QuickCSG: Fast Arbitrary Boolean Combinations of N Solids

QuickCSG computes the result for general N-polyhedron boolean expressions without an intermediate tree of solids. We propose a vertex-centric view of the problem, which simplifies the identification of final geometric contributions, and facilitates its spatial decomposition. The problem is then cast in a single KD-tree exploration, geared toward the result by early pruning of any region of space not contributing to the final surface. We assume strong regularity properties on the input meshes and that they are in general position. This simplifying assumption, in combination with our vertex-centric approach, improves the speed of the approach. Complemented with a task-stealing parallelization, the algorithm achieves breakthrough performance, one to two orders of magnitude speedups with respect to state-of-the-art CPU algorithms, on boolean operations over two to dozens of polyhedra. The algorithm also outperforms GPU implementations with approximate discretizations, while producing an output without redundant facets. Despite the restrictive assumptions on the input, we show the usefulness of QuickCSG for applications with large CSG problems and strong temporal constraints, e.g. modeling for 3D printers, reconstruction from visual hulls and collision detection

QuickCSG: Fast Arbitrary Boolean Combinations of N Solids

QuickCSG computes the result for general N-polyhedron boolean expressions without an intermediate tree of solids. We propose a vertex-centric view of the problem, which simplifies the identification of final geometric contributions, and facilitates its spatial decomposition. The problem is then cast in a single KD-tree exploration, geared toward the result by early pruning of any region of space not contributing to the final surface. We assume strong regularity properties on the input meshes and that they are in general position. This simplifying assumption, in combination with our vertex-centric approach, improves the speed of the approach. Complemented with a task-stealing parallelization, the algorithm achieves breakthrough performance, one to two orders of magnitude speedups with respect to state-of-the-art CPU algorithms, on boolean operations over two to dozens of polyhedra. The algorithm also outperforms GPU implementations with approximate discretizations, while producing an output without redundant facets. Despite the restrictive assumptions on the input, we show the usefulness of QuickCSG for applications with large CSG problems and strong temporal constraints, e.g. modeling for 3D printers, reconstruction from visual hulls and collision detection

Subdivision Surface based One-Piece Representation

Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject\u27s topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications

Solid modelling for manufacturing: from Voelcker's boundary evaluation to discrete paradigms

Herb Voelcker and his research team laid the foundations of Solid Modelling, on which Computer-Aided Design is based. He founded the ambitious Production Automation Project, that included Constructive Solid Geometry (CSG) as the basic 3D geometric representation. CSG trees were compact and robust, saving a memory space that was scarce in those times. But the main computational problem was Boundary Evaluation: the process of converting CSG trees to Boundary Representations (BReps) with explicit faces, edges and vertices for manufacturing and visualization purposes. This paper presents some glimpses of the history and evolution of some ideas that started with Herb Voelcker. We briefly describe the path from “localization and boundary evaluation” to “localization and printing”, with many intermediate steps driven by hardware, software and new mathematical tools: voxel and volume representations, triangle meshes, and many others, observing also that in some applications, voxel models no longer require Boundary Evaluation. In this last case, we consider the current research challenges and discuss several avenues for further research.Project TIN2017-88515-C2-1-R funded by MCIN/AEI/10.13039/501100011033/FEDER‘‘A way to make Europe’’Peer ReviewedPostprint (published version

Virtual reality based creation of concept model designs for CAD systems

This work introduces a novel method to overcome most of the drawbacks in traditional methods for creating design models. The main innovation is the use of virtual tools to simulate the natural physical environment in which freeform. Design models are created by experienced designers. Namely, the model is created in a virtual environment by carving a work piece with tools that simulate NC milling cutters. Algorithms have been developed to support the approach, in which the design model is created in a Virtual Reality (VR) environment and selection and manipulation of tools can be performed in the virtual space. The desianer\u27s hand movements generate the tool trajectories and they are obtained by recording the position and orientation of a hand mounted motion tracker. Swept volumes of virtual tools are generated from the geometry of the tool and its trajectories. Then Boolean operations are performed on the swept volumes and the initial virtual stock (work piece) to create the design model. Algorithms have been developed as a part of this work to integrate the VR environment with a commercial CAD/CAM system in order to demonstrate the practical applications of the research results. The integrated system provides a much more efficient and easy-to-implement process of freeform model creation than employed in current CAD/CAM software. It could prove to be the prototype for the next-generation CAD/CAM system

A Method of Rendering CSG-Type Solids Using a Hybrid of Conventional Rendering Methods and Ray Tracing Techniques

This thesis describes a fast, efficient and innovative algorithm for producing shaded, still images of complex objects, built using constructive solid geometry ( CSG ) techniques. The algorithm uses a hybrid of conventional rendering methods and ray tracing techniques. A description of existing modelling and rendering methods is given in chapters 1, 2 and 3, with emphasis on the data structures and rendering techniques selected for incorporation in the hybrid method. Chapter 4 gives a general description of the hybrid method. This method processes data in the screen coordinate system and generates images in scan-line order. Scan lines are divided into spans (or segments) using the bounding rectangles of primitives calculated in screen coordinates. Conventional rendering methods and ray tracing techniques are used interchangeably along each scan-line. The method used is detennined by the number of primitives associated with a particular span. Conventional rendering methods are used when only one primitive is associated with a span, ray tracing techniques are used for hidden surface removal when two or more primitives are involved. In the latter case each pixel in the span is evaluated by accessing the polygon that is visible within each primitive associated with the span. The depth values (i. e. z-coordinates derived from the 3-dimensional definition) of the polygons involved are deduced for the pixel's position using linear interpolation. These values are used to determine the visible polygon. The CSG tree is accessed from the bottom upwards via an ordered index that enables the 'visible' primitives on any particular scan-line to be efficiently located. Within each primitive an ordered path through the data structure provides the polygons potentially visible on a particular scan-line. Lists of the active primitives and paths to potentially visible polygons are maintained throughout the rendering step and enable span coherence and scan-line coherence to be fully utilised. The results of tests with a range of typical objects and scenes are provided in chapter 5. These results show that the hybrid algorithm is significantly faster than full ray tracing algorithms

Rational tensor product Bézier volumes

AbstractFree form volumes in rational Bézier representation are derived via homogeneous coordinates. Some properties and constructions are presented and two applications of free form volumes are discussed: definition of solid primitives and curve and surface modelling by the way of volume deformation

Free-form deformation of solid models in CSR.

Lai Chi-fai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 98-99).Abstracts in English and Chinese.Chapter 1. --- INTRODUCTION --- p.7Chapter 1.1 --- Motivations and objectives --- p.7Chapter 1.2 --- Thesis Organization --- p.10Chapter 2. --- related works --- p.11Chapter 2.1 --- Deformation Techniques --- p.11Chapter 2.1.1 --- Deformation techniques requiring a deformation tool --- p.11Chapter 2.1.2 --- Directly specified deformation techniques --- p.14Chapter 2.1.3 --- Comparison on Different Deformation Technique --- p.15Chapter 2.2 --- Application of Deformation --- p.16Chapter 2.2.1 --- Deforming superquadrics --- p.16Chapter 2.2.2 --- Volume wraping --- p.16Chapter 2.2.3 --- Deforming linear object --- p.17Chapter 2.2.4 --- FFD for animation synthesis --- p.17Chapter 2.2.5 --- Using FFD on feature-based Surface --- p.18Chapter 2.2.6 --- NURBS-BASED Free-Form Deformation (NFFD) --- p.18Chapter 2.3 --- Algebraic Patch Techniques --- p.20Chapter 2.3.1 --- Dahmen's scheme --- p.20Chapter 2.3.2 --- Lodha and Warren's technique --- p.20Chapter 2.3.3 --- Guo's method --- p.21Chapter 3. --- BACKGROUND THEORIES --- p.22Chapter 3.1 --- Algebraic Patches --- p.22Chapter 3.1.1 --- Bernstein-Bezier representation of a single patch --- p.22Chapter 3.1.2 --- Constructing free-form objects --- p.29Chapter 3.1.2.1 --- Bounding volumes for quadric patches --- p.29Chapter 3.1.2.2 --- Filling two-sided gaps --- p.31Chapter 3.2 --- Constructive Shell Representation --- p.35Chapter 3.2.1 --- Properties of quadric patches and its construction tetrahedron and trunctets --- p.38Chapter 3.3 --- Free-Form Deformation --- p.40Chapter 3.3.1 --- Formulating free-form deformation --- p.40Chapter 4. --- FREE-FORM DEFORMATION OF CSR SOLID MODELS --- p.43Chapter 4.1 --- Determination of Lattice Structure --- p.43Chapter 4.2 --- "Relation between weights, normals and shape of a trunctet" --- p.46Chapter 4.3 --- Applying FFD on CSR solid models --- p.49Chapter 4.3.1 --- Deforming normal at vertices --- p.52Chapter 4.3.2 --- Using vertices' neighborhoods --- p.54Chapter 4.4 --- Free-Form Deformation of CSR objects by Surface Fitting --- p.57Chapter 4.4.1 --- Deforming a single surface patch --- p.57Chapter 4.4.1.1 --- Locating surface points --- p.59Chapter 4.4.1.2 --- Conversion between barycentric and Cartesian coordinates --- p.61Chapter 4.4.1.3 --- Evaluating the deformed surface patch --- p.62Chapter 4.4.1.4 --- Saddle shape trunctet --- p.64Chapter 4.4.1.5 --- Using double tetrahedrons --- p.66Chapter 4.4.1.6 --- Surface subdivision --- p.69Chapter 4.4.2 --- Deforming Entire Solid Model --- p.72Chapter 4.4.3 --- Comparison on different approaches --- p.75Chapter 4.5 --- Conversion of CSG solid Models into CSR --- p.76Chapter 4.5.1 --- Converting halfspaces into CSR objects --- p.77Chapter 5. --- IMPLEMENTATION AND RESULTS --- p.82Chapter 5.1 --- Implementation --- p.82Chapter 5.2 --- Experimental Results --- p.84Chapter 6. --- CONCLUSION AND SUGGESTIONS FOR FURTHER WORK --- p.93Chapter 6.1 --- Conclusion --- p.93Chapter 6.2 --- Suggestions for further work --- p.9