Iso-level tool path planning for free-form surfaces

The aim of tool path planning is to maximize the efficiency against some given precision criteria. In practice, scallop height should be kept constant to avoid unnecessary cutting, while the tool path should be smooth enough to maintain a high feed rate. However, iso-scallop and smoothness often conflict with each other. Existing methods smooth iso-scallop paths one-by-one, which make the final tool path far from being globally optimal. This paper proposes a new framework for tool path optimization. It views a family of iso-level curves of a scalar function defined over the surface as tool path so that desired tool path can be generated by finding the function that minimizes certain energy functional and different objectives can be considered simultaneously. We use the framework to plan globally optimal tool path with respect to iso-scallop and smoothness. The energy functionals for planning iso-scallop, smoothness, and optimal tool path are respectively derived, and the path topology is studied too. Experimental results are given to show effectiveness of the proposed methods

Guided mesh normal filtering

The joint bilateral filter is a variant of the standard bilateral filter, where the range kernel is evaluated using a guidance signal instead of the original signal. It has been successfully applied to various image processing problems, where it provides more flexibility than the standard bilateral filter to achieve high quality results. On the other hand, its success is heavily dependent on the guidance signal, which should ideally provide a robust estimation about the features of the output signal. Such a guidance signal is not always easy to construct. In this paper, we propose a novel mesh normal filtering framework based on the joint bilateral filter, with applications in mesh denoising. Our framework is designed as a two-stage process: first, we apply joint bilateral filtering to the face normals, using a properly constructed normal field as the guidance; afterwards, the vertex positions are updated according to the filtered face normals. We compute the guidance normal on a face using a neighboring patch with the most consistent normal orientations, which provides a reliable estimation of the true normal even with a high-level of noise. The effectiveness of our approach is validated by extensive experimental results

Special Curve Patterns for Freeform Architecture

In recent years, freeform shapes are gaining more and more popularity in architecture. Such shapes are often challenging to manufacture, and have motivated an active research field called architectural geometry. In this thesis, we investigate patterns of special curves on surfaces, which find applications in design and realization of freeform architectural shapes. We first consider families of geodesic curves or piecewise geodesic curves on a surface, which are important for panelization of the surface and for interior design. We propose a method to propagate a series of such curves across a surface, starting from a given source curve, so that the distance functions between neighboring curves are close to given target distance functions. We use Jacobi fields as first order approximation of the distance functions from a curve to its neighboring curves, and select a Jacobi field which is closest to the target distance function. A neighboring curve is then computed according to the selected Jacobi field by solving an optimization problem. Using different target distance functions, we can generate different patterns of geodesic/piecewise geodesic curves. Our method provides an intuitive and controllable way to design geodesic patterns on freeform surfaces. We then present a method to compute functional webs, which are three families of curves with regular connectivity, where the curves have given special properties. We consider planar, circular and geodesic properties of the curves, which facilitate the fabrication of curve elements. We discretize a web as a regular triangle mesh, where the curves are represented by edge polylines of the mesh. The shape of the web is determined by optimizing a target functional which penalizes the deviation of the curves from their target properties. Furthermore, for webs where all curves are planar, we also show they can be computed in an exact way using three families of planes. By enabling the design of webs composed of curve elements which are easily manufacturable, our method addresses the challenge in realization of webs which have emerged in recent architectural designs

Interactive design exploration for constrained meshes

In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modifications that might not comply with the design intent. In addition, they only offer limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm. We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimization subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a unified way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved efficiently and accurately. Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system offers full control over the exploration process, by providing direct access to the specification of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces

Beyond developable: computational design and fabrication with auxetic materials

We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications

Static/Dynamic Filtering for Mesh Geometry

The joint bilateral filter, which enables feature-preserving signal smoothing according to the structural information from a guidance, has been applied for various tasks in geometry processing. Existing methods either rely on a static guidance that may be inconsistent with the input and lead to unsatisfactory results, or a dynamic guidance that is automatically updated but sensitive to noises and outliers. Inspired by recent advances in image filtering, we propose a new geometry filtering technique called static/dynamic filter, which utilizes both static and dynamic guidances to achieve state-of-the-art results. The proposed filter is based on a nonlinear optimization that enforces smoothness of the signal while preserving variations that correspond to features of certain scales. We develop an efficient iterative solver for the problem, which unifies existing filters that are based on static or dynamic guidances. The filter can be applied to mesh face normals followed by vertex position update, to achieve scale-aware and feature-preserving filtering of mesh geometry. It also works well for other types of signals defined on mesh surfaces, such as texture colors. Extensive experimental results demonstrate the effectiveness of the proposed filter for various geometry processing applications such as mesh denoising, geometry feature enhancement, and texture color filtering

A fast numerical solver for local barycentric coordinates

The local barycentric coordinates (LBC), proposed in Zhang et al (2014), demonstrate good locality and can be used for local control on function value interpolation and shape deformation. However, it has no closed- form expression and must be computed by solving an optimization problem, which can be time-consuming especially for high-resolution models. In this paper, we propose a new technique to compute LBC efficiently. The new solver is developed based on two key insights. First, we prove that the non-negativity constraints in the original LBC formulation is not necessary, and can be removed without affecting the solution of the optimization problem. Furthermore, the removal of this constraint allows us to reformulate the computation of LBC as a convex constrained optimization for its gradients, followed by a fast integration to recover the coordinate values. The reformulated gradient optimization problem can be solved using ADMM, where each step is trivially parallelizable and does not involve global linear system solving, making it much more scalable and efficient than the original LBC solver. Numerical experiments verify the effectiveness of our technique on a large variety of models

Robust RGB-D Face Recognition Using Attribute-Aware Loss

Existing convolutional neural network (CNN) based face recognition algorithms typically learn a discriminative feature mapping, using a loss function that enforces separation of features from different classes and/or aggregation of features within the same class. However, they may suffer from bias in the training data such as uneven sampling density, because they optimize the adjacency relationship of the learned features without considering the proximity of the underlying faces. Moreover, since they only use facial images for training, the learned feature mapping may not correctly indicate the relationship of other attributes such as gender and ethnicity, which can be important for some face recognition applications. In this paper, we propose a new CNN-based face recognition approach that incorporates such attributes into the training process. Using an attribute-aware loss function that regularizes the feature mapping using attribute proximity, our approach learns more discriminative features that are correlated with the attributes. We train our face recognition model on a large-scale RGB-D data set with over 100K identities captured under real application conditions. By comparing our approach with other methods on a variety of experiments, we demonstrate that depth channel and attribute-aware loss greatly improve the accuracy and robustness of face recognition