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Feature-based parametric modeling is the de facto standard in CAD. Boundary representation-based direct modeling is another CAD paradigm developed recently. They have complementary advantages and limitations, thereby offering huge potential for improvement towards an integrated CAD modeling scheme. Most existing integration methods are developed by industry and typically treat direct edits as pseudo-features, where little can be said about seamless integration. This paper presents an alternative method for seamless parametric/direct integration, which allows parametric and direct edits to work in a unified way. The fundamental issues and challenges of parametric/direct integration are first explained. A framework is then proposed to handle those information inconsistencies, based on a detection-then-resolution strategy. Algorithms that can systematically detect and resolve all possible types of information inconsistencies are also given to implement the framework. With them, model validity can be maintained during the whole model editing process, and then the discrepancy between direct edits and parametric edits can be resolved. The effectiveness of the proposed approach has been shown with a series of case studies and comparisons, based on a preliminary prototype., Comment: 19pages

This paper presents a comprehensive review of geometric constraint solving in parametric computer-aided design (CAD), with the major focus on its advances in the last 15 years. Geometric constraint solving can date back to the very first CAD prototype, Sketchpad, in the 1960s, but serious research studies were carried out only after parametric CAD was introduced in the late 1980s. In the following 30-year history of GCS research, two development stages may be identified: (1) the first 15 years (late 1980s - mid 2000s) were primarily devoted to geometric constraint decomposition for well-constrained systems or those with only structural constraint dependencies; and (2) the second 15 years (late 2000s - now) have seen research efforts shifted towards classification criteria and decomposition algorithms for general constraint systems (with and without non-structural constraint dependencies). Most existing reviews focused on the first 15 years. The problem researched in the second 15 years is, however, equally important, considering that a manually specified constraint system usually contains under- and over-constrained parts, and that such parts must be correctly detected and resolved before numerical solving can work. In this regard, this review paper covers both stages and will discusses what has already been made possible for handling general constraint systems, what developments can be expected in the near future, and which areas remain problematic., Comment: version 2. arXiv admin note: text overlap with arXiv:1904.00526

This paper presents a new method to generate tool paths for machining freeform surfaces represented either as parametric surfaces or as triangular meshes. This method allows for the optimal tradeoff between the preferred feed direction field and the constant scallop height, and yields a minimized overall path length. The optimality is achieved by formulating tool path planning as a Poisson problem that minimizes a simple, quadratic energy. This Poisson formulation considers all tool paths at once, without resorting to any heuristic sampling or initial tool path choosing as in existing methods, and is thus a globally optimal solution. Finding the optimal tool paths amounts to solving a well-conditioned sparse linear system, which is computationally convenient and efficient. Tool paths are represented with an implicit scheme that can completely avoid the challenging topological issues of path singularities and self-intersections seen in previous methods. The presented method has been validated with a series of examples and comparisons., Comment: under review

Boundary representation (B-rep) model editing plays an essential role in computer-aided design and motivates the very recent direct modeling paradigm, which features intuitive push-pull manipulation of the model geometry. In mechanical design, a substantial part of B-rep models being used are quadric models (composed of linear and quadric surfaces). However, push-pulling such models is not trivial due to the possible smooth face-face connections in the models. The major issue is that, during push-pull moves, it is often desirable to preserve these connections for functional, manufacturing, or aesthetic reasons, but this could cause complex inconsistencies between the geometry and topology in the model and lead to robustness issues in updating the model. The challenge lies in effectiveness towards detecting the instants when geometry-topology inconsistencies occur during push-pull moves. This paper proposes a novel reverse detection method to solve the challenge and then, based on it, presents a robust method for push-pull direct modeling while preserving smooth connections. Case studies and comparisons have been conducted to demonstrate the effectiveness of the method., Comment: 20 pages

Direct modeling is a very recent CAD paradigm that can provide unprecedented modeling flexibility. It, however, lacks the parametric capability, which is indispensable to modern CAD systems. For direct modeling to have this capability, an additional associativity information layer in the form of geometric constraint systems needs to be incorporated into direct modeling. This is no trivial matter due to the possible inconsistencies between the associativity information and geometry information in a model after direct edits. The major issue of resolving such inconsistencies is that there often exist many resolution options. The challenge lies in avoiding invalid resolution options and prioritizing valid ones. This paper presents an effective method to support the user in making decisions among the resolution options. In particular, the method can provide automatic information inconsistency reasoning, avoid invalid resolution options completely, and guide the choice among valid resolution options. Case studies and comparisons have been conducted to demonstrate the effectiveness of the method., Comment: 20 pages, 14 figures

This paper presents discussions on the limitations of the witness configuration method. These limitations have rarely been reported in previous studies. The witness configuration method is a very recent approach for geometric constraint solving, which is of critical importance for modern computer-aided design systems. The witness configuration method may be the most promising method to solve satisfactorily the challenges of geometric constraint solving. This method, in the current form, is however found to be limited for the three essential tasks in the geometric constraint solving domain. Examples are given to validate this work's statements on these limitations., Comment: 10 pages

The very recent CAD paradigm of direct modeling gives rise to the need of processing 3D geometric constraint systems defined on boundary representation (B-rep) models. The major issue of processing such variational B-rep models (in the STEP format) is that free motions of a well-constrained model involve more than just rigid-body motions. The fundamental difficulty lies in having a systematic description of what pattern these free motions follow. This paper proposes a geometric perturbation method to study these free motions. This method is a generalization of the witness method, allowing it to directly deal with variational B-rep models represented with the standard STEP scheme. This generalization is essentially achieved by using a direct, geometric representation of the free motions, and then expressing the free motions in terms of composites of several basis motions. To demonstrate the effectiveness of the proposed method, a series of comparisons and case studies are presented., Comment: 16 pages; journal paper

Direct modeling is a very recent CAD modeling paradigm featuring direct, intuitive push-pull interactions with the geometry of the model to much increase model editing flexibility. The major issue for push-pull direct modeling is the possible inconsistency between the altered geometry of the model and its unchanged topology. The challenge of resolving the geometry-topology inconsistency lies in ensuring that the resulting model remains as a valid solid model and that the model shape follows a continuous change pattern. Although push-pull direct modeling has been implemented in several CAD software packages, robustness towards generating valid modeling results and continuous shape changes still remains an open issue. This paper proposes a systematic method to handle the resolution of any possible inconsistent situation. The method formulates the continuous shape change requirement as successive Boolean operations on the model volume, thereby guaranteeing valid solid models and continuous shape changes. Further, this formulation allows for an easy implementation of push-pull direct modeling using existing CAD research and engineering results. In order to show the effectiveness of the proposed method, a software prototype is developed and the modeling results are compared with those of five leading CAD software packages., Comment: 17 pages, journal paper