Normal Umbrella: A new primitive for triangulating parametric surfaces

Typical methods for the triangulation of parametric surfaces use a sampling of the parameter space, and the wrong choice of parameterization can spoil a triangulation or even cause the algorithm to fail. We present a new method that uses a local tessellation primitive for almost-uniformly sampling and triangulating a surface, so that its parameterization becomes irrelevant. If sampling density or triangle shape has to be adaptive, the uniform mesh can be used either as an initial coarse mesh for a refinement process, or as a fine mesh to be reduced

Point cloud representation

Reconstructing a surface out of a three-dimensional set of points, which is obtained by sampling an object\u27s boundary, is done by generating an arbitrary triangular mesh. Our approach is to obviate the computation of such a mesh connectivity and to represent the object\u27s surface only by the point cloud. We discuss how such a point cloud representation can be visualized and present processing steps like coarsifying and smoothing, which are important for dealing with the objects. Further we apply a multiresolution method to point cloud representations and use this technique as well as others for modelling purposes

Edge-Sharpener: A geometric filter for recovering sharp features in uniform triangulations

3D scanners, iso-surface extraction procedures, and several recent geometric compression schemes sample surfaces of 3D shapes in a regular fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer these sharp features and thus exhibit significant errors. The new Edge-Sharpener filter introduced here identifies the chamfer edges and subdivides them and their incident triangles by inserting new vertices and by forcing these vertices to lie on intersections of planes that locally approximate the smooth surfaces that meet at these sharp features. This post-processing significantly reduces the error produced by the initial sampling process. For example, we have observed that the L2 error introduced by the SwingWrapper9 remeshing-based compressor can be reduced down to a fifth by executing Edge-Sharpener after decompression, with no additional information

Reconstrucción digital de estructuras de tejados históricos: desarrollo de un flujo de trabajo de análisis altamente automatizado

[EN] Planning on adaptive reuse, maintenance and restoration of historic timber structuresrequiresextensive architectural and structural analysis of the actual condition. Current methods for a modellingof roof constructions consist of several manual steps including the time-consuming dimensional modelling. The continuous development of terrestrial laser scanners increases the accuracy, comfort and speed of the surveying work inroof constructions. Resultingpoint clouds enabledetailed visualisation of theconstructionsrepresented by single points or polygonal meshes, but in fact donot containinformation about the structural system and the beam elements. The developed workflow containsseveral processing steps on the point cloud dataset. The most important among them arethenormal vector computation, the segmentation of points to extract planarfaces, a classification of planarsegmentsto detect the beam side facesand finally theparametric modelling of the beams on the basis of classified segments. Thisenablesa highly automated transitionfrom raw point cloud data to a geometric model containing beams of the structural system. The geometric model,as well as additional information about the structural properties of involved wooden beams and their joints,is necessaryinput for a furtherstructural modellingof timber constructions. The results of the workflow confirm that the proposed methods work well for beams with a rectangularcross-section and minor deformations. Scan shadows and occlusionof beamsby additional installationsor interlockingbeamsdecreases the modelling performance, but in generala high level ofaccuracy and completeness isachieved ata high degree of automation.[ES] Las estructuras históricas de madera requieren un análisis arquitectónico y estructural exhaustivo de su condición real en aras de planificar la reutilización flexible, el mantenimiento y la restauración. Los métodos actuales que modelan las construcciones de cubiertas pasan por aplicar varias etapas en modo manual, que incluye el lento modelado dimensional. El desarrollo continuo de escáneres láser terrestres aumenta la exactitud, la comodidad y la velocidad del trabajo topográfico en construcciones de tejados. Las nubes de puntos resultantes permiten la visualización detallada de las construcciones representadas por puntos o mallas poligonales, pero de hecho no contienen información sobre el sistema estructural y los elementos del travesaño. El flujo de trabajo desarrollado contiene varias etapas de procesamiento en el conjunto de datos de la nube de puntos. Los más importantes son el cálculo del vector normal, la segmentación de puntos que extraen caras planas, la clasificación de segmentos planos que detectan las caras laterales del travesaño y, finalmente, el modelado paramétrico de los travesaños en función de los segmentos clasificados. Esto permite una transición altamente automatizada de los datos de la nube de puntos brutos a un modelo geométrico que contiene los travesaños del sistema estructural. El modelo geométrico, así como la información adicional sobre las propiedades estructurales de las vigas de madera involucradas y de sus juntas, es información necesaria de entrada para el modelado estructural eventual de las construcciones de madera. Los resultados del flujo de trabajo confirman que los métodos propuestos funcionan bien en travesaños que presentan secciones transversales rectangulares y deformaciones menores. Las sombras en los escaneados y las oclusiones de los travesaños a partir de instalaciones adicionales o vigas entrelazados disminuye el rendimiento del modelado, pero en general se logra un nivel de exactitud e integridad elevado con un alto grado de automatización.Pöchtrager, M.; Styhler-Aydın, G.; Döring-Williams, M.; Pfeifer, N. (2018). Digital reconstruction of historic roof structures: developing a workflow for a highly automated analysis. Virtual Archaeology Review. 9(19):21-33. doi:10.4995/var.2018.8855SWORD2133919Attene, M., & Spagnuolo, M. (2000). Automatic surface reconstruction from point sets in space. Computer Graphics Forum, 19(3), 457-465. doi:10.1111/1467-8659.00438Baik, A., Yaagoubi, R., & Boehm, J. (2015). 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Reconstruction with Voronoi Centered Radial Basis Functions

The dinosaur model is courtesy of Cyberware, other models being courtesy of the AIM@SHAPE shape repositoryWe consider the problem of reconstructing a surface from scattered points sampled on a physical shape. The sampled shape is approximated as the zero level set of a function. This function is defined as a linear combination of compactly supported radial basis functions. We depart from previous work by using as centers of basis functions a set of points located on an estimate of the medial axis, instead of the input data points. Those centers are selected among the vertices of the Voronoi diagram of the sample data points. Being a Voronoi vertex, each center is associated with a maximal empty ball. We use the radius of this ball to adapt the support of each radial basis function. Our method can fit a user-defined budget of centers: The selected subset of Voronoi vertices is filtered using the notion of lambda medial axis, then clustered to fit the allocated budget

Graph matching a skeletonized theoretical morphospace with a cladogram for gomphonemoid-cymbelloid diatoms (Bacillariophyta)

A three-dimensional (3D) theoretical morphospace of gomphonemoid and cymbelloid diatoms was skeletonized using concepts from extended Reeb graph analysis and Morse theory. The resultant skeleton tree was matched to a cladogram of the same group of related taxa using adjacency matrices of the trees and ordinated with multidimensional scaling (MDS) of leaf nodes. From this, an unweighted path matrix based on the number of branches between leaf nodes was ordinated to determine degree of matched tree structures. A constrained MDS of the path matrix, weighted by ranked MDS leaf node groups as facets, was used to interpret taxon environmental tolerances and habitat preferences with respect to adaptive value. The methods developed herein provided a way to combine results from morphological and phylogenetic analyses and interpret those results with respect to an aspect of evolutionary process, namely, adaptation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83675/1/JLP-JBS2011.pdf-

Surface Reconstruction from Unorganized Point Cloud Data via Progressive Local Mesh Matching

This thesis presents an integrated triangle mesh processing framework for surface reconstruction based on Delaunay triangulation. It features an innovative multi-level inheritance priority queuing mechanism for seeking and updating the optimum local manifold mesh at each data point. The proposed algorithms aim at generating a watertight triangle mesh interpolating all the input points data when all the fully matched local manifold meshes (umbrellas) are found. Compared to existing reconstruction algorithms, the proposed algorithms can automatically reconstruct watertight interpolation triangle mesh without additional hole-filling or manifold post-processing. The resulting surface can effectively recover the sharp features in the scanned physical object and capture their correct topology and geometric shapes reliably. The main Umbrella Facet Matching (UFM) algorithm and its two extended algorithms are documented in detail in the thesis. The UFM algorithm accomplishes and implements the core surface reconstruction framework based on a multi-level inheritance priority queuing mechanism according to the progressive matching results of local meshes. The first extended algorithm presents a new normal vector combinatorial estimation method for point cloud data depending on local mesh matching results, which is benefit to sharp features reconstruction. The second extended algorithm addresses the sharp-feature preservation issue in surface reconstruction by the proposed normal vector cone (NVC) filtering. The effectiveness of these algorithms has been demonstrated using both simulated and real-world point cloud data sets. For each algorithm, multiple case studies are performed and analyzed to validate its performance