Arc Of Ellipse Research Articles

3D Modeling of the Tower Head Based on ObjectARX

Elliptical head is an important standard part of the separation tower equipment. It can not be generated by tensile method, rotation method, because the rotation axis can not pass region. This paper introduces the ObjectARX programming environment. It describes how to build the menu and the dialog box. ObjectARX is a secondary development tool of AutoCAD. With its function and its mechanical drawing once learned, four arcs of ellipse can be used to build 3d modeling of head.of tower equipment. The ObjectARX programming technology is applied to develop AutoCAD, making it more convenient to darw the professional 3d graphics.

Blending of the Trigonometric Polynomial Spline Curve with Arbitrary Continuous Orders

In order to develop the theory of trigonometric polynomial spline curve, the representation of trigonometric polynomial spline curve is blended to a general form based on blending of trigonometric polynomial curves. Moreover, some properties of the blending curve are discussed in details. The research shows that the basis of the trigonometric polynomial curve is relative simple, and the blending curve includes the original trigonometric polynomial spline curve and shows much better shape-control capability than the original curve. Meanwhile, the blending curve keeps the same degree of original one. It is easy to find that the curve can be reshaping by adjusting the shape factor. At the same time, a new method of the representation of closed curve is given and can also accurately represent the whole ellipse arc and other conic curve.

Computer graphics: principles and practice

1. Introduction. Image Processing as Picture Analysis. The Advantages of Interactive Graphics. Representative Uses of Computer Graphics. Classification of Applications. Development of Hardware and Software for Computer Graphics. Conceptual Framework for Interactive Graphics. 2. Programming in the Simple Raster Graphics Package (SRGP)/. Drawing with SRGP/. Basic Interaction Handling/. Raster Graphics Features/. Limitations of SRGP/. 3. Basic Raster Graphics Algorithms for Drawing 2d Primitives. Overview. Scan Converting Lines. Scan Converting Circles. Scan Convertiing Ellipses. Filling Rectangles. Fillign Polygons. Filling Ellipse Arcs. Pattern Filling. Thick Primiives. Line Style and Pen Style. Clipping in a Raster World. Clipping Lines. Clipping Circles and Ellipses. Clipping Polygons. Generating Characters. SRGP_copyPixel. Antialiasing. 4. Graphics Hardware. Hardcopy Technologies. Display Technologies. Raster-Scan Display Systems. The Video Controller. Random-Scan Display Processor. Input Devices for Operator Interaction. Image Scanners. 5. Geometrical Transformations. 2D Transformations. Homogeneous Coordinates and Matrix Representation of 2D Transformations. Composition of 2D Transformations. The Window-to-Viewport Transformation. Efficiency. Matrix Representation of 3D Transformations. Composition of 3D Transformations. Transformations as a Change in Coordinate System. 6. Viewing in 3D. Projections. Specifying an Arbitrary 3D View. Examples of 3D Viewing. The Mathematics of Planar Geometric Projections. Implementing Planar Geometric Projections. Coordinate Systems. 7. Object Hierarchy and Simple PHIGS (SPHIGS). Geometric Modeling. Characteristics of Retained-Mode Graphics Packages. Defining and Displaying Structures. Modeling Transformations. Hierarchical Structure Networks. Matrix Composition in Display Traversal. Appearance-Attribute Handling in Hierarchy. Screen Updating and Rendering Modes. Structure Network Editing for Dynamic Effects. Interaction. Additional Output Features. Implementation Issues. Optimizing Display of Hierarchical Models. Limitations of Hierarchical Modeling in PHIGS. Alternative Forms of Hierarchical Modeling. 8. Input Devices, Interaction Techniques, and Interaction Tasks. Interaction Hardware. Basic Interaction Tasks. Composite Interaction Tasks. 9. Dialogue Design. The Form and Content of User-Computer Dialogues. User-Interfaces Styles. Important Design Considerations. Modes and Syntax. Visual Design. The Design Methodology. 10. User Interface Software. Basic Interaction-Handling Models. Windows-Management Systems. Output Handling in Window Systems. Input Handling in Window Systems. Interaction-Technique Toolkits. User-Interface Management Systems. 11. Representing Curves and Surfaces. Polygon Meshes. Parametric Cubic Curves. Parametric Bicubic Surfaces. Quadric Surfaces. 12. Solid Modeling. Representing Solids. Regularized Boolean Set Operations. Primitive Instancing. Sweep Representations. Boundary Representations. Spatial-Partitioning Representations. Constructive Solid Geometry. Comparison of Representations. User Interfaces for Solid Modeling. 13. Achromatic and Colored Light. Achromatic Light. Chromatic Color. Color Models for Raster Graphics. Reproducing Color. Using Color in Computer Graphics. 14. The Quest for Visual Realism. Why Realism? Fundamental Difficulties. Rendering Techniques for Line Drawings. Rendering Techniques for Shaded Images. Improved Object Models. Dynamics. Stereopsis. Improved Displays. Interacting with Our Other Senses. Aliasing and Antialiasing. 15. Visible-Surface Determination. Functions of Two Variables. Techniques for Efficient Visible-Surface Determination. Algorithms for Visible-Line Determination. The z-Buffer Algorithm. List-Priority Algorithms. Scan-Line Algorithms. Area-Subdivision Algorithms. Algorithms for Octrees. Algorithms for Curved Surfaces. Visible-Surface Ray Tracing. 16. Illumination And Shading. Illumination Modeling. Shading Models for Polygons. Surface Detail. Shadows. Transparency. Interobject Reflections. Physically Based Illumination Models. Extended Light Sources. Spectral Sampling. Improving the Camera Model. Global Illumination Algorithms. Recursive Ray Tracing. Radiosity Methods. The Rendering Pipeline. 17. Image Manipulation and Storage. What Is an Image? Filtering. Image Processing. Geometric Transformations of Images. Multipass Transformations. Image Compositing. Mechanisms for Image Storage. Special Effects with Images. Summary. 18. Advanced Raster Graphic Architecture. Simple Raster-Display System. Display-Processor Systems. Standard Graphics Pipeline. Introduction to Multiprocessing. Pipeline Front-End Architecture. Parallel Front-End Architectures. Multiprocessor Rasterization Architectures. Image-Parallel Rasterization. Object-Parallel Rasterization. Hybrid-Parallel Rasterization. Enhanced Display Capabilities. 19. Advanced Geometric and Raster Algorithms. Clipping. Scan-Converting Primitives. Antialiasing. The Special Problems of Text. Filling Algorithms. Making copyPixel Fast. The Shape Data Structure and Shape Algebra. Managing Windows with bitBlt. Page Description Languages. 20. Advanced Modeling Techniques. Extensions of Previous Techniques. Procedural Models. Fractal Models. Grammar-Based Models. Particle Systems. Volume Rendering. Physically Based Modeling. Special Models for Natural and Synthetic Objects. Automating Object Placement. 21. Animation. Conventional and Computer-Assisted Animation. Animation Languages. Methods of Controlling Animation. Basic Rules of Animation. Problems Peculiar to Animation. Appendix: Mathematics for Computer Graphics. Vector Spaces and Affine Spaces. Some Standard Constructions in Vector Spaces. Dot Products and Distances. Matrices. Linear and Affine Transformations. Eigenvalues and Eigenvectors. Newton-Raphson Iteration for Root Finding. Bibliography. Index. 0201848406T04062001

Algebraic cubature by linear blending of elliptical arcs

We construct a cubature formula of algebraic degree of exactness n with n2/2+O(n) nodes, on the bidimensional domains generated by linear blending of two arcs of ellipses corresponding to the same angular interval. The construction is based on recent results on “subperiodic” trigonometric quadrature. Our formula generalizes several recent cubature formulas on standard circular sections. Among its numerous possible applications, we quote for example integration of functions with singularities, and integration on nonstandard circular sections arising in optical design or in meshfree methods with compactly supported radial bases.

An asymptotic solution of the Schrödinger equation for the elliptic wire in the magnetic field

An asymptotic solution of the Schrödinger equation with non-separable variables is obtained for a particle confined to an infinite elliptic cylinder potential well under an applied uniform longitudinal magnetic field. Using the standard-problem method, dimension-quantized eigenvalues have been calculated when the magnetic length is large enough in comparison with the half of the distance between the boundary ellipse focuses. In semi-classical approximation, the confined electron (hole) states are divided into the boundary states (BS), ring states (RS), hyperbolic caustic states (HCS) and harmonic oscillator states (HOS). For large angular momentum quantum numbers and small radial quantum numbers, the BS and RS are grouped into the ‘whispering gallery’ mode. They associate with particles moving along the wire cross section boundary. The motion is limited from the wire core by the elliptic caustic. Consisting of the HCS and HOS, the ‘jumping ball’ modes correspond to the states of particle moving along a wire diameter when the angular momentum quantum number is much less than the radial quantum number. In this case, the motion is restricted by the hyperbolic caustics and two boundary ellipse arcs. For excited hole states in a Bi wire, the energy spectrum and space probability distribution are analyzed.

Effects of bond parameters on the widths of supercooled liquid regions of ferrous BMGs

Correlation is investigated between supercooled liquid regions (SLRs) Δ T x (= T x − T g, where T x is the onset crystallization temperature and T g the glass transition temperature) of ferrous bulk metallic glasses (BMGs) and three bond parameters, i.e. electronegativity, atomic size and valent electron. From the available experimental data in literatures, Δ T x has strong correlation with the bond parameters. A semi-empirical equation is established to elucidate the correlation between Δ T x and the three bond parameters. In detail, Δ T x increases obviously with the increase of the atomic size parameter ( δ), and electronegativity difference (Δ x) and the electron concentration. An ellipse arc with thickness derived from the equation is drawn to determine the range of BMG with large SLR.

Search for the Optical Counterpart of PSR 1953+29

1) PSR B1953+29, the first millisecond binary pulsar discovered, has a low mass companion with a long orbital period (see parameters in Table 1).2) Shortly after its discovery the averaged pulse profile was observed to change shape in a discrete fashion: two different pulse profiles were alternating (Boriakoffet al1986). Each pulse profile remained the same for typical times of days. This is reminiscent of the mode-changing behaviour of slower pulsars, however, normally such pulsars remain in one mode for only a few minutes.3) Observations with a Cherenkov TeV Gamma-Ray detector have shown a large pulse-profile peak when the data is folded with the correct pulse period. Recent reprocessing of the original data shows the same peak (Bowdenet al1990).4) Comparison with optical photographs revealed a bright star (20-th magnitude) located less than 1 arcsec from the pulsar positions determined with the VLA and from timing. A star of ∼O.2M⊙is expected to be a white dwarf, at the distance of 3.5-5kpc it would be invisible.5) Optical spectral observations of the star with the 5-meter Palomar telescope showed a reddened spectrum without any emission or absorption lines. This is typical of very hot objects.6) CCD images obtained with the Russian 6 meter optical telescope in the Caucasus were taken to pinpoint the location of the star with accuracies better than a small fraction of an arc second. Imperfections of the CCD star images (saturation, etc.), in particular for bright 15-18 magnitude stars, had to be taken into account to pinpoint the center of the observed image. A technique was developed for finding the center of the image with an accuracy better than 0.17 arcsec, a single pixel of the CCD image. Arcs of ellipses were fitted to cross-sections of the star image at different light intensity levels. Down to very low light levels no pulsation was found.

Modelling of powder compaction and formation of composite materials: J. Xu and R. McMeeking (University of California, Santa Barbara, California, USA)

Fatigue endurance limit is a threshold stress-amplitude under which a solid subjected to a cyclic loading can sustain infinite life. Such a limit has been confirmed in ferrous materials but remains controversial in many advanced new materials, including bulk metallic glasses with superb strength. By using a combination of ultrasonic fatigue (USF) test and conventional fatigue test, we obtain the stress amplitude vs. loading cycle curve of the Vitreloy 1TM metallic glass, with loading cycles up to 109. There is a clear fatigue endurance limit (FEL) which is about 320 MPa, and is 17% of the strength of Vitreloy 1TM. The residual strength of survivals after 109 cycles is nearly the same as those of intact samples. We demonstrate that all fatigue cracks initiate from spherical pores which are inevitable and intrinsic amid casting and fast cooling, and the fatigue crack front resembles an ellipse arc till final rapid rapture of all tested samples. The size and position of a pore can be utilized to extract the fatigue initiation threshold K0th, and the elliptical fatigue crack front is used to obtain the mode I fracture toughness KIC, which are K0th=2.0±0.5MPam and KIC=18-20MPam for Vitreloy 1TM, respectively. The fatigue endurance limit and its intrinsic origin of Vitreloy 1TM pave the way to understand fatigue in other metallic glasses.

Aesthetic Measure for Constituent in a Fishery Harbour

This paper proposed the constituent model for the arrangement of coastal structures in a fishery harbour. The model consists of the arcs of circle and ellipse and the line segment. In order to determine the aesthetic measure for the whole fishery harbour, the popularity of the constituent for coastal structures was evaluated by a questionnaire survey. The symmetrical elements impress us favorably. The curved shape is favorable. The rectangular structures, which are mainly shaped by means of right angles and line segments without symmetry, are common in Japan but artificially impressed.

Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

Ellipse, arc of ellipse and elliptic spline

A general method for generating ellipses by using conjugate radii is presented. Elliptical arcs are then defined based on this method for generating ellipses. A 90° arc of ellipse is then used to generate a number of curves with slope constraints. Other arc of ellipse interpolations are then discussed. Three of these interpolations are used to define local elliptic splines with first order derivative continuity.

ChemInform Abstract: ELLIPTIC PHASE BOUNDARIES BETWEEN SMECTIC AND NEMATIC PHASES

Smectic–nematic phase boundaries that resemble arcs of ellipses can be analyzed by a quadratic expansion in temperature and pressure of the change ΔG of Gibbs function. If the change of entropy or volume is known, ΔG and its first two derivatives can be determined. Data on 8OCB and mixtures of 8OCB and 6OCB and of CB9A and CB7A fit an ellipse well, which suggests that the boundary is an ellipse. The smectic phase is therefore enclosed, which appears to be unique in single‐component systems and to disagree with simple mean‐field theory.

An improved shadow-mask design for in-line three-beam color picture tubes

In a color picture tube using an in-line arrangement of three beams and the conventional shadow mask, the transmission of the shadow mask must be made very low in the corner regions in order to avoid the overlapping of adjacent in-line trios of landed beam dots on the screen. An improved design of aperture alignment on a shadow mask was developed for the in-line three beams in order to avoid this overlapping without reducing the transmission. In this new shadow mask, the apertures are aligned not along straight lines as in the conventional shadow mask but along certain curved lines. The horizontal aperture alignment curves are a barrel-shaped group of arcs of ellipses, and the vertical aperture alignment curves are a pin-cushioned group of arcs of circles. Brightness and color purity of the picture in the corner regions of the screen were much improved by using this shadow mask.

Die Ersatzkugel in geodätischen Berechnungen

For precise geodetic computations over larger distances the reference surface of an ellipsoid of rotation should be used. However it is often replaced by a sphere of an adequate radius. The formulae are derived from figures which usually represent the conditions in a cross-section of the ellipsoid and the reference sphere through the normal plane. Equation (9) is given for the differences Δs of the length of the ellipse arc of the normal section and the corresponding arc of the circle with radius R. Also Eq. (19) is given for the distance d between the ellipse of the normal section and the circle (at the end point). Both equations are applied for various radii of the reference sphere. Table 1 shows the values Δs, Tab. 2 and Fig. 2 give the d-values for chosen lengths. It was found that especially the distance between the ellipsoid and the sphere need not always be negligible.

The Fatigue Strength under Bending, Torsional and Combined Stresses of Steel Test Pieces with Stress Concentrations

In previous investigations (Gough, Pollard, and Clenshaw 1951)§ under the same general research programme, determinations were made of the intrinsic and vee-notched fatigue strengths of the first seven steels here investigated, under various combinations of bending and torsion. The intrinsic fatigue limits were found to fit reasonably to an ellipse quadrant, and the notched fatigue limits to a two-constant displaced ellipse or ‘ellipse arc’. The bulk of the present paper concerns the behaviour under combinations of bending and torsional stresses of test pieces with transverse holes, for the same seven steels. The fatigue limits under the various stress combinations have been found to fit reasonably to an ellipse arc of the same form as for the vee-Notched Specimens. The similarity in form of the ellipse arcs for the seven materials supports the theoretical conclusion that the shape of the curve is dependent only on the shape of the hole, and is independent of the nature of the material. The information given on strength reduction factors under various combinations of bending and torsion, together with the tables of results of supplementary static tests, should be of use in such problems as crankshaft design. The paper also includes the results of flexural and torsional fatigue tests on an aircraft crankshaft steel, with other forms of stress concentration. These results are compared with those on two other steels of similar composition.

The Arc of the Ellipse

The Arc of the Ellipse

The Arc of the Ellipse

The Arc of the Ellipse

670. Fagnano’s Theorem on Arcs of an Ellipse

670. Fagnano’s Theorem on Arcs of an Ellipse