Showing papers in "ACM Transactions on Graphics in 1984"
TL;DR: It is shown that minimal representations (i.e., polyhedra) can be provided by a surface- based method using nearest neighbors structures or by a volume-based method using the Delaunay triangulation.
Abstract: Different geometric structures are investigated in the context of discrete surface representation. It is shown that minimal representations (i.e., polyhedra) can be provided by a surface-based method using nearest neighbors structures or by a volume-based method using the Delaunay triangulation. Both approaches are compared with respect to various criteria, such as space requirements, computation time, constraints on the distribution of the points, facilities for further calculations, and agreement with the actual shape of the object.
647 citations
TL;DR: Algorithmic procedures that have been implemented to reduce the computational expense of producing ray-traced images are described and examples that indicate the efficiency of these techniques for a variety of representative environments are presented.
Abstract: This paper describes algorithmic procedures that have been implemented to reduce the computational expense of producing ray-traced images. The selection of bounding volumes is examined to reduce the computational cost of the ray-intersection test. The use of object coherence, which relies on a hierarchical description of the environment, is then presented. Finally, since the building of the rayintersection trees is such a large portion of the computation, a method using image coherence is described. This visible-surface preprocessing method, which is dependent upon the creation of an "item buffer," takes advantage of a priori image information. Examples that indicate the efficiency of these techniques for a variety of representative environments are presented.
400 citations
TL;DR: A number of problems, such as the decomposition of simple polygons into convex, star, monotone, spiral, and trapezoidal polygons and the determination of edgevertex visibility, are linearly equivalent to the triangulation problem and therefore share the same lower bound.
Abstract: It' has long been known that the complexity of triangulation of simple polygons having an upper bound of 0 (n log n) but a lower bound higher than ~(n) has not been proved yet. We propose here an easily implemented route to the triangulation of simple polygons through the trapezoidization of simple polygons, which is currently done in O(n log n). Then the trapezoidized polygons are triangulated in O(n) time. Both of those steps can be performed on polygons with holes with the same complexity. We also show in this paper that a number of problems, such as the decomposition of simple polygons into convex, star, monotone, spiral, and trapezoidal polygons and the determination of edgevertex visibility, are linearly equivalent to the triangulation problem and therefore share the same lower bound. It is hoped that this will simplify the task of reducing the gap between the lower and upper bound for these problems.
236 citations
TL;DR: A new concept and method for line clipping is developed that describes clipping in an exact and mathematical form and can be easily generalized for clipping against any convex viewing volume.
Abstract: A new concept and method for line clipping is developed that describes clipping in an exact and mathematical form. The basic ideas form the foundation for a family of algorithms for two-dimensional, three-dimensional, and four-dimensional (homogeneous coordinates) line clipping. The line segment to be clipped is mapped into a parametric representation. From this, a set of conditions is derived that describes the interior of the clipping region. Observing that these conditions are all of similar form, they are rewritten such that the solution to the clipping problem is reduced to a simple max/min expression. For each dimension, the mathematics are discussed, an example is given, the algorithm is designed, and a performance test is conducted. The new algorithm is compared with the traditional Sutherland-Cohen clipping algorithm. Using randomly generated data, the new algorithm showed a 36 percent, 40 percent, and 79 percent improvement for two-dimensional, three-dimensional, and four- dimensional clipping, respectively. One of the advantages of this algorithm is the quick rejection of line segments that are invisible. In addition, this algorithm can be easily generalized for clipping against any convex viewing volume
160 citations
TL;DR: This paper describes a new method for triangulating a simple n-sided polygon, and is the first method whose performance is linear in the number of vertices, up to within a factor that depends only on the shape-complexity of the polygon.
Abstract: This paper describes a new method for triangulating a simple n-sided polygon. The algorithm runs in time O(n log s), with s _< n. The quantity s measures the sinuosity of the polygon, that is, the number of times the boundary alternates between complete spirals of opposite orientation. The value of s is in practice a very small constant, even for extremely winding polygons. Our algorithm is the first method whose performance is linear in the number of vertices, up to within a factor that depends only on the shape-complexity of the polygon. Informally, this notion of shape-complexity measures how entangled a polygon is, and is thus highly independent of the number of vertices. A practical advantage of the algorithm is that it does not require sorting or the use of any balanced tree structure. Aside from the notion of sinuosity, we are also able to characterize a large class of polygons for which the algorithm can be proven to run in O(n log log n) time. The algorithm has been implemented, tested, and empirical evidence has confirmed its theoretical claim to efficiency.
139 citations
TL;DR: An algorithm is described for the decomposition of a bounded concave region of E2 space into a settheoretic combination of convex regions, which exhibits a linear-time complexity for regions whose difference with their convex hull consists of only convex inner regions.
Abstract: An algorithm is described for the decomposition of a bounded concave region of E2 space into a settheoretic combination of convex regions. This algorithm finds the convex hull of the region and then recurses to find the convex hulls of the difference between the original region and its convex hull, until such regions are convex. It exhibits a linear-time complexity for regions whose difference with their convex hull consists of only convex inner regions, a quadratic worst-case complexity, and an average complexity a little worse than linear.
77 citations
TL;DR: It is shown that the proposed 0(1) search-time, O(n) space, and O( n) preprocessing-time algorithm is practically the most efficient among the tested algorithms.
Abstract: The point-location problem is stated as follows: Given a subdivision of the plane by a straight line planer graph G with n vertices and an arbitrary query point Q, determine which region of the subdivision contains Q. A new practical point-location algorithm is proposed. It has 0(1) search time, O(n) space, and O(n) preprocessing time in the average case. Existing point-location algorithms, as well as the one proposed here, have been implemented in FORTRAN, and their practical efficiencies are investigated by computational experiments on several planar subdivisions defined by graphs with 200-4000 vertices. It is shown that our 0(1) search-time, O(n) space, and O(n) preprocessing-time algorithm is practically the most efficient among the tested algorithms.
73 citations
TL;DR: Algorithms for performing the calculation of the intersection of a line with an object for objects defined by sweeping a planar cubic spline through space using translational, rotational, and conic sweeping are presented.
Abstract: The crucial step in a program based on ray tracing is the calculation of the intersection of a line with an object. In this paper, algorithms are presented for performing this calculation for objects defined by sweeping a planar cubic spline through space. Translational, rotational, and conic sweeping are treated. Besides solutions for the exact calculation, rectangle tests for improving efficiency are given. Possible extensions and improvements are discussed.
53 citations
TL;DR: An interactive pushdown automaton is defined as a model for user interface management dialogue control and examples are given for how various features present in otheruser interface management systems are modeled using the IPDA.
Abstract: An interactive pushdown automaton is defined as a model for user interface management dialogue control. The relationships between dialogue control and device handling are defined in terms of acquiring, releasing, enabling, and disabling of devices. Input modes are defined by sets of acquired devices and input states are defined by sets of enabled devices. A specified automaton describes the dialogue. Semantic controls of parse transitions, as well as pervasive transitions for exceptional conditions, are supported in the automaton. Algorithms are given to convert a specified automaton into an executable automaton. For the executable automaton an interpretation algorithm, which incorporates the control of input modes and states, is given. Examples are given for how various features present in other user interface management systems are modeled using the IPDA.
51 citations
TL;DR: The system architecture and protocols necessary to achieve virtual terminal support for both local and remote applications with a range of requirements, including graphics, are presented and an existing implementation is evaluated.
Abstract: One of the most important functions of an intelligent workstation is to provide a state-of-the-art user interface to distributed resources. One aspect of such an interface is virtual terminal support for both local and remote applications with a range of requirements, including graphics. To ensure good response for remote applications, in particular, the bulk of user interaction must be handled local to the workstation. Therefore, the terminal management software on the workstation must provide object modeling as well as viewing facilities, in contrast to most contemporary graphics systems. One way of doing this is to support structured display files. It is equally important to support simultaneous access to multiple applications; thus the terminal management software must provide window system Lscilities. Lastly, since the terminal management software should present a common interface to both local and remote applications, the workstation itself should be regarded as a multifunction component of the distributed system and not strictly as a terminal or a personal computer. This paper presents the system architecture and protocols necessary to achieve these goals and evaluates an existing implementation.
46 citations
TL;DR: An algorithmic solution to determining the outlines for an unconstrained brush and some ideas on a canonical brush and its use in solving the inverse problem, that is, determininl, the brushtrajectory description from given outlines are presented.
Abstract: The brush-trajectory method, a very natural scheme for describing two-dimensional shapes used in graphic arts and typesetting applications, has been used in only a few systems largely ¢,wing to the computational complexity involved in transforming such descriptions into raster bit maps. This paper addresses the problem. For some specific brushes and trajectories we derive algebraic solutions for describing the resulting outlines. The result of dynamic transformations on the brush as it moves along the trajectory is also studied. A special closed, smooth, convex brush defined by a Jburth-order parametric equation is introduced to describe more complex shapes. An algorithmic solution to determining the outlines for an unconstrained brush is then presented. Finally, we present some ideas on a canonical brush and its use in solving the inverse problem, that is, determininl, the brushtrajectory description from given outlines.
TL;DR: A novel algorithm for automatic finite-element mesh generation that has been implemented in two dimensions and is capable of generating predominantly "good" quadrilateral elements.
Abstract: A novel algorithm for automatic finite-element mesh generation is described. It uses constructive solid geometry to provide the geometric data for the object to be meshed. The geometric definition of the object and a value for the required mesh density are the only inputs. The method consists of two stages: point generation and mesh construction over the points. It has been implemented in two dimensions and is capable of generating predominantly "good" quadrilateral elements. Triangular elements are only created in circumstances under which quadrilateral elements are not feasible.
TL;DR: Markov chains are shown to be associated with solutions to the following three geometric problems: given a curve B[P](t), alter the shape of the curve by changing the blending functions B(t).
Abstract: The connection between probability theory and computer-aided geometric design is explored further. Markov chains are shown to be associated with solutions to the following three geometric problems: (1) Given a curve B[P](t), alter the shape of the curve by changing the control points P. (2) Given a curve B[P](t), alter the shape of the curve by changing the blending functions B(t.). (3) Given a curve B[P](t) and blending functions D(t), find control points Q so that D[Q](t) = B[P](t). Constraints imposed on these Markov chains by computer-aided geometric design are also derived.
TL;DR: The raster graphics architecture is an extension of the RasterOp model and supports operations for rectangle movement, text writing, curve drawing, flood, and fill and is intended for implementation by both closely and loosely coupled display subsystems.
Abstract: A raster graphics architecture and a raster graphics device are described. The graphics architecture is an extension of the RasterOp model and supports operations for rectangle movement, text writing, curve drawing, flood, and fill. The architecture is intended for implementation by both closely and loosely coupled display subsystems. The first implementation of the architecture is a remote raster display connected by fiber optics to a VAX minicomputer. The device contains a separate microprocessor, frame buffer, and additional local memory; it is capable of executing raster commands on operands in local memory or VAX host memory.
TL;DR: The idea for a Special Issue of Transactions on Graphics devoted to Computational Geometry arose from conversations between myself, Leo Guibas, and Jorge Nievergelt at Xerox Palo Alto Research Center in the spring of 1983, and it was therefore decided to publish two full Special Issues and include two papers in the next regular issue of TOG.
Abstract: The idea for a Special Issue of Transactions on Graphics devoted to Computational Geometry arose from conversations between myself, Leo Guibas, and Jorge Nievergelt at Xerox Palo Alto Research Center in the spring of 1983. We felt that it was time to attempt to bridge the historical divide between the two schools of computational geometry that had emerged during the 1970's, and that TOG was an appropriate forum. The call for papers produced more contributions than we had expected, many of high quality, and some lengthy. It was therefore decided to publish two full Special Issues (April 1984 and this one) and include two papers in the next regular issue of TOG {January 1985). We would like to thank contributors and referees for their help and valued advice. The earliest reference to computational geometry that I have been able to discover appears to be Minsky and Papert 's 1969 book "Perceptrons," subtitled "An Introduction to Computational Geometry." [1] Unfortunately the term is not defined, nor is it mentioned in the index, or as far as I recall, elsewhere in the book, and we are left to draw our own conclusions as to what the authors intended the term to mean! Independently, while at Cambridge University, I had decided that using computers to perform geometric calculations required a fresh approach to geometry and I defined computational geometry in 1971 as
TL;DR: The window controller developed for the computer animation system (TAN) of the human-body modeling and positioning system TEMPUS (Badler et al., 1983) is characterized, and its operation is illustrated with diagrams.
Abstract: The window controller developed for the computer animation system (TAN) of the human-body modeling and positioning system TEMPUS (Badler et al., 1983) is characterized, and its operation is illustrated with diagrams. The controller is associated with a screen viewport and comprises five nested squares related to five modifications of the window, including zooming in and out, translation, locking plus translation, and extension of extremes plus translation. The variations of the controller and its limitations are considered, and its advantages over the use of a miniworld in a separate viewport are indicated.