VC-Dimension of Exterior Visibility

In this paper, we study the Vapnik-Chervonenkis (VC)-dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VC-dimension of planar visibility systems is bounded by 23 if the cameras are allowed to be anywhere inside a polygon without holes [1]. Here, we consider the case of exterior visibility, where the cameras lie on a constrained area outside the polygon and have to observe the entire boundary. We present results for the cases of cameras lying on a circle containing a polygon (VC-dimension= 2) or lying outside the convex hull of a polygon (VC-dimension= 5). The main result of this paper concerns the 3D case: We prove that the VC-dimension is unbounded if the cameras lie on a sphere containing the polyhedron, hence the term exterior visibility

Solid reconstruction using recognition of quadric surfaces from orthographic views

International audienceThe reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided

Entropic Bonding in Nanoparticle and Colloidal Systems

Scientists and engineers will create the next generation of materials by precisely controlling their microstructure. One of the most promising and effective methods to control material microstructure is self-assembly, in which the properties of constituent “particles” guide their assembly into the desired structure. Self- assembly mechanisms rely on both inherent interactions between particles and emergent interactions resulting from the collective effects of all particles in the system. These emergent effects are of interest as they provide minimal mechanisms to control self-assembly, and thus can be used in conjunction with other assembly methods to create novel materials. Literature shows that complex phases can be obtained solely from hard, anisotropic particles, which are attracted via an emergent Directional Entropic Force. This thesis shows that this force gives rise to the entropic bond, a mesoscale analog to the chemical bond. In Chapter 3 I investigate the self- assembly of a system from a random tiling into an ordered crystal. Analysis of the emergent directional entropic forces reveal the importance of shape in the final self-assembled system as well as the ability for shape manipulation to control the final self-assembled structure. In Chapter 4, I investigate three-dimensional analogs of two-dimensional systems in Chapter 3, explaining the self-assembly behavior of these systems via understanding of the emergent directional entropic forces. In Chapter 5 I investigate the nature of the entropic bond, investigating two-dimensional systems of hexagonal nanoplatelets. The Entropic bond is quantified, and the ability to manipulate the bonds to produce similar self- assembly behavior to chemically-functionalized nanoparticles is demonstrated. Finally, Chapter 6 investigates the phase transitions of the general class of particle studied in Chapter 5, showing the ability for particle shape to change the type of phase transition present in a system of nanoparticles as well as stabilize phases otherwise not found. As a whole, this work details the nature of the entropic bond and its use in directing the self-assembly of systems of non- interacting anisotropic particles.PHDMaterials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144096/1/harperic_1.pd

Variable Resolution & Dimensional Mapping For 3d Model Optimization

Three-dimensional computer models, especially geospatial architectural data sets, can be visualized in the same way humans experience the world, providing a realistic, interactive experience. Scene familiarization, architectural analysis, scientific visualization, and many other applications would benefit from finely detailed, high resolution, 3D models. Automated methods to construct these 3D models traditionally has produced data sets that are often low fidelity or inaccurate; otherwise, they are initially highly detailed, but are very labor and time intensive to construct. Such data sets are often not practical for common real-time usage and are not easily updated. This thesis proposes Variable Resolution & Dimensional Mapping (VRDM), a methodology that has been developed to address some of the limitations of existing approaches to model construction from images. Key components of VRDM are texture palettes, which enable variable and ultra-high resolution images to be easily composited; texture features, which allow image features to integrated as image or geometry, and have the ability to modify the geometric model structure to add detail. These components support a primary VRDM objective of facilitating model refinement with additional data. This can be done until the desired fidelity is achieved as practical limits of infinite detail are approached. Texture Levels, the third component, enable real-time interaction with a very detailed model, along with the flexibility of having alternate pixel data for a given area of the model and this is achieved through extra dimensions. Together these techniques have been used to construct models that can contain GBs of imagery data

A system that learns to recognize 3-D objects

A system that learns to recognize 3-D objects from single and multiple views is presented. It consists of three parts: a simulator of 3-D figures, a Learner, and a recognizer. The 3-D figure simulator generates and plots line drawings of certain 3-D objects. A series of transformations leads to a number of 2-D images of a 3-D object, which are considered as different views and are the basic input to the next two parts. The learner works in three stages using the method of Learning from examples. In the first stage an elementary-concept learner learns the basic entities that make up a line drawing. In the second stage a multiple-view learner learns the definitions of 3-D objects that are to be recognized from multiple views. In the third stage a single-view learner learns how to recognize the same objects from single views. The recognizer is presented with line drawings representing 3-D scenes. A single-view recognizer segments the input into faces of possible 3-D objects, and attempts to match the segmented scene with a set of single-view definitions of 3-D objects. The result of the recognition may include several alternative answers, corresponding to different 3-D objects. A unique answer can be obtained by making assumptions about hidden elements (e. g. faces) of an object and using a multiple-view recognizer. Both single-view and multiple-view recognition are based on the structural relations of the elements that make up a 3-D object. Some analytical elements (e. g. angles) of the objects are also calculated, in order to determine point containment and conveziti. The system performs well on polyhedra with triangular and quadrilateral faces. A discussion of the system's performance and suggestions for further development is given at the end. The simulator and the part of the recognizer that makes the analytical calculations are written in C. The learner and the rest of the recognizer are written in PROLOG

View generated database

This document represents the final report for the View Generated Database (VGD) project, NAS7-1066. It documents the work done on the project up to the point at which all project work was terminated due to lack of project funds. The VGD was to provide the capability to accurately represent any real-world object or scene as a computer model. Such models include both an accurate spatial/geometric representation of surfaces of the object or scene, as well as any surface detail present on the object. Applications of such models are numerous, including acquisition and maintenance of work models for tele-autonomous systems, generation of accurate 3-D geometric/photometric models for various 3-D vision systems, and graphical models for realistic rendering of 3-D scenes via computer graphics

Perception of 3-D Surfaces from 2-D Contours

Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. We survey classes of techniques proposed in the past and provide a critical analysis. We propose that two kinds of symmetries in figures, which are known as parallel and skew symmetries, give significant information about surface shape for a variety of objects. We derive the constraints imposed by these symmetries and show how to use them to infer 3-D shape. We discuss the zero Gaussian curvature (ZGC) surfaces in depth and show results on the recovery of surface orientation for various ZGC surfaces. © 1993 IEE

GPU voxelization

Given a triangulated model, we want to identify which voxels of a voxel grid are intersected by the boundary of this model. There are other branch of implemented voxelizations, in which not only the boundary is detected, also the interior of the model. Often these voxels are cubes. But it is not a restriction, there are other presented techniques in which the voxel grid is the view frustum, and voxels are prisms. There are di erent kind of voxelizations depending on the rasterization behavior. Approximate rasterization is the standard way of rasterizing fragments in GPU. It means only those fragments whose center lies inside the projection of the primitive are identi ed. Conservative rasterization (Hasselgren et al. , 2005) involves a dilation operation over the primitive. This is done in GPU to ensure that in the rasterization stage all the intersected fragments have its center inside the dilated primitive. However, this can produce spurious fragments, non-intersected pixels. Exact voxelization detects only those voxels that we need.

The investigation of a method to generate conformal lattice structures for additive manufacturing

Additive manufacturing (AM) allows a geometric complexity in products not seen in conventional manufacturing. This geometric freedom facilitates the design and fabrication of conformal hierarchical structures. Entire parts or regions of a part can be populated with lattice structure, designed to exhibit properties that differ from the solid material used in fabrication. Current computer aided design (CAD) software used to design products is not suitable for the generation of lattice structure models. Although conceptually simple, the memory requirements to store a virtual CAD model of a lattice structure are prohibitively high. Conventional CAD software defines geometry through boundary representation (B-rep); shapes are described by the connectivity of faces, edges and vertices. While useful for representing accurate models of complex shape, the sheer quantity of individual surfaces required to represent each of the relatively simple individual struts that comprise a lattice structure ensure that memory limitations are soon reached. Additionally, the conventional data flow from CAD to manufactured part is arduous, involving several conversions between file formats. As well as a lengthy process, each conversion risks the generation of geometric errors that must be fixed before manufacture. A method was developed to specifically generate large arrays of lattice structures, based on a general voxel modelling method identified in the literature review. The method is much less sensitive to geometric complexity than conventional methods and thus facilitates the design of considerably more complex structures. The ability to grade structure designs across regions of a part (termed functional grading ) was also investigated, as well as a method to retain connectivity between boundary struts of a conformal structure. In addition, the method streamlines the data flow from design to manufacture: earlier steps of the data conversion process are bypassed entirely. The effect of the modelling method on surface roughness of parts produced was investigated, as voxel models define boundaries with discrete, stepped blocks. It was concluded that the effect of this stepping on surface roughness was minimal. This thesis concludes with suggestions for further work to improve the efficiency, capability and usability of the conformal structure method developed in this work