Surface Completion Using Laplacian Transform

Model acquisition process usually produce incomplete surfaces due to the technical constrains. This research presents the algorithm to perform surface completion using the available surface's context. Previous works on surface completions do not handle surfaces with near-regular pattern or irregular patterns well. The main goal of this research is to synthesize surface for hole that will have similar surface's context or geometric details as the hole's surrounding. This research uses multi-resolution approach to decompose the model into low-frequency part and high-frequency part. The low-frequency part is filled smoothly. The high-frequency part are transformed it into the Laplacian coordinate and filled using example-based synthesize approach. The algorithm is tested with planar surfaces and curve surfaces with all kind of relief patterns. The results indicate that the holes can be completed with the geometric detail similar to the surrounding surface

Topology-Aware Surface Reconstruction for Point Clouds

We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated in the optimization algorithm promote the correct topology. The result is a novel topology-aware technique which can: 1.) weed out topological noise from point scans, and 2.) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We showcase results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data

Iterative consolidation on unorganized point clouds and its application in design.

Chan, Kwan Chung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 63-69).Abstracts in English and Chinese.Abstract --- p.vAcknowledgements --- p.ixList of Figures --- p.xiiiList of Tables --- p.xvChapter 1 --- Introduction --- p.1Chapter 1.1 --- Main contributions --- p.4Chapter 1.2 --- Overview --- p.4Chapter 2 --- Related Work --- p.7Chapter 2.1 --- Point cloud processing --- p.7Chapter 2.2 --- Model repairing --- p.9Chapter 2.3 --- Deformation and reconstruction --- p.10Chapter 3 --- Iterative Consolidation on Un-orientated Point Clouds --- p.11Chapter 3.1 --- Algorithm overview --- p.12Chapter 3.2 --- Down-sampling and outliers removal --- p.14Chapter 3.2.1 --- Normal estimation --- p.14Chapter 3.2.2 --- Down-sampling --- p.15Chapter 3.2.3 --- Particle noise removal --- p.17Chapter 3.3 --- APSS based repulsion --- p.19Chapter 3.4 --- Refinement --- p.22Chapter 3.4.1 --- Adaptive up-sampling --- p.22Chapter 3.4.2 --- Selection of up-sampled points --- p.23Chapter 3.4.3 --- Sample noise removal --- p.23Chapter 3.5 --- Set constraints to sample points --- p.24Chapter 4 --- Shape Modeling by Point Set --- p.27Chapter 4.1 --- Principle of deformation --- p.27Chapter 4.2 --- Selection --- p.29Chapter 4.3 --- Stretching and compressing --- p.30Chapter 4.4 --- Bending and twisting --- p.30Chapter 4.5 --- Inserting points --- p.30Chapter 5 --- Results and Discussion --- p.37Chapter 5.1 --- Program environment --- p.37Chapter 5.2 --- Results of iterative consolidation on un-orientated points --- p.37Chapter 5.3 --- Effect of our de-noising based on up-sampled points --- p.44Chapter 6 --- Conclusions --- p.49Chapter 6.1 --- Advantages --- p.49Chapter 6.2 --- Factors affecting our algorithm --- p.50Chapter 6.3 --- Possible future works --- p.51Chapter 6.3.1 --- Improve on the quality of results --- p.51Chapter 6.3.2 --- Reduce user input --- p.52Chapter 6.3.3 --- Multi-thread computation --- p.52Chapter A --- Finding Neighbors --- p.53Chapter A.1 --- k-d Tree --- p.53Chapter A.2 --- Octree --- p.54Chapter A.3 --- Minimum spanning tree --- p.55Chapter B --- Principle Component Analysis --- p.57Chapter B.1 --- Principle component analysis --- p.57Chapter C --- UI of the program --- p.59Chapter C.1 --- User Interface --- p.59Chapter D --- Publications --- p.61Bibliography --- p.6

Toward Controllable and Robust Surface Reconstruction from Spatial Curves

Reconstructing surface from a set of spatial curves is a fundamental problem in computer graphics and computational geometry. It often arises in many applications across various disciplines, such as industrial prototyping, artistic design and biomedical imaging. While the problem has been widely studied for years, challenges remain for handling different type of curve inputs while satisfying various constraints. We study studied three related computational tasks in this thesis. First, we propose an algorithm for reconstructing multi-labeled material interfaces from cross-sectional curves that allows for explicit topology control. Second, we addressed the consistency restoration, a critical but overlooked problem in applying algorithms of surface reconstruction to real-world cross-sections data. Lastly, we propose the Variational Implicit Point Set Surface which allows us to robustly handle noisy, sparse and non-uniform inputs, such as samples from spatial curves

Some Basis Function Methods for Surface Approximation

This thesis considers issues in surface reconstruction such as identifying approximation methods that work well for certain applications and developing efficient methods to compute and manipulate these approximations. The first part of the thesis illustrates a new fast evaluation scheme to efficiently calculate thin-plate splines in two dimensions. In the fast multipole method scheme, exponential expansions/approximations are used as an intermediate step in converting far field series to local polynomial approximations. The contributions here are extending the scheme to the thin-plate spline and a new error analysis. The error analysis covers the practically important case where truncated series are used throughout, and through off line computation of error constants gives sharp error bounds. In the second part of this thesis, we investigates fitting a surface to an object using blobby models as a coarse level approximation. The aim is to achieve a given quality of approximation with relatively few parameters. This process involves an optimization procedure where a number of blobs (ellipses or ellipsoids) are separately fitted to a cloud of points. Then the optimized blobs are combined to yield an implicit surface approximating the cloud of points. The results for our test cases in 2 and 3 dimensions are very encouraging. For many applications, the coarse level blobby model itself will be sufficient. For example adding texture on top of the blobby surface can give a surprisingly realistic image. The last part of the thesis describes a method to reconstruct surfaces with known discontinuities. We fit a surface to the data points by performing a scattered data interpolation using compactly supported RBFs with respect to a geodesic distance. Techniques from computational geometry such as the visibility graph are used to compute the shortest Euclidean distance between two points, avoiding any obstacles. Results have shown that discontinuities on the surface were clearly reconstructed, and th

Regenerisanje NC koda primenom 3D identifikacije i analize geometrijskih odstupanja

REZIME: Proizvodnja delova na numerički upravljanim mašinama alatkama jedna je od najzastupljenijih tehnika korišćenih u savremenim proizvodnim procesima. Čak i kod preciznog hladnog i toplog oblikovanja delova ili livenja delova, mnogi od završnih postupaka obrade i delova se obavljaju rezanjem na mašinama alatkama, a takođe se i alati za ove mašine, ovim tehnologijama obrađuju. CAD/CAM sistemi mogu da generišu NC programe na osnovu geometrije dela, ali ne pomažu programerima u izboru odgovarajućih strategija rezanja, geometrije alata i drugih parametara procesa. Komercijalni CAM softveri generišu CNC programe uglavnom sa matematičke tačke gledišta i obično sadrže konstantne parametre rezanja za određenu putanju alata i ne simuliraju očekivani kvalitet i tačnost obrađenih površina, a takođe ne uzimaju u obzir mehaničke aspekte procesa glodanja kao što su sile rezanja i devijacija reznog alata. Savremena merna oprema je sve prisutnija u mašinskoj industriji, pa se može reći da su koordinatne merne mašine postale standard i da se proizvodnja i dokumentacija velikim delom prilagođava koordinatnim mernim mašinama. Sa druge strane se još intenzivnije razvijaju beskontaktni (optički i laserski) merni sistemi. Ovi merni sistemi podrazumevaju kao razultat merenja oblak tačaka, koji zahteva procesiranje i generisanje površina u cilju merenja i kontrole. U okviru disertacije dat je pregled savremene merne opreme i predstavljeni su postupci generisanja površina i merenja odstupanja pomoću softvera, kao što su CATIA, GOM Inspect, PC DMIS i sl. Eksperimentalna istraživanja obuhvataju veoma veliki broj eksperimenata. U okviru prvog eksperimenta analiziran je uticaj širine rezanja na tačnost obrađenog dela. Sledećim eksperimentom obuhvaćen je uticaj brzine rezanja i pomoćnog kretanja na hrapavost obrađenog dela kao i na dimenzionalna i geometrijska odstupanja: ravnost, upravnost i paralelnost. Narednim eksperimentima istraživan je uticaj greške postavljanja (paralelne pomerenosti ose i nagnutosti ose) glodala kao i radijalnog odstupanja zuba glodala, na topografiju površine. Poslednjim eksperimentalnim ispitivanjima određivan je uticaj promene dubine rezanja, odnosno putanje glodala na dobijene dužinske i geometrijske mere. Realizovana eksperimentalna istraživanja su pokazala korelativnu zavisnost između parametara obrade i dobijenih parametara kvaliteta obrađenog dela. Odstupanja obrađenih delova identifikovana su i merena pomoću koordinatne merne mašine i različitih optičkih mernih sistema (ATOS) uz primenu odgovarajućih softvera za merenje. Takođe su izvršena poređenja dobijenih rezultata sa različitih mernih uređaja. Razvijen je algoritam za regenerisanje postojećeg NC koda u cilju korekcije odstupanja obrađenog dela koje se javljaju usled grešaka obrade. Algoritam predviđa postojanje baze podataka koje se potrepljuju eksperimentalnim istraživanjima, podacima iz obradnih procesa, rezultatima modeliranja i simulacija zavisnosti parametara obrade od tačnosti obrade. Regenerisanjem NC koda vrše se korekcije grešaka obrade, odnosno predupređuju se uzroci nastanka grešaka obrade.ABSTRACT: The production of parts using numerically controlled machine tools is one of the most used techniques in modern production processes. Even at the precise cold and hot shaping of parts or casting of parts, most of fine machining and parts are performed with cutting on machine tools, and the tools for these machines are also processed with these technologies. CAD/CAM systems can generate NC programs based on the geometry of a part, but do not help programmers in the selection of the proper cutting strategies, tool geometry and other processing parameters. Commercial CAM software develop CNC programs mostly from the mathematical point of view and commonly contain constant cutting parameters for a specific tool path and they do not simulate the expected quality and accuracy of the machined surfaces, and they also do not take into consideration the mechanical aspects of milling process such as cutting forces and cutting tool deviation. Modern measurement equipment is more present in manufacturing industries, so it can be said that the measuring machine coordinates have became the standard and that the manufacturing and documentation are adjusting to the coordinate measuring machines in a great deal. On the other hand, the non-contact (optical and laser) measuring systems are more intensively developed. These measuring systems as a result include a point cloud, which requires the processing and generating of surfaces for the purpose of measuring and control. In the framework of the dissertation is given the review of modern measuring equipment and the surface generating procedures and deviation measurements using the software, such as CATIA, Gom Inspect, PC DMIS, etc, are presented. Experimental researches include a very large number of experiments. Within the firs experiment, the impact of cutting width on the accuracy of processed part was analyzed. The following experiment included the impact of cutting speed and auxiliary movement of the roughness of the processed part as well as on the dimensional and geometrical deviations: flatness, perpendicularity and parallelism. Subsequent experiments examined the impact of error setup (parallel offset of axis and inclination of the axis) of the milling cutter as well as the radial deviation of mill tooth on the surface topography. In the final experiments the impact of the change of cutting depth, i.e., milling cutter path, on the obtained longitudinal and geometrical measures is determined. Conducted experimental researches have shown the correlative dependence between the cutting parameters and obtained quality parameters of machined part. Deviations of machined parts are identified and measured using the coordinate measuring machine and different optical measuring systems (ATOS) with the application of corresponding measuring software. The comparisons of the results obtained from the different measuring devices are also performed. An algorithm for generation of the existing NC code for the correction of the machined part deviations that occur due to machining error is developed. The algorithm predicts the existence of database that is supported by experimental research, data from machining processes, results of modeling and simulation of machining parameters dependence on the accuracy of the processing. Regeneration of NC code By regenerating the NC code the correction of processing errors is made, i.e., the causes of processing errors are prevented