We introduce RibbonSculpt, the first method for interactive freeform shape design in VR through progressive sketching of sparse, oriented ribbons. Instead of reconstructing a surface from a fully drawn VR sketch, our method allows the real-time creation and progressive refinement of a closed surface of any topological genus, thanks to the continuous update of a volumetric proxy. The latter corresponds to a filtered subset of the Voronoi balls defined by the user-sketched ribbons. At each visualization step, a mesh extracted from the proxy is beautified through Laplacian-based energy minimization, yielding a smooth surface that interpolates the ribbons. Guided by this surface, users can easily refine their design by adding or removing ribbons, which sculpts, in return, the set of Voronoi balls forming the proxy. Our results, supported by user studies, show that RibbonSculpt allows VR users to easily and quickly draft the 3D shapes they have in mind.

Abstract Although intuitive, sketching a closed 3D shape directly in an immersive environment results in an unordered set of arbitrary strokes, which can be difficult to assemble into a closed surface. We tackle this challenge by introducing VRSurf, a surfacing method inspired by a balloon inflation metaphor: Seeded in the sparse scaffold formed by the strokes, a smooth, closed surface is inflated to progressively interpolate the input strokes, sampled into lists of points. These are treated in a divide‐and‐conquer manner, which allows for automatically triggering some additional balloon inflation followed byfusion ifthe current inflation stops due to a detected concavity. While the input strokes are intended to belong to the same smooth 3D shape, our method is robust to coarse VR input and does not require strokes to be aligned. We simply avoid intersecting strokes that might give an inconsistent surface position due to the roughness of the VR drawing. Moreover, no additional topological information is required, and all the user needs to do is specify the initial seeding location for the first balloon. The results show that VRsurf can efficiently generate smooth surfaces that interpolate sparse sets of unoriented strokes. Validation includes a side‐by‐side comparison with other reconstruction methods on the same input VR sketch. We also check that our solution matches the user's intent by applying it to strokes that were sketched on an existing 3D shape and comparing what we get to the original one.

This Special Section of Computers & Graphics (C&G), features the full papers presented at the Shape Modeling International 2024 conference — SMI 2024 (https://smiconf.github.io/2024/). The conference was organised by the Computer Graphics and Imaging Lab and hosted at Wayne State University, July 11 to 13, 2024.

Abstract This paper is devoted to a category of metamaterials called auxetics, identified by their negative Poisson's ratio. Our work consists in exploring geometrical strategies to generate irregular auxetic structures. More precisely we seek to reduce the Poisson's ratio ν, by pruning an irregular network based solely on geometric criteria. We introduce a strategy combining a pure geometric pruning algorithm followed by a physics‐based testing phase to determine the resulting Poisson's ratio of our structures. We propose an algorithm that generates sets of irregular auxetic networks. Our contributions include geometrical characterization of auxetic networks, development of a pruning strategy, generation of auxetic networks with low Poisson's ratio, as well as validation of our approach. We provide statistical validation of our approach on large sets of irregular networks, and we additionally laser‐cut auxetic networks in sheets of rubber. The findings reported here show that it is possible to reduce the Poisson's ratio by geometric pruning, and that we can generate irregular auxetic networks at lower processing times than a physics‐based approach.

Abstract Contour trees are extensively used in scalar field analysis. The contour tree is a data structure that tracks the evolution of level set topology in a scalar field. Scalar fields are typically available as samples at vertices of a mesh and are linearly interpolated within each cell of the mesh. A more suitable way of representing scalar fields, especially when a smoother function needs to be modeled, is via higher order interpolants. We propose an algorithm to compute the contour tree for such functions. The algorithm computes a local structure by connecting critical points using a numerically stable monotone path tracing procedure. Such structures are computed for each cell and are stitched together to obtain the contour tree of the function. The algorithm is scalable to higher degree interpolants whereas previous methods were restricted to quadratic or linear interpolants. The algorithm is intrinsically parallelizable and has potential applications to isosurface extraction.

We present an interactive method that manipulates perceived object shape from a single input color image thanks to a warping technique implemented on the GPU. The key idea is to give the illusion of shape sharpening or rounding by exaggerating orientation patterns in the image that are strongly correlated to surface curvature. We build on a growing literature in both human and computer vision showing the importance of orientation patterns in the communication of shape, which we complement with mathematical relationships and a statistical image analysis revealing that structure tensors are indeed strongly correlated to surface shape features. We then rely on these correlations to introduce a flow-guided image warping algorithm, which in effect exaggerates orientation patterns involved in shape perception. We evaluate our technique by 1) comparing it to ground truth shape deformations, and 2) performing two perceptual experiments to assess its effects. Our algorithm produces convincing shape manipulation results on synthetic images and photographs, for various materials and lighting environments.

In this paper we present a user study on the use of Depth of Field for depth perception in Direct Volume Rendering. Direct Volume Rendering with Phong shading and perspective projection is used as the baseline. Depth of Field is then added to see its impact on the correct perception of ordinal depth. Accuracy and response time are used as the metrics to evaluate the usefulness of Depth of Field. The onsite user study has two parts: static and dynamic. Eye tracking is used to monitor the gaze of the subjects. From our results we see that though Depth of Field does not act as a proper depth cue in all conditions, it can be used to reinforce the perception of which feature is in front of the other. The best results (high accuracy & fast response time) for correct perception of ordinal depth occurs when the front feature (out of the two features users were to choose from) is in focus and perspective projection is used.

Interactive visualization applications benefit from simplification techniques that generate good-quality coarse meshes from high-resolution meshes that represent the domain. These meshes often contain interesting substructures, called embedded structures, and it is desirable to preserve the topology of the embedded structures during simplification, in addition to preserving the topology of the domain. This paper describes a proof that link conditions, proposed earlier, are sufficient to ensure that edge contractions preserve the topology of the embedded structures and the domain. Excluding two specific configurations, the link conditions are also shown to be necessary for topology preservation. Repeated application of edge contraction on an extended complex produces a coarser representation of the domain and the embedded structures. An extension of the quadric error metric is used to schedule edge contractions, resulting in a good-quality coarse mesh that closely approximates the input domain and the embedded structures.

The display of space filling data is still a challenge for the community of visualization. Direct volume rendering (DVR) is one of the most important techniques developed to achieve direct perception of such volumetric data. It is based on semitransparent representations, where the data are accumulated in a depth-dependent order. However, it produces images that may be difficult to understand, and thus several techniques have been proposed so as to improve its effectiveness, using for instance lighting models or simpler representations (e.g., maximum intensity projection). In this article, we present three perceptual studies that examine how DVR meets its goals, in either static or dynamic context. We show that a static representation is highly ambiguous, even in simple cases, but this can be counterbalanced by use of dynamic cues (i.e., motion parallax) provided that the rendering parameters are correctly tuned. In addition, perspective projections are demonstrated to provide relevant information to disambiguate depth perception in dynamic displays.

Although deforming surfaces are frequently used in numerous domains (scientific applications, games...), only few works have been proposed until now for simplifying such data. However, these time-varying surfaces are generally represented as oversampled triangular meshes with a static connectivity, involving a large number of unnecessary details for some frames. Among the related works, some methods provide globally good results, but fine details appearing during the animation are not always well-preserved, because of a static geometry sampling. We propose a new simplification method for deforming surfaces based on a dynamic geometry sampling. The idea is to compute one coarse version at the first frame, and then to progressively update the coarse sampling for the subsequent frames. In order to optimally approximate each frame, vertices are added or removed following the appearance or disappearance of fine details in the frames. Our approach is fast, easy to implement, and produces good quality time-varying approximations with well-preserved fine details, at any given frame.

Abstract Geometric constraints have proved to be efficient for enhancing the realism of shape animation. The present paper addresses the computation and the preservation of the volume enclosed by multiresolution meshes. A wavelet based representation allows the mesh to be handled at any level of resolution. The key contribution is the calculation of the volume as a trilinear form with respect to the multiresolution coefficients. Efficiency is reached thanks to the pre‐processing of a sparse 3D data structure involving the transposition of the filters while represented as a lifting scheme. A versatile and interactive method for preserving the volume during a deformation process is then proposed. It is based on a quadratic minimization subject to a linearization of the volume constraint. A closed form of the solution is derived.

We present a method for deforming piecewise linear 3D curves with constant length constraint. We show how this constraint can be integrated into a multiresolution editing tool allowing an intuitive control of the deformation’s extent and aspect. The constraint is enforced following two steps. A first step consists in approximating the initial length by modifying the multiresolution decomposition at some specified scale. In a second step the constraint is exactly enforced by constrained minimization of a smoothness criterion. This process then provides the core of an integrated wrinkling tool for soft tissues modelling. A curve on the mesh is deformed, providing a deformation profile which is propagated in a user-defined neighbourhood on the surface.

The recent ability to measure quickly and inexpensively dense sets of points on physical objects has deeply influenced the way engineers represent shapes in CAD systems, animation software or in the game industry. Many researchers advocated to completely bypass smooth surface representations, and to stick to a dense mesh model throughout the design process. Yet smooth analytic representations are still required in standard CAD systems and animation software, for reasons of compactness, control, appearance and manufacturability. In this paper we present a new method for fitting a smooth adoptively refinable triangular spline surface of arbitrary topology to an arbitrary dense triangular mesh. The key ingredient in our solution is that adaptive fitting is achieved by 4-splitting triangular surface patches locally therefore no particular attention has to be paid the validity of an underlying subdivided mesh. Furthermore, the final surface is composed of low-degree polynomial patches that always join with Gl-continuity. The ability to adoptively refine the model allows to achieve a given approximation error with a minimal number of patches.

Smooth parametric surfaces interpolating triangular meshes are very useful for modeling surfaces of arbitrary topology. Several interpolants based on these kind of surfaces have been developed over the last fifteen years. However, with current 3D acquisition equipments, models are becoming more and more complex. Since previous interpolation methods lack a local refinement property, there is no way to locally adapt the level of detail. In this article, we introduce a hierarchical triangular surface model. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent plane continuity. This model enables designers to create a complex smooth surface of arbitrary topology composed of a small number of patches to which details can be added by locally refining the patches until an arbitrary small size is reached. It is implemented as a hierarchical data structure where the top layer describes a coarse, smooth base surface and the lower levels encode the details in local frame coordinates.

Triangular Bezier patches are an important tool for defining smooth surfaces over arbitrary triangular meshes. The previously introduced 4-split method interpolates the vertices of a 2-manifold triangle mesh by a set of tangent plane continuous triangular Bezier patches of degree five. The resulting surface has an explicit closed form representation and is defined locally. In this paper, we introduce a new method for visually smooth interpolation of arbitrary triangle meshes based on a regular 4-split of the domain triangles. Ensuring tangent plane continuity of the surface is not enough for producing an overall fair shape. Interpolation of irregular control-polygons, be that in 1D or in 2D, often yields unwanted undulations. Note that this undulation problem is not particular to parametric interpolation, but also occurs with interpolatory subdivision surfaces. Our new method avoids unwanted undulations by relaxing the constraint of the first derivatives at the input mesh vertices: The tangent directions of the boundary curves at the mesh vertices are now completely free. Irregular triangulations can be handled much better in the sense that unwanted undulations due to flat triangles in the mesh are now avoided.

Polyhedral meshes are used for visualization, computer graphics or geometric modeling purposes and result from many applications like iso-surface extraction, surface reconstruction or CAD/CAM. The paper introduces a method for constructing smooth surfaces from a triangulated polyhedral mesh of arbitrary topology. It presents a new algorithm which generalizes and improves the triangle 4-split method (S. Hahmann and G.-P. Bonneau) in the crucial point of boundary curve network construction. This network is then filled in by a visual smooth surface from which an explicit closed form parametrization is given. Furthermore, the method becomes now completely local and can interpolate normal vector input at the mesh vertices.

Multiresolution analysis based on FWT (Fast Wavelet Transform) is now widely used in scientific visualization. Spherical biorthogonal wavelets for spherical triangular grids were introduced by P. Schroder and W. Sweldens (1995). In order to improve on the orthogonality of the wavelets, the concept of nearly orthogonality, and two new piecewise-constant (Haar) bases were introduced by G.M. Nielson (1997). We extend the results of Nielson. First we give two one-parameter families of triangular Haar wavelet bases that are nearly orthogonal in the sense of Nielson. Then we introduce a measure of orthogonality. This measure vanishes for orthogonal bases. Eventually, we show that we can find an optimal parameter of our wavelet families, for which the measure of orthogonality is minimized. Several numerical and visual examples for a spherical topographic data set illustrates our results.

We introduce multiresolution analysis (MRA) algorithms intended to be used in scientific visualization, and based on a non-nested set of approximating spaces. The need for non-nested spaces arises from the fact that the required scaling functions do not fulfil any refinement equation. Therefore we introduce in the first part the concept of the approximated refinement equation, that allows to generalize the filter bank and exact reconstruction algorithms. The second part shows how this concept enables to define an MRA scheme for piecewise constant data defined on an arbitrary planar or spherical triangular mesh. The ability to deal with arbitrary triangular meshes, without subdivision connectivity, can be achieved only through the use of non-nested approximating spaces, as introduced in the first part.

In this article, we build a multi-resolution framework intended to be used for the visualization of continuous piecewise linear functions defined over triangular planar or spherical meshes. In particular, the data set can be viewed at different level of detail, that's to say as a piecewise linear function defined over any simplification of the base mesh. In his multi-resolution form, the function requires strictly the same volume of data than the original input: It is then possible to go through consecutive levels by the use of so-called detail coefficients, with exact reconstruction if desired. We also show how to choose a decimation sequence that leads to a good compromise between the resulting approximation error and the number of removed vertices. The theoretical tools used here are inspired from wavelet-based techniques and extended in the sense that they can handle non-nested approximation spaces.

Wavelet-based methods have proven their efficiency for visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all wavelet-based methods is a hierarchy of meshes that satisfies subdivision-connectivity. This hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree uniform 2D meshes, octree uniform 3D meshes, or 4-to-1 split triangular meshes. In particular, the necessity of subdivision-connectivity prevents the application of wavelet-based methods on irregular triangular meshes. In this paper, a "wavelet-like" decomposition is introduced that works on piecewise constant data sets over irregular triangular surface meshes. The decomposition/reconstruction algorithms are based on an extension of wavelet-theory allowing hierarchical meshes without property. Among others, this approach has the following features: it allows exact reconstruction of the data set, even for nonregular triangulations, and it extends previous results on Haar-wavelets over 4-to-1 split triangulations.

In the last five years, there has been numerous applications of wavelets and multiresolution analysis in many fields of computer graphics as different as geometric modelling, volume visualization or illumination modelling. Classical multiresolution analysis is based on the knowledge of a nested set of functional spaces in which the successive approximations of a given function converge to that function, and can be efficiently computed. This paper first proposes a theoretical framework which enables multiresolution analysis even if the functional spaces are not nested, as long as they still have the property that the successive approximations converge to the given function. Based on this concept, we finally introduce a new multiresolution analysis with exact reconstruction for large data sets defined on uniform grids. We construct a one-parameter family of multiresolution analyses which is a blending of Haar and linear multiresolution, using BLaC (Blending of Linear and Constant) wavelets.

Abstract The generation of technical smooth surfaces from a mesh of three‐dimensional data points is an important problem in geometric modelling. In this publication we give a survey of some new techniques based on a calculus of variation approach. Apart from the pure construction of these surfaces, the analysis of their quality is equally important in the design and manufacturing process. Generalized focal surfaces are presented here as a new surface interrogation tool.