Hidden Surface Elimination Research Articles

Point-Based Rendering of Non-Manifold Surfaces

We are concerned with producing high-quality images of parametric and implicit surfaces, in particular those with non-manifold features. We present a point-based technique for rendering implicit surfaces that uses octree spatial subdivision with a natural interval exclusion test that guarantees that no parts of the surface are missed. This allows us to render non-manifold implicit surfaces at speeds comparable to parametric surfaces. We also derive criteria that guarantee complete pixel coverage of the surface. The point-based method allows for hidden surface elimination using a z-buffer, and shadow casting using a shadow buffer. We illustrate the technique with a number of surfaces, and discuss its advantages and disadvantages.

Fast inverse offset computation using polygon rendering hardware

Mold and die parts are usually fabricated using 3-axis numerically controlled milling machines with ball-end, flat-end or round-end cutters. The cutter location (CL) surface representing a trajectory surface of the cutter's reference point when the cutter is slid over a part is important for preventing the gouging problem. This surface is equivalent to the inverse offset shape of the part, which is the top surface of the swept volume of the inverse cutter moving around the part surface. The author proposes a fast computation method of the inverse offset shape of a polyhedral part using the hidden-surface elimination mechanism of the polygon rendering hardware. In this method, the CL surface is obtained by simply rendering the component objects of the swept volume. An experimental program is implemented and demonstrated.

ＮＣ加工結果の高速な可視化手法 ３次元グラフィックス表示装置の利用

Molds and dies with sculptured surfaces are usually fabricated using numerically controlled (NC) 3-axis milling machines with a spherical cutter. Most CAM systems compute the tool path using the geometric model of designed surfaces in a semi-automatic manner. In order to detect potential problems of the tool path, geometric verifications of the NC milling result are necessary prior to actual machining. Result shape of the workpiece can be computed by subtracting successive tool swept volumes along the path from a solid model representing the stock shape. In this paper, the authors propose an acceleration method of the subtracting operations using the hidden-surface elimination mechanism of the 3-dimensional graphics acceleration hardware. Computation time of the proposed method is basically proportional to the total number of polygons approximating the component surfaces of the swept volumes. Some portions of the component surfaces do not contribute the result shape of the workpiece. Our algorithm reduces the number of polygons by properly excluding such surface portions from the tessellation. An experimental program is implemented and geometric verifications of some sculptured surface milling operations are demonstrated. The program can visualize the complex milling result in a few seconds.

Sweep methods for parallel computational geometry

In this paper we give efficient parallel algorithms for a number of problems from computational geometry by using versions of parallel plane sweeping. We illustrate our approach with a number of applications, which include:General hidden-surface elimination (even if the overlap relation contains cycles).CSG boundary evaluation.Computing the contour of a collection of rectangles.Hidden-surface elimination for rectangles. There are interesting subproblems that we solve as a part of each parallelization. For example, we give an optimal parallel method for building a data structure for line-stabbing queries (which, incidentally, improves the sequential complexity of this problem). Our algorithms are for the CREW PRAM, unless otherwise noted.

Photorealistic terrain imaging and flight simulation

Photorealistic terrain visualization results from combining two data sets. The first contains information about terrain color (texture), usually from a vertical view angle, such as an aerial or satellite image. The second data set contains information about terrain topography, in the form of elevation samples. This data set is also known as a digital terrain model, or DTM. We can reconstruct the 3D terrain from the DTM using various methods. The conventional approach triangulates the terrain into a continuous surface consisting of relatively large planar facets. An alternative approach uses a regular array of atomic values called voxels to represent the terrain. After terrain surface reconstruction, we render the oblique perspective terrain image by a process called phototexturing-the mapping of the corresponding texture onto this surface. Before doing this, we must register the texture and DTM so that the overlay is accurate. This corrects geometric distortions in the data sets, which originate in measurement device or sensor inaccuracies. We obtain the final image by projecting the colored surface onto a viewing plane, incorporating hidden surface elimination.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Output-Sensitive Methods for Rectilinear Hidden Surface Removal

We present an algorithm for the hidden-surface elimination problem for rectangles, which is also known as window rendering. The time complexity of our algorithm is dependent on both the number of input rectangles, n, and on the size of the output, k. Our algorithm obtains a trade-off between these two components, in that its running time is O(r(n1+1/r + k)), where 1 ≤ r ≤ log n is a tunable parameter. By using this method while adjusting the parameter r "on the fly" one can achieve a running time that is O(n log n + k(log n/log(1+k/n))). Note that when k is Θ(n), this achieves an O(n log n) running time, and when k is Θ(n1+ϵ) for any positive constant ϵ, this achieves an O(k) running time, both of which are optimal.

Three views of virtual reality: nonimmersive virtual reality

Nonimmersive virtual reality (VR), which places the user in a 3D environment that can be directly manipulated with a conventional graphics workstation using a monitor, a keyboard; and a mouse, is discussed. The scene is displayed with the same 3D depth cues used in immersive VR: perspective view, hidden-surface elimination, color, texture, lighting, shading and shadows. As in immersive VR, animation and simulation are interactively controlled in response to the user's direct manipulation. Much of the technology used to support immersive and nonimmersive VR is the same. They use the same 3D modeling and rendering and many of the same interaction techniques. The advantages and applications of nonimmersive VR systems are discussed. Immersive and nonimmersive VR systems are compared and hybrid possibilities are reviewed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Hidden Surface Elimination on Parallel Processors

With the wide availability of general purpose parallel computers, there is a need to reconsider hidden surface elimination (HSE) algorithms with respect to parallel implementation. This paper considers MIMD parallel implementations off our common image space HSE algorithms - recursive subdivision, scan line, painter's, and z-buffer. Their suitability for parallel implementation is investigated and their relative performance in multiprocessor systems is measured using polygonal scene descriptions of between 200 and 2500 polygons. Dependence on the size of scene description is measured and results are extrapolated to larger scene descriptions. It is shown that HSE algorithms may be efficiently parallelised. A distributed z-buffer is shown to be a fast and efficient method of solving HSE problems using parallel computers.

A polygonal approach to hidden-line and hidden-surface elimination

We present algorithms for the well-known hidden-line and hidden-surface elimination problems. Our algorithms are optimal in the worst case, and are also able to take advantage of problem instances that are “simpler” than in the worst case. Specifically, our algorithms run in O( n log n + k + t) time, where n is the number of edges, and k (resp. t) is the number of intersecting pairs of line segments (resp. polygons) in the projection plane π. Our algorithms are based on a polygon-based strategy, rather than an edge-based strategy, and are quite simple.

A fast algorithm for determining the insolation at the surface of the earth

AbstractA digital terrain model is a two‐dimensional array which contains elevations of the surface of the Earth. The elevation data are sampled at regular mesh points of appropriate resolution. This paper presents a fast algorithm for determining the isolation on the surface patches at each mesh point.In the case where it can be assumed that it is sufficient to consider only direct rays from a single light source, the insolation at a point in time can easily be computed by employing a hidden surface elimination algorithm having the viewpoint at the light source. In general, however, at the point where the insolation must be determined considering scattered light integrated over an interested period, it is necessary to execute the hidden surface eliminations applied in every direction from the celestial sphere.The algorithm herein has a time complexity of O m n2. This is smaller than those of O(m n2) of naive algorithms employing hidden surface eliminations applied in m directions, where the resolution of digital terrain is n × n. An implemented program shows that our algorithm is 33 times faster than the naive one for m≒;8 100 and 67 times for m≒32,400.

On parallel scan-conversion algorithms for transputer networks

Two fundamental scan line procedures are considered from the point of view of parallel implementation on transputer networks. The paper describes algorithms for the scan conversion of polygons, and the related hidden surface elimination problem for three-dimensional models with polygonal data structures. In each case parallel designs have been implemented and timed in various configurations against a functionally equivalent, but not necessarily optimized, single processor code. The results presented demonstrate that scan line algorithms can be efficiently implemented on suitably configured networks of transputers.

A Framework for Functional Specification and Transformation of Hidden Surface Elimination Algorithms

AbstractThis paper deals with the theory of hidden surface elimination algorithms in Computer Graphics. A set of functions and abstract data types are defined to help concisely specify a class of hidden surface elimination algorithms in a purely functional language. A formal study of these algorithms is presented here along with theorems of equivalence between some of the specifications. It is shown here that such proofs of equivalence will help in the construction of existing as well as new algorithms. We bring in the importance of such a study to exploit alternative parallel architectures for implementation of these algorithms. The other benefits of formal specification and analysis are due to its use as a teaching aid and effective method for rapid prototyping of these algorithms.

Polygon rendering on a dual-paradigm parallel processor

The Disputer is a general purpose parallel processor which incorporates both Single Instruction Multiple Data stream (SIMD) and Multiple Instruction Multiple Data stream (MIMD) parallelism. It is shown how the polygon rendering operations of filling and hidden surface elimination can be efficiently distributed among the SIMD and the MIMD parts of the Disputer. Apart from being a useful graphics application, this work illustrates some of the issues involved in programming the Disputer efficiently and, in particular, the need to keep communication between the SIMD and the MIMD parts low.

The structure of experts: A parallel processor system for 3‐dimensional graphics

AbstractA parallel processor system, called EXPERTS, is developed to generate realistic images of three‐dimensional (3‐D) scenes at a high speed. EXPERTS inputs a list of 3‐D objects defined by a polyhedron model, executes hidden surface elimination by utilizing a scan‐line algorithm, and calculates a frame of pixel values. To perform these processes efficiently, EXPERTS is constructed as a two‐level hierarchical bus‐connected multiprocessor system. This system architecture is derived from the processing scheme employed in which the scan‐line algorithm is divided into two succeeding stages and parallelism is introduced to each stage, respectively. Two types of special‐purpose processor elements were designed to speed up these two processes: that for the former stage is called Scan‐Line Processor (SLP), and that for the latter stage is called PiXel processor (PXP). This paper describes the parallel processing method of scan‐line algorithm, the interconnection scheme of the processor elements, and the details of their hardware architecture. Performance estimation of the system is also presented.

The BRUGEL package: toward computer-aided design of macromolecules

The BRUGEL package: toward computer-aided design of macromolecules

Incremental Polygon Rendering on a SIMD Processor Array

AbstractWe demonstrate how both area coherence and parallelism can be exploited in order to speed up rendering operations on a SIMD square array of processors. Our algorithms take advantage of the method of differences, in order to incrementally compute the values of a linear polynomial function at discrete intervals and thus implement area rendering operations efficiently. We discuss how filling of convex polygons, hidden surface elimination and smooth shading can be implemented on an N × N processor array that supports planar arithmetic, that is, arithmetic operations performed on N × N matrices in parallel for all matrix elements. A major attraction of the method we present is that it is based on a SIMD processor array; such machines are now recognised as highly general purpose given the wide range of applications successfully implemented on them.

A Processor for an Object‐Oriented Rendering System

AbstractAn object oriented approach to the real‐time rendering of raster images is described. The architecture is based on a set of object processors arranged in a pipeline. These object processors scan convert the objects in the scene and interpolate depth and normal vectors across the objects. Hidden surface elimination is distributed along the pipeline. The structure of the object processors and of the algorithms employed are described in detail.Computing Reviews Classification: C. 1.2, C.3, 1.3.1

Displaying Random Surfaces

This paper presents some techniques for simplifying the display of random surfaces created by a regular facet-evolution method similar to that which we described in an earlier paper.1 We concentrate on the problems of hidden surface elimination and shadowing, and show how these can be handled in a way that achieves economy of storage whilst avoiding program complexity. The techniques presented are image space ones, and the emphasis is on producing realistic looking pictures rather than achieving strict mathematical accuracy.

Working with occam: a program for generating display images

It is assumed that a host processor computes the corner coordinates of surfaces and outputs these sequentially, in ranked order, to the components described in an OCCAM program. The data is precomputed and stored in a sequential file. A scheduler controls the activity of a number of zone management processors (ZMPs), all running in parallel, and a special memory buffer. Each ZMP handles only one surface at a time. A processor can pick up a new surface for display when the previous surface has been completed. Only one ZMP can write into a given raster scanline at one time. Others may be writing into the same column of other lines at the same time. Hidden surface elimination is achieved by processing the surfaces in an order ranked on distance from the viewing point. This ranking is done in the host processor. The ranked data is held on a file, which is read sequentially in 512 byte blocks. This data has been previously computed and stored as a sequence of double-byte integers in the required order for a series of picture frames, one frame per 512 byte block. The occam implementation on the Apple II europlus running under UCSD version 4 is very slow. It is postulated that an implementation using separate occam professor hardware units for each appropriate process would run in real time. There is considerable communication between the processors. The activity of each processor is generally sequential and all the processors run in parallel. Comments are made about some of the problems and advantages of programming in occam in an appendix.

Shaded Display of Digital Maps

Improved techniques of surface interpolation, clipping, and hidden-surface elimination help solve some problems in generating perspective views of digital terrain data.