Generating subdivision surfaces from profile curves

The construction of freeform models has always been a challenging task. A popular approach is to edit a primitive object such that its projections conform to a set of given planar curves. This process is tedious and relies very much on the skill and experience of the designer in editing 3D shapes. This paper describes an intuitive approach for the modeling of freeform objects based on planar profile curves. A freeform surface defined by a set of orthogonal planar curves is created by blending a corresponding set of sweep surfaces. Each of the sweep surfaces is obtained by sweeping a planar curve about a computed axis. A Catmull-Clark subdivision surface interpolating a set of data points on the object surface is then constructed. Since the curve points lying on the computed axis of the sweep will become extraordinary vertices of the subdivision surface, a mesh refinement process is applied to adjust the mesh topology of the surface around the axis points. In order to maintain characteristic features of the surface defined with the planar curves, sharp features on the surface are located and are retained in the mesh refinement process. This provides an intuitive approach for constructing freeform objects with regular mesh topology using planar profile curves.     

An approach to recognize interacting features from B-Rep CAD models of prismatic machined parts using a hybrid (graph and rule based) technique

This paper presents a new hybrid (graph + rule based) approach for recognizing the interacting features from B-Rep CAD models of prismatic machined parts. The developed algorithm considers variable topology features and handles both adjacent and volumetric feature interactions to provide a single interpretation for the latter. The input CAD part model in B-Rep format is preprocessed to create the adjacency graphs for faces and features of associated topological entities and compute their attributes. The developed FR system initially recognizes all varieties of the simple and stepped holes with flat and conical bottoms from the feature graphs. A new concept of Base Explicit Feature Graphs and No-base Explicit Feature Graphs has been proposed which essentially delineates between features having planar base face like pockets, blind slots, etc. and those without planar base faces like passages, 3D features, conical bottom features, etc. Based on the structure of the explicit feature graphs, geometric reasoning rules are formulated to recognize the interacting feature types. Extracted data has been post-processed to compute the feature attributes and their parent-child relationships which are written into a STEP like native feature file format. The FR system was extensively tested with several standard benchmark components and was found to be robust and consistent. The extracted feature file can be used for integration with various downstream applications like CAPP.     

Generative regular-freeform surface recognition for generating material removal volume from stock model

The present paper illustrates the development of generative surface recognition for regular and freeform. To obtain the final form of product, material removal volume generation from a stock model is also discussed. Only a few studies integrated the regular and freeform surfaces to provide a comprehensive definition of surface recognition as well as for the volumetric estimation of removal material in finishing and roughing operations. The current research deploys a comprehensive surface recognition approach that can recognise both regular and freeform surfaces based on the geometry as well as loop entity of a face. In contrast to the regular surface that can be categorised into a particular group of geometrical shape, such as cylindrical shape, the proposed approach enables the recognition of a freeform surface that cannot be defined as a generic geometrical shape. In addition, the new method also simplifies the existing surface recognition for regular surfaces. The material removal volumes created consist of machining volumes for finishing and roughing operations needed to be machined to obtain the final form of the product. The present research provides a unique user customisation feature that enables user to specify the volumetric thickness for material removal volume in the finishing operation as well as the size for the stock model. These estimated volumes are prepared for subsequent manufacturing applications, such as sequencing of machining operation.     

Feature-based 3D non-manifold freeform object construction

This paper presents a novel technique for modeling a 3D non-manifold freeform model around a 3D reference model. To represent both the design abstractions and the incomplete topological information, a new non-manifold data structure is first defined. Our data structure embodies the functional vitalities of both the boundary representation data structure and the complex-based data structure. Along with our data structure, a set of topological operators is defined to manipulate the entities in the data structure. Based on the non-manifold data structure and the topological operators, we develop a technique to construct 3D freeform objects around a reference model. Intuitive 2D sketches are adopted to specify the detailed profile of the object constructed. The construction method is feature-based – every reference model has pre-defined features, and the feature template of the constructed object is related to the features of the reference model by feature node encoding. Therefore, the surfaces derived from one reference model can be regenerated automatically on another reference model with the same features. The geometry coverage of our geometric modeling approach includes both manifold and non-manifold 3D freeform objects.     

3D clipping algorithm for feature mapping across domains

This paper describes an algorithm based on 3D clipping for mapping feature models across domains. The problem is motivated by the need to identify feature models corresponding to different domains. Feature mapping (also referred to as feature conversion) involves obtaining a feature model in one domain given a feature model in another. This is in contrast to feature extraction which works from the boundary representation of the part. Most techniques for feature mapping have focused on obtaining negative feature models only. We propose an algorithm that can convert a feature model with mixed features (both positive and negative) to a feature model containing either only positive or only negative features.The input to the algorithm is a feature model in one domain. The algorithm for mapping this model to another feature model is based on classification of faces of features in the model and 3D clipping. 3D clipping refers to the splitting of a solid by a surface. The feature mapping process involves three major steps. In the first step, faces forming the features in the input model are classified with respect to one another. The spatial arrangement of faces is used next to derive the dependency relationship amongst features in the input model and a Feature Relationship Graph (FRG) is constructed. In the second step, using the FRG, features are clustered and interactions between features (if any) are resolved. In the final step, the 3D clipping algorithm is used to determine the volumes corresponding to the features in the target domain. These volumes are then classified to identify the features for obtaining the feature model in the target domain. Multiple feature sets (where possible) can be obtained by varying the sequence of faces used for clipping. Results of implementation are presented.     

Generating assembly features onto split solid models

A large model can be split into smaller components where by assembly features can be created and attached onto the components so that they can be reassembled to form the original model. The assembly features may function as positioning or interlocking purposes depending on the mating requirement. This paper describes a method for creating assembly features onto the solid components automatically. The main idea of the method is to construct spatial rectangular assembly cells inside the original model. This is done by ray tracing the tool surface that is used to split the model, provided that there is no undercut on the split surface along the assembly direction. The spatial cells represent solid regions in which assembly features can be attached. Different kinds of assembly features can be mapped to the spatial cells, which are then attached to the split components. The split surface can be planar, quadrics or higher order freeform surfaces, thus allowing a high degree of flexibility in creating the assembly feature shapes.     

带自由曲面的三视图重建算法研究

针对蕴含自由曲面的三视图,提出了通过恢复边界线和轮廓线进而根据这些恢复 的空间曲线重建自由曲面的算法。首先分析并证明了自由曲面在三视图中的投影性质,从而提 出边界投影和轮廓投影的匹配算法。针对视图中存在的被打断的样条曲线,提出了分段样条曲 线的爬坡算法来解决此类曲线不能匹配的问题。然后基于投影匹配序列重建出自由曲面的边界 线,再由边界投影上的点和轮廓投影端点的对应关系重建出空间轮廓线。由轮廓线等参采样构 造截面线并和边界线一起蒙皮生成最终自由曲面。本文提出的算法扩展了工程图的重建域。     

Recognition of machining features for cast then machined parts

Mechanical parts are typically manufactured using multiple manufacturing processes. Primary processes such as casting realize the primary shape of the part, while secondary processes such as machining generate more detailed shape of the part. This paper presents a feature recognition method to support machining process planning for cast-then-machined parts. From the part model including the specification of machined faces, we generate the starting workpiece for machining, which represents the casting output in sufficient detail to support machining process planning. The starting workpiece is generated by identifying faces to be made by casting followed by machining, then offsetting the part through these faces by a uniform machining thickness to obtain cast faces, and combining the halfspaces induced by machined faces and the halfspaces induced by their bounding cast faces to enclose removal volumes. Machining features are then recognized from the removal volumes using a volume decomposition method called Alternating Sum of Volumes with Partitioning.     

Spiral tool path generation for diamond turning optical freeform surfaces of quasi-revolution

Space Archimedean spiral is defined firstly in this paper. Thereafter, a new spiral tool path generation based on space Archimedean spiral is proposed for diamond turning optical freeform surfaces of quasi-revolution, which is defined as a surface close to some surface of revolution. By projecting the space Archimedean spiral onto the freeform surface along the normal direction of the base surface instead of a fixed direction like traditional method, a quasi-uniform spiral tool path on the freeform surface can be obtained. This method can be used on diamond turning optical freeform surfaces. Finally, two examples are presented to prove its effectiveness and adaptability.     

Functional webs for freeform architecture

Rationalization and construction‐aware design dominate the issue of realizability of freeform architecture. The former means the decomposition of an intended shape into parts which are sufficiently simple and efficient to manufacture; the latter refers to a design procedure which already incorporates rationalization. Recent contributions to this topic have been concerned mostly with small‐scale parts, for instance with planar faces of meshes. The present paper deals with another important aspect, namely long‐range parts and supporting structures. It turns out that from the pure geometry viewpoint this means studying families of curves which cover surfaces in certain well‐defined ways. Depending on the application one has in mind, different combinatorial arrangements of curves are required. We here restrict ourselves to so‐called hexagonal webs which correspond to a triangular or tri‐hex decomposition of a surface. The individual curve may have certain special properties, like being planar, being a geodesic, or being part of a circle. Each of these properties is motivated by manufacturability considerations and imposes constraints on the shape of the surface. We investigate the available degrees of freedom, show numerical methods of optimization, and demonstrate the effectivity of our approach and the variability of construction solutions derived from webs by means of actual architectural designs.?     

Efficient Hausdorff Distance computation for freeform geometric models in close proximity

We present an interactive-speed algorithm for computing the Hausdorff Distance (HD) between two freeform geometric models represented with NURBS surfaces. The algorithm is based on an effective technique for matching a surface patch from one model to the corresponding nearby surface patch on the other model. To facilitate the matching procedure, we employ a bounding volume hierarchy (BVH) for freeform NURBS surfaces, which provides a hierarchy of Coons patches and bilinear surfaces approximating the NURBS surfaces (Kim et al., 2011 [1]). Comparing the local HD upper bound against a global HD lower bound, we can eliminate the majority of redundant surface patches from further consideration. The resulting algorithm and the associated data structures are considerably simpler than the previous BVH-based HD algorithms. As a result, we can compute the HD of two freeform geometric models efficiently and robustly even when the two models are in close proximity. We demonstrate the effectiveness of our approach using several experimental results.     

基于层次B样条的自由形状特征重用

借助层次B样条技术提出了一种自由形状特征的重用算法.首先利用低通滤波和泊松方程对源曲面上特征区域进行基面与细节特征的分离操作,求得基面与特征之间的偏移矢量场;然后利用平面参数化将偏移矢量场应用到目标曲面上完成特征重构;最后借助层次B样条技术优化重用结果.实验结果表明,该算法能够有效地完成自由形状特征的重用.     

Freeform surface flattening based on fitting a woven mesh model

This paper presents a robust and efficient surface flattening approach based on fitting a woven-like mesh model on a 3D freeform surface. The fitting algorithm is based on tendon node mapping (TNM) and diagonal node mapping (DNM), where TNM determines the position of a new node on the surface along the warp or weft direction and DNM locates a node along the diagonal direction. During the 3D fitting process, strain energy of the woven model is released by a diffusion process that minimizes the deformation between the resultant 2D pattern and the given surface. Nodes mapping and movement in the proposed approach are based on the discrete geodesic curve generation algorithm, so no parametric surface or pre-parameterization is required. After fitting the woven model onto the given surface, a continuous planar coordinate mapping is established between the 3D surface and its counterpart in the plane, based on the idea of geodesic interpolation of the mappings of the nodes in the woven model. The proposed approach accommodates surfaces with darts, which are commonly utilized in clothing industry to reduce the stretch of surface forming and flattening. Both isotropic and anisotropic materials are supported.     

The Convex Hull of Freeform Surfaces

We present an algorithm for computing the convex hull of freeform rational surfaces. The convex hull problem is reformulated as one of finding the zero-sets of polynomial equations; using these zero-sets we characterize developable surface patches and planar patches that belong to the boundary of the convex hull.     

Composite freeform surface reconstruction using recursive interpolating subdivision scheme

Composite freeform surface reconstruction from 3D scanned data of a physical model has become a more and more important topic in the field of CAD/CAE/CAM. By repeated application of a fixed set of recursive interpolation subdivision schemes on the initial mesh of the 3D sparse scanned data of a physical model, a polygonal model of composite freeform surface can be constructed. In the paper, the algorithm for constructing the initial triangular mesh from 3D sparse scanned data is presented. The unified recursive interpolating subdivision scheme for triangular mesh is proposed. A special quad-tree data structure is suggested to store all the necessary information of the vertices and elements of the polygonal model. Examples of composite surface reconstruction are provided to explain the distinguished superiority of subdivision scheme for reconstructing the arbitrary topological complex surface.     

Efficient offset trimming for deformable planar curves using a dynamic hierarchy of bounding circular arcs

We present an efficient algorithm for computing a family of trimmed offsets for planar freeform curves under deformation. The algorithm is based on a dynamic bounding volume hierarchy (BVH) for the untrimmed offsets of a given planar curve, which can be generated efficiently using a hierarchy of recursive bisections of the given curve. The proposed algorithm is effective for deformable planar curves. At each time frame, we segment the input curve into monotone spiral pieces (Barton and Elber, 2011), which is the only pre-processing needed for the dynamic BVH construction. To speed up the on-line generation of dynamic BVH, we employ the bounding circular arcs (BCA) of Meek and Walton (1995) that can be computed very efficiently using the position and tangent information at the endpoints of each monotone spiral curve segment. Using several experimental results, we demonstrate the performance improvement of our algorithm over the previous biarc-based algorithm of Kim et al. (2012).