AN ELEMENTARY TREATISE ON COORDINATE GEOMETRY OF THREE DIMENSIONS

By P. MILAK

INTRODUCTION THE CONTEXT: MEASUREMENT UNCERTAINTY IN INDUSTRIAL (GEOMETRICAL) METROLOGY THE MOTIVATION THE AIM THE OUTLINE CONTRIBUTION TO OWN PUBLICATIONS AND STUDENTS’ THESES MATHEMATICAL NOTATION 3D COORDINATE METROLOGY PROMINENT REPRESENTATIVES OF MEASUREMENT SYSTEMS TACTILE COORDINATE MEASUREMENT SYSTEMS STRUCTURED-LIGHT 3D SCANNER INDUSTRIAL X-RAY COMPUTED TOMOGRAPHY COMPARISON OF THE PRESENTED MEASUREMENT SYSTEMS MEASUREMENT AND GEOMETRY DATA REPRESENTATION POINT CLOUD THE DESCRIPTION OF GEOMETRY BASED ON STEP CAD TRIANGLE MESH CONSTRAINED DELAUNAY TRIANGULATIONS METROLOGICAL TRACEABILITY AND MEASUREMENT UNCERTAINTY PROBLEM STATEMENT AND OBJECTIVE RELATED WORK THE DATA PROCESSING PIPELINE FOR CALCULATION OF SPATIALLY DISCRETE METROLOGICAL DESCRIPTORS EXTENDED TRIANGLE MESH DATA STRUCTURE MEASUREMENT DATA POST-PROCESSING CORRUPTED TRIANGLES TRIANGLE MESH SELF INTERSECTIONS VOLUMETRIC MODEL REPAIR DISTANCE METRICS BETWEEN TWO TRIANGLE MESHES CLOSEST EDGE POINT (CEP) SHORTEST DISTANCE (SD) SHORTEST DISTANCE FROM THE PLANE DEFINED BY THE SAM- PLING START POINT AND ITS VERTEX NORMAL VECTOR (SDSP) SHORTESTDISTANCETOPLANEDEFINED BYTHE HITCOORDINATE AND ITS NORMALISED GRADIENT (SDHP) VERTEX NORMAL VECTOR (VNV) TRIANGLE MESH AFÏNITY (TMA) PREPARATION OF NOMINAL GEOMETRY DATA PREPARATION OF REFERENCE MEASUREMENT DATA TACTILE CMS REFERENCE MEASUREMENT REPRESENTED BY A POINT CLOUD REFERENCE MEASUREMENT REPRESENTED BY A TRIANGLE MESH ALIGNMENT OF COORDINATE SYSTEMS (REGISTRATION) MANUAL REGISTRATION BASED ON GEOMETRY ELEMENTS AUTOMATED GLOBAL ”BEST FIT” REGISTRATION PERFORMANCE EVALUATION FOR DIFFERENT METHODS SIMULTANEOUS REGISTRATION OF MULTIPLE GEOMETRIES ALTERNATIVE REGISTRATION METHODS SUMMARY OF THE REGISTRATION DECISION TREE DETERMINATION OF METROLOGICAL DESCRIPTORS CONVENTIONAL METROLOGICAL DESCRIPTORS UNCONVENTIONAL METROLOGICAL DESCRIPTORS SPATIAL CORRELATION OF METROLOGICAL DESCRIPTORS SUMMARY OF THE DATA PROCESSING PIPELINE SELECTED APPLICATIONS OF THE SPATIALLY DISCRETE METROLOGICAL DESCRIPTOR FRAMEWORK ANALYSIS OF MEASUREMENT SYSTEMS AND TASKS EVALUATING THE PRECISION OF TCMS MEASUREMENTS SPATIALLY DISCRETE METROLOGICAL DESCRIPTORS FOR OPTICAL MEASUREMENTS VALIDATING SURFACE POINT QUALITY PARAMETERS FOR CT MEASUREMENT DURATION VS UNCERTAINTY FOR CT THE IMPACT OF PROJECTION AVERAGING SETTINGS FOR CT THE IMPACT OF FBP RECONSTRUCTION FILTERS AND BINNING ACCURACY OF DIGITAL TWINS FOR METROLOGICAL CT SYSTEMS INVESTIGATING VGS MESH EXPORT PRESETS DIFFERENCES BETWEEN THE AVAILABLE DISTANCE METRICS WEIGHTED GEOMETRY ELEMENT REGRESSION ANALYSIS AND DATA FUSION FORTOL: IMPROVING TOLERANCE SPECIFICATIONS HETEROGENEOUS COMPUTING FOR DATA PARALLEL PROBLEMS PROBLEM SIZE AND ALGORITHMIC PROPERTIES FUNDAMENTAL DESIGN CHOICES THE BASICS OF PARALLEL PROGRAMMING BUILDING HETEROGENEOUS SOLUTIONS WITH CUDA PERFORMANCE EVALUATION OF THE GPU IMPLEMENTATIONS DISCUSSION SUMMARY AND OUTLOOK