Advanced Metrology: Freeform Surfaces

Front Matter
Copyright
Preface
Acknowledgments
Free-form surface sampling
	Introduction
	The state of the art
		Primitive surfaces
		Free-form surfaces
			Model-adapted sampling strategies
			Self-adaptive sampling strategies
	Surface reconstruction
		Tensor product B-spline reconstruction
		Delaunay triangulation reconstruction
	Curvature based sampling
		Curve sampling
		Surface sampling
	Adaptive sampling strategy
		Method description
			Profile adaptive compression sampling
			Areal adaptive scanning
		Performance validation
			Experimental settings
			Results and discussion
	Triangular mesh sampling
	Summary
	References
Fundaments for free-form surfaces
	Introduction
	Free-form surface representation
		Free-form surface requirements
		Surface representation models
		Discrete surface representations
		Continuous surface representations
			Subdivision surfaces
			Ruled surfaces
		Other surfaces methods
			Skinned surfaces or multisection surfaces
			Swept surfaces
			Swung surfaces
	Free-form analysis
		Sampling and reconstruction
			Feature- or attribute-based sampling
			Sampling based on orthogonal functions
			Simplification of meshes
		Free-form form fitting
			Nominal form is known
			Nominal form is not known
		Free-form filtration and multiscale decomposition
			Diffusion filtering
			Morphological filtering
			Segmentation
			Wavelets
		Free-form analytics
			Form parameters
			Shape parameters
			Surface texture field parameters
			Surface texture feature parameters
	Summary
	References
Free-form surface sampling
	Introduction
	The state of the art
		Primitive surfaces
		Free-form surfaces
			Model-adapted sampling strategies
			Self-adaptive sampling strategies
	Surface reconstruction
		Tensor product B-spline reconstruction
		Delaunay triangulation reconstruction
	Curvature based sampling
		Curve sampling
		Surface sampling
	Adaptive sampling strategy
		Method description
			Profile adaptive compression sampling
			Areal adaptive scanning
		Performance validation
			Experimental settings
			Results and discussion
	Triangular mesh sampling
	Summary
	References
Geometrical fitting of free-form surfaces
	Introduction
	Geometrical representations
	Algebraic fitting and geometrical fitting
		Geometric fitting for explicit functions
		Geometric fitting for implicit/parametric functions
			Experimental validation
	Robust estimators
		Statistical fundaments
		Commonly used error metrics
			M-Estimators
			L-Estimators
			R-Estimators
			lp Norm estimators
		Surrogate functions
			Experimental validation
	Minimum zone fitting
		Definition of tolerance zone
		Interior point method
			Experimental validation
		Exponential penalty function
			Experimental validation
	Summary
	References
Free-form surface reconstruction
	Introduction
	Triangular mesh parametrization
		Case studies
	Surface reconstruction with B-splines and NURBS
		Surface reconstruction
		Case studies
	Surface reconstruction with local B-splines models
		Truncated hierarchical B-splines
		Locally refined B-splines
		Test cases
	Surface reconstruction with triangular Bezier surfaces
		Degree 2 interpolation
		Degree 5 interpolation
		Case studies
	Implicit function surface reconstruction
		Marching cubes
		Adaptive surface reconstruction
		Test case
	Summary
	References
Free-form surface filtering using the diffusion equation
	Introduction
	Linear Gaussian filters
	Diffusion filtering and relationship with Gaussian filters
		Diffusion equation
		The relationship between the diffusion time parameter and the Gaussian cutoff wavelength
	Laplace-Beltrami operator
	Mean curvature motion
	Discrete differential geometry
		Discrete Laplace-Beltrami operators
		Criteria for convergence
		Numerical solutions of the diffusion equation
	Application approach
		Surfaces without boundaries
		Surfaces without boundaries
		Simulation test case
		Experimental test case
		Mean curvature flow: Simulation test case
	Summary
	References
Morphological filtering of free-form surfaces
	Introduction
	Mathematical morphology and morphological operations
		Morphology operations on set
		Morphological operations on functions
	Morphological operations in surface metrology
		Surface scanning
		Real mechanical surface reconstruction
		Closing and opening filtering
		Form approximation
		Contact points
		Uncertainty zone for continuous surface reconstruction
		Scale-space analysis
	Alpha shape algorithms for morphological filtering
		Alpha shape theory
		Link between alpha hull and morphological envelopes
		Morphological envelope computation based on the alpha shape
		Divide and conquer optimization
	Contact points and their searching procedures
		Redundancy of the Delaunay triangulation
		Definition of contact points
		Propositions for searching contact points
	Case studies
	Summary
	References
Segmentation of topographical features on free-form surfaces
	Introduction
	Watershed segmentation and its application
		Watershed segmentation in geography
		Watershed segmentation in image processing
		Watershed segmentation in engineering surface analysis
		Watershed segmentation of free-form surfaces
		General strategy of applying the watershed method on free-form surfaces
	Watershed segmentation of topographical features on free-form surfaces
		Extraction of surface topography
		Construction of the Pfaltz graph
		Oversegmentation merging
	Case studies
	Summary
	References
	Further reading
Free-form surface filtering using wavelets and multiscale decomposition
	Introduction
	Wavelet multiscale analysis
	Implementations methods of wavelet multiscale analysis
		First-generation wavelet: The filter bank method
		Second-generation wavelet: The lifting scheme method
	Wavelets generations for surface texture characterization
	Wavelet multiscale decomposition for 3-D triangular meshes
	Free-form surface filtering using lifting wavelets
		Split operator
			Random split operator
			Shortest-edge split operator
			Quadric error metric (QEM) split operator
		Prediction operator
			Laplacian prediction operator
			Gaussian prediction operator
		Update operator
		Mesh simplification (the approximation)
		The details (wavelet coefficients)
		Merge operator
		Filtration algorithm
	Multiscale free-form surface decomposition using a Laplacian mesh relaxation
		Laplacian mesh relaxation
		Multiscale decomposition using a relaxation scheme
		Scale-limited surfaces using mesh relaxation
	Case studies
		Computer-generated surfaces
			Lifting wavelets filtration results
			Laplacian mesh decomposition results
		Bioengineering surfaces
			Lifting wavelets filtration results
			Laplacian mesh decomposition results
		Comparisons
	Summary
	References
	Further reading
Characterization of free-form surfaces
	Introduction
	Surface representation
	Reference form computation
		Plane estimation
		Cylinder estimation
		Sphere estimation
	Areal texture parameters definition
		Height parameters
		Hybrid parameters
		Functional parameters
		Comparison with ISO 25178-2
		Triangular mesh approximation
	Test cases
		Portion of lattice structure
			Comparison between the grid and mesh methods
			Comparison of different reconstruction and form estimation methods
		Ball bearing surface
		Heavy-duty stick-on Velcro surface
		Portion of turbine blade
	Feature parameters
	Summary
	References
Characterization of free-form structured surfaces
	Introduction
	Characterization framework of free-form structured surface
	F-operator for the form removal of the free-form structured surface
		Robust spline filter
			Generalized robust spline filter
			M-estimation
			Iteratively reweighted least squares solution for generalized spline filter
				L2 norm-Linear spline filter
				Proposed nonlinear spline filter
			Experimental results
		Robust Gaussian regression filter
	PDE-based surface characterization
		Linear diffusion for regular lattice grid surface analysis
		Adaptive diffusion filter for surface analysis
		Wavelet regularization PDE-based surface characterization
		Numerical solution and experiments
			Profile analysis
			Areal surface analysis
	Feature extraction
		Sobel edge operator
		Segmentation
		Wolf pruning
	Case studies for the characterization of MEMs surfaces
	Methodology to characterize tessellation surfaces
		Methodology
		AACF
		Lattice building
		Case studies
	Summary
	References
	Further reading
Smart surface design and metrology platform
	Introduction
	Semantics of surface design and metrology
		Semantic flows among the four conceptual realms
		Representing the semantics
			CSL semantics
				Basic semantics
				Enriched semantics
				Hierarchical semantics
			CSL reasoning
	Semantics of surface texture specification
		Hierarchical operation model
		Reasoning on the semantics
	CatSurf: An integrated surface texture information system
		CatSurf: System architecture and components
			Design your specifications with functionality and production capability
			Intelligent specification generation
			Guidance and analysis of measurement
			Using CatSurf in CAD systems
		Test cases
			PST specification design for a helical gear in AutoCAD
			Areal specification design for a stepped shaft in solidworks
	Summary
	Appendix
		Basic category concepts
		High-level categorical concepts
	References
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	Z