Showing papers in "Computer-aided Design in 1983"
TL;DR: A recursive algorithm for the evaluation of rational Bezier curves is presented; it consists of a construction that works with a constant cross ratio and is carried over to other algorithms.
Abstract: A recursive algorithm for the evaluation of rational Bezier curves is presented; it consists of a construction that works with a constant cross ratio. This geometric principle is carried over to other algorithms.
152 citations
TL;DR: The method of solution presented is based on viewing a part as consisting of several elementary objects and on recognizing these from their specific patterns in the 2D representation.
Abstract: One possible way of specifying the geometry of mechanical parts in CAD follows a two-step procedure: input of a graphics-oriented 2D representation corresponding to views and cuts; and interpretation of this data to give the explicit 3D description. This paper is concerned with the problem of automating the interpretation step. The method of solution presented is based on viewing a part as consisting of several elementary objects and on recognizing these from their specific patterns in the 2D representation. A detailed algorithm is given for the case of three-view representations of parts whose constituent elementary objects are of the uniform-thickness type.
109 citations
TL;DR: In this paper, a plane cubic spline segment is used to approximate the offset line of a plane with respect to the plane's offset line, and the known curvatures and tangents at the end-points of the offset-line are used to calculate the corresponding spline.
Abstract: A plane cubic spline segment is given. We want to approximate its offset line by another cubic spline segment. Therefore we take the known curvatures and tangents at the end-points of the offset line and calculate the corresponding spline. Finally examples are given.
104 citations
TL;DR: In this article, a method of using vectors to represent excess material removed by numerically controlled milling is described and a method for calculating vector intersections with a cylinder representing a milling cutter is developed.
Abstract: The paper describes a method of using vectors to represent excess material removed by numerically controlled milling and develops a method of calculating vector intersections with a cylinder representing a milling cutter. Tests can be made of cutter violations. Major advantages of the method are its applicability to 3-, 4- or 5-axis numerically controlled machine tools and the need for only one algorithm to process any shape.
96 citations
TL;DR: A method for interactive smoothing is outlined and a smoothing algorithm is described which is mathematically comparable to manual smoothing with a physical spline.
Abstract: The most common curve representation in CADCAM systems of today is the cubic parametric spline. Unfortunately this curve will sometimes oscillate and cause unwanted inflexions which are difficult to deal with. This paper has developed from the need to eliminate oscillations and remove inflexions from such splines, a need which may occur for example when interpolating data measured from a model. A method for interactive smoothing is outlined and a smoothing algorithm is described which is mathematically comparable to manual smoothing with a physical spline.
93 citations
TL;DR: This paper considers polynominal curves represented in the rational quadratic, cubic or rational cubic form and algorithms for drawing and curve-curve intersection are described.
Abstract: A new class of algorithms for the processing of parametrically defined curves is presented. All the algorithms are based on the 'divide and conquer' (subdivision) paradigm. An important feature which marks out this class of algorithms from earlier subdivision-based algorithms is that the curve is characterized algebraically and not geometrically. Curve shape properties needed for the processing tasks are derived from the algebraic form of the curve. As long as the necessary properties can be derived, any mathematical from of the curve may be used. In particular this paper considers polynominal curves represented in the rational quadratic, cubic or rational cubic form. Shape properties such as linearity and Euclidean bounds are derived and algorithms for drawing and curve-curve intersection are described.
64 citations
TL;DR: The algorithm to create knots is a modification of de Boor's knot placement scheme and has been realized in the CADCAM system SYRKO, a Daimler-Benz development for car body design and manufacturing.
Abstract: For piecewise polynomial representation of curves, an algorithm to create knots is presented. The aim is to minimize the interpolation error for a given number of knots or, conversely, the number of knots needed to interpolate within a tolerance. The method used is a modification of de Boor's knot placement scheme. The algorithm described in this paper has been realized in the CADCAM system SYRKO, a Daimler-Benz development for car body design and manufacturing.
58 citations
TL;DR: It will be shown that such algorithms can be generated by constructing higher dimensional degenerate Bezier simplices and using their triangular subsimplices to subdivide the original triangular surface.
Abstract: In an earlier paper the author studied subdivision algorithms for Bezier curves. These algorithms were generated by constructing degenerate Bezier triangles and tetrahedra and using their edges to subdivide the original curve. In this paper we take up the study of subdivision algorithms for the triangular Bezier surfaces first introduced by Sabin. It will be shown that such algorithms can be generated by constructing higher dimensional degenerate Bezier simplices and using their triangular subsimplices to subdivide the original triangular surface.
55 citations
TL;DR: This paper describes a method for moving datapoints in a curve net to new ‘smoother’ positions and different techniques to analyse the result of the smoothing are discussed.
Abstract: Bicubic parametric surfaces are often used to represent complex shapes in systems for computer-aided design and manufacture. Such as surface can be defined by a topologically rectangular mesh of cubic parametric splines, a curve which is an approximate mathematical model of the linear elastic beam. Smoothing a bicubic parametric surface can be done by smoothing the curve net that defines it. This paper describes a method for moving datapoints in a curve net to new ‘smoother’ positions. Different techniques to analyse the result of the smoothing are also discussed.
47 citations
TL;DR: Four subdivision algorithms for multivariate splines are discussed in a geometrical manner and the proofs given are mostly geometric also and thus easy to follow.
Abstract: Four subdivision algorithms for multivariate splines are discussed in a geometrical manner. The proofs given are mostly geometrical also and thus easy to follow. An illustrative example demonstrates the effect of the algorithms to a sample surface.
42 citations
TL;DR: A graph theoretic interpretation of the array partitioning problem and the implementation of partitioned arrays as block folded or parallel connected PLAs is presented and an efficient heuristic algorithm is presented.
Abstract: This paper presents a new approach to optimal topological design of PLAs (programmed logic arrays). In particular we address the array partitioning problem and the implementation of partitioned arrays as block folded or parallel connected PLAs. We present a graph theoretic interpretation of the problem and an efficient heuristic algorithm. A computer program, Smile, is described and experimental results are reported.
TL;DR: In this article, the problem is reduced to one of solving a system of algebraic equations that can be either linear or nonlinear, and the method proposed here is illustrated with problems arising from several engineering disciplines.
Abstract: A wide class of tecnical problems involves the determination of shape complying with certain local geometric conditions, such as prescribed — or bounded — values of slope and curvature. Traditionally these problems have been solved by resorting to well-known curves described by algebraic formulae. The class of such curves available is limited, however, and in general curves comply with the desired conditions only at certain intervals. By the introduction of periodic splines it is shown how curves can be synthesized that meet local geometric conditions at a finite set of points that may be located arbitrarily throughout the whole interval of interest. The problem is then reduced to one of solving a system of algebraic equations that can be either linear or nonlinear. The method proposed here is illustrated with problems arising from several engineering disciplines.
TL;DR: Practical aims are the reduction of input effort, the efficient use of memory space and the development of tools for translating machine codes implemented in programmable binary control devices back to graphical representations.
Abstract: This paper deals with the automatic generation of logic schematics. Practical aims are the reduction of input effort, the efficient use of memory space and the development of tools for translating machine codes implemented in programmable binary control devices back to graphical representations. The emphasis lies on the determination of such sequences of logic units that result in a minimal number of line intersections. A new heuristic algorithm that decreases the intersection number successively is proposed. First results of computer experiments are presented.
TL;DR: The Prolog fact dependency system is discussed, together with the facilities it offers architects, and its role in integrated CAAD systems is discussed.
Abstract: A review of integrated CAAD systems and selected research work is presented. The Prolog fact dependency system is discussed, together with the facilities it offers architects.
TL;DR: In this article, a greedy channel-router is presented, where the greedy router wires the channel left-to-right, column-by-column, wiring each column completely before starting the next.
Abstract: A ‘greedy’ channel-router is presented. It is quick, simple and effective. It always suceeds, usually using no more than one track more than required by channel density. It may be forced in rare cases to make a few connections ‘off the end’ of the channel, in order to succeed. It assumes that all pins and wirling lie on a common grid, and that vertical wires are on one layer, horizontal on another. The greedy router wires the channel left-to-right, column-by-column, wiring each column completely before starting the next. Within each column the router tries to maximize the utility of the wiring produced, using simple, ‘greedy’ heuristics. It may place a net on more than one track for a few columns, and collapse the net to a single track later on, using a vertical jog. It may also use a jog to move a net to a track closer to its pin in some future column. The router may occasionally add a new track to the channel, to avoid getting stuck.
TL;DR: This algorithm for displaying curved surfaces with hidden lines eliminated divides the screen space into small 3D boxes to reduce the number of subpatches to be checked to determine the visibility of each grid point.
Abstract: An algorithm for displaying curved surfaces with hidden lines eliminated is described. The surfaces are displayed as rectangular grids of straight segments which approximate those surfaces. The algorith is essentially one of brute force. However, it divides the screen space into small 3D boxes to reduce the number of subpatches to be checked to determine the visibility of each grid point. It turned out that this division process made this algorithm about 10 times faster than the algorithm which had no use of the division. Expanding the algorithm for making contour drawings is very easy. Some methods for drawing silhouette lines are considered.
TL;DR: Application of these techniques to analysing the clarity, consistency, and completeness of existing building design standards, and to developing new standards, are suggested to reduce the effort and cost required to maintain CABD systems applicable and current.
Abstract: This article discusses a set of techniques for expressing and organizing the contents of building design standards, and suggests that application of these techniques, in conjunction with a restructuring of data flow strategies within CABD (computer-aided building design) software systems, are needed to reduce the effort and cost required to maintain CABD systems applicable and current. The article stresses application of these techniques to analysing the clarity, consistency, and completeness of existing building design standards, and to developing new standards. The SASE (Standards Analysis, Synthesis, and Expression) software system, a convenient implementation of the techniques, is presented. The method of use of standards represented by these techniques within a CABD environment is discussed as are implications of the logical expression of standards for constructing expert systems for the building process.
TL;DR: Among curves and surfaces defined by parametric polynomials, the cases dealt with here are those which only have to comply with the requirement to run through a certain number of points previously located in space.
Abstract: Among curves and surfaces defined by parametric polynomials, the cases dealt with here are those which only have to comply with the requirement to run through a certain number of points previously located in space. The process can be totally automatic, but the results are liable to be altered by arbitrary decisions.
TL;DR: This paper considers planar segmented Bezier curves of degree 3 (4) which have all the edges of a given convex polygon as tangents and the segments of which are C^2-(C^3-) continuous in their common joins.
Abstract: This paper considers planar segmented Bezier curves of degree 3 (4) which have all the edges of a given convex polygon as tangents and the segments of which are C^2-(C^3-) continuous in their common joins. Also, the nodes of the B-spline curves which have the same shapes as these Bezier curves are constructed.
TL;DR: The system operates as an interpreter of the user's instructions, storing his decision and the conclusions inferred from those decisions, and automatically maintains consistency from a user's point of view.
Abstract: We describe experimental work in logic programming for architects, leading to the setting up of a fact dependency system. The system operates as an interpreter of the user's instructions, storing his decision and the conclusions inferred from those decisions. Consistency from a user's point of view is automatically maintained. A separate introduction to the Prolog logic programming language is appended to this paper.
TL;DR: The major approaches to database system design are analysed and examples of CAD software systems which have utilized them are indicated and an integraged approach to databaseSystem is proposed as an alternative for further investigations.
Abstract: This paper concerns the application of database theories formulated mostly in the commercial and business area of data processing to CAD software design. The major approaches to database system design are analysed and examples of CAD software systems which have utilized them are indicated. An integraged approach to database system is proposed as an alternative for further investigations.
[...]
TL;DR: The influence of representation technology on concepts and methods in CADCAM is discussed, and the influences of communication between computers, and of knowledge-based programs are considered to throw light on possible scenarios for the future working environment.
Abstract: The paper discusses conceptual changes observed as CADCAM systems progress from one generation to another. The influence of representation technology on concepts and methods in CADCAM is discussed, and then the influences of communication between computers, and of knowledge-based programs are considered. Taken together, these various aspects of computer technology throw light on possible scenarios for the future working environment.
TL;DR: In this paper, a method of constructing a C^1 surface which interpolates to a function and derivative function on an arbitrary triangle is developed, and its polynomial precision set includes all polynomials of degree four or less.
Abstract: A method of constructing a C^1 surface which interpolates to a function and derivative function on an arbitrary triangle is developed. The calculations involved are simple and efficient, and its polynomial precision set includes all polynomials of degree four or less. The approximate errors of the interpolation function are estimated. An example is presented.
TL;DR: An algorithm that calculates the following information for an arbitrary orientable mesh, simplifying the mesh by operations similar to the so-called Euler operators, and may be extended to establish a sequence of Euler operations capable of constructing the mesh.
Abstract: A mesh of quasidisjoint polygons is a useful representation of a surface for many applications of computer graphics and CAD. We present an algorithm that calculates the following information for an arbitrary orientable mesh: • • the number of connected components of the mesh • • for each component whether it is closed or not • • for each open component its boundary curve(s) • • for each component its topological genus If the mesh is not orientable, an error message is generated. For a mesh of n polygons, the algorithm takes O( n log n ) time. The algorithm works by simplifying the mesh by operations similar to the so-called Euler operators. It may be extended to establish a sequence of Euler operations capable of constructing the mesh.
TL;DR: An example relational model is presented as a complementary logical scheme for viewing the shape database that facilitates compact storage and supports non-manipulative query operations through the projection, selection and join operators defined for the relational model, without requiring expert knowledge of the manipulative structure.
Abstract: As the heart of any solid modelling system, much effort has been spent on formulating the data models which represent the shape of a polyhedral solid object within the computer in an accurate, unique and complete manner. Most of this effort has been devoted to make the models manipulateable in terms of computational efficiency, and preserve their semantic integrity. The price paid for achieving these goals is a proliferation of cross-reference data links which, coupled with multiple redundancy, renders the models inefficient for storage or transmission over communication channels. Moreover, the interrogation of these models by non-manipulative applications is usually unsupported functionally, requiring direct accesses to the data, which involves extensive pointer chasing and therefore high familiarity with the manipulative data structure. This paper presents an example relational model as a complementary logical scheme for viewing the shape database that facilitates compact storage and supports non-manipulative query operations through the projection, selection and join operators defined for the relational model, without requiring expert knowledge of the manipulative structure. The flexibility of the relational model, compared with that of the hierarchical, manipulative one, allows easy extensibility and the association of non-geometric attributes with each data item.
TL;DR: It is shown that the usual methods applied by workers in computer graphics are theoretically sound provided care is exercised in defining the range of the coordinate chart.
Abstract: Some mathematical aspects of homogeneous coordinates are presented It is shown that the usual methods applied by workers in computer graphics are theoretically sound provided care is exercised in defining the range of the coordinate chart The mechanics of the linear representation of transformations are explained in terms of commutative diagrams Finally some familiar examples are discussed
TL;DR: In this paper, an integrated solids modelling system for representing and manipulating polyhedral objects bounded by bicubic parametric surfaces is presented, such that the surface underlying any face can be replaced by another surface that has been modelled independently.
Abstract: Since the beginning of geometric modelling as a field of CAD a decade ago, the methods for interactive design of solid objects and interactive design of free-formed surfaces (of degree three and higher) were developed along parallel yet disjoint lines One led to the development of techniques for representing and manipulating the shape of polyhedral solids bounded mostly by planes, while the other led to the development of techniques for the mathematical representation of curved surfaces, without paying attention to their combination into volumetric solids Though the need for integrating solid object modelling with surface modelling for the design of such artefacts as machine parts, aircraft, cars and ships has been widely recognized, there is so far no single modelling system which provides such capabilities in a general way An integrated solids modelling system for representing and manipulating polyhedral objects bounded by bicubic parametric surfaces is presented Its basic capabilities include the representation of solids through a surface-based model, such that the surface underlying any face can be replaced by another surface that has been modelled independently Other functionalities include scaling, rotation and translation of shapes and their pairwise combination into more complex shapes by means of spatial set operators
TL;DR: Techniques for producing pictures with a microcomputer showing surfaces defined by heights on a regular rectangular grid and five types of isometric drawing with hidden lines removed on common types of plotting devices are described.
Abstract: Techniques for producing pictures with a microcomputer showing surfaces defined by heights on a regular rectangular grid are described. The production of contour maps and five types of isometric drawing with hidden lines removed on common types of plotting devices are considered. Examples of pictures are given.
TL;DR: The algorithm has applications as a new means of generating geometric models and, in the CAD/CAM field, for simulating bending processes used to manufacture parts.
Abstract: A geometric algorithm for performing bending operations on polyhedral objects is described. The hypotheses, conditions and model of the bending process are defined, and then the mathematical model of bending is developed for each element of the boundary representation of a polyhedron. The algorithm has applications as a new means of generating geometric models and, in the CAD/CAM field, for simulating bending processes used to manufacture parts. The algorithm has been implemented and examples are given of objects transformed by the bending operation.
IBM1
TL;DR: A special-purpose system which can cut verification time by several orders of magnitude is described, including compiler, linker and register-level language translator, Ysetran, architecture.
Abstract: Gate-level logic simulation takes up more CPU time as system complexity increases. A special-purpose system which can cut verification time by several orders of magnitude is described. The Yorktown Simulation Engine (YSE) is a highly parallel programmable machine which can simulate up to 1 M gates at a speed of over 2000M gate simulations per second. It is estimated that the IBM 3081 processor could have been simulated at over 1 000 instructions per second on YSE. Gate-level logic simulation is reviewed and the architecture and hardware implementation of the YSE is described. The software architecture, including compiler, linker and register-level language translator, Ysetran, architecture, are detailed.