Herb Voelcker and his research team laid the foundations of Solid Modelling, on which Computer-Aided Design is based. He founded the ambitious Production Automation Project, that included Constructive Solid Geometry (CSG) as the basic 3D geometric representation. CSG trees were compact and robust, saving a memory space that was scarce in those times. But the main computational problem was Boundary Evaluation: the process of converting CSG trees to Boundary Representations (BReps) with explicit faces, edges and vertices for manufacturing and visualization purposes. This paper presents some glimpses of the history and evolution of some ideas that started with Herb Voelcker. We briefly describe the path from “localization and boundary evaluation” to “localization and printing”, with many intermediate steps driven by hardware, software and new mathematical tools: voxel and volume representations, triangle meshes, and many others, observing also that in some applications, voxel models no longer require Boundary Evaluation. In this last case, we consider the current research challenges and discuss several avenues for further research.

Slicing a model (computing thin slices of a geometric or volumetric model with a sweeping plane) is necessary for several applications ranging from 3D printing to medical imaging. This paper introduces a technique designed to compute these slices efficiently, even for huge and complex models. We voxelize the volume of the model at a required resolution and show how to encode this voxelization in an out-of-core octree using a novel Sweep Encoding linearization. This approach allows for efficient slicing with bounded cost per slice. We discuss specific applications, including 3D printing, and compare these octrees’ performance against the standard representations in the literature.

The analysis of protein-ligand interactions is a time-intensive task. Researchers have to analyze multiple physico-chemical properties of the protein at once and combine them to derive conclusions about the protein-ligand interplay. Typically, several charts are inspected, and 3D animations can be played side-by-side to obtain a deeper understanding of the data. With the advances in simulation techniques, larger and larger datasets are available, with up to hundreds of thousands of steps. Unfortunately, such large trajectories are very difficult to investigate with traditional approaches. Therefore, the need for special tools that facilitate inspection of these large trajectories becomes substantial. In this paper, we present a novel system for visual exploration of very large trajectories in an interactive and user-friendly way. Several visualization motifs are automatically derived from the data to give the user the information about interactions between protein and ligand. Our system offers specialized widgets to ease and accelerate data inspection and navigation to interesting parts of the simulation. The system is suitable also for simulations where multiple ligands are involved. We have tested the usefulness of our tool on a set of datasets obtained from protein engineers, and we describe the expert feedback.

Abstract Several visual representations have been developed over the years to visualize molecular structures, and to enable a better understanding of their underlying chemical processes. Today, the most frequently used atom‐based representations are the Space‐filling, the Solvent Excluded Surface, the Balls‐and‐Sticks, and the Licorice models. While each of these representations has its individual benefits, when applied to large‐scale models spatial arrangements can be difficult to interpret when employing current visualization techniques. In the past it has been shown that global illumination techniques improve the perception of molecular visualizations; unfortunately existing approaches are tailored towards a single visual representation. We propose a general illumination model for molecular visualization that is valid for different representations. With our illumination model, it becomes possible, for the first time, to achieve consistent illumination among all atom‐based molecular representations. The proposed model can be further evaluated in real‐time, as it employs an analytical solution to simulate diffuse light interactions between objects. To be able to derive such a solution for the rather complicated and diverse visual representations, we propose the use of regression analysis together with adapted parameter sampling strategies as well as shape parametrization guided sampling, which are applied to the geometric building blocks of the targeted visual representations. We will discuss the proposed sampling strategies, the derived illumination model, and demonstrate its capabilities when visualizing several dynamic molecules.

Abstract The analysis of protein‐ligand interactions is complex because of the many factors at play. Most current methods for visual analysis provide this information in the form of simple 2D plots, which, besides being quite space hungry, often encode a low number of different properties. In this paper we present a system for compact 2D visualization of molecular simulations. It purposely omits most spatial information and presents physical information associated to single molecular components and their pairwise interactions through a set of 2D InfoVis tools with coordinated views, suitable interaction, and focus+context techniques to analyze large amounts of data. The system provides a wide range of motifs for elements such as protein secondary structures or hydrogen bond networks, and a set of tools for their interactive inspection, both for a single simulation and for comparing two different simulations. As a result, the analysis of protein‐ligand interactions of Molecular Simulation trajectories is greatly facilitated.

Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point clouds. Previous techniques have developed approximations to convolutions for restricted conditions. Unfortunately, their applicability is limited and cannot be used for general point clouds. We propose an efficient and effective method to learn convolutions for non-uniformly sampled point clouds, as they are obtained with modern acquisition techniques. Learning is enabled by four key novelties: first, representing the convolution kernel itself as a multilayer perceptron; second, phrasing convolution as a Monte Carlo integration problem, third, using this notion to combine information from multiple samplings at different levels; and fourth using Poisson disk sampling as a scalable means of hierarchical point cloud learning. The key idea across all these contributions is to guarantee adequate consideration of the underlying non-uniform sample distribution function from a Monte Carlo perspective. To make the proposed concepts applicable to real-world tasks, we furthermore propose an efficient implementation which significantly reduces the GPU memory required during the training process. By employing our method in hierarchical network architectures we can outperform most of the state-of-the-art networks on established point cloud segmentation, classification and normal estimation benchmarks. Furthermore, in contrast to most existing approaches, we also demonstrate the robustness of our method with respect to sampling variations, even when training with uniformly sampled data only. To support the direct application of these concepts, we provide a ready-to-use TensorFlow implementation of these layers at https://github.com/viscom-ulm/MCCNN.

Molecular simulations are used in many areas of biotechnology, such as drug design and enzyme engineering. Despite the development of automatic computational protocols, analysis of molecular interactions is still a major aspect where human comprehension and intuition are key to accelerate, analyze, and propose modifications to the molecule of interest. Most visualization algorithms help the users by providing an accurate depiction of the spatial arrangement: the atoms involved in inter-molecular contacts. There are few tools that provide visual information on the forces governing molecular docking. However, these tools, commonly restricted to close interaction between atoms, do not consider whole simulation paths, long-range distances and, importantly, do not provide visual cues for a quick and intuitive comprehension of the energy functions (modeling intermolecular interactions) involved. In this paper, we propose visualizations designed to enable the characterization of interaction forces by taking into account several relevant variables such as molecule-ligand distance and the energy function, which is essential to understand binding affinities. We put emphasis on mapping molecular docking paths obtained from Molecular Dynamics or Monte Carlo simulations, and provide time-dependent visualizations for different energy components and particle resolutions: atoms, groups or residues. The presented visualizations have the potential to support domain experts in a more efficient drug or enzyme design process.

We propose to measure the quality of an affine motion by its steadiness, which we formulate as the inverse of its Average Relative Acceleration (ARA). Steady affine motions, for which ARA=0, include translations, rotations, screws, and the golden spiral. To facilitate the design of pleasing in-betweening motions that interpolate between an initial and a final pose (affine transformation), B and C , we propose the Steady Affine Morph (SAM), defined as A t ∘ B with A = C ∘ B -1 . A SAM is affine-invariant and reversible. It preserves isometries (i.e., rigidity), similarities, and volume. Its velocity field is stationary both in the global and the local (moving) frames. Given a copy count, n , the series of uniformly sampled poses, A i/n ∘ B , of a SAM form a regular pattern which may be easily controlled by changing B , C , or n , and where consecutive poses are related by the same affinity A 1/n . Although a real matrix A t does not always exist, we show that it does for a convex and large subset of orientation-preserving affinities A . Our fast and accurate Extraction of Affinity Roots (EAR) algorithm computes A t , when it exists, using closed-form expressions in two or in three dimensions. We discuss SAM applications to pattern design and animation and to key-frame interpolation.

Abstract We explore the automatic recovery of solids from their binary volumetric discretizations. In particular, we propose an approach, called Pressing, for smoothing isosurfaces extracted from binary volumes while recovering their large planar regions (flats). Pressing yields a surface that is guaranteed to contain the samples of the volume classified as interior and exclude those classified as exterior. It uses global optimization to identify flats and constrained bilaplacian smoothing to eliminate sharp features and high frequencies from the rest of the isosurface. It recovers sharp edges between flat regions and between flat and smooth regions. Hence, the resulting isosurface is usually a very accurate approximation of the original solid. Furthermore, the segmentation of the isosurface into flat and curved faces and the sharp/smooth labelling of their edges may be valuable for shape recognition, simplification, compression and various reverse engineering and manufacturing applications.

Abstract Relief impostors have been proposed as a compact and high‐quality representation for high‐frequency detail in 3D models. In this paper we propose an algorithm to represent a complex object through the combination of a reduced set of relief maps. These relief maps can be rendered with very few artifacts and no apparent deformation from any view direction. We present an efficient algorithm to optimize the set of viewing planes supporting the relief maps, and an image‐space metric to select a sufficient subset of relief maps for each view direction. Selected maps (typically three) are rendered based on the well‐known ray‐height‐field intersection algorithm implemented on the GPU. We discuss several strategies to merge overlapping relief maps while minimizing sampling artifacts and to reduce extra texture requirements. We show that our representation can maintain the geometry and the silhouette of a large class of complex shapes with no limit in the viewing direction. Since the rendering cost is output sensitive, our representation can be used to build a hierarchical model of a 3D scene.

Abstract Given a tetrahedral mesh immersed in a voxel model, we present a method to refine the mesh to reduce the discrepancy between interpolated values based on either scheme at arbitrary locations. An advantage of the method presented is that it requires few subdivisions and all decisions are made locally at each tetrahedron. We discuss the algorithm's performance and applications.

Abstract This paper describes a method to obtain a closed surface that approximates a general 3D data point set with nonuniform density. Aside from the positions of the initial data points, no other information is used. Particularly, neither the topological relations between the points nor the normal to the surface at the data points are needed. The reconstructed surface does not exactly interpolate the initial data points, but approximates them with a bounded maximum distance. The method allows one to reconstruct closed surfaces with arbitrary genus and closed surfaces with disconnected shells.

Abstract The computation of the largest planar region approximating a 3D object is an important problem with wide applications in modeling and rendering. Given a voxelization of the 3D object, we propose an efficient algorithm to solve a discrete version of this problem. The input of the algorithm is the set of grid edges connecting the interior and the exterior of the object (called sticks). Using a voting‐based approach, we compute the plane that slices the largest number of sticks and is orientation‐compatible with these sticks. The robustness and efficiency of our approach rests on the use of two different parameterizations of the planes with suitable properties. The first of these is exact and is used to retrieve precomputed local solutions of the problem. The second one is discrete and is used in a hierarchical voting scheme to compute the global maximum. This problem has diverse applications that range from finding object signatures to generating simplified models. Here we demonstrate the merits of the algorithm for efficiently computing an optimized set of textured impostors for a given polygonal model. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling

This paper describes a multiresolution method for implicit curves and surfaces. The method is based on wavelets, and is able to simplify the topology. The implicit curves and surfaces are defined as the zero‐valued piece‐wise algebraic isosurface of a tensor‐product uniform cubic B‐spline. A wavelet multiresolution method that deals with uniform cubic B‐splines on bounded domains is proposed. In order to handle arbitrary domains the proposed algorithm dynamically adds appropriate control points and deletes them in the synthesis phase.

Medical imaging is constantly advancing due to technological improvements in both data gathering devices and data processing of their output. In this progress the heart presents special demands because of its incessant and brisk movement, and intrinsic characteristics. In this paper we briefly survey techniques that can be used to construct a three-dimensional model of a heart, and discuss our approach within an ongoing effort to produce accurate models of a patient's beating heart for both diagnosis and medical training.