Converting Hybrid Wire-frames to B-rep Models

International audienceSolid reconstruction from engineering drawings is one of the efficient technologies to product solid models. The B-rep oriented approach provides a practical way for reconstructing a wide range of objects. However, its major limitation is the computational complexity involved in the search for all valid faces from the intermediate wire-frame, especially for objects with complicated face topologies. In previous work, we presented a hint-based algorithm to recognize quadric surfaces from orthographic views and generate a hybrid wire-frame as the intermediate model of our B-rep oriented method. As a key stage in the process of solid reconstructing, we propose an algorithm to convert the hybrid wire-frame to the final B-rep model by extracting all the rest faces of planes based on graph theory. The entities lying on the same planar surface are first collected in a plane graph. After all the cycles are traced in a simplified edge-adjacency matrix of the graph, the face loops of the plane are formed by testing loop containment and assigning loop directions. Finally, the B-rep model is constructed by sewing all the plane faces based on the M¨obius rule. The method can efficiently construct 2- manifold objects with a variety of face topologies, which is illustrated by results of implementatio

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

3D reconstruction of curved objects from single 2D line drawings.

Wang, Yingze.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 42-47).Abstract also in Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Related Work --- p.5Chapter 2.1 --- Line labeling and realization problem --- p.5Chapter 2.2 --- 3D reconstruction from multiple views --- p.6Chapter 2.3 --- 3D reconstruction from single line drawings --- p.7Chapter 2.3.1 --- Face identification from the line drawings --- p.7Chapter 2.3.2 --- 3D geometry reconstruction --- p.9Chapter 2.4 --- Our research topic and contributions --- p.13Chapter 3 --- Reconstruction of Curved Manifold Objects --- p.14Chapter 3.1 --- Assumptions and terminology --- p.14Chapter 3.2 --- Reconstruction of curved manifold objects --- p.17Chapter 3.2.1 --- Distinguishing between curved and planar faces --- p.17Chapter 3.2.2 --- Transformation of Line Drawings --- p.20Chapter 3.2.3 --- Regularities --- p.23Chapter 3.2.4 --- 3D Wireframe Reconstruction --- p.26Chapter 3.2.5 --- Generating Curved Faces --- p.28Chapter 3.2.6 --- The Complete 3D Reconstruction Algorithm --- p.33Chapter 4 --- Experiments --- p.35Chapter 5 --- Conclusions and Future Work --- p.40Chapter 5.1 --- Conclusions --- p.40Chapter 5.2 --- Future work --- p.40Bibliography --- p.4

Passive method for 3D reconstruction of human jaw: theory and application.

Oral dental applications based on visual data pose various challenges. There are problems with lighting (effect of saliva, tooth dis-colorization, gum texture, and other sources of specularity) and motion (even inevitable slight motions of the upper/ lower jaw may lead to errors far beyond the desired tolerance of sub-millimeter accuracy). Nowadays, the dental CAM systems have become more compromised and accurate to obtain the geometric data of the jaw from the active sensor (laser scanner). However, they have not met the expectations and the needs of dental professionals in many ways. The probes in these systems are bulky { even their newer versions - and are hard to maneuver. It requires multiple scans to get full coverage of the oral cavity. In addition, the dominant drawback of these systems is the cost. Stereo-based 3D reconstruction provides the highest accuracy among vision systems of this type. However, the evaluation of it\u27s performance for both accuracy results and the number of 3D points that are reconstructed would be affected by the type of the application and the quality of the data that is been acquired from the object of interest. Therefore, in this study, the stereo-based 3D reconstruction will vi be evaluated for the dental application. The handpiece of sensors holder would reach to areas inside the oral cavity, the gap between the tooth in the upper jaw and the tooth in the lower jaw in these areas would be very small, in such the stereo algorithms would not be able to reconstruct the tooth in that areas because of the distance between the optical sensors and the object of interest \tooth as well as the configuration of optical sensors are contradicted the geometric constraint roles of the stereo-based 3D reconstruction. Therefore, the configuration of the optical sensors as well as the number of sensors in the hand piece of sensors holder will be determined based on the morphological of the teeth surfaces. In addition to the 3D reconstruction, the panoramic view of a complete arch of human teeth will be accomplished as an application of dental imaging. Due to the low rate of features on teeth surfaces, the normal tooth surface is extracted using shape from shading. The extracted surface normals impact many imprecise values because of the oral environment; hence an algorithm is being formulated to rectify these values and generate normal maps. The normal maps reveal the impacted geometric properties of the images inside an area, boundary, and shape. Furthermore, the unrestricted camera movement problem is investigated. The camera may be moved along the jaw curve with different angles and distances due to handshaking. To overcome this problem, each frame is tested after warping it, and only correct frames are used to generate the panoramic view. The proposed approach outperforms comparing to the state-of-art auto stitching method

3D model reconstruction from vector perpendicular projections

This scientific monograph deals with the issue of 3D model reconstruction of a rotation part from its orthogonal projections recorded on a digitalized drawing in vector format and with computer-aided automation of the process. The topic is a partial task of the domain focused on generating the 3D part model or product from a technical drawing. The introduction comments on the analysis of the current state of information in the field. The rules of projecting the parts in a technical drawing are described as well as the related terminology and methods in computer graphics, mathematics and geometry. The computer-aided ways of modeling solids are analyzed. The introductory part is complemented by an overview of existing solutions by other authors and by the possibilities of my own method development. The monograph core is focused on the proposal of proceedings and algorithms for transformation process automation of 2D vector record comprising orthogonal projections representing the rotation part on a 3D model. The pilot implementations of algorithms and their verification by testing on the selected sample of geometric shapes are added

Parameter optimization and learning for 3D object reconstruction from line drawings.

Du, Hao.Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.Includes bibliographical references (p. 61).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- 3D Reconstruction from 2D Line Drawings and its Applications --- p.1Chapter 1.2 --- Algorithmic Development of 3D Reconstruction from 2D Line Drawings --- p.3Chapter 1.2.1 --- Line Labeling and Realization Problem --- p.4Chapter 1.2.2 --- 3D Reconstruction from Multiple Line Drawings --- p.5Chapter 1.2.3 --- 3D Reconstruction from a Single Line Drawing --- p.6Chapter 1.3 --- Research Problems and Our Contributions --- p.12Chapter 2 --- Adaptive Parameter Setting --- p.15Chapter 2.1 --- Regularities in Optimization-Based 3D Reconstruction --- p.15Chapter 2.1.1 --- Face Planarity --- p.18Chapter 2.1.2 --- Line Parallelism --- p.19Chapter 2.1.3 --- Line Verticality --- p.19Chapter 2.1.4 --- Isometry --- p.19Chapter 2.1.5 --- Corner Orthogonality --- p.20Chapter 2.1.6 --- Skewed Facial Orthogonality --- p.21Chapter 2.1.7 --- Skewed Facial Symmetry --- p.22Chapter 2.1.8 --- Line Orthogonality --- p.24Chapter 2.1.9 --- Minimum Standard Deviation of Angles --- p.24Chapter 2.1.10 --- Face Perpendicularity --- p.24Chapter 2.1.11 --- Line Collinearity --- p.25Chapter 2.1.12 --- Whole Symmetry --- p.25Chapter 2.2 --- Adaptive Parameter Setting in the Objective Function --- p.26Chapter 2.2.1 --- Hill-Climbing Optimization Technique --- p.28Chapter 2.2.2 --- Adaptive Weight Setting and its Explanations --- p.29Chapter 3 --- Parameter Learning --- p.33Chapter 3.1 --- Construction of A Large 3D Object Database --- p.33Chapter 3.2 --- Training Dataset Generation --- p.34Chapter 3.3 --- Parameter Learning Framework --- p.37Chapter 3.3.1 --- Evolutionary Algorithms --- p.38Chapter 3.3.2 --- Reconstruction Error Calculation --- p.39Chapter 3.3.3 --- Parameter Learning Algorithm --- p.41Chapter 4 --- Experimental Results --- p.45Chapter 4.1 --- Adaptive Parameter Setting --- p.45Chapter 4.1.1 --- Use Manually-Set Weights --- p.45Chapter 4.1.2 --- Learn the Best Weights with Different Strategies --- p.48Chapter 4.2 --- Evolutionary-Algorithm-Based Parameter Learning --- p.49Chapter 5 --- Conclusions and Future Work --- p.53Bibliography --- p.5

Interactive visualization tools for topological exploration

Thesis (Ph.D.) - Indiana University, Computer Science, 1992This thesis concerns using computer graphics methods to visualize mathematical objects. Abstract mathematical concepts are extremely difficult to visualize, particularly when higher dimensions are involved; I therefore concentrate on subject areas such as the topology and geometry of four dimensions which provide a very challenging domain for visualization techniques. In the first stage of this research, I applied existing three-dimensional computer graphics techniques to visualize projected four-dimensional mathematical objects in an interactive manner. I carried out experiments with direct object manipulation and constraint-based interaction and implemented tools for visualizing mathematical transformations. As an application, I applied these techniques to visualizing the conjecture known as Fermat's Last Theorem. Four-dimensional objects would best be perceived through four-dimensional eyes. Even though we do not have four-dimensional eyes, we can use computer graphics techniques to simulate the effect of a virtual four-dimensional camera viewing a scene where four-dimensional objects are being illuminated by four-dimensional light sources. I extended standard three-dimensional lighting and shading methods to work in the fourth dimension. This involved replacing the standard "z-buffer" algorithm by a "w-buffer" algorithm for handling occlusion, and replacing the standard "scan-line" conversion method by a new "scan-plane" conversion method. Furthermore, I implemented a new "thickening" technique that made it possible to illuminate surfaces correctly in four dimensions. Our new techniques generate smoothly shaded, highlighted view-volume images of mathematical objects as they would appear from a four-dimensional viewpoint. These images reveal fascinating structures of mathematical objects that could not be seen with standard 3D computer graphics techniques. As applications, we generated still images and animation sequences for mathematical objects such as the Steiner surface, the four-dimensional torus, and a knotted 2-sphere. The images of surfaces embedded in 4D that have been generated using our methods are unique in the history of mathematical visualization. Finally, I adapted these techniques to visualize volumetric data (3D scalar fields) generated by other scientific applications. Compared to other volume visualization techniques, this method provides a new approach that researchers can use to look at and manipulate certain classes of volume data