SETS AND VARIETIES PRIME IDEALS AND RADICALS GR¨OBNER BASES LEXICOGRAPHIC TERM ORDERING AND LEADING TERMS REWRITING AND NORMAL-FORM ALGORITHMS A MEMBERSHIP TEST FOR IDEALS BUCHBERGER’S THEOREM AND CONSTRUCTION OF GR¨OBNER BASES IMPROVED BASIS CONSTRUCTION AND REDUCED GR¨OBNER BASES ADMISSIBLE TERM ORDERINGS SOLVING ALGEBRAIC EQUATIONS TRIANGULARIZING ALGEBRAIC EQUATIONS FINDING SURFACE INTERSECTIONS BASIS DETERMINATION WITH SYMBOLIC QUANTITIES OPERATIONS ON CURVES AND SURFACES IMPLICITIZATION AND INVERSION O?SET SURFACES GEOMETRIC THEOREM PROVING OUTLINE OF THE PROOF METHOD TRANSLATING GEOMETRIC CON?GURATIONS FORMULA MANIPULATION CHOICE OF COORDINATE AXES AND OTHER HEURISTICS COMPLEXITY SIMPLE BASIS EXPERIMENTS LARGE BASIS COMPUTATIONS COE?CIENT GROWTH BASIS CONVERSION COMPUTING IN THE RESIDUE CLASS RING BASIS CONVERSION FOR ZERO-DIMENSIONAL IDEALS VARIABLE ELIMINATION