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In recent years, there has been a lot of research on how to achieve interaction between users and virtual objects using augmented reality. Interaction technologies in augmented reality need to enable users to handle virtual objects intuitively. In addition, since hands are the main means of interaction with objects in real life, it is also necessary to enable interaction operations with hands on virtual objects [1]. In order to make it possible to intuitively handle objects in virtual space using hands in real space, it is necessary to consider whether physical phenomena in real space and virtual space are correctly superimposed (physical consistency). In this study, we proposed a system that allows users to intuitively handle the deformation, movement, and merging of virtual objects in augmented reality. The system was then used by four university students to compare it with existing studies [2].

In Computer Graphics, the two main approaches to rendering and visibility involve ray tracing and rasterization. However, a limitation of both approaches is that they essentially use point sampling. This is the source of noise and aliasing, and also leads to significant difficulties for differentiable rendering. In this work, we present a new rendering method, which we call vectorization, that computes 2D point-to-region integrals analytically, thus eliminating point sampling in the 2D integration domain such as for pixel footprints and area lights. Our vectorization revisits the concept of beam tracing, and handles the hidden surface removal problem robustly and accurately. That is, for each intersecting triangle inserted into the viewport of a beam in an arbitrary order, we are able to maintain all the visible regions formed by intersections and occlusions, thanks to our Visibility Bounding Volume Hierarchy structure. As a result, our vectorization produces perfectly anti-aliased visibility, accurate and analytic shading and shadows, and most important, fast and noise-free gradients with Automatic Differentiation or Finite Differences that directly enables differentiable rendering without any changes to our rendering pipeline. Our results are inherently high-quality and noise-free, and our gradients are one to two orders of magnitude faster than those computed with existing differentiable rendering methods.

We investigate the problem of finding the visible pieces of a scene of objects from a specified viewpoint. In particular, we are interested in the design of an efficient hidden surface removal algorithm for a scene comprised of iso-oriented rectangles. We propose an algorithm where given a set of [Formula: see text] iso-oriented rectangles we report all visible surfaces in [Formula: see text] time and linear space, where [Formula: see text] is the number of surfaces reported. The previous best result by Bern [Journal of Computer and System Sciences 40 (1990) 49–69], has the same time complexity but uses [Formula: see text] space.

Computer-generated hologram runs into difficulty with multi-perspective rendering because it handles threedimensional images. In this study, we propose a hidden surface removal method that enables continuous motion parallax by ray tracing from a point light source placed on a virtual object to the hologram plane. This method allows us to investigate in detail whether light from a point source reaches each pixel of the hologram plane, which in turn enables the removal of hidden surfaces and shading corresponding to continuous viewpoint movement. Although ray tracing is computationally intensive and takes a long time, NVIDIA’s Turing architecture GPUs, which have computation cores specialized for ray tracing, enable fast calculation.

Conventional swept-volume displays can provide accurate physical cues for depth perception. However, the corresponding texture reproduction does not have high quality because such displays employ high-speed projectors with low bit-depth and low resolution. In this study, to address the limitation of swept-volume displays while retaining their advantages, a novel swept-volume three-dimensional (3D) display is proposed by incorporating physical materials as screens. Physical materials such as wool, felt, and so on are directly used for reproducing textures on a displayed 3D surface. Furthermore, we introduce the adaptive pattern generation based on real-time viewpoint tracking to perform the hidden-surface removal. Our algorithm leverages the ray-tracing concept and can run at high speed on GPU.

We have developed an output device for a computer-generated hologram (CGH) named a fringe printer, which can output a 0.35- &mu, m plane-type hologram. We also proposed several CGH with a fringe printer. A computer-generated rainbow hologram (CGRH), which can reconstruct a full color 3D image, is one of our proposed CGH. The resolution of CGRH becomes huge (over 50 Gpixels) due to improvement of the fringe printer. In the calculation, it is difficult to calculate the whole fringe pattern of CGRH at the same time by a general PC. Furthermore, since the fine pixel pitch provides a wide viewing angle in CGRH, object data, which are used in fringe calculation, should be created from many viewpoints to provide a proper hidden surface removal process. The fringe pattern of CGRH is calculated in each horizontal block. Therefore, the object data from several view points should be organized for efficient computation. This paper describes the calculation algorithm for huge resolution CGRH and its output results.

3D CAD models are widely used to improve management of large-scale engineering projects. Examples include Building Information Modeling (BIM) and Oil & Gas industrial plants. Maintaining these facilities is a critical task that often involves anti-corrosive painting of equipment and metallic structures. Existing CAD software estimates the painting area including hidden surfaces that are not actually painted in the field. To improve these computations, we propose an approach based on Adaptively-Sampled Distance Fields (ADFs) exploiting the relationship between object areas and Constructive Solid Geometry (CSG) operations. Tests with synthetic models demonstrate that our technique achieves an accuracy of 99%. In real-world 3D CAD models, we were able to reduce the estimated area by 38% when compared to the naive calculations. These result in significant cost savings in material provision and workforce required for maintaining these facilities.

Hidden images contain one or several concealed foregrounds which can be recognized with the assistance of clues preserved by artists. Experienced artists are trained for years to be skilled enough to find appropriate hidden positions for a given image. However, it is not an easy task for amateurs to quickly find these positions when they try to create satisfactory hidden images. In this paper, we present an interactive framework to suggest the hidden positions and corresponding results. The suggested results generated by our approach are sequenced according to the levels of their recognition difficulties. To this end, we propose a novel approach for assessing the levels of recognition difficulty of the hidden images and a new hidden image synthesis method that takes spatial influence into account to make the foreground harmonious with the local surroundings. During the synthesis stage, we extract the characteristics of the foreground as the clues based on the visual attention model. We validate the effectiveness of our approach by performing two user studies, including the quality of the hidden images and the suggestion accuracy.

most popular lines clipping algorithms are Cohen- Sutherland and Liang-Barsky line clipping algorithm. These algorithms are complex and the steps of calculation are very high. This paper proposes a simple new line clipping algorithm for 2D space which uses the parametric equation of the line. This algorithm further easily extended to the polygon clipping by considering the edge of the polygon as a line. The proposed algorithm is numerically tested for a numbers of random line segments and the results show the simplicity and less complex behavior of the algorithm. Keywordsclipping algorithm, Cohen-Sutherland line clipping algorithm, Liang-Barsky line clipping algorithm. 2D space

This paper presents the processing technique of hidden hypersurface removal for 4-D space visualization. When 4-D space and objects are visualized in 3-D space by perspective projection, if a 4-D scene includes multiple 4-D objects and intricate structures, visibility becomes a fundamental problem in 4-D space visualization. To address this problem and improve the perception of 4-D space, we extend Warnock's area-subdivision algorithm, which is used for hidden surface removal in the domain of 2-D projections of a 3-D scene, to the domain of 3-D projections of a 4-D scene. The visualization results show that our algorithm can display a 4-D scene with correct visibility, and suggest that the hidden hypersurface removal can help us understand the spatial relationship of the 4-D scene.

Traditional hidden surface removal algorithm based on hardware Z-Buffer technique cannot give attention to precision or efficiency at the same time when dealing with the non-uniform triangulated SAR (Synthetic Aperture Radar) scene model. A novel high-precision hidden surface removal approach using fast ray-tube splitting algorithm is proposed, where the SAR scene hidden surface removal problem is decomposed into two simple procedures, i.e. a Delaunay triangulator is used to generate the initial ray tubes from the projected point clouds of all incident visible vertices, then an adaptive ray-tube splitting method is adopted to carry out the complex scene shading situations and resultant visible model reconstruction. Simulation results of typical aircraft and T-72 tank show that, the new approach is feasible and effective.

This paper presents a calculation method of computer-generated holograms that involves removing the hidden surface and provides realistic rendering. The method was based on the ray-tracing method that simulates rays traveling paths. Rays are cast from every elementary hologram into virtual objects and then the traveling paths of the rays are determined. Since the method is considering intersection with objects, absorption, reflection, and refraction, the method is capable of rendering realistic images. Multiple reflections and refraction are expressed by casting additional rays into the reflection direction and the transmission direction and calculating the length of the light path. To express the quality of materials, the Phong reflection model and Cook-Torrance reflection model were used. Results of optical reconstructions show that the hidden surface removal was conducted. Moreover, the texture of material appeared as well as other effects by the proposed method.

Graphic clipping algorithm is a hotspot all the time in computer graphics. Based upon non-intersect polygon boundary, a clipping algorithm on vector graphics is proposed in this paper. The proposed algorithm can be divided into three steps. First, eliminating the boundary which has no intersection with vector graphics and calculating effective intersections; second, dividing graphics into several parts; finally, determining whether each part within boundaries and achieving graphic clipping. Besides, it can be demonstrated by experiments that compared with traditional algorithm, the proposed algorithm is clear, simple, effective and can be applied widely. Furthermore, the proposed algorithm only consumes about 7 seconds in millions of data and the memory consumption nearly unchanged.

This paper focuses on the identification of hidden lines and junctions from natural sketches of drawings that exhibit an extended-trihedral geometry. Identification of hidden lines and junctions is essential in the creation of a complete 3D model of the sketched object, allowing the interpretation algorithms to infer what the unsketched back of the object should look like. This approach first labels the sketched visible edges of the object with a geometric edge label, obtaining a labelled junction at each of the visible junctions of the object. Using a dictionary of junctions with visible and hidden edges, these labelled visible junctions are then used to deduce the edge interpretation and orientation of some of the hidden edges. A genetic algorithm is used to combine these hidden edges into hidden junctions, evolving the representation of the hidden edges and junctions until a feasible hidden view representation of the object is obtained., peer-reviewed

Sometimes, in computer graphics, there is a need to show a part or a piece of a specific picture to study it accurately. For this purpose a window can be used to select the interested part of the picture for display out of other parts. This window is called a clipping window and this process is called a clipping process .On the other hand, clipping is required when a part of a moving image becomes out of the visible zone for display. So the clipping process is one of the important issues in the field of computer graphic specially for real time applications. Therefore a study of the line clipping with respect to a rectangular window while looking to various methods to achieve clipping process in the image space is presented in this paper. In addition to that, performance measurements are conducted and compared. The paper develops a method to perform clipping in the object space in which the line segment is clipped against a viewing volume. Finally, pipelining is adopted to realize clipping algorithm in hardware.

A novel method for hidden-surface removal is proposed for accelerating computation of full-parallax computer-generated holograms (CGHs). When creating high-definition CGHs, the silhouette method is probably the only realistic technique to produce occluded 3D scenes. However, the conventional silhouette method is inefficient and more time-consuming for calculating sparse 3D scenes that include many small objects. Although derived from the silhouette method, the proposed method considerably reduces the computation time for sparse scenes by using Babinet's principle and partial wave field propagation. A definite algorithm as well as formulation is presented in this paper. Furthermore, high-definition CGHs created by the proposed method are demonstrated for verifying the validity of the method.

In order to expand the area of use of beam tracing method, the comprehensive beam tracing method (CBTM) was developed. CBTM is best suited for acoustic and hydro-acoustic simulation of non-homogenous environments. CBTM can trace both refraction as well as reflection of sound wave, using triangular beams. The geometry of scene in CBTM is based on triangles meshes rather than polygons, so complex, irregular shaped objects can be simulated. Furthermore, CBTM traces beams thorough several volumes with different media, allowing for non-convex volumes. This paper presents the algorithms and data structures used for the process of beam division that occurs during the interaction of beam with complex, non-convex environment. Paper also brings measurements of the implemented beam division code and comparison of measured results with results of other methods.

We investigate the computer-generated hologram with full parallax and which can be reconstructed with white light. The object of the hologram is processed from three-dimensional computer graphics polygon data and has shaded surface for hidden surface removal. The optically reconstructed image from the printed hologram is evaluated.

Time-frequency analysis is usually used to reveal the appearance of different frequency components varying with time, in signals, of which time-frequency spectrogram is an important visual tool to display the information. The Mesh Surface Generation (MSG) algorithm is widely used in three-dimensional (3D) modeling. Removing hidden lines from the mesh plot is an essential process that produces explicit depth information. In this paper, a fast and effective method has been proposed for a time-frequency Spectrogram Mesh Surface Generation (SMSG) display, especially, based on the painter&rsquo, s algorithm. In addition, most portable fault diagnosis devices have little function to generate a 3D spectrogram, which generally needs a general computer to realize the complex time-frequency analysis algorithms and a 3D display. However, general computer is not portable and then not suitable for field test. Hence, the proposed SMSG algorithm is applied to an embedded fault diagnosis device, which is light, low-cost, and real-time. The experimental results show that this approach can realize a high degree of accuracy and save considerable time.

We give an output-sensitive algorithm for computing the visibility map of a set of n constant-complexity convex fat polyhedra or curved objects in 3-space. Our algorithm runs in O((n+k) polylog n) time, where k is the combinatorial complexity of the visibility map. This is the first algorithm for computing the visibility map of fat objects that does not require a depth order on the objects and is faster than the best known algorithm for general objects. It is also the first output-sensitive algorithm for curved objects that does not require a depth order.

In this paper, we provide a new architecture by using the programmable graphics processing unit (GPU) to move all electro- magnetic computing code to graphical hardware, which significantly accelerates Graphical electromagnetic computing (GRECO) method. We name this method GPUECO. The GPUECO method not only employs the hidden surface removal technique of graphics hardware to identify the surfaces and wedges visible from the radar direction, but also utilizes the formidable of computing power in programmable GPUs to predict the scattered fields of visible surfaces and wedges us- ing the Physical Optical (PO) and Equivalent Edge Current (EEC). The computational efficiency of the scattered field in fragment pro- cessors is further enhanced using the Z-Cull and parallel reduction techniques, which avoid the inconsistent branching and the addition of the scattered fields in CPU, respectively. Numerical results show excellent agreement with the exact solution and measured data and, the GPUECO method yields approximately 30times faster results.

For practical 3-D computer-generated holograms (CGH), it is important to display surface model shaded images like computer graphics (CG). We have developed a simple process that is used to obtain 3-D data for CGH from two CG images. The first image is a shaded CG image. The second image is a depth-cued image, i.e., image intensity is modulated by the depth of the object. We use a Z-buffer, which is usually used for hidden-surface removal, to make the depth-cued image. We have improved the process to eliminate the problem of the absence of the hidden surface's data, which should appear when a viewer moves. We adapted our process so that it can be used to make a master disk hologram, meaning that, CGHs from processed 3-D Data are displayed on a disk hologram.

We describe a hidden surface removal algorithm for two-dimensional layered scenes built from arbitrary primitives, particularly suited to interaction and animation in rich scenes (for example, in illustration). The method makes use of a set-based raster representation to implement a front-to-back rendering model which analyses and dramatically reduces the amount of rasterization and composition required to render a scene. The method is extended to add frame-to-frame coherence analysis and caching for interactive or animated scenes. A powerful system of primitive-combiners called filters is described, which preserves the efficiencies of the algorithm in highly complicated scenes. The set representation is extended to solve the problem of correlated mattes, leading to an efficient solution for high quality antialiasing. A prototype implementation has been prepared.

Methods of creating digital terrain and landscape models for regional and site specific visualisations are described. A number of alternative approaches are discussed and their relative accuracies are considered. This is followed by a review of the computer graphics procedures which can be used to render such models. Particular attention is directed towards methods for depth cueing, hidden surface removal, shading and texturing. The effects of the atmosphere and methods of producing shadows are also examined. The paper then presents varied applications of such visualisations, including small scale, regional examples and large scale, site specific applications. In conclusion, the role of photogrammetry in the process of visualisation is assessed and possible future developments in this field are identified.

The trajectory of the ball-center point of a ball-end mill slid along a concave-edge region on a part surface becomes a pencil curve, and the ball-end milling along the pencil curve is called pencil curve machining. Presented in the paper is a procedure for computing pencil curves for 3-axis sculptured surface machining. The proposed algorithm traces pencil curves from an offset triangular mesh having numerous intersections (self-intersections). Since the outer skin of an offset triangular mesh makes the valid CL-surface, pencil curves can be obtained by connecting valid intersections lying on the outer skin of the offset mesh. The underlying concept of the proposed algorithm is that visible intersections are always valid for pencil curves. To obtain the visibility data of intersections, the proposed algorithm uses a graphics board, which performs hidden surface removal at a rate of up to a million polygons per second. Various examples have been tested with implementation of the algorithm, and some examples are presented for illustration.

A mono-static high frequency acoustic target strength analysis scheme was developed for underwater targets, based on the far-field Kirchhoff approximation. An adaptive triangular beam method and a concept of virtual surface were adopted for c onsidering the effect of hidden surfaces and multiple reflections of an underwater targe t, respectively. A test of a simple target showed that the suggested hidden surface removal scheme is valid. Then some numerical analyses, for several underwater targets, were carried out; (1) for several simple underwater targets, like sphere, square plate, cylinder, trihedral corner reflector, and (2) for a generic submarine model. The former was exactly coinc ident with the theoretical results including beam patterns versus azimuth angles, and the latter suggested that multiple reflections have to be considered to estimate more accurate target strength of underwater targets. ※Keywords: High frequency acoustic scattering(고주파수 음향산란), Underwater target(수중표 적), Sonar cross section(소나 단면적), Target strength(표적강도), Kirchhoff approximation(키르 코프 근사), Hidden surface removal(은면삭제), Multiple reflection effect(다중반사 효과)

We show that a collection of lines in 3-space can be cut into a subquadratic number of pieces, such that all depth cycles defined by triples of lines are eliminated. This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.

A platform-independent occlusion culling library for dynamic environments, dPVS, can benefit such applications as CAD and modeling tools, time-varying simulations, and computer games. Visibility optimization is currently the most effective technique for improving rendering performance in complex 3D environments. The primary reason for this is that during each frame the pixel processing subsystem needs to determine the visibility of each pixel individually. Currently, rendering performance in larger scenes is input sensitive, and most of the processing time is wasted on rendering geometry not visible in the final image. Here we concentrate on real-time visualization using mainstream graphics hardware that has a z-buffer as a de facto standard for hidden surface removal. In an ideal system only the complexity of the geometry actually visible on the screen would significantly impact rendering time - 3D application performance should be output sensitive.

A novel algorithm is presented for hidden-surface removal in digitally synthetic holograms. The algorithm is able to work with full-parallax holograms and remove obstructed fields in the object wave emitted from threedimensional (3-D) surface objects. This algorithm is initially discussed as a rigorous procedure to obtain fields behind a tilted planar surface by using the rotational transformation of wave fields, and finally results in the silhouette approximation for reduction of computation time. Reconstructions of holograms created by using the algorithm are demonstrated.

We propose clipping methods that are capable of using complex geometries for volume clipping. The clipping tests exploit per-fragment operations on the graphics hardware to achieve high frame rates. In combination with texture-based volume rendering, these techniques enable the user to interactively select and explore regions of the data set. We present depth-based clipping techniques that analyze the depth structure of the boundary representation of the clip geometry to decide which parts of the volume have to be clipped. In another approach, a voxelized clip object is used to identify the clipped regions. Furthermore, the combination of volume clipping and volume shading is considered. An optical model is introduced to merge aspects of surface-based and volume-based illumination in order to achieve a consistent shading of the clipping surface. It is demonstrated how this model can be efficiently incorporated in the aforementioned clipping techniques.

Since the BSP tree algorithm was introduced, many extended or applied algorithms for the original BSP tree algorithm have been reported. Most of the previous work dealt with polygons that are components of polyhedra. If a scene consists of many polyhedra and they are allowed to move, the management cost of a BSP tree becomes expensive and the size of the tree becomes large. This paper presents an object-oriented BSP tree algorithm that can more efficiently deal with a large number of moving polyhedra.

We consider the following problem as defined by Grove et al. [Internat. J. Comput. Geom. Appl. 9 (1999) 207–217]: Given a set of n isothetic rectangles in 3D space determine the subset of rectangles, that are not completely hidden. We present an optimal algorithm for this problem that runs in O( n log n ) time and O( n ) space. Our result is an improvement over the one of Grove et al. by a logarithmic factor in storage and is achieved by using a different approach. An analogous approach gives non-trivial solutions for other kinds of objects too.

In this paper, a new technique for occlusion processing is proposed in computer holography. The new technique based on the silhouette method is very fast as compared with the conventional methods. This technique allows us to remove hidden-surfaces of self-occlude objects and makes it possible to reconstruct fine spatial 3D images that are comparable to that in classical holography. The performance and optical reconstruction is reported.

In this paper, we present an algorithm for visible edge determination from moving viewpoint in 2D-space by an easier approach. We show implementation details and performance analysis of the algorithm to justify the efficiency and correctness of the proposed algorithm. The time complexity of the algorithm is O(n 2 ) in the worst case but we hope time complexity can be reduced practically because of the effective optimization in case of sorting angularly and finding intersection of points in a fixed range. Further modification of this algorithm is expected to determine the visible surface from moving perspective yielding the near optimal solution in 3D-space.

High-definition computer holography based on the polygon-based method commonly uses the silhouette method to shield light behind objects for hidden surface removal. However, the light-shielding is not perfect and causes leakage light passing through many gaps between silhouette-shaped masks. Although we have proposed the principle of more rigorous technique to remove the leakage light, the technique has never been applied to the actual high-definition computer holography because of its long computation time. We propose some techniques to reduce the computation time and apply the rigorous technique to high-definition computer holography. A CGH created by the proposed method is demonstrated.

A novel technique for hidden-surface removal, called switch-back technique, is proposed for fast generation of full-parallax CGHs. The basic theory based on Bibinet’s law as well as the performances are presented with the reconstruction of CGHs.

A computer-generated hologram(CGH) is an ideal three-dimensional(3D) display technology. CGHs are calculated by simulating wave propagation from 3D objects using a computer.

We describe an efficient parallel algorithm for hidden-surface removal for terrain maps. The algorithm runs in O(log 4 n) steps on the CREW PRAM model with a work bound of O((n+k) \polylog ( n)) where n and k are the input and output sizes, respectively. In order to achieve the work bound we use a number of techniques, among which our use of persistent data structures is somewhat novel in the context of parallel algorithms.

Computing the visible portions of curved surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics, and machining applications in manufacturing. Most of the early work has focused on discrete methods based on polygonization or ray-tracing and hidden curve removal. In this paper we present an algorithm for decomposing a given surface into regions so that each region is either completely visible or hidden from a given viewpoint. Initially, it decomposes the domain of each surface based on silhouettes and boundary curves. To compute the exact visibility, we introduce a notion of visibility curves obtained by projection of silhouette and boundary curves and decomposition of the surface into nonoverlapping regions. These curves are computed using marching methods and we present techniques to compute all the components. The nonoverlapping and visible portions of the surface are represented as trimmed surfaces and we present a representation based on polygon trapezoidation algorithms. The algorithms presented use some recently developed algorithms from computational geometry like triangulation of simple polygons and point location. Given the nonoverlapping regions, we use an existing randomized algorithm for visibility computation. We also present results from a preliminary implementation of our algorithm.

The Binary Space Partitioning (BSP) tree achieves fast hidden surface removal for most practical applications where an observer can move through a scene of static objects. However, the BSP algorithm generally increases the number of polygons in a scene due to its splitting stage resulting in a detrimental effect on the priority ordering and more significantly, the display calculations (shading, lighting, shadows, etc.) of the rendering pipeline. We present the Conflict Neutralization algorithm which attempts to reduce the number of splits more effectively than existing techniques whilst maintaining the ‘standard’ model of a BSP tree. Our idea is similar to Conflict Minimization proposed by Fuchs; the significant difference is that our algorithm recognizes that a polygon suitable for selection in the Minimization criterion may subsequently stop the remainder of polygons achieving some reductions in cuts—with Conflict Neutralization, such a polygon is demoted. We compare the results of Conflict Neutralization against Conflict Minimization, the Least-crossed with Most-crossed tie-breaking criterion and our own, enhanced implementation of Conflict Minimization. We show how these techniques fall into different ‘depths of analysis’.

We present a rasterization processor architecture named SPARP (single-pass antialiased rasterization processor), which exploits antialiased rendering in a single pass. Our architecture is basically based on the A-buffer (Carpenter, Computer graphics 1985;19:69–78) algorithm. We have modified the A-buffer algorithm to enhance the efficiency of hardware implementation and quality of the image rendered, such as the data structure of pixel storage elements, the merging scheme of partial-coverage pixels, and the blending of partial-coverage or non-opaque pixels. For the scan conversion and generation of subpixel masks, we use the representation of edges that was proposed by Schilling (Computer graphics 1991;25:131–41). We represent partial-coverage pixels for a pixel location by a front-to-back sorted list as in the A-buffer and dynamically manage the list storage. We have devised a dynamic memory management scheme that extremely simplifies the memory managing overheads so that we can build it by hard-wired logic circuitry. In our architecture we can render an antialiased scene with the same rendering context of Z -buffer method. Depending on the scene complexity, proposed architecture requires rasterization time 1.4–1.7 times as much as a Z -buffer rasterizer does. The buffer memory requirements can vary depending on the scene complexity; the average storage requirement is 2.75 times that of the Z -buffer for our example scenes. Our architecture can be used with most rendering algorithms to produce high-quality antialiased images at the minimally increased rendering time and buffer memory cost, but due to the improvements in semiconductor technology we can expect that antialiased rasterization processors will be widely adopted in the near future.

Hidden surface removal can be achieved using the priority face determination (PFD) tree to create a priority ordering of n polygons in log 4/3 n time. In this paper, we show how the number of polygons stored in the tree and drawn to the screen can be minimized significantly by determining, at the pre-processing stage, which polygons are completely hidden by other polygons from particular regions of the scene. The removal of hidden polygons at the pre-processing stage means that there is no need to even consider them at run time. The cost for the resulting decrease in run time is an increase in the pre-processing time, but techniques for reducing this are presented.

We define a new model of complexity, called object complexity, for measuring the performance of hidden-surface removal algorithms. This model is more appropriate for predicting the performance of these algorithms on current graphics rendering systems than the standard measure of scene complexity used in computational geometry. We also consider the problem of determining the set of visible windows in scenes consisting of n axis-parallel windows in ℝ3. We present an algorithm that runs in optimal Θ(n log n) time. The algorithm solves in the object complexity model the same problem that Bern3 addressed in the scene complexity model.

We devise techniques to manipulate a collection of loosely interpenetrating spheres in three-dimensional space. Our study is motivated by the representation and manipulation of molecular configurations, modeled by a collection of spheres. We analyze the sphere model and point to its favorable properties that make it more easy to manipulate than an arbitrary collection of spheres. For this special sphere model we present efficient algorithms for computing its union boundary and for hidden surface removal. The efficiency and practicality of our approach are demonstrated by experiments on actual protein data.

Two points p and q are circularly-visible from each other, if there exists a circular arc connecting p and q that does not intersect any obstacles. Circularly-hidden surface removal is to identify the circularly-visible portion of an environment, using the circular rays that are generated by rotating the points on a given half-plane about its bounding line. We first characterize the circularly-projected images of polygonal faces. Then, we show that circularly-hidden surface removal for polyhedral objects can be accomplished in O(n2α(n)) time, where n is the total number of edges of given polyhedrons.