CSGNet: Neural Shape Parser for Constructive Solid Geometry

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on shape primitives defined recursively. Bottom-up techniques for this shape parsing task rely on primitive detection and are inherently slow since the search space over possible primitive combinations is large. In contrast, our model uses a recurrent neural network that parses the input shape in a top-down manner, which is significantly faster and yields a compact and easy-to-interpret sequence of modeling instructions. Our model is also more effective as a shape detector compared to existing state-of-the-art detection techniques. We finally demonstrate that our network can be trained on novel datasets without ground-truth program annotations through policy gradient techniques.Comment: Accepted at CVPR-201

Voxelization of Free-Form Solids Represented by Catmull-Clark Subdivision Surfaces

www.cs.uky.edu/∼cheng Abstract. A voxelization technique and its applications for objects with arbitrary topology are presented. It converts a free-form object from its continuous geometric representation into a set of voxels that best approximates the geometry of the object. Unlike traditional 3D scan-conversion based methods, our voxelization method is performed by recursively subdividing the 2D parameter space and sampling 3D points from selected 2D parameter space points. Moreover, our voxelization of 3D closed objects is guaranteed to be leak-free when a 3D flooding operation is performed. This is ensured by proving that our voxelization results satisfy the properties of separability, accuracy and minimality.

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

BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples

A voxel-based method of constructing and skinning conformal and functionally graded lattice structures suitable for additive manufacturing

Additive Manufacturing (AM) enables the production of geometrically complex parts that are difficult to manufacture by other means. However, conventional CAD systems are limited in the representation of such parts. This issue is exacerbated when lattice structures are combined or embedded within a complex geometry. This paper presents a computationally efficient, voxel-based method of generating lattices comprised of practically any cell type that can conform to an arbitrary external geometry. The method of conforming involves the tessellation and trimming of unit cells that can leave ‘hanging’ struts at the surface, which is a possible point of weakness in the structure. A method of joining these struts to form an external two dimensional lattice, termed a ‘net-skin’ is also described. Traditional methods of manufacturing lattice structures generally do not allow variation of cell properties within a structure; however, additive manufacturing enables graded lattices to be generated that are potentially more optimal. A method of functionally grading lattices is, therefore, also described to take advantage of this manufacturing capability

Extracting datums to reconstruct CSG models from 2D engineering sketches of polyhedral shapes

Our goal is to automatically generate CAD 3D models from 2D sketches as part of a design chain where models should be procedural, containing features arranged in a model tree and linked to suitable datums. Current procedural models capture much about the design intent and are easy to edit, but must be created from scratch during the detailed design state—given conceptual sketches as used by designers in the early part of the design process, current sketch-based modeling approaches only output explicit models. Thus, we describe an approach to extract high-level information directly from 2D engineering wireframe sketches and use it to complete a CSG feature tree, which serves as a model tree for a procedural 3D CAD model. Our method extracts procedural model information directly from 2D sketches in the form of a set of features, plus a set of datums and relationships between these features. We detect and analyze features of 2D sketches in isolation, and define the CSG feature tree by the parent–child relationships between features, and combine this information to obtain a complete and consistent CSG feature tree that can be transferred to a 3D modeler, which reconstructs the model. This paper focuses on how to extract the feature datums and the extrusion operation from an input 2D sketch.Funding for open access charge: CRUE-Universitat Jaume

An Exact Representation of Polygonal Objects by C1-continuous Scalar Fields Based on Binary Space Partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of function-based modelling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples