Showing papers on "Line segment published in 1981"

Algorithms for Graphics and Image Processing

Abstract: 1: Introduction.- 1.1 Graphics, Image Processing, and Pattern Recognition.- 1.2 Forms of Pictorial Data.- 1.2.1 Class 1: Full Gray Scale and Color Pictures.- 1.2.2 Class 2: Bilevel or "Few Color" pictures.- 1.2.3 Class 3: Continuous Curves and Lines.- 1.2.4 Class 4: Points or Polygons.- 1.3 Pictorial Input.- 1.4 Display Devices.- 1.5 Vector Graphics.- 1.6 Raster Graphics.- 1.7 Common Primitive Graphic Instructions.- 1.8 Comparison of Vector and Raster Graphics.- 1.9 Pictorial Editor.- 1.10 Pictorial Transformations.- 1.11 Algorithm Notation.- 1.12 A Few Words on Complexity.- 1.13 Bibliographical Notes.- 1.14 Relevant Literature.- 1.15 Problems.- 2: Digitization of Gray Scale Images.- 2.1 Introduction.- 2.2 A Review of Fourier and other Transforms.- 2.3 Sampling.- 2.3.1 One-dimensional Sampling.- 2.3.2 Two-dimensional Sampling.- 2.4 Aliasing.- 2.5 Quantization.- 2.6 Bibliographical Notes.- 2.7 Relevant Literature.- 2.8 Problems.- Appendix 2.A: Fast Fourier Transform.- 3: Processing of Gray Scale Images.- 3.1 Introduction.- 3.2 Histogram and Histogram Equalization.- 3.3 Co-occurrence Matrices.- 3.4 Linear Image Filtering.- 3.5 Nonlinear Image Filtering.- 3.5.1 Directional Filters.- 3.5.2 Two-part Filters.- 3.5.3 Functional Approximation Filters.- 3.6 Bibliographical Notes.- 3.7 Relevant Literature.- 3.8 Problems.- 4: Segmentation.- 4.1 Introduction.- 4.2 Thresholding.- 4.3 Edge Detection.- 4.4 Segmentation by Region Growing.- 4.4.1 Segmentation by Average Brightness Level.- 4.4.2 Other Uniformity Criteria.- 4.5 Bibliographical Notes.- 4.6 Relevant Literature.- 4.7 Problems.- 5: Projections.- 5.1 Introduction.- 5.2 Introduction to Reconstruction Techniques.- 5.3 A Class of Reconstruction Algorithms.- 5.4 Projections for Shape Analysis.- 5.5 Bibliographical Notes.- 5.6 Relevant Literature.- 5.7 Problems.- Appendix 5.A: An Elementary Reconstruction Program.- 6: Data Structures.- 6.1 Introduction.- 6.2 Graph Traversal Algorithms.- 6.3 Paging.- 6.4 Pyramids or Quad Trees.- 6.4.1 Creating a Quad Tree.- 6.4.2 Reconstructing an Image from a Quad Tree.- 6.4.3 Image Compaction with a Quad Tree.- 6.5 Binary Image Trees.- 6.6 Split-and-Merge Algorithms.- 6.7 Line Encodings and the Line Adjacency Graph.- 6.8 Region Encodings and the Region Adjacency Graph.- 6.9 Iconic Representations.- 6.10 Data Structures for Displays.- 6.11 Bibliographical Notes.- 6.12 Relevant Literature.- 6.13 Problems.- Appendix 6.A: Introduction to Graphs.- 7: Bilevel Pictures.- 7.1 Introduction.- 7.2 Sampling and Topology.- 7.3 Elements of Discrete Geometry.- 7.4 A Sampling Theorem for Class 2 Pictures.- 7.5 Contour Tracing.- 7.5.1 Tracing of a Single Contour.- 7.5.2 Traversal of All the Contours of a Region.- 7.6 Curves and Lines on a Discrete Grid.- 7.6.1 When a Set of Pixels is not a Curve.- 7.6.2 When a Set of Pixels is a Curve.- 7.7 Multiple Pixels.- 7.8 An Introduction to Shape Analysis.- 7.9 Bibliographical Notes.- 7.10 Relevant Literature.- 7.11 Problems.- 8: Contour Filling.- 8.1 Introduction.- 8.2 Edge Filling.- 8.3 Contour Filling by Parity Check.- 8.3.1 Proof of Correctness of Algorithm 8.3.- 8.3.2 Implementation of a Parity Check Algorithm.- 8.4 Contour Filling by Connectivity.- 8.4.1 Recursive Connectivity Filling.- 8.4.2 Nonrecursive Connectivity Filling.- 8.4.3 Procedures used for Connectivity Filling.- 8.4.4 Description of the Main Algorithm.- 8.5 Comparisons and Combinations.- 8.6 Bibliographical Notes.- 8.7 Relevant Literature.- 8.8 Problems.- 9: Thinning Algorithms.- 9.1 Introduction.- 9.2 Classical Thinning Algorithms.- 9.3 Asynchronous Thinning Algorithms.- 9.4 Implementation of an Asynchronous Thinning Algorithm.- 9.5 A Quick Thinning Algorithm.- 9.6 Structural Shape Analysis.- 9.7 Transformation of Bilevel Images into Line Drawings.- 9.8 Bibliographical Notes.- 9.9 Relevant Literature.- 9.10 Problems.- 10: Curve Fitting and Curve Displaying.- 10.1 Introduction.- 10.2 Polynomial Interpolation.- 10.3 Bezier Polynomials.- 10.4 Computation of Bezier Polynomials.- 10.5 Some Properties of Bezier Polynomials.- 10.6 Circular Arcs.- 10.7 Display of Lines and Curves.- 10.7.1 Display of Curves through Differential Equations.- 10.7.2 Effect of Round-off Errors in Displays.- 10.8 A Point Editor.- 10.8.1 A Data Structure for a Point Editor.- 10.8.2 Input and Output for a Point Editor.- 10.9 Bibliographical Notes.- 10.10 Relevant Literature.- 10.11 Problems.- 11: Curve Fitting with Splines.- 11.1 Introduction.- 11.2 Fundamental Definitions.- 11.3 B-Splines.- 11.4 Computation with B-Splines.- 11.5 Interpolating B-Splines.- 11.6 B-Splines in Graphics.- 11.7 Shape Description and B-splines.- 11.8 Bibliographical Notes.- 11.9 Relevant Literature.- 11.10 Problems.- 12: Approximation of Curves.- 12.1 Introduction.- 12.2 Integral Square Error Approximation.- 12.3 Approximation Using B-Splines.- 12.4 Approximation by Splines with Variable Breakpoints.- 12.5 Polygonal Approximations.- 12.5.1 A Suboptimal Line Fitting Algorithm.- 12.5.2 A Simple Polygon Fitting Algorithm.- 12.5.3 Properties of Algorithm 12.2.- 12.6 Applications of Curve Approximation in Graphics.- 12.6.1 Handling of Groups of Points by a Point Editor.- 12.6.2 Finding Some Simple Approximating Curves.- 12.7 Bibliographical Notes.- 12.8 Relevant Literature.- 12.9 Problems.- 13: Surface Fitting and Surface Displaying.- 13.1 Introduction.- 13.2 Some Simple Properties of Surfaces.- 13.3 Singular Points of a Surface.- 13.4 Linear and Bilinear Interpolating Surface Patches.- 13.5 Lofted Surfaces.- 13.6 Coons Surfaces.- 13.7 Guided Surfaces.- 13.7.1 Bezier Surfaces.- 13.7.2 B-Spline Surfaces.- 13.8 The Choice of a Surface Partition.- 13.9 Display of Surfaces and Shading.- 13.10 Bibliographical Notes.- 13.11 Relevant Literature.- 13.12 Problems.- 14: The Mathematics of Two-Dimensional Graphics.- 14.1 Introduction.- 14.2 Two-Dimensional Transformations.- 14.3 Homogeneous Coordinates.- 14.3.1 Equation of a Line Defined by Two Points.- 14.3.2 Coordinates of a Point Defined as the Intersection of Two Lines.- 14.3.3 Duality.- 14.4 Line Segment Problems.- 14.4.1 Position of a Point with respect to a Line.- 14.4.2 Intersection of Line Segments.- 14.4.3 Position of a Point with respect to a Polygon.- 14.4.4 Segment Shadow.- 14.5 Bibliographical Notes.- 14.6 Relevant Literature.- 14.7 Problems.- 15: Polygon Clipping.- 15.1 Introduction.- 15.2 Clipping a Line Segment by a Convex Polygon.- 15.3 Clipping a Line Segment by a Regular Rectangle.- 15.4 Clipping an Arbitrary Polygon by a Line.- 15.5 Intersection of Two Polygons.- 15.6 Efficient Polygon Intersection.- 15.7 Bibliographical Notes.- 15.8 Relevant Literature.- 15.9 Problems.- 16: The Mathematics of Three-Dimensional Graphics.- 16.1 Introduction.- 16.2 Homogeneous Coordinates.- 16.2.1 Position of a Point with respect to a Plane.- 16.2.2 Intersection of Triangles.- 16.3 Three-Dimensional Transformations.- 16.3.1 Mathematical Preliminaries.- 16.3.2 Rotation around an Axis through the Origin.- 16.4 Orthogonal Projections.- 16.5 Perspective Projections.- 16.6 Bibliographical Notes.- 16.7 Relevant Literature.- 16.8 Problems.- 17: Creating Three-Dimensional Graphic Displays.- 17.1 Introduction.- 17.2 The Hidden Line and Hidden Surface Problems.- 17.2.1 Surface Shadow.- 17.2.2 Approaches to the Visibility Problem.- 17.2.3 Single Convex Object Visibility.- 17.3 A Quad Tree Visibility Algorithm.- 17.4 A Raster Line Scan Visibility Algorithm.- 17.5 Coherence.- 17.6 Nonlinear Object Descriptions.- 17.7 Making a Natural Looking Display.- 17.8 Bibliographical Notes.- 17.9 Relevant Literature.- 17.10 Problems.- Author Index.- Algorithm Index.

A Three-Dimensional Edge Operator

Abstract: Modern scanning techniques, such as computed tomography, have begun to produce true three-dimensional imagery of internal structures. The first stage in finding structure in these images, like that for standard two-dimensional images, is to evaluate a local edge operator over the image. If an edge segment in two dimensions is modeled as an oriented unit line segment that separates unit squares (i.e., pixels) of different intensities, then a three-dimensional edge segment is an oriented unit plane that separates unit volumes (i.e., voxels) of different intensities. In this correspondence we derive an operator that finds the best oriented plane at each point in the image. This operator, which is based directly on the 3-D problem, complements other approaches that are either interactive or heuristic extensions of 2-D techniques.

Numerically controlled method of machining cams and other parts

Abstract: Milling machine apparatus and method for controlling the relative movement between a working surface and a cutting edge in which said relative movement approximates a mathematically definable path and occurs in a series of line segments each intersecting said path at first and second points with the second point of each line segment being the first point of the next successive line segment. The system comprises first means for determining a maximum distance d' between each successive line segment and said path measured along a line extending from a predetermined reference and passing between said first and second points, where d'=d+Δd, a predetermined range of value. Also provided are second means responsive to the determination of d' for each successive line segment to then establish the first point of intersection of the next successive line segment, and control means responsive to the determined points of intersection to generate prime moving control signals. Prime moving means respond to said control signals to cause the cutting edge to cut along the successive line segments with respect to said working surface.

Line segment video display apparatus

Abstract: A raster type display apparatus includes interlaced even-and-odd frames. A digital memory of a computer stores line segment data in locations which are sequentially read out to form a line segment display with overlapping line segments. The first line of one field is defined by a "O" start location and a third removed location for the end. The second line is defined by the fourth and seventh locations, and so forth. The first line of the second field starts with the last data taken plus two to access and define the line by the second and fifth locations, and so forth. The first field again reads the start to third locations, fourth to seventh, etc. Data points equal to twice the scan lines are displayed with each scan line spread over four data points. An off-scale detector prevents a line segment directly between the data points and creates a pair of line segments at the top and bottom of the display screen. An extended line from a break point in a curve to screen bottom is also prevented. Resettable registers monitor the carrier bits of digital multiplier and adder and are connected by an even-odd detector to actuate an exclusive "OR" gate to complement the output and generate the appropriate split display. A display control assigns a data words as a control which are loaded in memory by the computer. A detection network controls an "ANDED" routing network for coded control of the line segment definition, such as blanking and channel changes.

Shading of regions on vector display devises

Abstract: Given an arbitrary simple polygon with N vertices we present an algorithm for shading the interior of the polygon with a set of parallel lines where the slope and the distance between lines are prespecified. If the number of shading line segments is M, the algorithm described in the paper runs in 0(N log N + M) time. The algorithm is generalizable to shade any region or regions of an arbitrary planar subdivision.

Twisting geometry optical system utilizing imaging array with time delay segments

Abstract: The invention relates to an optical scanning system which utilizes a tilted lens array to image scan line segments onto an area array of detector units. Each line segment is imaged onto a multiple time integration segment which enhances effective exposure by integration of multiple scans for each line segment.

Plane - sweep algorithms for intersecting geometric figures

Abstract: Algorithms in computational geometry are of increasing importance in computer-aided design, for example, in the layout of integrated circuits. The efficient computation of the intersection of several superimposed figures is a basic problem. Plane figures defined by points connected by straight line segments are considered, for example, polygons (not necessarily simple) and maps (embedded planar graphs). The regions into which the plane is partitioned by these intersecting figures are to be processed in various ways such as listing the boundary of each region in cyclic order or sweeping the interior of each region. Let m be the total number of points of all the figures involved and s be the total number of intersections of all line segments. A two plane-sweep algorithm that solves the problems above is presented; in the general case (non convexity) in time O((n+s)log-n) and space O(n+s); when the regions of each given figure are convex, the same can be achieved in time O(n log n +s) and space O(n)

Discriminating method of type of line in pattern recognizer

Abstract: PURPOSE:To discriminate the type of line (solid line, broken line, and chain line), based on the distribution of the frequency of the length of line segment constituting the line. CONSTITUTION:Figure 1 is stored in the video memory 3 with the photo electric converter 2. The solid line path recognizer 4 recognizes the number of end point of each segment, folded point and points, and the result is stored in the characteristic memory 5. The broken line path recognizer 6 obtains the segment connectable (near and in the same direction) to each segment, when the lines are broken and chain lines and stores the connection information to the memory 7. The line length measuring circuit 81 obtains the length of line of segment. The hystogram of the length of line is formed with the circuits 82, 84 and stored in the memory 83. The types of line can be discriminated at the circuit 85 from the characteristics that the solid line has the distribution of long line length, broken line has the distribution of shorted parts, and chain line has the double peak having the same height.

Optical line scanner system

Abstract: An optical line scanning system utilizes a lens array (24) positioned between a scan line (22) and a detector array (26) and inclined at an angle to the axis of the scanned line. The lens array consists of a staggered two-row arrangement, each lens along the same center line imaging alternate line segments, in tiered fashion, onto the detector array.

Hidden Line Algorithms

Abstract: All the three-dimensional diagrams drawn so far have been ‘wire figures’, pictures of objects in which all edges and vertices may be seen. If an object is solid, then naturally the edges and vertices behind the volume of the object would be invisible to an observer, for example, the dashed lines in figure 8.1. So we have to produce a Hidden Line Algorithm that will draw only the visible line segments on a solid object or set of objects. We shall assume that all vertices are the end points of line segments.

Electronic display for periodic function - uses stored line segments joining successive points to provide beam modulation signal

Abstract: The display has a function curve built-up from individual line segments of varying lengths. A memory (M) stores each segment joining two points on the curve representing two successive values, the scanning beam modulated via a circuit comprising a D/A converter (DAC), a sample and hold circuit (E), two comparators (C1,C2) and a points generator (P). One of the inputs of each comparator (C1,C2) receives the output of a sawtooth generator (G) controlled by the line return pulses. The other inputs of the comparator respectively receive the input and output signal of the sample and hold circuit (E). The outputs of the comparators go to the modulation mixer (M) via a logic combining circuit and via the points generator (P). The mixer output is used as the modulation signal. The display allows a continuous representation of a curve defined by discrete points.