Incremental feature generation and modification during design evolution

Feature modification in incremental feature generation

This paper presents a unified differentiable boolean operator for implicit solid shape modeling using Constructive Solid Geometry (CSG). Traditional CSG relies on min, max operators to perform boolean operations on implicit shapes. But because these boolean operators are discontinuous and discrete in the choice of operations, this makes optimization over the CSG representation challenging. Drawing inspiration from fuzzy logic, we present a unified boolean operator that outputs a continuous function and is differentiable with respect to operator types. This enables optimization of both the primitives and the boolean operations employed in CSG with continuous optimization techniques, such as gradient descent. We further demonstrate that such a continuous boolean operator allows the modeling of both sharp mechanical objects and smooth organic shapes with the same framework. Our proposed boolean operator opens up new possibilities for future research toward fully continuous CSG optimization.

Ordinary triangular mesh model can be constructed from discrete point cloud. However, this kind of model contains large amount of data. It is not only difficult to split, but also lacks topological relation information. We proposed a CSG---BRep (Constructive Solid Geometry--Boundary Representation) topological model to overcome these problems. CSG---BRep model can record topological relationship of 3D model in great detail. We first introduced aspects of the topological model: location, orientation and sub-shape. Then we proposed two algorithms to access topological structure. We also proposed algorithms for performing Boolean operation on CSG---BRep models. Finally, we demonstrated CSG---BRep construction using LIDAR point cloud as a data source. We would show that, compared to ordinary triangular mesh model, CSG---BRep model is composable and can effectively reduce data volume. In addition, CSG---BRep model has detailed topological relation information, allowing further querying and analysis of 3D spatial topological information.

Face area evaluation algorithm for solids

Solid modeling is the technique for representing and manipulating a complete description of physical objects. Valid representations of solid are developed base on a mathematical description of rigid object. A valid solid representation scheme provides sufficient information for geometric operations on objects, e.g. Boolean operations, collision detection. The description here introduces the Fundamental concepts in solid modeling are introduced. Characteristics of a solid representation scheme are discussed. Two popular solid representation schemes, the constructive solid geometry and the boundary representation schemes, are described. The fundamental algorithms for solid modeling, point membership classification, and Boolean operations, are also discussed. Validity of the boundary representation scheme, the Euler operators, as well as the Winged‐edge data structure for the implementation of boundary representation scheme are also presented.

CAD models serve as the fundamental carriers for representing geometric structures and design logic. Understanding the underlying construction logic of complex shapes facilitates the reuse, editing, and optimization of designs. Constructive Solid Geometry (CSG) offers a viable approach for shape parsing by representing complex geometries through combinations of simple primitives. This paper proposes a novel method for parsing 3D CAD shapes based on CSG representations. Leveraging quadric surfaces as the fundamental modeling primitives, our approach employs a dual-branch architecture— “composition–subtraction”—to construct target 3D shapes via Boolean operations. Each branch receives either voxel grids or point clouds as input and uses an auto-encoder to extract shape features, which are then used to predict a set of intermediate shapes. The final reconstruction is obtained through set difference operations. To enhance the model’s expressive capacity under a fixed Boolean operation sequence, we introduce rotation parameters and dual primitive designs. Moreover, we adopt a staged training framework that progressively guides the model from learning approximate signed distance functions to precise structural modeling. A regularization loss is incorporated to promote geometric diversity and plausibility of the primitives. After training, we further propose a post-processing strategy based on signed distance influence to remove redundant primitives, resulting in more compact and interpretable CSG sequences. Experimental comparisons on the ABC dataset demonstrate that our method reduces the 3D chamfer distance and edge chamfer distance by 72.1% and 31.1%, respectively, and improves the normal vector consistency by 9.48%, compared to SECAD-Net, and achieves better results in visual metrics.

In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C(1)-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation.

Fetuses are extremely radiosensitive and the protection of pregnant females against ionizing radiation is of particular interest in many health and medical physics applications. Existing models of pregnant females relied on simplified anatomical shapes or partial-body images of low resolutions. This paper reviews two general types of solid geometry modeling: constructive solid geometry (CSG) and boundary representation (BREP). It presents in detail a project to adopt the BREP modeling approach to systematically design whole-body radiation dosimetry models: a pregnant female and her fetus at the ends of three gestational periods of 3, 6 and 9 months. Based on previously published CT images of a 7-month pregnant female, the VIP-Man model and mesh organ models, this new set of pregnant female models was constructed using 3D surface modeling technologies instead of voxels. The organ masses were adjusted to agree with the reference data provided by the International Commission on Radiological Protection (ICRP) and previously published papers within 0.5%. The models were then voxelized for the purpose of performing dose calculations in identically implemented EGS4 and MCNPX Monte Carlo codes. The agreements of the fetal doses obtained from these two codes for this set of models were found to be within 2% for the majority of the external photon irradiation geometries of AP, PA, LAT, ROT and ISO at various energies. It is concluded that the so-called RPI-P3, RPI-P6 and RPI-P9 models have been reliably defined for Monte Carlo calculations. The paper also discusses the needs for future research and the possibility for the BREP method to become a major tool in the anatomical modeling for radiation dosimetry.For more information on this article, see medicalphysicsweb.org

The generation of 3-D solid objects, and more generally solid geometric modelling, is very important in Computer Aided Design (CAD). An important role is played by the Constructive Solid Geometry (CSG) representation scheme. In CSG, objects are described by trees of Boolean operations on half-spaces or boundaries of primitive solids. The study of techniques to speed up the rendering of scenes modelled with the CSG scheme is an attractive field of research; in this paper we propose a new algorithm which reduces the computational complexity for ray casting approaches. Our strategy identifies a set of areas on the plane of view where the rays starting from the observer have to be traced; for each zone, only a portion of the entire CSG tree has to be considered for intersection tests, instead of the whole database of the primitive objects. A comparison of our algorithm with a ray caster that adopts bounding volume hierarchies and with a freeware ray tracer called POV-Ray shows that, for the examples considered, we may reduce the intersection tests to one third of those performed when standard optimizations are adopted.

Octree reinforced thin-shell rapid prototyping

: Described is a set of algorithms for efficiently rendering a CSG- defined objective directly into a frame buffer without converting first to a boundary representation. The method requires only that the frame buffer contain sufficient memory to hold two color values, two z values, and three one-bit flags. The algorithm first converts the CSG tree to a normalized form that is analogous to the sum-of-products form for boolean switching functions. Expanding on results previously reported the authors, introduce 1) an improved algorithm for converting a CSG expression to sum-of-products form, 2) a technique for minimizing the tree using don't care conditions based on geometry, 3) the dynamic interleaving of the above two algorithms, allowing very efficient rendering for most CSG objects, 4) a method for extending the technique to non- convex primitives, and 5) an implementation of these ideas in an interactive CSG design system on Pixelplanes 4. In this system the designer directly manipulates the CSG structure while continuously viewing the color rendering of the object under design. It is believed these algorithms will attain similar speeds on many of the next generation high-performance graphics system that have frame buffers with many bits per pixel.

Accelerated robust Boolean operations based on hybrid representations

This work presents the role of 3D visualization and analysis of monuments and archaeological sites in producing useful data regarding their preservation condition. The progress made in 3D digitization technologies, in combination with the development of new data processing algorithms, has enabled reliable and highly detailed digitization of the characteristics of different parts of the monuments. Due to both the effects of nature and human intervention, monuments and sites all over the world have undergone changes over time. The use of analog documentation data can help significantly towards this direction. In this work, we use as a case study a luxurious residential complex in the Athenian Agora, known as the Omega House. We use a retrospective 3D model, created with photographs taken in the late 60’s and early 70’s, in comparison with a 3D model made with contemporary digital photos, taken in 2017. All models are georeferenced. The old model is derived using analog terrestrial photographs and aerial photos taken by a blimp. The new one is created by terrestrial digital photographs in combination with images taken by an unmanned aerial vehicle, commonly known as a drone. The 3D models have been divided into smaller parts so that we can analyze them with greater accuracy separately, and then the whole models were compared as well. The Constructive Solid Geometry (CSG) modelling scheme is used and Boolean operations are applied to find the difference and intersection of the models. The comparison that is carried out in the current work elaborates on legacy data usefulness and their utility for monitoring the Omega House condition. The type of investigation proposed in this work proves that legacy data can be repurposed and can attain a new role through change detection techniques.

A feature-based topological optimization for structure design

This paper describes a fast algorithm for the volume conversion and rendering of CSG models constructed from both geometric and volumetric primitives. Using 3D texture mapping and frame buffer pixel operations, the algorithm can interactively generate a binary volume of the CSG model. The result can be used for volume rendering and other applications. Boolean operations are implicitly computed by a Point-Classification Map, and implemented by a hardware assisted frame buffer pixel map. The algorithm can be applied to any regions of interest of the model, thus provides a multi-resolution rendering solution through dynamic voxelization of the viewing regions. Since no pre-processing is required for any change of the CSG tree, it can be used as an effective rendering tool in a volumetric CSG modeling environment.