Procedural Content Generation (PCG) has demonstrated its capability to create compelling game content across various domains, including racing games. In this paper, a novel approach utilizing PCG is presented that aims to generate racetracks with the primary objective of ensuring fairness and balanced gameplay regardless of the player’s vehicle choice1. The proposed framework comprises three distinct phases: During the first phase, modular racetrack segments are procedurally generated in order to enhance track variety, which plays a crucial role in providing an engaging gaming experience. In the second phase, AI car controllers are employed on different vehicles to simulate driving through all generated racetrack segments, gathering various statistics. This step allows for the collection of data that will inform decision-making during the final assembly of the complete racetrack. Finally, in the third phase, the collected data is utilized to select and assemble the most suitable racetrack segments, ensuring fairness for all simulated vehicle types by avoiding any potential unfair advantages or disadvantages. To further support this innovative framework, its theoretical foundation is explored, and detailed explanations of each step involved in the process are provided.

A maze is a common structure in a game level. When we design game levels having a different purpose of each level, we may desire mazes with different topological properties, such as lots of branches or long straight-ways. Thus, we need the ability to design mazes based on our game mechanics. In this paper, we introduce our design-centric maze generation in which designers can input their desired properties to create their own mazes. Our method also enables the designers to control the topology of the solution path of a maze. Additionally, this method can provide several mazes which satisfy the given desired properties allowing designers to choose the best maze and use it to build game content for a game level. To demonstrate how useful our design-centric method is, this paper provides several use-cases of building actual game levels and shows that we can design the levels effectively using our method.

Abstract One of the standard techniques to visualize three‐dimensional flow is to use geometry primitives. This solution, when opaque primitives are used, results in high levels of occlusion, especially with dense streamline seeding. Using semi‐transparent geometry primitives can alleviate the problem of occlusion. However, with semi‐transparency some parts of the data set become too vague and blurry, while others are still heavily occluded. We conducted a user study that provided us with results on perceptual limits of using semi‐transparent geometry primitives for flow visualization. Texture models for semi‐transparent streamlines were introduced. Test subjects were shown multiple overlaying layers of streamlines and recorded how many different flow directions they were able to perceive. The user study allowed us to identify a set of top scoring textures. We discuss the results of the user study, provide guidelines on using semi‐transparency for three‐dimensional flow visualization and show how varying textures for different streamlines can further enhance the perception of dense streamlines. We also discuss the strategies for dealing with very high levels of occlusion. The strategies are per‐pixel filtering of flow directions, when only some of the streamlines are rendered at a particular pixel, and opacity normalization, a way of altering the opacity of overlapping streamlines with the same direction. We illustrate our results with a variety of visualizations.

Visualization of flow fields with geometric primitives is often challenging due to occlusion that is inevitably introduced by 3D streamlines. In this paper, we present a novel view-dependent algorithm that can minimize occlusion and reveal important flow features for three dimensional flow fields. To analyze regions of higher importance, we utilize Shannon's entropy as a measure of vector complexity. An entropy field in the form of a three dimensional volume is extracted from the input vector field. To utilize this view-independent complexity measure for view-dependent calculations, we introduce the notion of a maximal entropy projection (MEP) framebuffer, which stores maximal entropy values as well as the corresponding depth values for a given viewpoint. With this information, we develop a view-dependent streamline selection algorithm that can evaluate and choose streamlines that will cause minimum occlusion to regions of higher importance. Based on a similar concept, we also propose a viewpoint selection algorithm that works hand-in-hand with our streamline selection algorithm to maximize the visibility of high complexity regions in the flow field.

No abstract available.

This paper presents a new three-dimensional display system using a reconfigurable projection manifold. The display surface is warped interactively into a non-planar manifold according to the scene image's depth information for the current view. Scene images are projected onto the display using computer graphics and a post-process warping. We currently use two projections to provide a complete coverage of the manifold surface from oblique projection angles. In this paper, we describe the overall design issues and goals of the projector-based rendering process, introduce the algorithms to model the projection manifold surface and describe the algorithms used to create the pre-warped images from the scene image. Our current prototype is a discrete tile-based approximation to the depth manifold. We describe our experiments with two such prototypes, one using a static test configuration, and another actuated using linear motion controllers for each discrete tile. This second prototype can be configured dynamically, as the depth information in the scene changes.

Some applications require scenes mixing polygonal and volumetric objects and shadows make the scenes more realistic. This paper describes a shadow algorithm for mixed polygonal and volumetric data, including the generation of soft shadows for area light sources. Our volume shader leverages advanced graphics GPU for an accelerated and feasible solution. The shadow and soft shadow algorithm applies to all combinations of volumes and polygons, without any restriction on the geometric positioning and overlap of the volumes and polygons. For realistic rendering where we have a high albedo participating media, multiple scattering is significant. We extend our algorithm to handle both multiple forward scattering and back scattering with light attenuation. This constitutes a complete system for shadow generation and light propagation.

Traditional flow volumes construct an explicit geometrical or parametrical representation from the vector field. The geometry is updated interactively and then rendered using an unstructured volume rendering technique. Unless a detailed refinement of the flow volume is specified for the interior, information inside the underlying flow volume is lost in the linear interpolation. These disadvantages can be avoided and/or alleviated using an implicit flow model. An implicit flow is a scalar field constructed such that any point in the field is associated with a termination surface using an advection operator on the flow. We present two techniques, a slice-based three-dimensional texture mapping and an interval volume segmentation coupled with a tetrahedron projection-based renderer, to render implicit stream flows. In the first method, the implicit flow representation is loaded as a 3D texture and manipulated using a dynamic texture operation that allows the flow to be investigated interactively. In our second method, a geometric flow volume is extracted from the implicit flow using a high dimensional isocontouring or interval volume routine. This provides a very detailed flow volume or set of flow volumes that can easily change topology, while retaining accurate characteristics within the flow volume. The advantages and disadvantages of these two techniques are compared with traditional explicit flow volumes.

We present an algorithm for constructing isosurfaces in any dimension. The input to the algorithm is a set of scalar values in a d-dimensional regular grid of (topological) hypercubes. The output is a set of (d-1)-dimensional simplices forming a piecewise linear approximation to the isosurface. The algorithm constructs the isosurface piecewise within each hypercube in the grid using the convex hull of an appropriate set of points. We prove that our algorithm correctly produces a triangulation of a (d-1)-manifold with boundary. In dimensions three and four, lookup tables with 2(8) and 2(16) entries, respectively, can be used to speed the algorithm's running time. In three dimensions, this gives the popular Marching Cubes algorithm. We discuss applications of four-dimensional isosurface construction to time varying isosurfaces, interval volumes, and morphing.

No abstract available.

This paper describes an efficient algorithm to model the light attenuation due to a participating media with low albedo. Here, we consider the light attenuation along a ray, as well as the light attenuation emanating from a surface. The light attenuation is modeled using a splatting volume renderer for both the viewer and the light source. During the rendering, a 2D shadow buffer accumulates the light attenuation. We first summarize the basic shadow algorithm using splatting. Then, an extension of the basic shadow algorithm for projective textured light sources is described. The main part of this paper is an analytic soft shadow algorithm based on convolution techniques. We describe and discuss the soft shadow algorithm, and generate soft shadows, including umbra and penumbra, for extended light sources.

This paper describes an efficient algorithm to model the light attenuation due to a participating media with low albedo. The light attenuation is modeled using splatting volume renderer for both the viewer and the light source. During the rendering, a 2D shadow buffer attenuates the light for each pixel. When the contribution of a footprint is added to the image buffer, as seen from the eye, we add the contribution to the shadow buffer, as seen from the light source. We have generated shadows for point lights and parallel lights using this algorithm. The shadow algorithm has been extended to deal with multiple light sources and projective textured lights.

Distance fields are an important volume representation. A high quality distance field facilitates accurate surface characterization and gradient estimation. However, due to Nyquist's law, no existing volumetric methods based on the linear sampling theory can fully capture surface details, such as comers and edges, in 3D space. We propose a novel complete distance field representation (CDFR) that does not rely on Nyquist's sampling theory. To accomplish this, we construct a volume where each voxel has a complete description of all portions of surface that affect the local distance field. For any desired distance, we are able to extract a surface contour in true Euclidean distance, at any level of accuracy, from the same CDFR representation. Such point-based iso-distance contours have faithful per-point gradients and can be interactively visualized using splatting, providing per-point shaded image quality. We also demonstrate applying CDFR to a cutting edge design for manufacturing application involving high-complexity parts at unprecedented accuracy using only commonly available computational resources.

Visualization algorithms have seen substantial improvements in the past several years. However, very few algorithms have been developed for directly studying data in dimensions higher than three. Most algorithms require a sampling in three-dimensions before applying any visualization algorithms. This sampling typically ignores vital features that may be present when examined in oblique cross-sections, and places an undo burden on system resources when animation through additional dimensions is desired. For time-varying data of large data sets, smooth animation is desired at interactive rates. We provide a fast Marching Cubes like algorithm for hypercubes of any dimension. To support this, we have developed a new algorithm to automatically generate the isosurface and triangulation tables for any dimension. This allows the efficient calculation of 4D isosurfaces, which can be interactively sliced to provide smooth animation or slicing through oblique hyperplanes. The former allows for smooth animation in a very compressed format. The latter provide better tools to study time-evolving features as they move downstream. We also provide examples in using this technique to show interval volumes or the sensitivity of a particular isovalue threshold.

Splatting is widely applied in many areas, including volume, point-based and image-based rendering. Improvements to splatting, such as eliminating popping and color bleeding, occasion-based acceleration, post-rendering classification and shading, have all been recently accomplished. These improvements share a common need for efficient frame-buffer accesses. We present an optimized software splatting package, using a newly designed primitive, called FastSplat, to scan-convert footprints. Our approach does not use texture mapping hardware, but supports the whole pipeline in memory. In such an integrated pipeline, we are then able to study the optimization strategies and address image quality issues. While this research is meant for a study of the inherent trade-off of splatting, our renderer, purely in software, achieves 3- to 5-fold speedups over a top-end texture hardware implementation (for opaque data sets). We further propose a method of efficient occlusion culling using a summed area table of opacity. 3D solid texturing and bump mapping capabilities are demonstrated to show the flexibility of such an integrated rendering pipeline. A detailed numerical error analysis, in addition to the performance and storage issues, is also presented. Our approach requires low storage and uses simple operations. Thus, it is easily implementable in hardware.

Splatting is a volume rendering algorithm that combines efficient volume projection with a sparse data representation. Only voxels that have values inside the iso-range need to be considered, and these voxels can be projected via efficient rasterization schemes. In splatting, each projected voxel is represented as a radially symmetric interpolation kernel, equivalent to a fuzzy ball. Projecting such a basis function leaves a fuzzy impression, called a footprint or splat, on the screen. Splatting traditionally classifies and shades the voxels prior to projection, and thus each voxel footprint is weighted by the assigned voxel color and opacity. Projecting these fuzzy color balls provides a uniform screen image for homogeneous object regions, but leads to a blurry appearance of object edges. The latter is clearly undesirable, especially when the view is zoomed on the object. In this work, we manipulate the rendering pipeline of splatting by performing the classification and shading process after the voxels have been projected onto the screen. In this way volume contributions outside the iso-range never affect the image. Since shading requires gradients, we not only splat the density volume, using regular splats, but we also project the gradient volume, using gradient splats. However alternative to gradient splats, we can also compute the gradients on the projection plane using central differencing. This latter scheme cuts the number of footprint rasterization by a factor of four since only the voxel densities have to be projected.

Splatting is a popular volume rendering algorithm that pairs good image quality with an efficient volume projection scheme. The current axis-aligned sheet-buffer approach, however, bears certain inaccuracies. The effect of these is less noticeable in still images, but clearly revealed in animated viewing, where disturbing popping of object brightness occurs at certain view angle transitions. In previous work, we presented a new variant of sheet-buffered splatting in which the compositing sheets are oriented parallel to the image plane. This scheme not only eliminates the condition for popping, but also produces images of higher quality. In this paper, we summarize this new paradigm and extend it in a number of ways. We devise a new solution to render rectilinear grids of equivalent cost to the traditional approach that treats the anisotropic volume as being warped into a cubic grid. This enables us to use the usual radially symmetric kernels, which can be projected without inaccuracies. Next, current splatting approaches necessitate the projection of all voxels in the iso-interval(s), although only a subset of these voxels may eventually be visible in the final image. To eliminate these wasteful computations we propose a novel front-to-back approach that employs an occlusion map to determine if a splat contributes to the image before it is projected, thus skipping occluded splats. Additional measures are presented for further speedups. In addition, we present an efficient list-based volume traversal scheme that facilitates the quick modification of transfer functions and iso-values.

Splatting is a fast volume rendering algorithm which achieves its speed by projecting voxels in the form of pre-integrated interpolation kernels, or splats. Presently, two main variants of the splatting algorithm exist: (i) the original method, in which all splats are composited back-to-front, and (ii) the sheet-buffer method, in which the splats are added in cache-sheets, aligned with the volume face most parallel to the image plane, which are subsequently composited back-to-front. The former method is prone to cause bleeding artifacts from hidden objects, while the latter method reduces bleeding, but causes very visible color popping artifacts when the orientation of the compositing sheets changes suddenly as the image screen becomes more parallel to another volume face. We present a new variant of the splatting algorithm in which the compositing sheets are always parallel to the image plane, eliminating the condition for popping, while maintaining the insensitivity to color bleeding. This enables pleasing animated viewing of volumetric objects without temporal color and lighting discontinuities. The method uses a hierarchy of partial splats and employs an efficient list-based volume traversal scheme for fast splat access. It also offers more accuracy for perspective splatting as the decomposition of the individual splats facilitates a better approximation to the diverging nature of the rays that traverse the splatting kernels.

The paper describes three new results for volume rendering algorithms utilizing splatting. First, an antialiasing extension to the basic splatting algorithm is introduced that mitigates the spatial aliasing for high resolution volumes. Aliasing can be severe for high resolution volumes or volumes where a high depth of field leads to converging samples along the perspective axis. Next, an analysis of the common approximation errors in the splatting process for perspective viewing is presented. In this context, we give different implementations, distinguished by efficiency and accuracy, for adding the splat contributions to the image plane. We then present new results in controlling the splatting errors and also show their behavior in the framework of our new antialiasing technique. Finally, current work in progress on extensions to splatting for temporal antialiasing is demonstrated. We present a simple but highly effective scheme for adding motion blur to fast moving volumes.

The paper discusses the problem of subdividing unstructured mesh topologies containing hexahedra, prisms, pyramids and tetrahedra into a consistent set of only tetrahedra, while preserving the overall mesh topology. Efficient algorithms for volume rendering, iso-contouring and particle advection exist for mesh topologies comprised solely of tetrahedra. General finite-element simulations however, consist mainly of hexahedra, and possibly prisms, pyramids and tetrahedra. Arbitrary subdivision of these mesh topologies into tetrahedra can lead to discontinuous behaviour across element faces. This will show up as visible artifacts in the iso-contouring and volume rendering algorithms, and lead to impossible face adjacency graphs for many algorithms. The authors present various properties of tetrahedral subdivisions, and an algorithm SOP determining a consistent subdivision containing a minimal set of tetrahedra.

Splatting is a popular direct volume rendering algorithm. However, the algorithm does not correctly render cases where the volume sampling rate is higher than the image sampling rate (e.g. more than one voxel maps into a pixel). This situation arises with orthographic projections of high-resolution volumes, as well as with perspective projections of volumes of any resolution. The result is potentially severe spatial and temporal aliasing artifacts. Some volume ray-casting algorithms avoid these artifacts by employing reconstruction kernels which vary in width as the rays diverge. Unlike ray-casting algorithms, existing splatting algorithms do not have an equivalent mechanism for avoiding these artifacts. The authors propose such a mechanism, which delivers high-quality splatted images and has the potential for a very efficient hardware implementation.

Real time rendering of iso contour surfaces is problematic for large complex data sets. An algorithm is presented that allows very rapid representation of an interval set surrounding an iso contour surface. The algorithm draws upon three main ideas. A fast indexing scheme is used to select only those data points near the contour surface. Hardware assisted splatting is then employed on these data points to produce a volume rendering of the interval set. Finally, by shifting a small window through the indexing scheme or data space, animated volumes are produced showing the changing contour values. In addition to allowing fast selection and rendering of the data, the indexing scheme allows a much compressed representation of the data by eliminating "noise" data points.

Vector field rendering is difficult in 3D because the vector icons overlap and hide each other. We propose four different techniques for visualizing vector fields only near surfaces. The first uses motion blurred particles in a thickened region around the surface. The second uses a voxel grid to contain integral curves of the vector field. The third uses many antialiased lines through the surface, and the fourth uses hairs sprouting from the surface and then bending in the direction of the vector field. All the methods use the graphics pipeline, allowing real time rotation and interaction, and the first two methods can animate the texture to move in the flow determined by the velocity field.>

Simulation of complex 3-dimensional phenomena generate data sets which are hard to comprehend using conventional 2-dimensionally oriented visualization tools. One way to overcome this limitation is to employ various volume visualization techniques. While early volume visualization techniques worked well on simple scalar volumes they failed to exploit frame buffer hardware capabilities and handle higher order data such as vector fields. Work at Lawrence Livermore National Laboratory has centered on developing new techniques and extending existing techniques. This paper describes the various algorithms developed for volume rendering, and presents new methods of examining vector fields in a volumetric fashion.

Volume visualization is becoming an important tool for understanding large 3D data sets. A popular technique for volume rendering is known as splatting. With new hardware architectures offering substantial improvements in the performance of rendering texture mapped objects, we present textured splats. An ideal reconstruction function for 3D signals is developed which can be used as a texture map for a splat. Extensions to the basic splatting technique are then developed to additionally represent vector fields.>

Flow volumes are the volumetric equivalent of stream lines. They provide more information about the vector field being visualized than do stream lines or ribbons. Presented is an efficient method for producing flow volumes, composed of transparently rendered tetrahedra, for use in an interactive system. The problems of rendering, subdivision, sorting, composing artifacts, and user interaction are dealt with. Efficiency comes from rendering only the volume of the smoke, and using hardware texturing and compositing.>

In order to visualize both clouds and wind in climate simulations, clouds were rendered using a 3D texture which was advected by the wind flow. The simulation is described. Rendering, the advection of texture coordinates, and haze effects are discussed. Results are presented.>

Methods for displaying scientific data using textures and raster operations rather than geometric techniques are described. The flexibility and simplicity of raster operations allow a greater choice of visualization techniques with only a small set of basic operations. In addition, texture mapping techniques that allow the representation of several variables simultaneously, without a high degree of clutter, are shown. The combination of traditional geometric techniques, image composition techniques, and image rendering techniques can be integrated into a single framework for the display of scientific data. A system for generating and operating on textures and images for the purposes of scientific visualization is presented. To illustrate its advantage, the development of bump maps for vector filters and contour lines is demonstrated.>