Showing papers in "ACM Transactions on Graphics in 1991"

Task-analytic approach to the automated design of graphic presentations

Abstract: BOZ is an automated graphic design and presentation tool that designs graphics based on an analysis of the task for which a graphic is intended to support. When designing a graphic, BOZ aims to optimize two ways in which graphics help expedite human performance of information-processing tasks: (1) allowing users to substitute simple perceptual inferences in place of more demanding logical inferences, and (2) streamlining users' search for needed information. BOZ analyzes a logical description of a task to be performed by a human user and designs a provably equivalent perceptual task by substituting perceptual inferences in place of logical inferences in the task description. BOZ then designs and renders an accompanying graphic that encodes and structures data such that performance of each perceptual inference is supported and visual search is minimized. BOZ produces a graphic along with a perceptual procedure describing how to use the graphic to complete the task. A key feature of BOZ's approach is that it is able to design different presentations of the same information customized to the requirements of different tasks. BOZ is used to design graphic presentations of airline schedule information to support five different airline reservation tasks. Reaction time studies done with real users for one task and graphic show that the BOZ-designed graphic significantly reduces users' performance time to the task. Regression analyses link the observed efficiency savings to BOZ's two key design principles: perceptual inference substitutions and pruning of visual search.

A triangulation algorithm from arbitrary shaped multiple planar contours

Abstract: Conventional triangulation algorithms from planar contours suffer from some limitations. For instance, incorrect results can be obtained when the contours are not convex, or when the contours in two successive slices are very different. In the same way, the presence of multiple contours in a slice leads to ambiguities in defining the appropriate links. The purpose of this paper is to define a general triangulation procedure that provides a solution to these problems. We first describe a simple heuristic triangulation algorithm which is extended to nonconvex contours. It uses an original decomposition of an arbitrary contour into elementary convex subcontours. Then the problem of linking one contour in a slice to several contours in an adjacent slice is examined. To this end, a new and unique interpolated contour is generated between the two slices, and the link is created using the previously defined procedure. Next, a solution to the general case of linking multiple contours in each slice is proposed. Finally, the algorithm is applied to the reconstitution of the external surface of a complex shaped object: a human vertebra.

Efficient Delaunay triangulation using rational arithmetic

Abstract: Many fundamental tests performed by geometric algorithms can be formulated in terms of finding the sign of a determinant. When these tests are implemented using fixed precision arithmetic such as floating point, they can produce incorrect answers; when they are implemented using arbitrary-precision arithmetic, they are expensive to compute. We present adaptive-precision algorithms for finding the signs of determinants of matrices with integer and rational elements. These algorithms were developed and tested by integrating them into the Guibas-Stolfi Delaunay triangulation algorithm. Through a combination of algorithm design and careful engineering of the implementation, the resulting program can triangulate a set of random rational points in the unit circle only four to five times slower than can a floating-point implementation of the algorithm. The algorithms, engineering process, and software tools developed are described.

A general framework for visualizing abstract objects and relations

Abstract: Pictorial representations significantly enhance our ability to understand complicated relations and structures, which means that information systems strongly require user interfaces that support the visualization of many kinds of information with a wide variety of graphical forms. At present, however, these difficult visualization problems have not been solved. We present a visualization framework for translating abstract objects and relations, typically represented in textual forms, into pictorial representations, and describe a general visualization interface based on this framework. In our framework, abstract objects and relations are mapped to graphical objects and relations by user-defined mapping rules. The kernel of our visualization process is to determine a layout of graphical objects under geometric constraints. A constraint-based object layout system named COOL has been developed to handle this layout problem. COOL introduces the concept of rigidity of constraints in order to reasonably handle, a set of conflicting constraints by use of the least squares method. As applications of our system, we show the generation of kinship diagrams, list diagrams, Nassi-Shneiderman diagrams, and entity-relationship diagrams.

Automating the lexical and syntactic design of graphical user interfaces: the UofA* UIMS

Abstract: The primary goal of the UofA* UIMS is to address a key problem with UIMSS: their inability to help in the initial design of user interfaces, Because of this inability, most existing UIMSS require the interface designer to work with low level syntactic and lexical detail, which can be very time-consuming and expensive in terms of effort required. The UofA* approach to this problem is to produce the initial design specification and implementation of the user interface automatically , and then enable the interface designer to improve its appearance and effectiveness through an interactive refinement process, The interface designer, in this approach, works at the conceptual and semantic levels of the user interface and produces a high-level description of the commands the interface is to support. Based on this description the syntactic and lexical levels of the interface are automatically designed and implemented. This interface can be refined by the designer to improve the resulting interaction with the user. The UofA* UIMS facilitates exploration in interface design by using user’s preferences and designer’s guidelines as optional inputs. It allows the creation of interfaces in which many different types of syntaxes can coexist.

Using multivariate resultants to find the intersection of three quadric surfaces

Abstract: Macaulay’s concise but explicit expression for nmltivariate resultants has many potential applications in computer-aided geometric design. Here we describe its use in solid modeling for finding the intersections of three implicit quadric surfaces. By B6zout’s theorem, three quadric surfaces have either at most eight or intlnitely many intersections. Our method finds the intersections, when there are finitely many, by generating a polynomial of degree at most eight whose roots are the intersection coordinates along an appropriate axis. Only addition, subtraction, and multiplication are required to find the polynomial. But when there are pmsibilities of extraneous roots, division and greatest common divisor computations are necessary to identify and remove them.

Integer forward differencing of cubic polynomials: analysis and algorithms

Abstract: Two incremental cubic interpolation algorithms are derived and analysed. Each is based on a known linear interpolation algorithm and modified for third order forward differencing. The tradeoff between overflow avoidance and loss of precision has made forward differencing a method which, although known to be fast, can be difficult to implement. It is shown that there is one particular family of curves which represents the worst case, in the sense that if a member of this family can be accurately drawn without overflow, then any curve which fits in the bounding box of that curve can be. From this the limitations in terms of step count and screen resolution are found for each of the two algorithms.

Closed smooth piecewise bicubic surfaces

Abstract: Two classes of closed piecewiee bicubic surfaces are considered. These surfaces are geometrically smooth about each extraordinary point and, for a large mesh and a large control polyhedron, they are parametrically smooth away from the extraordinary points. Furthermore, free parameters are available for manipulating the shape of the surface without changing the control polyhedron. The control is local for a large control polyhedron.

Drawing antialiased cubic spline curves

Abstract: Cubic spline curves have many nice properties that make them desirable for use in comptuer graphics, and the advantages of antialiasing have been known for some years. Yet, only recently has there been any attempt at directly antialiasing spline curves. Parametric spline curves have resisted antialiasing in several ways: single segments may cross or become tangent to themselves. Cusps and small loops are easily missed entirely. Thus, short pieces of the curve cannot necessarily be rendered in isolation. Finding the distance from a pixel center to the curve accurately and efficiently—usually an essential part of antialiasing—is an unsolved problem. The method presented by Lien, Shantz, and Pratt [21] is a good start, although it considers pixel-length pieces of the curve in isolation and lacks robustness in the handling of certain curves. This paper provides an improved method that is more robust, and is able to handle intersections and tangency.

Rendering curves and surfaces with hybrid subdivision and forward differencing

Abstract: We present a Hybrid Rendering Algorithm (HRA) for rendering parametric curves and surfaces. The algorithm uses a series of Direct Rendering Criteria (DRC) for determining whether the curve surface can be directly rendered by forward differencing with a constant step size. The DRCS test the geometric flatness of the curve/surface, its parametric uniformity, and the ability to use only integer arithmetic in the forward differencing algorithm. If any of the DRCS is not fulfilled, the curve, surface is subdivided, The location of the subdivision in parameter space is chosen to increase the chances that the new segments will satisfy the DRCS, For the integer arithmetic DRC we introduce a general method for determining an alignment of tbe forward differences. We show that for cubic [quartic) curves whose control points lie in a 128K x 128K space this alignment enables up to 2 ‘3(21 L) forward steps. The method is applicable to curves of any order.

Depth-order point classification techniques for CSG display algorithms

Abstract: Constructive Solid Geometry (CSG) defines objects as Boolean combinations (CSG trees) of primitive solids. To display such objects, one must classify points on the surfaces of the primitive solids with respect to the resulting composite object, to test whether these points lie on the boundary of the composite object or not. Although the point classification is trivial compared to the surface classification (i.e., the computation of the composite object), for CSG models with a large number of primitive solids (large CSG trees), the point classification may still consume a considerable fraction of the total processing time. This paper presents an overview of existing and new efficiency-improving techniques for classifying points in depth order. The different techniques are compared through experiments.

Turning point preserving planar interpolation

Abstract: Consider the digital electronic storage of a contour map where the input source may be a printed map or a map in raster form obtained, for example, from satellite imagery. In the case of a printed map, the turning points would be visually selected and digitized. In the case of a map in raster form, the turning points would be determined by critical point detection techniques such as described by l’hapa [8]. When reproducing the map, it is desirable that the computer-generated turning points occur at and only at the points originally input as turning points. For contour maps this requirement is more important than the visual smoothness required for applications such as the design of highways or automobile bodies. The turning points characterize the contour lines and are also known as characteristics points, Marino [51. A turning point, as used here, may be defined as follows: Let Q(u) be a parametrically defined curve. A turning point occurs at the point P = Q( Ul) if, in a small neighborhood of P, the curvature along the curve decreases as u increases for u > UI or as u decreases for u < U1. The curvature need not be uniquely defined at P.

Numerically stable implicitization of cubic curves

Abstract: We give efficient, numerically-stable techniques for converting polynomial, and rational cubic curves to implicit form. We achieve numerical stability by working in a rotated coordinak system and using carefully chosen expressions for the coetlicients that appear in the implicit form. This is more practical than previously known methods which can be numerically unstable unless all computations are done in exact rational arithmetic.

A linear time Oslo algorithm

Abstract: One method of displaying a B-spline surface is to develop a polygonal approximation to the true surface, allowing a polygon-based rendering technique to be employed [1, 4, 5, 8]. Among other applications, the OSZO algorithm provides a way to determine this approximation from an initial B-spline specification [2, 7]. This paper presents an efficient variation to the Oslo algorithm which is appropriate for use in a single-processor environment. The discussion is geared toward curves, and the results are easily applied to surfaces. }

Editorial: Looking back. Looking ahead

Abstract: —increased the annual page count by 33 percent; —created an effective and usable computer system for tracking papers submitted to the journal; —codified and documented our procedures and policies; —taken the journal from publishing a year behind schedule to being on schedule; —maintained, and even increased, the already high quality of papers published in the journal; —considerably decreased the time to review papers submitted to the journal; and —effectively transitioned his responsibilities, records, and computerized system to his successor.”