Visible Surface Algorithm Research Articles

Visibility in Computer Graphics

Visibility computation was crucial for computer graphics from its very beginning. The first visibility algorithms in computer graphics aimed to determine visible surfaces in a synthesized image of a three-dimensional scene. Nowadays there are many different visibility algorithms for various visibility problems. We propose a new taxonomy of visibility problems that is based on a classification according to the problem domain. We provide a broad overview of visibility problems and algorithms in computer graphics grouped by the proposed taxonomy. We survey visible surface algorithms, visibility culling algorithms, visibility algorithms for shadow computation, global illumination, point-based and image-based rendering, and global visibility computations. Finally, we discuss common concepts of visibility algorithm design and several criteria for the classification of visibility algorithms.

Using Image Depth Variables as Predictors of Visual Quality

Depth is an important part of our understanding and appreciation of landscape. Attempts made to measure attributes of photographs of landscapes and to develop predictive models of scenic beauty have either failed to include depth or included it by subjective separation of the foreground, mid-ground, and background within the photograph. The process of measurement from photographs is also limiting because it does not provide a mechanism for readily assessing the effect on visual qualities of proposed landscape changes. The process described here requires a detailed digital model of the environment but is then able to generate variables relating to land-cover type, their depth, and patterns of depth in any view direction. Among these variables are several which are closely correlated with scenic beauty and which can together make a good predictive model. Computer systems, which include hardware implementations of three-dimensional visible surface algorithms, offer the possibility of very fast generation of scenic beauty estimates from any location. Such estimates are among the requirements for autonomous agent-based modelling of landscape behaviour.

UTILIZING PARAMETRIC HYPERPATCH METHODS FOR MODELING AND DISPLAY OF FREE-FORM SOLIDS

This paper introduces methods of creating, modifying and visualizing free-form geometric models, by use of the B-spline hyperpatch. Modeling tools for the hyperpatch, including local control-point interactions, lofting operations and sweeping operations, are described. These operations, together with modeling tools generated for free-form surface design, form a powerful tool hierarchy for the design of complex solids. Techniques are also described by which these hyperpatches may be integrated into conventional visible-surface algorithms. With the defined methods, and the hyperpatch model, the complexity of free-form solid object construction was found to be significantly simplified.

Interference detection through rasterization

AbstractInterference detection is a useful technique, but it is also generally time‐consuming. In this paper, a new type of interference detection algorithm is proposed for real‐time interference detection. The algorithm first rasterizes the projection of the target objects and calculates the z‐values, just as done by the z‐buffer visible surface algorithm. For interference detection, all z‐values and pointers to the corresponding faces of objects are saved in a z‐list for each pixel. Sorting the z‐list against the z‐values allows the detection of overlapping objects in the z‐direction at each pixel position and, thus, finds interfering faces by referring to the face pointers in the z‐list.The algorithm is simple and easy to implement. Its computational complexity is directly proportional to the number of polygons, and, in addition, standard graphics hardware can be used to greatly accelerate execution. Another advantage is that the algorithm can be applied to all ‘ray‐traceable’ objects, including algebraic surfaces, and procedurally defined objects; traditionally these were not suitable subjects for interference detection.The algorithm is implemented on a graphics workstation using a standard graphics library. Interference detection at a practical interaction speed is achieved for complicated objects such as polyhedra with thousands of polygons. The algorithm can be used in two ways: for inexpensive interference detection, and as an efficient culling method for more precise collision/interference detection algorithms.

Antialiasing scan-line data

The output of a scan-line visible-surface algorithm is a collection of scan-line segments with associated simple shading functions, which together define the shading as a function of a continuous variable along each scan line. A hybrid antialiasing method that uses this information fully is presented. The method extends to the case where an image transform maps the scan lines into slanted lines in the output raster coordinates. Edge-slope information can be used to infer data along extra scan lines to improve antialiasing. Results obtained with the method are given. >

Computer graphics and animation

This article surveys the theory and techniques of computer graphics and animation. The main topics are modeling primitives, transformations and colors, visible surface algorithms, light and shadows, ray-tracing, texture, phenomena modeling, principles of computer animation, classification of computer animation methods, key-frame animation, and animation of synthetic actors.

Near real-time shadow generation using BSP trees

This paper describes an object-space shadow generation algorithm for static polygonal environments illuminated by movable point light sources. The algorithm can be easily implemented on any graphics system that provides fast polygon scan-conversion and achieves near real-time performance for environments of modest size. It combines elements of two kinds of current shadow generation algorithms: two-pass object-space approaches and shadow volume approaches. For each light source a Binary Space Partitioning (BSP) tree is constructed that represents the shadow volume of the polygons facing it. As each polygon's contribution to a light source's shadow volume is determined, the polygon's shadowed and lit fragments are computed by filtering it down the shadow volume BSP tree. The polygonal scene with its computed shadows can be rendered with any polygon-based visible-surface algorithm. Since the shadow volumes and shadows are computed in object space, they can be used for further analysis of the scene. Pseudocode is provided, along with pictures and timings from an interactive implementation.

Incremental display of CSG models using local updating

Local updating is a strategy for making incremental changes to a geometric model and its displayed image for constant viewing position. Only those parts of a model that are affected by modifications are recomputed and redisplayed, which considerably increase efficiency compared to updating the complete model and its display. Methods are presented for local updating in a solid modelling system with a CSG scanline visible-surface algorithm that can display shaded images directly from a CSG tree using polyhedral primitives. Special attention is given to precise determination of the screen areas that must be updated. It is performed in three stages: rectangular areas, edges, and parts of scanlines of interest are successively determined.

セグメントチェイン法による自由曲面の隠れ面消去処理

This paper presents a fast visible surface algorithm for free form bodies. Conventional algorithms for such objects require a lot of computing time as well as much memory capacity. The proposed algorithm approximates the objects with many small triangles. It makes use of a special triangle data structure which preserves topological information between neighboring triangles and requires comparatively small memory storage. By employing the segment chain method, the algorithm exhibits much faster characteristics compared with the Watkins' algorithm.

Integrated analytic spatial and temporal anti-aliasing for polyhedra in 4-space

A visible surface algorithm with integrated analytic spatial and temporal anti-aliasing is presented. This algorithm models moving polygons as four dimensional (X,Y,Z,T) image space polyhedra, where time (T) is treated as an additional spatial dimension. The linearity of these primitives allows simplification of the analytic algorithms. The algorithm is exact for non-intersecting primitives, and exact for the class of intersecting primitives generated by translation and scaling of 3-d (X,Y,Z) polygons in image space. This algorithm is an extension of Catmull's analytic visible surface algorithm for independent pixel processing, based on the outline of integrated spatial and temporal anti-aliasing given by Korien and Badler. An analytic solution requires that the visible surface calculations produce a continuous representation of visible primitives in the time and space dimensions. Visible surface algorithm, graphical primitives, and filtering algorithm, (by Feibush, Levoy and Cook) are extended to include continuous representation of the additional dimension of time. A performance analysis of the algorithm contrasted with a non-temporally anti-aliased version is given.

An analytic visible surface algorithm for independent pixel processing

An algorithm is presented that solves the visible surface problem at each pixel independently. This allows motion blur and depth of field blurring to be integrated into the algorithm. It also allows parallel processing. The algorithm works on large numbers of polygons. An analytic Gaussian filter is used. The filter can be elongated or scaled differently for each polygon to adjust for its speed or distance from the focal plane. This is achieved by shrinking or scaling the polygon prior to solving the hidden surface problem so that blurring is correctly presented when objects obscure each other.

Near real-time shaded display of rigid objects

Described is a visible surface algorithm and an implementation that generates shaded display of objects with hundreds of polygons rapidly enough for interactive use — several images per second. The basic algorithm, introduced in [Fuchs, Kedem and Naylor, 1980], is designed to handle rigid objects and scenes by preprocessing the object data base to minimize visibility computation cost. The speed of the algorithm is further enhanced by its simplicity, which allows it to be implemented within the internal graphics processor of a general purpose raster system.

An improved illumination model for shaded display

To accurately render a two-dimensional image of a three-dimensional scene, global illumination information that affects the intensity of each pixel of the image must be known at the time the intensity is calculated. In a simplified form, this information is stored in a tree of “rays” extending from the viewer to the first surface encountered and from there to other surfaces and to the light sources. A visible surface algorithm creates this tree for each pixel of the display and passes it to the shader. The shader then traverses the tree to determine the intensity of the light received by the viewer. Consideration of all of these factors allows the shader to accurately simulate true reflection, shadows, and refraction, as well as the effects simulated by conventional shaders. Anti-aliasing is included as an integral part of the visibility calculations. Surfaces displayed include curved as well as polygonal surfaces.

Predetermining visibility priority in 3-D scenes (Preliminary Report)

The principal calculation performed by all visible surface algorithms is the determination of the visible polygon at each pixel in the image. Of the many possible speedups and efficiencies found for this problem, only one published algorithm (developed almost a decade ago by a group at General Electric) took advantage of an observation that many visibility calculations could be performed without knowledge of the eventual viewing position and orientation— once for all possible images . The method is based on a “potential obscuration” relation between polygons in the simulated environment. Unfortunately, the method worked only for certain objects; unmanagable objects had to be manually (and expertly!) subdivided into managable pieces. Described in this paper is a solution to this problem which allows substantial a priori visibility determination for all possible objects without any manual intervention. The method also identifies the ( hopefully, few) visibility calculations which remain to be performed after the viewing position is specified. Also diescussed is the development of still stronger solutions which could further reduce the number of these visibility calculations remaining at image generation time. The reduction in overall processing and memory requirements enabled by this approach may be quite significant, especially for those applications (e.g., 3-D simulation, animation, interactive design) in which numerous visible surface images are generated from a relatively stable data base.

A terrain and cloud computer image generation model

A method is presented that produces a realistic simulation of terrain using source data from the Defense Mapping Agency (DMA). Spatially compact objects are presently modeled with some success at realism. Because terrain is large in extent it exhibits special problems. These problems include: data base size and generation, masking priority, and shading. An array of height values can be created from the DMA terrain file. Height is a single valued function of the array coordinate pair. The pair has implicit positional information. A masking priority algorithm is used which has no restriction on observer geometry. The algorithm searches the height array along the line of sight for the first visible position in the array. This approach requires no clipping or depth sorting of surface representations. The height array indices are used to access the pixel shade from a registered, orthonormal texture array. The use of texture provides a simple way to add nonlinear shading for a realistic representation with flexible data base generation. Atmospheric attenuation is a method used to increase realism. Methods are in use which produce haze or fog with constant attenuation. The line-of-sight search is used to produce realistic clouds with spatially variable attenuation. Terrain and clouds are adequately simulated using this method of modeling. The data structures of height and texture arrays are simple, easily generated, and make good use of storage resources. Resolving masking priority along the line of sight is a visible surface algorithm which has advantages over hidden surface algorithms. Realistic representations such as texture and atmospheric attenuation are used with some success.

An improved illumination model for shaded display

To accurately render a scene, global illumination information that affects the intensity of each pixel of the image must be known at the time the intensity is calculated. In a simplified form, this information is stored in a tree of “rays” extending from the viewer to the first surface encountered and from there to other surfaces and to the light sources. The visible surface algorithm creates this tree for each pixel of the display and passes it to the shader. The shader then traverses the tree to determine the intensity of the light received by the viewer. Consideration of all of these factors allows the shader to accurately simulate true reflection, shadows, and refraction as well as the effects simulated by conventional shaders. Anti-aliasing is included as an integral part of the visibility calculations. Surfaces displayed include curved as well as polygonal surfaces.

A graph-theoretic real-time visible surface editing technique

Efficient visible surface (hidden surface) algorithms must make use of information about the structure of the environment, constraints on viewpoint locations and the coherence between successive views in a sequence. Here the visible surface problem is posed as a problem in graph theory. A new technique based on 'updating cut-sets in a graph is presented as a means to streamline the culling of back faces during visible surface computations. The technique can be used for general environments that contain some convex polyhedra. Since the method saves the most computation when convex polyhedra having many faces appear in the environment, it is particularly appropriate for handling geodesic domes and polyhedral approximations to spheres. A direct extension for nonconvex polyhedra is suggested.

Hierarchical geometric models for visible surface algorithms

The geometric structure inherent in the definition of the shapes of three-dimensional objects and environments is used not just to define their relative motion and placement, but also to assist in solving many other problems of systems for producing pictures by computer. By using an extension of traditional structure information, or a geometric hierarchy, five significant improvements to current techniques are possible. First, the range of complexity of an environment is greatly increased while the visible complexity of any given scene is kept within a fixed upper limit. Second, a meaningful way is provided to vary the amount of detail presented in a scene. Third, “clipping” becomes a very fast logarithmic search for the resolvable parts of the environment within the field of view. Fourth, frame to frame coherence and clipping define a graphical “working set,” or fraction of the total structure that should be present in primary store for immediate access by the visible surface algorithm. Finally, the geometric structure suggests a recursive descent, visible surface algorithm in which the computation time potentially grows linearly with the visible complexity of the scene.

Hierarchical geometric models for visible-surface algorithms

The research described in this paper addresses the problems associated with the design of systems for efficiently producing computer-generated pictures and picture sequences of very complex, three-dimensional environments. The thesis of the research is that the geometric structure inherent in the definition of the shapes of three-dimensional objects and environments must be used not just to define their relative motion and placement but also to assist in solving many other problems of systems for producing pictures by computer.The implications are that by using an extension of traditional structure information, or a geometric hierarchy, five significant improvements to current techniques are possible. First, the range of complexity of an environment is greatly increased while the visible complexity of any given scene is kept within a fixed upper limit. Second, a meaningful way is provided to vary the amount of detail presented in a scene both according to the screen area occupied by the objects in the scene and according to camera and object motions. Third, by using the geometric hierarchy, "clipping" becomes a very fast logarithmic search for the resolvable parts of the environment within the field-of-view. Fourth, by using this positional hierarchy in conjunction with a storage hierarchy of the sort used in virtual memory computing systems, frame-to-frame coherence and clipping define a graphical "working set", or fraction of the total structure that should be present in primary store for immediate access by the visible-surface algorithms. Finally, the proposed structural framework suggests a new recursive descent visible-surface algorithm in which the computation time grows almost linearly with a scene's visible complexity rather than as a worse than linear function of its object-space complexity.

Visible surface algorithms for quadratic patches: Mahl, R.Inst. Elect. Electron. Eng. Trans. Comput., Vol C-21, No 1, (January 1972) pp 1–4

Visible surface algorithms for quadratic patches: Mahl, R.Inst. Elect. Electron. Eng. Trans. Comput., Vol C-21, No 1, (January 1972) pp 1–4