Subdivision surface fitting to a dense mesh using ridges and umbilics

Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach

Application des surfaces de Bézier pour la reconstruction 3-D

Dans ce travail, nous présentons une méthode de reconstruction 3-D basée sur l’utilisation des surfaces de Bézier, combinée au lissage tridimensionnel. L’idée principale est de générer, à partir d’un nuage de points issus de la numérisation d’un objet 3-D, une représentation de surfaces à partir de la quelle nous procédons à la reconstruction 3-D de l’objet en question. Ensuite nous présentons les résultats de notre méthode appliquées à quelques objets

Subdivide and Conquer: Adapting Non-Manifold Subdivision Surfaces to Surface-Based Representation and Reconstruction of Complex Geological Structures

Methods from the field of computer graphics are the foundation for the representation of geological structures in the form of geological models. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered, and the capacities and limitations of different algorithms are not always evident. In this work, we therefore review surface-based geological modelling methods from both a geological and computer graphics perspective. Specifically, we investigate the use of NURBS (non-uniform rational B-splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of the two approaches. Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention—even if subdivision surfaces support arbitrary topologies and watertight boundary representation, two aspects that make them an appealing choice for complex geological modelling. It is worth mentioning that watertight models are an important basis for subsequent process simulations. Many complex geological structures require a combination of smooth and sharp edges. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterise the resistance of a mesh structure to the subdivision procedure. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology, is described. Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison with the complex geological structure

Scientific visualizations

Visualizations for three different categories of problems are presented: measurements of object parameters as they vary over time, constructing surfaces from unorganized sets of points, and representing the internal structure of volumes using isosurfaces. Problem backgrounds are discussed as well as the operational details of each visualization. Visualizations were written with ease of use in mind for Spiegel, a programmable visualization environment

Reconstruction locale et visualisation de nuages de points par surfaces de subdivision

National audienceLes surfaces de points, qu'elles soient directement acquises par scanner ou issues de la conversion d'autres modèles, permettent de stocker et de transmettre des objets complexes de manière économique, mais sont mal adaptées aux architectures matérielles existantes qui s'appuient sur une description géométrique à base de surfaces polygonales. Cet article propose une technique permettant d'obtenir une visualisation efficace des surfaces de points, entièrement à l'aide du pipeline de rendu matériel. L'idée centrale présentée ici est d'effectuer une reconstruction surfacique locale par triangulation d'un nuage de points, en générant un agrégat de 2-variétés se recouvrant, et en procurant une continuité visuelle dans les zones de recouvrements à l'aide des surfaces de subdivision

Intuitive freeform modeling using subdivision surfaces.

Lai Yuen-hoo.Thesis submitted in: November 2004.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 100-102).Abstracts in English and Chinese.Abstract --- p.i摘要 --- p.iiAcknowledgment --- p.iiiList of Figures --- p.ivTable of Content --- p.viiChapter 1. --- Introduction --- p.1Chapter 1.1. --- Problem Definition --- p.1Chapter 1.2. --- Proposed Solution --- p.2Chapter 1.3. --- Thesis Contributions --- p.2Chapter 2. --- Modeling Approaches --- p.4Chapter 2.1. --- Polygon Modeling --- p.4Chapter 2.2. --- Patch Modeling --- p.6Chapter 2.3. --- Freehand Sketch-based Modeling --- p.7Chapter 2.4. --- Template Based Modeling --- p.8Chapter 2.5. --- Curve Interpolation Method --- p.9Chapter 3. --- Surface Operations --- p.11Chapter 3.1. --- Surface Blending --- p.11Chapter 3.2. --- Surface Trimming --- p.13Chapter 3.3. --- Boolean Operations --- p.14Chapter 4. --- Subdivision Surface --- p.16Chapter 4.1. --- Basic Principle --- p.16Chapter 4.2. --- Catmull-Clark Surface --- p.17Chapter 5. --- Modeling Algorithm Overview --- p.21Chapter 6. --- Subdivision Surface Generation --- p.23Chapter 6.1. --- Input Curves --- p.23Chapter 6.2. --- Surface Sweeping --- p.24Chapter 6.3. --- Subdivision Surface Fitting --- p.29Chapter 7. --- Surface Blending --- p.32Chapter 7.1. --- Introduction --- p.32Chapter 7.2. --- Problem Definition --- p.32Chapter 7.3. --- Algorithm Overview --- p.36Chapter 7.4. --- Blend Region Detection --- p.39Chapter 7.4.1. --- Collision Detection --- p.40Chapter 7.4.2. --- Result and Analysis --- p.42Chapter 7.5. --- "Mesh Refinement, Surface Fitting and Region Removal" --- p.46Chapter 7.5.1. --- Mesh Refinement --- p.46Chapter 7.5.1.1. --- Adaptive Subdivision --- p.46Chapter 7.5.1.2. --- Additional Subdivision Constraint --- p.47Chapter 7.5.2. --- Surface Fitting --- p.49Chapter 7.5.2.1. --- General Approach --- p.49Chapter 7.5.2.2. --- Surface Point Correspondence --- p.50Chapter 7.5.2.3. --- Numerical Fitting Method --- p.51Chapter 7.5.3. --- Unwanted Region Removal --- p.55Chapter 7.5.4. --- Result and Analysis --- p.56Chapter 7.6. --- Boundary Smoothing --- p.58Chapter 7.6.1. --- General Approach --- p.59Chapter 7.6.2. --- Constraint on Deformation Direction of Vertex --- p.61Chapter 7.6.3. --- Result and Analysis --- p.63Chapter 7.7. --- Blend Curves --- p.65Chapter 7.7.1. --- Problem Definition --- p.65Chapter 7.7.2. --- Proposed Solution Overview --- p.66Chapter 7.7.3. --- Maintenance of Regular Vertex Valence along Blend Curve --- p.67Chapter 7.7.3.1. --- Pairing Up Blend Boundary Vertices --- p.70Chapter 7.7.4. --- Minimization of Distortion Caused by Extraordinary Vertices --- p.72Chapter 7.7.5. --- Blend Vertex Position Optimization Function --- p.74Chapter 7.7.5.1. --- Face Normal Expression --- p.74Chapter 7.7.5.2. --- Face Normal Difference Energy Function --- p.77Chapter 7.7.5.3. --- Midpoint Distance Energy Function --- p.78Chapter 7.7.5.4. --- Weighted Least Square Energy Minimization --- p.78Chapter 8. --- Implementation --- p.81Chapter 8.1. --- Data Structure --- p.81Chapter 8.2. --- User Interface --- p.82Chapter 9. --- Results --- p.83Chapter 9.1. --- Surface Generation --- p.83Chapter 9.2. --- Surface Blending --- p.86Chapter 9.2.1. --- Ideal Case --- p.86Chapter 9.2.2. --- Angle of Insertion --- p.87Chapter 9.2.3. --- Surface Feature Near Intersection --- p.88Chapter 9.2.4. --- Comparison --- p.89Chapter 9.2.5. --- Other Examples --- p.92Chapter 9.3. --- Overall Performance --- p.94Chapter 9.4. --- Limitations --- p.97Chapter 9.4.1. --- Limitation on Generated Shape --- p.97Chapter 9.4.2. --- Limitation on Input Surfaces --- p.98Chapter 10. --- Conclusion and Future Work --- p.99References --- p.10