Showing papers on "Line segment published in 1984"

A fast sequential method for polygonal approximation of digitized curves

Abstract: A new and very fast algorithm for polygonal approximation is presented. It uses a scan-along technique where the approximation depends on the area deviation for each line segment. The algorithm outputs a new line segment when the area deviation per length unit of the current segment exceeds a prespecified value. Pictures are included, showing the application of the algorithm to contour coding of binary objects. Some useful simplifications of the algorithms are suggested.

Discrete Representation of Straight Lines

Abstract: If a continuous straight line segment is digitized on a regular grid, obviously a loss of information occurs. As a result, the discrete representation obtained (e.g., a chaincode string) can be coded more conveniently than the continuous line segment, but measurements of properties (such as line length) performed on the representation have an intrinsic inaccuracy due to the digitization process. In this paper, two fundamental properties of the quantization of straight line segments are treated. 1) It is proved that every ``straight'' chaincode string can be represented by a set of four unique integer parameters. Definitions of these parameters are given. 2) A mathematical expression is derived for the set of all continuous line segments which could have generated a given chaincode string. The relation with the chord property is briefly discussed.

A New Concept and Method for Line Clipping

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

Fourier Coding of Image Boundaries

Abstract: A transform coding scheme for closed image boundaries on a plane is described The given boundary is approximated by a series of straight line segments Depending on the shape, the boundary is represented by the (x-y) coordinates of the endpoints of the line segments or by the magnitude of the successive radii vectors that are equispaced in angle around the given boundary Due to the circularity present in the data, the discrete Fourier transform is used to exactly decorrelate the finite boundary data By fitting a Gaussian circular autoregressive model to represent the boundary data, estimates of the variances of the Fourier coefficients are obtained Using the variances of the Fourier coefficients and the MAX quantizer, the coding scheme is implemented The scheme is illustrated by an example

On-line recognition method and apparatus for a handwritten pattern

Abstract: Coordinates of a handwritten pattern drawn on a tablet are sequentially sampled by a pattern recognition unit to prepare pattern coordinate data. Based on an area encircled by segments created by the sampled pattern coordinate data of one stroke and a line connecting a start point and an end point of the one-stroke coordinate data, the sampled pattern coordinate data of the one stroke is converted to a straight line and/or curved line segments. The converted segments are quantized and normalized. The segments of the normalized input pattern are rearranged so that the input pattern is drawn in a predetermined sequence. Differences between direction angles for the rearranged segments are calculated. Those differences are compared with differences of the direction angles of the dictionary patterns read from a memory to calculate a difference therebetween. The matching of the input pattern and the dictionary pattern is determined in accordance with the difference. If the matching fails, the first or last inputted segment of the input pattern is deleted or the sampled pattern coordinate data of the next stroke is added, to continue the recognition process.

A data reduction algorithm for planar curves

Abstract: A planar curve may be represented by a sequence of connected line segments. Existent algorithms for reducing the number of line segments used to represent a curve are examined. An efficient (linear time), computationally simple algorithm is developed. This algorithm achieves a high degree of data reduction while producing a representation that is accurate for even the most complex curves.

Curvilinear interpolation system and method

Abstract: A curvilinear interpolation system and method for use in a numerical control apparatus such as a machine tool or a robot having two or more drive axes and movable while effecting linear interpolation on a given curve with a plurality of line segments. For each line segment a curvature K p of the curve is calculated at a current curve interpolating point P p , and a curvature K n calculated at a point P n on the curve spaced a given search length l S from the point P p along the curve. Then, a curvature K s is set equal to K p when K p ≧K n and set equal to K n when K p

Some Methods of Computational Geometry Applied to Computer Graphics

Abstract: Windowing a two-dimensional picture means to determine those line segments of the picture that are visible through an axis-parallel window. A study of some algorithmic problems involved in windowing a picture is offered. Some methods from computational geometry are exploited to store the picture in a computer such that (1) those line segments inside or partially inside of a window can be determined efficiently, and (2) the set of those line segments can be maintained efficiently while the window is moved parallel to a coordinate axis and/or it is enlarged or reduced.

Intersecting is easier than sorting

Abstract: This paper settles a long-standing open question of computational geometry: Is it possible to compute all k intersections between n arbitrary line segments in time linear in k? We answer this question affirmatively by presenting the first algorithm with a running time of the form O(k + f(n)), where f is a subquadratic function of n. The function f we achieve is actually quasi-linear in n, which makes our algorithm the most efficient to date for each value of k. To obtain this result we must turn away from traditional, sweep-line-based schemes. Instead, we introduce a new hierarchical strategy for dealing with segments without ever reducing the dimensionality of the problem. This framework is used to solve other related problems. In particular, we are able to present the first subquadratic algorithm for counting intersections (as opposed to reporting each of them explicitly), and we give the first optimal algorithm for computing the intersections of a line arrangement with a query segment. Using duality arguments we also present an improved algorithm for a point enclosure problem.

Clipping to the boundary of a circular-arc polygon

Abstract: This paper presents an algorithm for partitioning line segments and circular arcs according to a circular-arc polygon boundary. That is, given a line or circular arc and a boundary made up of line segments and circular arcs, partition the given line or circular arc into the pieces that lie inside and those that lie outside the boundary. The algorithm works on nonself-intersecting polygonal boundaries. This problem arises in computer graphics, when a circular-arc polygon boundary is used as a window on a scene. It is also related to geometrical problems that arise in integrated circuit design.

Structural matching of line drawings using the geometric relationship between line segments

Abstract: A new method for matching line drawings is presented. “Neighboring relations” between line segments are first defined. The neighboring relation defined here is not a topological relation such as an intersection, but a general geometric relation between a pair of (spatially separated) line segments. In the matching process, geometric properties of neighboring line segments are used as “matching keys,” and clustering in the parameter space is used to determine the geometric transformation between line drawings. Several experimental results are given to show the versatility of the matching algorithm.

Finding Rectangle Intersections by Divide-and-Conquer

Abstract: In this correspondence we reconsider three geometrical problems for which we develop divide-and-conquer algorithms. The first problem is to find all pairwise intersections among a set of horizontal and vertical line segments. The second is to report all points enclosures occurring in a mixed set of points and rectangles, and the third is to find all pairwise intersections in a set of isooriented rectangles. We derive divide-and-conquer algorithms for the first two problems which are then combined to solve the third. In each case a space-and time-optimal algorithm is obtained, that is O(n) space and O(n log n + k) time, where n is the number of given objects and k is the number of reported pairs. These results show that divide-and-conquer can be used in place of line sweep, without additional asymptotic cost, for some geometrical problems. This raises the natural question: For which class of problems are the line sweep and divide-and-conquer paradigms interchangeable?

Duality and an Algorithm for a Class of Continuous Transportation Problems

Abstract: In this paper we treat the problem of transferring mass at least cost from one line segment to another, when there is a continuous cost function cx, y giving the cost of transferring material from the point x on the first line segment to the point y on the second. The mass has to be arranged with uniform density on the second line segment after the transfer. This is a one-dimensional form of the well-known mass-transfer problem. It is an infinite-dimensional linear program. We discuss duality theory for this problem and give an algorithm which converges to an optimal solution.

Space Searching For Intersecting Objects

Abstract: Determining or counting geometric objects that intersect another geometric query object is at the core of algorithmic problems in a number of applied areas of computer science. This article presents a family of space-efficient data structures that realize sublinear query time for points, line segments, lines and polygons in the plane, and points, line segments, plaraes, and polyhedra in three dimensions.

Solving Visibility Problems by Using Skeleton Structures

Abstract: This paper presents solutions to several visibility problems which can be considered as simplified versions of the hidden line elimination problem. We present a technique which allows to translate many line sweep algorithms involving sets of iso-oriented objects into algorithms for sets of non iso-oriented objects such that the asymptotic worst case time and space requirements do not change.

Single track line capacity model

Abstract: The objective of the research described in this paper was to develop a model for computation of an ultimate capacity of a single track line and to provide a sensitivity analysis of this capacity to the parameters which influence it. The model is based in a concept of mathematical expectation of capacity and can be applied under saturation conditions i.e. a constant demand for service. It can serve for planning purposes, computation of single track line capacity on the base of which estimations are possible concerning a single track line performance under given conditions, as well as commercial time‐tables planning, decisions about a partial or complete construction of the second parallel track along the line in service, intermediate stations locations planning and the necessary facilities along the line under construction. In the sensitivity analysis, the model allows a change of parameters upon which the capacity depends. These are: the length of the line segment which is considered to be bottleneck for ...

Protective device for coaxial line

Abstract: The device comprises a coaxial main line segment 1 and a coaxial closed line segment 2. In order to significantly reduce in particular the proportions of the device, the inner and outer conductors 111-112; 121-122, 22 of the line segments are fully insulated throughout their length by an insulating material 4. The insulating material 4 preferably has a dielectric constant greater than about 2.5, such as epoxy resin. The closed line segment 2 is preferably curved 90 DEG starting from one end 21, 23 connected to the main line segment 1, and bent back against and parallel to the outer conductor 121-122 of the main line segment 1.

High-speed processing method of line segment coordinates

Abstract: To determine the coordinate values of quantized sequential dots on a line segment connecting desired two points (x 1 , y 1 ), (x 2 , y 2 ) in a two-dimensional quantized coordinate system, line segment coordinates are processed at high speed by providing counters, each of which employs one quantum unit as the reference clock signal thereof, respectively for the x-axis and y-axis, controlling reference clock signals, which are to be input to the counters, in accordance with the information on the two points (x 1 , y 1 ), (x 2 , y 2 ), and employing output values of the counters as coordinate values of the quantized sequential dots. The above method features high-speed processing operations.

Pattern recognition device

Abstract: PURPOSE:To improve the ability of recognition, by extracting a characteristic amount from pieces of segmented information and performing the specified operation processing CONSTITUTION:A character and a figure being an object is image picked up with a camera 1, and an obtained video signal is binary-coded at a binary-coding circuit 2 The picture data binary-coded, ie, processed for segment is inputted to a characteristic extraction circuit 3, where characteristics are extracted and stored in an RAM4 A mu-CPU5 analyzes the connect property of segment information stored for classifying an unknown pattern into a set of segment and cuts out the unknown pattern with a circumscribed quadrangle having a prescribed size, the quadrangle is split longitudinally and laterally with plural line segments, the presence or absence of the pattern is checked at each region and the pattern is recognized by comparing the pattern with the prescribed pattern and an output is given from a discriminating output section 8

Diagram input device

Abstract: PURPOSE:To form intrinsic geometrical information of a line drawing by analyzing a characteristic amount representing the linearity, and discriminating a line segment, angle and circular arc of an original diagram to obtain a split data for splitting point strings. CONSTITUTION:A distance (characteristic amount) between line segments tying a noted picture element and n-set of picture elements before and after the noted picture element is calculated by a characteristic amount calculating device 8. A characteristic amount analyzing device 9 discriminates the characteristic from the characteristic amounts stored in a storage device 4 and forms the split data to split a point series data into straight lines and circular arcs. A diagram data forming device 10 forms information such as start point and end point of a straight line for a straight line section, start point and end point of a circular arc, center position and direction of turning for a circular arc section from the split data and point strings data stored in the storage device 4.

Signal propagating device for a plurality of memory cells

Abstract: There is provided a signal propagating device for receiving an input signal at an input end thereof and supplying the input signal to a plurality of memory cells arranged in one row. The signal propagating device includes a word line connected to transmit the input signal and having a plurality of line segments electrically coupled to the memory cells. A preceding one of the line segments is formed to have a larger average width than a succeeding one of the line segments.

Clip circuit of crt display units

Abstract: A clip circuit (17) of a CRT display unit clips off, by means of a simple operation, the portion of a polygon (5) protruding from the three-dimensional space (4) when the polygon (5) is partially inserted into the three-dimensional space. More specifically, a window register (175) stores therein the data on the primary to tertiary planes forming the three-dimensional space, respectively comprised of a pair of planes. A host computer (10) provides three-dimensional coordinate data representing the respective vertexes of the polygon. An ALU (177) first extracts from the vectors constituting the polygon, a line segment existing in a field bounded by a pair of primary planes, according to the three-dimensional coordinate data from the window-register and the three-dimensional plane data from the host computer. Then, from the above stated line segment, the ALU (177) extracts a line segment existing in a field bounded by a pair of secondary planes and further extracts from this line segment, a line segment existing in a field bounded by a pair of tertiary planes, so that the other portions excluding the extracted line segments are clipped off. Accordingly, the unnecessary portions of a polygon can be clipped off only by one processing operation for each pair of primary to tertiaty planes, which means that only three processing operations are required.

Data processing device

Abstract: PURPOSE:To output efficient tool passing route data, by performing interpolation processing on a line segment or circular arc in accordance with the surface shape of an objective shape CONSTITUTION:When an objective shape is inputted into a shape inputting device 1, a shape data constructing means 2 constructs the objective shape in its inside from the inputted data A tool passing route coordinate calculating means 3 which receives the output of the constructing means 2, calculates tool passing route coordinate values required for working the surface shape and sends the calculated result to an interpolation processing means 16 The processing means 16 performs interpolation processing on sections, which can be interpolated by a line segment or circular arc, in accordance with the surface unevenness of the objective shape as much as possible The interpolated tool passing route data are outputted from an output device 17 By performing the interpolation processing in such a way, efficient tool passing route data can be outputted

Device for processing input and output of information

Abstract: PURPOSE:To output a linear drawing with good quality by calculating a line segment length and a line width of scanned linear drawing information and correcting the informaton so as to reproduce the original linear drawing. CONSTITUTION:A paper sheet 1 on which picture information including character information and a linear drawing is recorded is scanned by an optical system. The picture information is converted into an electric signal by a detector 31 through an optical lens 2 and further converted into a digital quantity by a binary-coding circuit 32. The information processed by an input device 3 is stored in a character picture data storage device 4 and then, a processing unit 5 separates the character information and the picture information in the storage device 4 and transfers the picture information to a storage device 6 for correcting picture. Further, a data in the storage device 6 is brought into a fine line by a fine line forming device 7, and moreover the line segment length and the line width of the linear drawing information are calculated and the inforation is corrected so as to reproduce the original linear drawing. The corrected data pattern is outputted from an output device 8.