Isometric Projection Research Articles

An algorithm for the production of an isometric projection of a three-dimensional surface: Hall, C. 75.36 National Physical Laboratory, Teddington, UK (November 1973) 27 pp

An algorithm for the production of an isometric projection of a three-dimensional surface: Hall, C. 75.36 National Physical Laboratory, Teddington, UK (November 1973) 27 pp

Hall effectB-Hloop recorder for thin magnetic films

An instrument for recording B-H loops of evaporated magnetic films is described. A Hall effect probe is used to measure the normal component of magnetic field at the film surface along an edge of the film. The instrument is arranged also to record a map of the normal field over the area of the film in isometric projection form. The field maps indicate the uniformity of the domain structure when the film is in a partially switched state.

The effect of strain rate on the post-yield flow of mild steel

A brief description is given of a rapid-loading hydraulic test machine which was used in an earlier investigation of delayed yielding under constant stress. A modification to the machine is also described, which makes it possible to perform tests at approximately constant strain rate. Results are given of constant-stress tests on mild steel specimens of four different mean ferrite grain sizes. Some of these results are compared with those obtained in constant strain-rate tests on specimens of similar grain size. The experimental data are discussed and it is concluded that they may be reasonably represented by an ‘equation of state’ relating stress, strain and strain rate. For one grain size this equation is depicted by means of a surface shown in isometric projection.

Application of the Eccentric and True Anomalies of the Ellipse to Isometric and Axometric Projection

The terminology of three-dimensional projection is examined and axometric projections compared. A method is introduced which enables a pictorial view to be drawn from orthographic views without using direct projections or special set-squares.

Objectives and Organization in Elementary-School Art Programs

FOR the sake of establishing perspective, any statement of the modern concepts in art-teaching might well begin with a historical review. In the schools of America, art entered the curriculum during the early and middle part of the nineteenth century. In the beginning it was not the art that we know today but drawing, with the chief emphasis on form. Instruction was highly formal and mechanical in all the grades; and the records show that even first-grade children dealt with such concepts as the axis of symmetry, the tangential union of lines, semi-diagonals, and concentric squares.' Object-drawing frequently was done with the aid of mechanical instruments; linear drawing and the study of perspective were common parts of the program in all grades; and courses in drawing and art, which were never clearly separated, bore such titles as Isometric Projection and Shadows, Size, Geometric Design, Orthographic Projection and Shadows, and Linear Drawing and Measuring (freehand). Art, even in the elementary school, was taught largely as a vocational trade subject, and a further emphasis was placed on the learning of formal, stereotyped skills and facts which comprised a superficial cultural training, especially for girls. Originality, freedom, expression, appreciation -these concepts were rare in the early development of art. Form, design, perspective, and accuracy were given the greatest emphasis. The approach to art-teaching, in its earlier years, was strictly through copying. The forms were highly conventionalized, and adherence to the rules and principles was rigidly required. In large part, the focus was on form and specific skills until after the Civil War period. By the close of the nineteenth century, drawing and various other forms of art work were well intrenched in the elementary schools of America. In 1879 the National Association of School Superintendents had met in ' Twenty-seventh A nnual Report of the Board of President and Directors of the St. Louis Public Schools for the Year Ending August i, 188r, pp. 266-67. St. Louis, Missouri: St. Louis Public Schools, 1882.

Construction of Perspective Drawings from Contoured Maps by means of a Camera Lucida

Several combined link and slide devices have been described, by means of which block diagrams can be constructed from contoured maps (1, 2). Briefly, their mode of use is as follows: (a) On tracing a contour with the tracing point of the mechanical device, the drawing pencil reproduces the contour as its isometric projection, i.e. distances along the supposed line of sight are reduced relative to distances measured at right-angles to this direction, the reduction factor being determined by the angle at which the area is assumed to be viewed. (b) Before drawing the isometric projection of the next lower contour, the sheet of paper on which the diagram is being made is moved relative to the map in a direction depend-ing on the type of device by a distance which depends on the scale of the map, the contour interval, the angle at which the area is viewed, and any factor of vertical scale magnification relative to the horizontal scale which is deemed necessary to bring out the topography (2). Each successive contour is treated in this manner, preferably starting with the highest contour and finishing with the lowest. In drawing the isometric projections of the contours, such parts are omitted as their inter-sections with the higher contour projections show to be obscured by the intervention of high topography between them and the point from which the area is viewed. (c) Finally hill sky-lines are filled in, roads, rivers, etc, are drawn by sketching between the points where they have been marked as crossing contours in dealing with each contour, and such artistic additions are made as will enhance the impression of relief.

Our Present Dilemma Regarding the Values of the Natural Constantse,mandh. A New Graphical Method of Presentation

Fourteen experiments each of which determines some function of one or more of the constants $e$, $m$ and $h$, are classified, according to the function determined, into nine groups. The latter number is reduced to seven by the elimination of five of the thirteen experiments as unreliable in the light of our present knowledge. Three cardinally good experiments, the directly measured x-ray values of $e$, the many concordant measurements of $\frac{e}{m}$ and the values of $\frac{h}{e}$ from the limit-of the continuous x-ray spectrum are exhibited on a new type of diagram showing separately results of all independent reliable determinations to portray the consistencies graphically. The indubitable nature of the discrepancy is thus made evident and the remaining four experimental values also plotted on the diagram seem to give better support to the first two named cardinal experiments than to the last. The new type of diagram is an isometric projection of a cartesian coordinate system whose axes represent the relative deviations of $e$, $m$ and $h$ from conventionally assumed values. Planes in this space represent the different experimental determinations of functions of $e$, $m$ and $h$ and the discussion brings out the absolute geometric property that five of these planes are cozonal (parallel to a common axis). Though there are seven equations it thus appears that to solve for $e$, $m$ and $h$ either the direct $e$, equation or alternately the ${R}_{\ensuremath{\infty}}$ equation is indispensable.The results are briefly recounted of a careful examination both by the author and others of numerous possible experimental and theoretical sources of the discrepancy. Modified diagrams are shown for (a) the assumption that the velocity of propagation of radiation in vacuum suffers a slow decline with increasing frequency (the velocity for 20,000-volt x-rays is assumed to be \textonequarter{} percent lower than the low frequency optical value); (b) the alternative assumption that the Bohr-Rydberg formula must be revised to include a factor ($1\ensuremath{-}\ensuremath{\alpha}$). Both assumptions rectify the diagram as regards the three cardinal experiments but throw the remaining experiments out of line with them. Since the two assumptions named are about equally objectionable both on theoretical grounds and in their results on the diagram they are now rejected as unlikely. The author concludes that in all probability some unsuspected theoretical or experimental flaw in the determination of $\frac{h}{e}$ by the continuous x-ray spectrum method is the source of the discrepancy and emphasizes the need for renewed study of this experiment along with x-ray ionization and excitation potentials over a wider range of voltages with better spectral resolution. The weakness of low voltage measurements of ionization and excitation potentials is pointed out. It is emphasized that when systematic error is as glaringly evident as at present the temptation to obtain compromise or best values of the natural constants by least-squares methods should be strongly resisted for it is not inconceivable that the discrepancy may reveal some important error of principle or theory.

The mode of formation of Neumann bands. Part II.–The evidence that the bands are twins

1. Any discussion of the significance of Neumann bands must involve the geometrical relationships between them and the matrix. The orientation of the cube lattice of a meteorite having been determined by X-ray or other methods, a section parallel to a cube face can be cut, polished and etched, and the angles which the traces of the Neumann bands make with the sides or the diagonals of the cube face can be measured. If the bands are parallel to the twelve planes of the icositetrahedron {112}, their traces will lie in the directions shown in fig. 5, PVUT representing the orientation of the cube face. The spatial relationships of the planes producing such {112} traces can be visualised by means of fig. 6, an isometric projection of a cube, in which the planes producing the traces shown in fig. 5 are indicated by their traces on three mutually perpendicular planes, e. g ., PVUT (010), PTQX (001) and PXWV (100).

Oblique and Isometric Projection. By J. Watson. (Edward Arnold. 3s. 6d.)

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Oblique and Isometric Projection

Oblique and Isometric Projection

A Treatise on Practical Plane and Solid Geometry

IN these 400 pages the joint authors present the student, particularly the one who wishes to restrict his work to the Science and Art Department syllabus of the honours stage of the annual examination held in geometry, with the solutions of a series of problems arranged in an orderly and progressive manner. The problems are, for the most part, those which have been set at the examinations held during the years 1887 to 1896, and their solutions are accompanied, in many cases, by useful hints. There are also included the theories of isometric projection, shadows, and perspective, and several interesting miscellaneous examples, besides some of the less difficult problems which are of fundamental importance. It is not advisable for a student to limit himself entirely to the reading of such a book as this, but using it in connection with a good text-book its value will be very much enhanced: for this reason, the authors have made ample references to existing standard works. No less important are the excellent and clearly printed figures, to the number of 200, which accompany the text; these should be well studied, and, in most cases, re-drawn by the reader himself. For advanced students and teachers this collection of problems and proofs will, without doubt, prove a most useful help in their work.

Practical Plane Geometry and Projection for Science Classes, Schools, and Colleges

A VERY practical and useful book by an experienced teacher: it is designed to meet the requirements of students at the Royal School of Mines, at the Royal Military Academy, at Cooper's Hill, and elsewhere, and embraces great part of the two higher stages of the Science and Art Department syllabus. There is no great scope for absolute novelty in such a work, and our author acknowledges his indebtedness to the works of many, if not most, of his well-known predecessors, but the arrangement appears to be judicious, and the constructions good and clearly enunciated. In the Practical Geometry (six chapters) the student is taught the use and construction of scales, of triangles and polygons, and there are numerous problems on areas, on circles in contact, and on other plane curves with their tangents and normals. The orthographical portion treats of the projection of the five regular solids, of other simple solids, of flat and curved surfaces, intersected by cutting planes, and of solids inscribed in, or circumscribed to, the surfaces of other solids; of the interpenetration of solids, of the projection of shadows, on isometric projection, on the solution of the spherical triangle, and on horizontal projection—a very extensive and varied bill of fare. In addition there are numerous questions for practice, many of which are taken from examination papers, and the text is illustrated by several clearly-drawn figures. Part ii. contains eighty-one large-page plates to further illustrate the constructions. The two parts together ought to enable any painstaking student to take a creditable place in his examination and to acquire a solid acquaintance with the subject.