Pyramidal Volume Research Articles

The Volume and Centroid of the Step Pyramid of Zoser

The Volume and Centroid of the Step Pyramid of Zoser

The Volume and Centroid of the Step Pyramid of Zoser

The Volume and Centroid of the Step Pyramid of Zoser

Hierarchical splatting

This paper presents a progressive refinement algorithm for volume rendering which uses a pyramidal volume representation. Besides storing average values, the pyramid stores estimated error, so an octtree can be fit to the pyramid given a user-supplied precision. This octtree is then drawn using a set of splats, or footprints, each scaled to match the size of the projection of a cell. The splats themselves are approximated with RGBA Gouraud-shaded polygons, so that they can be drawn efficiently on modern graphics workstations. The result is a real-time rendering algorithm suitable for interactive applications.

Real-time 3-D ultrasonic diagnostic imaging

Real-time phased-array two-dimensional ultrasound imaging has gained worldwide acceptance as a valuable diagnostic tool. In the past years, a parallel receive processing scheme for phased-array systems, called Explososcanning, which permits imaging of several B-mode lines for each transmitted acoustic burst, has been developed. Now this receive processing is being utilized in conjunction with newly developed two-dimensional arrays to electrically scan the ultrasound beam in three dimensions. The current 2-D transducers consist of 256 elements, operate at approximately 2 MHz and measure 16 by 16 mm at the site of skin contact. The 3-D echo data obtained from the pyramidal scan volume can be displayed as multiple sectors at preselected azimuth and elevation directions, as a two-dimensional projectional image with perspective or as stereoscopic pairs. Parallel processing will permit the formation of approximately 9000 look directions within the pyramidal scan volume at TV rates.

Statistical geometry of some dense random packing of hard spheres model structures: I. Description of local order

The sensitivity of some parameters describing the short range order of amorphous model structures is investigated. Two binary dense random packing of hard spheres models built with and without the constraint that metalloids may not be in hard contact are compared. Besides the partial pair correlation functions, Voronoi polyhedron volumes and conventional coordination numbers defined by a cut-off distance, a new coordination number defined by the pyramidal volume contributions of the generalized Voronoi polyhedron is introduced and tested. Because this coordination number is real and it changes continuously with any continuous variation of the structure, it is more adequate to describe minor differences of the local order than the usual integer coordination numbers. It is shown that the use of integer coordination numbers leads to the overestimation of the disorder of the structure.

Digital processing of contrast echocardiograms: A new technique for measuring right ventricular ejection fraction

Imaging of the right ventricle with 2-dimensional echocardiography (2-D echo) is hampered by trabeculation of the right ventricular (RV) endocardial surface and by limited echocardiographic resolution. Determination of RV ejection fraction (EF) is thus often an inconsistent and tedious procedure. The process of digital subtraction contrast echocardiography was developed to maximize echocardiographic definition of the right ventricle and to assess RVEF with minimal operator interaction. Videotaped 2-D echocardiograms recorded during i.v. injection of agitated saline were digitized. Masks were constructed from end-systolic and end-diastolic apical 4-chamber and parasternal RV short-axis images. Masks were subtracted from corresponding images recorded with contrast in the right ventricle; images of the contrast alone were extracted and their areas determined. EF was calculated from raw area measurements and after conversion to volume. Comparison with RVEF measured by first-pass radionuclide angiography yielded the following correlation coefficients: 4-chamber RV area, r = 0.79; parasternal short-axis RV area, r = 0.59; ellipsoid approximation RV volume, r = 0.84; pyramidal RV volume, r = 0.79; and Simpson's rule triangular cylinder RV volume, r = 0.62. Digital subtraction contrast echocardiography is a new method that can be used for semiautomated determination of RVEF. Further studies to assess the clinical values of digital image processing of 2-D echocardiograms to measure RV function appear warranted.

Models for Certain Pyramids

The proof for the volume of a triangular pyramid involves showing that the pyramid is one of theee equal pyramids that form a prism. To make paper models of the three pyramids most pupils make the prism first and then measure certain lines in it to find the edges of the pyramids. But even when making the oblique prism the pupil has no direct geometric method for making the third lateral face after he has constructed two of the faces; that is, after making a pattern for ΔABC, for parallelogram ABDF, and for parallelogram BCED, he cannot construct parallelogram ACEF because he knows neither the diagonal CF, nor the angles at the vertices, nor any altitude of the parallelogram.

1590. The volume of the pyramid

1590. The volume of the pyramid

THE QUANTITATIVE DISTRIBUTION OF THE PYRAMIDAL TRACT IN MAN

It is an axiom, generally recognized in neurophysiology, that the development of skilled acts in the upper and lower extremities of the highest forms of animal life is intimately connected with the size of the pyramidal tracts. The work of Schaefer1is quoted as giving experimental evidence of this thesis, and Tilney2concluded from comparative studies of the central nervous system of apes and man that it is in relation to the progressive adaptation apparent in the upper extremities that the pyramidal system is most intimately connected.... It seems permissible to conclude that the increment in pyramidal volume is proportional to that increasing demand for control of motor performances made possible through the progressive development of the hand. In studying the literature on this subject one finds that comparative measurements of the pyramids in the medulla oblongata and the size of the nonmedullated tract in new-born animals form

On the Treatment in School Texts of the Sphere, Cone and Pyramid

An important note in the Proc. Edin. Math. Soc. of May 1904 pointed out that the then prevalent School method of tangents made it difficult for the pupil to gain sound knowledge in his later studies. The same criticism may, I submit, be directed against the treatment, now prevalent in school texts, of (1) surface of sphere, (2) volume of sphere, and (3) volume of cone and pyramid.

31. Elementary Proof That the Volume of a Pyramid or Cone Is 1/3 Base X Height, by Assuming the Properties of Similar Figures

31. Elementary Proof That the Volume of a Pyramid or Cone Is 1/3 Base X Height, by Assuming the Properties of Similar Figures