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• Introduction of Riemannian global illumination. • A path tracer algorithm to approximate the solution of the Riemannian global illumination. • A map of the algorithm to the GPU, using the RTX platform. • We apply the Non-Euclidean path tracer to render "Photorealistic" inside views of the 3D flat torus, Poincaré sphere, and the hyperbolic mirrored dodecahedron. These are examples of the Euclidean, spherical, and hyperbolic spaces: the Thurston classical geometries. This paper presents a novel path tracer algorithm for immersive visualization of Riemannian manifolds. To do this, we introduce Riemannian illumination, a generalization of classical Computer Graphics illumination models. In this context, global light transport is expressed by extending the rendering equation to Riemannian manifolds. Using Monte Carlo integration to solve this equation results in the novel path tracer for Non-Euclidean spaces. We discuss its basic principles, as well as the general CPU algorithm. Additionally, we discuss in detail how to implement a GPU version, using the RTX pipeline. Finally, we apply the algorithm to render "photorealistic" inside views of the flat torus, Poincaré sphere, and the hyperbolic mirrored dodecahedron. These are examples of Euclidean, spherical, and hyperbolic spaces: the Thurston classical geometries. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new method to control scene sampling in complex ray-based rendering environments. It proposes to constrain image sampling density with a combination of object features, which are known to be well perceived by the human visual system, and image space saliency, which captures effects that are not based on the object''s geometry. The presented method uses Non-Photorealistic Rendering techniques for the object space feature evaluation and combines the image space saliency calculations with image warping to infer quality hints from previously generated frames. In order to map different feature types to sampling densities, we also present an evaluation of the object space and image space features'' impact on the resulting image quality. In addition, we present an efficient, adaptively aligned fractal pattern that is used to reconstruct the image from sparse sampling data. Furthermore, this paper presents an algorithm which uses our method in order to guarantee a desired minimal frame rate. Our scheduling algorithm maximizes the utilization of each given time slice by rendering features in the order of visual importance values until a time constraint is reached. We demonstrate how our method can be used to boost or stabilize the rendering time in complex ray-based image generation consisting of geometric as well as volumetric data. [Copyright &y& Elsevier]

This paper presents a novel gradient-based image completion algorithm for removing significant objects from natural images or photographs. Our method reconstructs the region of removal in two phases. Firstly, the gradient maps in the removed area are completed through a patch-based filling algorithm. After that, the image is reconstructed from the gradient maps by solving a Poisson equation. A new patch-matching criterion is developed in our approach to govern the completion of gradient maps. Both the gradient and the color information are incorporated in this new criterion, so a better image completion result is obtained. Several examples and comparisons are given at the end of the paper to demonstrate the performance of our gradient-based image completion approach. [Copyright &y& Elsevier]

Video segmentation is an important preprocessing step for many computer vision and graphics tasks. Its main goal is to group the voxels in the video volume with similar appearance and motion into spatio-temporally consistent supervoxels. In this paper, we formulate video segmentation as an L 0 gradient minimization problem, so that the spatio-temporal coherence can be effectively enforced through a gradient sparsity pursuit way. In our method, the appearance and motion descriptor space is first built for over-segmented image patches of each video frame. Then the L 0 gradient minimization is performed in the descriptor space, for both spatial and temporal dimensions. To solve the non-convex L 0 norm minimization problem, we extend the fused coordinate descent algorithm from 2D image grids to 3D video volume. We conduct quantitative evaluation of our method in a public video segmentation benchmark LIBSVX. The experimental results demonstrate our superior performance to state-of-the-arts in segmentation accuracy and undersegmentation error, and comparable performance in boundary recall and explained variation. [ABSTRACT FROM AUTHOR]

Abstract: Realistic rain simulation is a challenging problem due to the variety of different phenomena to consider. In this paper we propose a new rain rendering algorithm that extends present state of the art in the field, achieving real-time rendering of rain streaks and splashes with complex illumination effects, along with fog, halos and light glows as hints of the participating media. Our algorithm creates particles in the scene using an artist-defined storm distribution (e.g., provided as a 2D cloud distribution). Unlike previous algorithms, no restrictions are imposed on the rain area dimension or shape. Our technique adaptively samples the storm area to simulate rain particles only in the relevant regions and only around the observer. Particle simulation is executed entirely in the graphics hardware, by placing the particles at their updated coordinates at each time-step, also checking for collisions with the scene. To render the rain streaks, we use precomputed images and combine them to achieve complex illumination effects. Several optimizations are introduced to render realistic rain with virtually millions of falling rain droplets. [Copyright &y& Elsevier]

Abstract: In many applications, the first step into the topological analysis of a discrete point set P sampled from a manifold is the construction of a simplicial complex with vertices on P. In this paper, we present an algorithm for the efficient computation of the Čech complex of P for a given value of the radius of the covering balls. Experiments show that the proposed algorithm can generally handle input sets of several thousand points, while for the topologically most interesting small values of can handle inputs with tens of thousands of points. We also present an algorithm for the construction of all possible Čech complices on P. [Copyright &y& Elsevier]

Abstract: Polycube map is a global cross-surface parameterization technique, where the polycube shape can roughly approximate the geometry of modeled objects while retaining the same topology. The large variation of shape geometry and its complex topological type in real-world applications make it difficult to effectively construct a high-quality polycube that can serve as a good global parametric domain for a given object. In practice, existing polycube map construction algorithms typically require a large amount of user interaction for either pre-constructing the polycubes with great care or interactively specifying the geometric constraints to arrive at the user-satisfied maps. Hence, it is tedious and labor intensive to construct polycube maps for surfaces of complicated geometry and topology. This paper aims to develop an effective method to construct polycube maps for surfaces with complicated topology and geometry. Using our method, users can simply specify how close the target polycube mimics a given shape in a quantitative way. Our algorithm can both construct a similar polycube of high geometric fidelity and compute a high-quality polycube map in an automatic fashion. In addition, our method is theoretically guaranteed to output a one-to-one map. To demonstrate the efficacy of our method, we apply the automatically-constructed polycube maps in a number of computer graphics applications, such as seamless texture tiling, T-spline construction, and quadrilateral mesh generation. [Copyright &y& Elsevier]

Abstract: This paper presents an algorithm for approximating arbitrary polygonal meshes with subdivision surfaces, with the objective of preserving the relevant features of the object while searching the coarsest possible control mesh. The main idea is to firstly extract the feature lines of the object, and secondly construct the subdivision surface over this network. Control points are created by approximating these lines while the connectivity is built with respect to the anisotropy of the object. Our algorithm reinforces the similarity between the subdivision surface and the original shape by affecting an integer sharpness degree to each control edge in order to accurately reproduce the different curvature radii of corresponding fillets and blends. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a novel method that represents the highly complex point sets by clustering and reconstructing the points to normal-mapped B-spline surfaces (NBSs). The main idea is to construct elaborate normal maps on simple surfaces for the realistic rendering of complex point-set models. Based on this observation, we developed the coarse, NBSs to approximate the original point datasets with fine surface details. In our algorithm, a genetic clustering algorithm is proposed to automatically segment the point samples into several clusters according to their statistical properties, and a network of B-spline patches with normal maps are constructed according to the clustering results. In respect to signal processing, our algorithm decouples the original data into two collections: coarse geometry information and fine surface details. The multi-level B-spline surfaces are employed to describe the coarse geometry information, and the normal maps are constructed to capture the fine surface details. Our experimental results show that this representation facilitates the modeling and rendering of complex point sets without losing the visual qualities. [Copyright &y& Elsevier]

Abstract: The winged- and half-edge data structures are commonly used representations for polyhedron models. Due to the complexity, students in an introductory course to computer graphics usually have difficulty in handling these data structures and developing applications. This paper describes the authors’ effort in the development of a visualization and animation tool for teaching and learning these data structures. This tool also includes a simple pseudo-code-like language for algorithm design. Instructors may employ this tool for presentation and demonstration purposes. Students may use the simple language to develop and experiment with new algorithms before their actual implementation. The visualization and animation system may be used to explore and understand the relationship among mesh elements and algorithm execution. [Copyright &y& Elsevier]

The Pythagorean tree is a fractal figure with a branching structure based upon the Pythagorean theorem. This paper describes the use of a greedy algorithm to encourage a homogenous spread of detail for asymmetrical trees and avoid localized regions of high detail. A model of prioritized branch growth based on this idea is used to optimize tree shape, allowing more visually interesting trees to be grown using significantly fewer segments. A comparison of the fractal dimension of the resulting shapes supports the general success of this approach. [Copyright &y& Elsevier]

The paper presents a new algorithm for point-in-polygon queries. By decomposing a polygon into a set of convex polygons and then constructing a BSP tree, the algorithm performs an inclusion query against the polygon in two steps. In the first step, it finds the convex polygon that is most likely to contain the query point through the BSP tree, and then in the second step, it tests whether the query point is in the convex polygon by employing advanced techniques for point-in-convex-polygon queries. The new algorithm is immune of singularity and has a performance of conducting a query by time demand in O(log n), and storage requirement in O(n). The time complexity of the preprocessing is O(n log n) for convex decomposition and BSP tree construction. The new algorithm has its performance in various aspects comparable to the state-of-art algorithms based on trapezoidation. Furthermore, as the number of convex polygons is always much fewer than the number of trapezoids in partitioning a polygon, and a high-quality search tree can always be constructed to manage the convex polygons, the new algorithm can run much faster than the trapezoidation-based algorithms, up to over double folds in maximum. [Copyright &y& Elsevier]

In this paper, we present a search method with multi-class probability estimates for sketch-based 3D engineering part retrieval. The purpose of using probabilistic output from classification is to support high-quality part retrieval by motivating user relevance feedback from a ranked list of top categorical choices. Given a free-hand user sketch, we use an ensemble of classifiers to estimate the likelihood of the sketch belonging to each predefined category by exploring the strengths of various individual classifiers. Complementary shape descriptors are used to generate classifiers with probabilistic output using support vector machines (SVM). A weighted linear combination rule, called adapted minimum classification error (AMCE), is developed to concurrently minimize the classification errors and the log likelihood errors. Experiments are conducted using our Engineering Shape Benchmark database to evaluate the proposed combination rule. User studies show that users can easily identify the desired classes and then the parts under the proposed method and algorithms. Compared with the best individual classifier, the classification accuracy using AMCE increased by 7% for 3D models, and the average best rank improved by 11.6% for sketches. [Copyright &y& Elsevier]

Triangle surface models belong to the most popular type of geometric objects description in computer graphics. Therefore, the problem of fast visualization of this type of data is often solved. One popular approach is stripification, i.e., a conversion of a triangulated object surface into strips of triangles. This enables a reduction of the rendering time by reducing the data size which avoids redundant lighting and transformation computations. The problem of finding an optimal decomposition of triangle surface models to a set of strips is NP-hard and there exist a lot of different heuristic stripification techniques. This paper should help to orient in the jungle of stripification algorithms. We present an overview of existing stripification methods and detailed description of several important stripification methods for fully triangulated meshes. As different authors usually use different data sets and different architectures, it is nearly impossible to compare the quality of stripification methods. For this reason we also present a set of tests of these methods to give the reader a better possibility to compare these methods. [Copyright &y& Elsevier]

In this paper we solve the following optimization problem: given a simple polygon P, what is the maximum-area polygon that is axially symmetric and is contained in P? This problem pops up in shape reasoning when planar shapes are approximated by simpler shapes, e.g., symmetric shapes, or when they are decomposed hierarchically into simpler shapes. We propose an algorithm for solving the problem, analyze its running time, and describe our implementation of it (for the case of a convex polygon). The algorithm is based on building and investigating a planar map, each cell of which corresponds to a different configuration of the inscribed polygon. We prove that the complexity of the map is , where n is the complexity of P. For a convex polygon the complexity is in the worst case. A substantial part of the work concentrates on calculation and analysis of arcs of the planar map. Arcs represent topological changes of the structure of the inscribed polygon, and are determined by the geometry of the original polygon. For each face of the map we calculate the area function of the inscribed polygons and look for a global maximum of the compound area function. We achieve this goal by using a numerical method. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new approach to line drawing that attempts to maintain a uniform packing density of horizontal segments to diagonal segments throughout the line. While the conventional line drawing algorithms perform linear time computations to find the location of the pixels, our algorithm takes logarithmic time. Also, experimental results show that the quality of line is acceptable and comparable to the well-known Bresenham''s line-drawing algorithm. [Copyright &y& Elsevier]

Abstract: Image morphing has been extensively studied in computer graphics and it can be summarized as follows: given two input images, morphing algorithms produce a sequence of inbetween images which transforms the source image into the target image in a visually pleasant way. In this paper, we propose an algorithm, based on recent advances from texture-from-sample ideas, which synthesizes a metamorphosis sequence targeted specifically for textures. We use the idea of binary masks—or texton masks—to control and drive the morphing sequence. Our solution provides an automatic mapping from source texels into target texels and thus guarantees a coherent and visually smoothing transition from the source texture into the target texture. We compare our morphing results with prior work and with simple interpolation between corresponding pixels in the same source and target images. [Copyright &y& Elsevier]

Abstract: This paper presents an intuitive, freehand sketching application for Computer Aided Design (CAD) that can reconstruct a 3D object from a single, flat, freehand sketch. A pen is used to draw 2D sketches consisting of straight and curved strokes connected at vertices. The sketches are processed by a reconstruction algorithm that uses the angular distribution of the strokes and their connectivity to determine an orthogonal 3D axis system whose projection correlates with the observed stroke orientations. The axis system is used to determine a plausible depth for each vertex. This approach works well for drawings of objects whose edges predominantly conform to some overall orthogonal axis system. A second, independent optimization procedure is then used to reconstruct each curved stroke in the original sketch, assuming that the curve is planar. New strokes can be attached to the 3D object, or drawn directly onto the object''s faces. An implementation of the reconstruction algorithm based on Levenberg–Marquardt optimization allows objects with over 50 strokes to be reconstructed in interactive time. [Copyright &y& Elsevier]

Abstract: Impostors can be used as an alternative representation of distant objects in complex 3D scenes. They work by replacing the distant object with a simple texture map. Although this texture map must be updated as the viewpoint moves around the scene, it is not necessary to do this every frame. The saving inherent in not completely rendering the entire scene for every frame means that using impostors can significantly improve frame rate. One of the main challenges presented by the implementation of such a rendering algorithm is the capture, organisation and tracking of the impostor textures needed for every object. This paper explores some ways of doing this using OpenGL in ways that make the best use of current consumer level graphics hardware. [Copyright &y& Elsevier]

The field of computer graphics is expanding and evolving rapidly. Past computer graphics courses addressed low-level topics such as line drawing algorithms (Computers and Graphics 2000;24(1):151–155) while the graphics industry has moved toward scene graph representations of three-dimensional scenes. This discrepancy has moved some educators to suggest graphics courses exclude 2D topics for concentration on 3D. This paper suggests that such a switch is unnecessary and provides a course outline blending old and new topics to provide breadth and relevancy without abandoning the basics. [Copyright &y& Elsevier]