Joel Daniels

Robust Smooth Feature Extraction from Point Clouds

Defining sharp features in a given 3D model facilitates a better understanding of the surface and aids visualizations, reverse engineering, filtering, simplification, non-photo realism, reconstruction and other geometric processing applications. We present a robust method that identifies sharp features in a point cloud by returning a set of smooth curves aligned along the edges. Our feature extraction is a multi-step refinement method that leverages the concept of robust moving least squares to locally fit surfaces to potential features. Using Newtons method, we project points to the intersections of multiple surfaces then grow polylines through the projected cloud. After resolving gaps, connecting corners, and relaxing the results, the algorithm returns a set of complete and smooth curves that define the features. We demonstrate the benefits of our method with two applications: surface meshing and point-based geometry compression.

Quadrilateral mesh simplification

We introduce a simplification algorithm for meshes composed of quadrilateral elements. It is reminiscent of edge-collapse based methods for triangle meshes, but takes a novel approach to the challenging problem of maintaining the quadrilateral connectivity during level-of-detail creation. The method consists of a set of unit operations applied to the dual of the mesh, each designed to improve mesh structure and maintain topological genus. Geometric shape is maintained by an extension of a quadric error metric to quad meshes. The technique is straightforward to implement and efficient enough to be applied to real-world models. Our technique can handle models with sharp features, and can be used to re-mesh general polygonal, i.e. tri- and quad-dominant, meshes into quadonly meshes.

Interactive Vector Field Feature Identification

We introduce a flexible technique for interactive exploration of vector field data through classification derived from user-specified feature templates. Our method is founded on the observation that, while similar features within the vector field may be spatially disparate, they share similar neighborhood characteristics. Users generate feature-based visualizations by interactively highlighting well-accepted and domain specific representative feature points. Feature exploration begins with the computation of attributes that describe the neighborhood of each sample within the input vector field. Compilation of these attributes forms a representation of the vector field samples in the attribute space. We project the attribute points onto the canonical 2D plane to enable interactive exploration of the vector field using a painting interface. The projection encodes the similarities between vector field points within the distances computed between their associated attribute points. The proposed method is performed at interactive rates for enhanced user experience and is completely flexible as showcased by the simultaneous identification of diverse feature types.

Semi-regular quadrilateral-only remeshing from simplified base domains

Semi‐regular meshes describe surface models that exhibit a structural regularity that facilitates many geometric processing algorithms. We introduce a technique to construct semi‐regular, quad‐only meshes from input surface meshes of arbitrary polygonal type and genus. The algorithm generates a quad‐only model through subdivision of the input polygons, then simplifies to a base domain that is homeomorphic to the original mesh. During the simplification, a novel hierarchical mapping method, keyframe mapping, stores specific levels‐of‐detail to guide the mapping of the original vertices to the base domain. The algorithm implements a scheme for refinement with adaptive resampling of the base domain and backward projects to the original surface. As a byproduct of the remeshing scheme, a surface parameterization is associated with the remesh vertices to facilitate subsequent geometric processing, i.e. texture mapping, subdivision surfaces and spline‐based modeling.

Spline-based feature curves from point-sampled geometry

Defining sharp features in a 3D model facilitates a better understanding of the surface and aids geometric processing and graphics applications, such as reconstruction, filtering, simplification, reverse engineering, visualization, and non-photo realism. We present a robust method that identifies sharp features in a point-based model by returning a set of smooth spline curves aligned along the edges. Our feature extraction leverages the concepts of robust moving least squares to locally project points to potential features. The algorithm processes these points to construct arc-length parameterized spline curves fit using an iterative refinement method, aligning smooth and continuous curves through the feature points. We demonstrate the benefits of our method with three applications: surface segmentation, surface meshing and point-based compression.

Localized quadrilateral coarsening

In this paper we introduce a coarsening algorithm for quadrilateral meshes that generates quality, quad‐only connectivity during level‐of‐coarsening creation. A novel aspect of this work is development and implementation of a localized adaptation of the polychord collapse operator to better control and preserve important surface components. We describe a novel weighting scheme for automatic deletion selection that considers surface attributes, as well as localized queue updates that allow for improved data structures and computational performance opportunities over previous techniques. Additionally, this work supports optional and intuitive user controls for tailored simplification results.

iLAMP: Exploring high-dimensional spacing through backward multidimensional projection

Ever improving computing power and technological advances are greatly augmenting data collection and scientific observation. This has directly contributed to increased data complexity and dimensionality, motivating research of exploration techniques for multidimensional data. Consequently, a recent influx of work dedicated to techniques and tools that aid in understanding multidimensional datasets can be observed in many research fields, including biology, engineering, physics and scientific computing. While the effectiveness of existing techniques to analyze the structure and relationships of multidimensional data varies greatly, few techniques provide flexible mechanisms to simultaneously visualize and actively explore high-dimensional spaces. In this paper, we present an inverse linear affine multidimensional projection, coined iLAMP, that enables a novel interactive exploration technique for multidimensional data. iLAMP operates in reverse to traditional projection methods by mapping low-dimensional information into a high-dimensional space. This allows users to extrapolate instances of a multidimensional dataset while exploring a projection of the data to the planar domain. We present experimental results that validate iLAMP, measuring the quality and coherence of the extrapolated data; as well as demonstrate the utility of iLAMP to hypothesize the unexplored regions of a high-dimensional space.

SMI 2011: Full Paper: Template-based quadrilateral meshing

Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthogonality, alignment and adaptivity; however, they cannot make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features.

Interactive Quadrangulation with Reeb Atlases and Connectivity Textures

Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the users own subjective requirements.

Template-based quadrilateral mesh generation from imaging data

This paper describes a novel template-based meshing approach for generating good quality quadrilateral meshes from 2D digital images. This approach builds upon an existing image-based mesh generation technique called Imeshp, which enables us to create a segmented triangle mesh from an image without the need for an image segmentation step. Our approach generates a quadrilateral mesh using an indirect scheme, which converts the segmented triangle mesh created by the initial steps of the Imesh technique into a quadrilateral one. The triangle-to-quadrilateral conversion makes use of template meshes of triangles. To ensure good element quality, the conversion step is followed by a smoothing step, which is based on a new optimization-based procedure. We show several examples of meshes generated by our approach, and present a thorough experimental evaluation of the quality of the meshes given as examples.