Interactive modeling of complex geometric details based on empirical mode decomposition for multi-scale 3D shapes

In this paper we develop an interactive modeling system for complex geometric details transformation based on empirical mode decomposition (EMD) on multi-scale 3D shapes. Given two models, we aim to transfer geometric details from one model to another one in an interactive manner. Taking full advantages of the multi-scale representation computed via EMD, different-scale geometric details can be transferred individually or in a concerted way, which makes our algorithm much more flexible than cut-and-paste and cloning based methods in transferring geometry details. In this process, the target surface with new transferred details could be generated by a mesh reconstruction method widely used in Laplacian surface editing. With the original positions of target surface serving as the soft constraints, the overall shape of the target model will be fully preserved. Our method can also support real-time continuous details transfer. Compared with state-of-the-art algorithms, our method provides an easier-to-use modeling tool and produces varied modeling results. We demonstrate the effectiveness of our modeling tool with various applications, such as detail transfer and enrichment, model reuse and recreation, and detail recovery for shape completion.     

Parallel and adaptive surface reconstruction based on implicit PHT-splines

We present a new surface reconstruction framework, which uses the implicit PHT-spline for shape representation and allows us to efficiently reconstruct surface models from very large sets of points. A PHT-spline is a piecewise tri-cubic polynomial over a 3D hierarchical T-mesh, the basis functions of which have good properties such as nonnegativity, compact support and partition of unity. Given a point cloud, an implicit PHT-spline surface is constructed by interpolating the Hermitian information at the basis vertices of the T-mesh, and the Hermitian information is obtained by estimating the geometric quantities on the underlying surface of the point cloud. We take full advantage of the natural hierarchical structure of PHT-splines to reconstruct surfaces adaptively, with simple error-guided local refinements that adapt to the regional geometric details of the target object. Examples show that our approach can produce high quality reconstruction surfaces very efficiently. We also present the multi-threaded algorithm of our approach and show its parallel scalability.     

High frequency geometric detail manipulation and editing for point-sampled surfaces

In this paper, based on the new definition of high frequency geometric detail for point-sampled surfaces, a new approach for detail manipulation and a detail-preserving editing framework are proposed. Geometric detail scaling and enhancement can always produce fantastic effects by directly manipulating the geometric details of the underlying geometry. Detail-preserving editing is capable of preserving geometric details during the shape deformation of point-sampled model. For efficient editing, the point set of the model is first clustered by a mean shift scheme, according to its anisotropic geometric features and each cluster is abstracted as a simplification sample point (SSP). Our editing operation is implemented by manipulating the SSP first and then diffusing the deformation to all sample points on the underlying geometry. As a postprocessing step, a new up-sampling and relaxation procedure is proposed to refine the deformed model. The effectiveness of the proposed method is demonstrated by several examples.     

Efficient feature tracking of time-varying surfaces using multi-scale motion flow propagation

This paper presents a framework for efficient feature tracking of time-varying surfaces. The framework can not only capture the dynamic geometry features on time-varying surfaces, but can also compute the accurate boundaries of the geometry features. The basic idea of the proposed approach is using the multi-scale motion flow and surface matching information to propagate the feature frame on time-varying surfaces. We first define an effective multi-scale geometry motion flow for the time-varying surfaces, which efficiently propagates the geometry features along the time direction of the time-varying surfaces. By combining both the approximately invariant signature vectors and geometry motion flow vectors, we also incorporate the shape matching into the system to process feature tracking for time-varying surfaces in large deformation while with low frame sampling rate. Our approach does not depend on the topological connection of the underlying surfaces. Thus, it can process both mesh-based and point-based time-varying surfaces without vertex-to-vertex correspondence across the frames. Feature tracking results on different kinds of time-varying surfaces illustrate the efficiency and effectiveness of the proposed method.     

A unified method for appearance and geometry completion of point set surfaces

This paper presents a novel approach for appearance and geometry completion over point-sampled geometry. Based on the result of surface clustering and a given texture sample, we define a global texture energy function on the point set surface for direct texture synthesis. The color texture completion is performed by minimizing a constrained global energy using the existing surface texture on the surface as the input texture sample. We convert the problem of context-based geometry completion into a task of texture completion on the surface. The geometric detail is then peeled and converted into a piece of signed gray-scale texture on the base surface of the point set surface. We fill the holes on the base surface by smoothed extrapolation and the geometric details over these patches are reconstructed by a process of gray-scale texture completion. Experiments show that our method is flexible, efficient and easy to implement. It provides a practical texture synthesis and geometry completion tool for 3D point set surfaces.     

Generation of accurate integral surfaces in time-dependent vector fields

We present a novel approach for the direct computation of integral surfaces in time-dependent vector fields. As opposed to previous work, which we analyze in detail, our approach is based on a separation of integral surface computation into two stages: surface approximation and generation of a graphical representation. This allows us to overcome several limitations of existing techniques. We first describe an algorithm for surface integration that approximates a series of time lines using iterative refinement and computes a skeleton of the integral surface. In a second step, we generate a well-conditioned triangulation. Our approach allows a highly accurate treatment of very large time-varying vector fields in an efficient, streaming fashion. We examine the properties of the presented methods on several example datasets and perform a numerical study of its correctness and accuracy. Finally, we investigate some visualization aspects of integral surfaces.     

PointProNets: Consolidation of Point Clouds with Convolutional Neural Networks

With the widespread use of 3D acquisition devices, there is an increasing need of consolidating captured noisy and sparse point cloud data for accurate representation of the underlying structures. There are numerous algorithms that rely on a variety of assumptions such as local smoothness to tackle this ill‐posed problem. However, such priors lead to loss of important features and geometric detail. Instead, we propose a novel data‐driven approach for point cloud consolidation via a convolutional neural network based technique. Our method takes a sparse and noisy point cloud as input, and produces a dense point cloud accurately representing the underlying surface by resolving ambiguities in geometry. The resulting point set can then be used to reconstruct accurate manifold surfaces and estimate surface properties. To achieve this, we propose a generative neural network architecture that can input and output point clouds, unlocking a powerful set of tools from the deep learning literature. We use this architecture to apply convolutional neural networks to local patches of geometry for high quality and efficient point cloud consolidation. This results in significantly more accurate surfaces, as we illustrate with a diversity of examples and comparisons to the state‐of‐the‐art.     

Multi-level differential surface representation based on local transformations

One crucial issue of multi-resolution surface representations is how to effectively record and reconstruct geometric details among surface levels. Standard multi-resolution techniques encode details directly as local displacements in the vertices, and may produce unplausible results when the base level endures large deformations. In this paper we propose an alternative detail representation and reconstruction scheme, based on local transformations on a per-triangle basis. While more storage is required, recording details as local transformations favors global coupling of geometric details and allows for large-scale surface manipulations. By modeling the scale components of the surface modifications as a set of deforming factors, we achieved detail-preserving reconstruction results naturally under very large deformations. Comprehensive experimental results verify the efficiency and robustness of our approach. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Geometry Textures and Applications†

Geometry textures are a novel geometric representation for surfaces based on height maps. The visualization is done through a graphics processing unit (GPU) ray casting algorithm applied to the whole object. At rendering time, the fine‐scale details (mesostructures) are reconstructed preserving original quality. Visualizing surfaces with geometry textures allows a natural level‐of‐detail (LOD) behaviour. There are numerous applications that can benefit from the use of geometry textures. In this paper, besides a mesostructure visualization survey, we present geometry textures with three possible applications: rendering of solid models, geological surfaces visualization and surface smoothing.     

Geometric texturing using level sets

We present techniques for warping and blending (or subtracting) geometric textures onto surfaces represented by high resolution level sets. The geometric texture itself can be represented either explicitly as a polygonal mesh or implicitly as a level set. Unlike previous approaches, we can produce topologically connected surfaces with smooth blending and low distortion. Specifically, we offer two different solutions to the problem of adding fine-scale geometric detail to surfaces. Both solutions assume a level set representation of the base surface which is easily achieved by means of a mesh-to-level-set scan conversion. To facilitate our mapping, we parameterize the embedding space of the base level set surface using fast particle advection. We can then warp explicit texture meshes onto this surface at nearly interactive speeds or blend level set representations of the texture to produce high-quality surfaces with smooth transitions.     

Multi-scale anisotropic heat diffusion based on normal-driven shape representation

Multi-scale geometric processing has been a popular and powerful tool in graphics, which typically employs isotropic diffusion across scales. This paper proposes a novel method of multi-scale anisotropic heat diffusion on manifold, based on the new normal-driven shape representation and Edge-weighted Heat Kernels (EHK). The new shape representation, named as Normal-Controlled Coordinates (NCC), can encode local geometric details of a vertex along its normal direction and rapidly reconstruct surface geometry. Moreover, the inner product of NCC and its corresponding vertex normal, called Normal Signature (NS), defines a scalar/heat field over curved surface. The anisotropic heat diffusion is conducted using the weighted heat kernel convolution governed by local geometry. The convolution is computed iteratively based on the semigroup property of heat kernels toward accelerated performance. This diffusion is an efficient multi-scale procedure that rigorously conserves the total heat. We apply our new method to multi-scale feature detection, scalar field smoothing and mesh denoising, and hierarchical shape decomposition. We conduct various experiments to demonstrate the effectiveness of our method. Our method can be generalized to handle any scalar field defined over manifold.     

Generalized B-spline subdivision-surface wavelets for geometry compression

We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail is expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform is computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.     

A diffusion wavelet approach for 3-D model matching

This paper proposes a new 3D shape retrieval approach based on diffusion wavelets which generalize wavelet analysis and associated signal processing techniques to functions on manifolds and graphs. Unlike current works on 3D matching, which are based either on the topological information of the model or its scatter point distribution information, this approach uses both information for more effective matching. Diffusion wavelets enable both global and local analyses on graphs, and can capture the topology of a surface with the diffusion map of its mesh representation. As a result, both multi-scale properties of the 3D geometric model and the topology among the meshes can be extracted for use in 3D geometric model retrieval. Tests using 3D benchmarks demonstrate that the approach based on diffusion wavelets is effective and performs better than those by spherical wavelet and spherical harmonics in 3D model matching.     

Multiresolution Shape Deformations for Meshes with Dynamic Vertex Connectivity

Multiresolution shape representation is a very effective way to decompose surface geometry into several levels of detail. Geometric modeling with such representations enables flexible modifications of the global shape while preserving the detail information. Many schemes for modeling with multiresolution decompositions based on splines, polygonal meshes and subdivision surfaces have been proposed recently. In this paper we modify the classical concept of multiresolution representation by no longer requiring a global hierarchical structure that links the different levels of detail. Instead we represent the detail information implicitly by the geometric difference between independent meshes. The detail function is evaluated by shooting rays in normal direction from one surface to the other without assuming a consistent tesselation. In the context of multiresolution shape deformation, we propose a dynamic mesh representation which adapts the connectivity during the modification in order to maintain a prescribed mesh quality. Combining the two techniques leads to an efficient mechanism which enables extreme deformations of the global shape while preventing the mesh from degenerating. During the deformation, the detail is reconstructed in a natural and robust way. The key to the intuitive detail preservation is a transformation map which associates points on the original and the modified geometry with minimum distortion. We show several examples which demonstrate the effectiveness and robustness of our approach including the editing of multiresolution models and models with texture.     

Signed algebraic level sets on NURBS surfaces and implicit Boolean compositions for isogeometric CAD–CAE integration

Boundary-representation (B-rep) geometrical models, often mathematically represented using Non-Uniform Rational B-Spline (NURBS) surfaces, are the starting point for complex downstream product life-cycle evaluations including Computer-Aided Engineering (CAE). Boolean operations during B-rep model generation require surface intersection computations to describe the composed entity. However, for parametric NURBS surfaces, intersection operations are non-trivial and typically carried out numerically. The numerical intersection computations introduce challenges relating to the accuracy of the resulting representation, efficiency with which the computation is carried out, and robustness of the result to small variations in geometry. Often, for downstream CAE evaluations, an implicit, procedural knowledge of the Boolean operations between the composed objects that can resolve point containment queries (exact to the original NURBS bounding surfaces) maybe sufficient during quadrature. However, common point containment queries on B-rep models are numerical, iterative and relatively expensive. Thus, the first goal of the present paper is to describe a purely algebraic, and therefore non-iterative, approach to carrying out point containment queries on complex B-rep models built using low-degree NURBS surfaces. For CAE operations, the boundary representation of B-rep solids is, in general, not convenient and as a result, the B-rep model is converted to a meshed volumetric approximation. The major challenges to such a conversion include capturing the geometric features accurately when constructing the secondary (meshed) representation, apart from the efficiency of carrying out such a mesh generation step repeatedly as the geometric shape evolves. Thus, an ideal analysis procedure would operate directly on B-rep CAD models, without needing a secondary mesh, and would procedurally unify the geometric operations during CAD as well as CAE stages. Therefore, the second and broader goal of the present paper is to demonstrate CAD–CAE integration using signed algebraic level set operations directly on B-rep models by embedding or immersing the bounding surfaces within a discretized domain while preserving the geometric accuracy of the surfaces exact to the original NURBS representation during analysis.     

Fast hierarchical animated object decomposition using approximately invariant signature

In this paper, we introduce a novel method to hierarchically decompose the animated 3d object efficiently by utilizing high-dimensional and multi-scale geometric information. The key idea is to treat the animated surface sequences as a whole and extract the near-rigid components from it. Our approach firstly detects a set of the multi-scale feature points on the animated object and computes approximately invariant signature vectors for these points. Then, exploiting both the geometric attributes and the local signature vector of each point (vertex) of the animated object, all the points (vertices) of the animated object can be clustered efficiently using a GPU-accelerated mean shift clustering algorithm. To refine the decomposition boundaries, the initially-generated boundaries of the animated object can be further improved by applying a boundary refinement technique based on Gaussian Mixture Models (GMMs). Furthermore, we propose a hierarchical decomposition technique using a topology merging strategy without introducing additional computations.     

A Framework for Interactive Hypertexture Modelling

Hypertexturing can be a powerful way of adding rich geometric details to surfaces at low memory cost by using a procedural three‐dimensional (3D) space distortion. However, this special kind of texturing technique still raises a major problem: the efficient control of the visual result. In this paper, we introduce a framework for interactive hypertexture modelling. This framework is based on two contributions. First, we propose a reformulation of the density modulation function. Our density modulation is based on the notion of shape transfer function. This function, which can be easily edited by users, allows us to control in an intuitive way the visual appearance of the geometric details resulting from the space distortion. Second, we propose to use a hybrid surface and volume‐point‐based representation in order to be able to dynamically hypertexture arbitrary objects at interactive frame rates. The rendering consists in a combined splat‐ and raycasting‐based direct volume rendering technique. The splats are used to model the volumetric object while raycasting allows us to add the details. An experimental study on users shows that our approach improves the design of hypertextures and yet preserves their procedural nature.     

Algorithmic shape modeling with subdivision surfaces

We present methods for synthesizing 3D shape features on subdivision surfaces using multi-scale procedural techniques. Multi-scale synthesis is a powerful approach for creating surfaces with different levels of detail. Our methods can also blend multiple example multi-resolution surfaces, including procedurally defined surfaces as well as captured models.     

Material-aware differential mesh deformation using sketching interface

In this paper, we present a material-aware mesh deformation method using a sketching interface. Guided by user-specified material properties, our method can deform the surface mesh in a non-uniform way, while previous deformation techniques are mainly designed for uniform materials. The non-uniform deformation is achieved by material-dependent gradient field manipulation and Poisson-based reconstruction. Compared with previous material-oblivious deformation techniques, our method supplies better control of the deformation process and can generate more realistic results. We propose a novel detail representation that transforms geometric details between successive surface levels as a combination of dihedral angles and barycentric coordinates. This detail representation is similarity-invariant and fully compatible with material properties. Based on these two methods, we implement a multi-resolution deformation tool, allowing the user to edit a mesh inside a hierarchy in a material-aware manner. We demonstrate the effectiveness and robustness of our methods by several examples with real-world data.     

Geodesic-driven visual effects over complex surfaces

Texture mapping is an important technique for adding visual details to geometric models. Image-based texture mapping is the most popular approach, but it relies on pre-computed images which often limit their use to static effects. For adding dynamic effects, procedural-based texturing is more adequate. Since it rely on functions to describe texturing patterns, procedural texturing allows for a more compact representation and control of visual effects by a simple change of parameters. In this work we describe GeoTextures, an approach that uses geodesic distance fields defined from multiple sources at different locations over a model surface to place, advect, and combine procedural visual effects over complex surfaces. The use of geodesics extends the scope of common procedural textures which are usually limited to using spatial 3D coordinates or 2D texture coordinates. We illustrate the flexibility of our real-time approach with a range of visual effects, such as time-based propagation of weathering phenomena, transparency effects, and mesh displacement over surfaces with smooth silhouettes using hardware based tessellation available in current graphics cards.