scholarly journals Real quartic surfaces containing16skew lines

2004 ◽  
Vol 2004 (44) ◽  
pp. 2331-2345
Author(s):  
Isidro Nieto
Keyword(s):  
Three Dimensional ◽  
Real Surface ◽  
Two Dimensional ◽  
Viewing Angle ◽  
Complex Surfaces ◽  
Quartic Surface ◽  
The Real ◽  
Visual Properties ◽  
Quartic Surfaces

It is well known that there is an open three-dimensional subvarietyMsof the Grassmannian of lines inℙ3which parametrizes smooth irreducible complex surfaces of degree 4 which are Heisenberg invariant, and each quartic contains 32 lines but only 16 skew lines, being determined by its configuration of lines, are called adouble 16. We consider here the problem of visualizing in a computer the real Heisenberg invariant quartic surface and the real double 16. We construct a family of pointsl∈Msparametrized by a two-dimensional semialgebraic variety such that under a change of coordinates oflinto its Plüecker, coordinates transform into the real coordinates for a lineLinℙ3, which is then used to construct a program in Maple 7. The program allows us to draw the quartic surface and the set of transversal lines toL. Additionally, we include a table of a group of examples. For each test example we specify a parameter, the viewing angle of the image, compilation time, and other visual properties of the real surface and its real double 16. We include at the end of the paper an example showing the surface containing the double 16.

scholarly journals On a set of quartic surfaces in space of four dimensions; and a certain involutory transformation

1926 ◽  
Vol 110 (756) ◽  
pp. 700-708
Keyword(s):  
Present Note ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Quartic Surface ◽  
Four Dimensions ◽  
Cubic Surfaces ◽  
Mutual Relations ◽  
Quartic Surfaces ◽  
Three Dimensional Space

There exists in space of four dimensions an interesting figure of 15 lines and 15 points, first considered by Stéphanos (‘Compt. Rendus,’ vol. 93, 1881), though suggested very clearly by Cremona’s discussion of cubic surfaces in three-dimensional space. In connection with the figure of 15 lines there arises a quartic surface, the intersection of two quadrics, which is of importance as giving rise by projection to the Cyclides, as Segre has shown in detail (‘Math. Ann.,’ vol. 24, 1884). The symmetry of the figure suggests, howrever, the consideration of 15 such quartic surfaces; and it is natural to inquire as to the mutual relations of these surfaces, in particular as to their intersections. In general, two surfaces in space of four dimensions meet in a finite number of points. It appears that in this case any two of these 15 surfaces have a curve in common; it is the purpose of the present note to determine the complete intersection of any two of these 15 surfaces. Similar results may be obtained for a system of cubic surfaces in three dimensions, corresponding to those here given for this system of quartic surfaces in four dimensions, since the surfaces have one point in common, which may be taken as the centre of a projection.

scholarly journals Rancang Bangun Aplikasi Augmented Reality Museum Bali Berbasis Android Studi Kasus Gedung Karangasem dan Gedung Tabanan

2016 ◽  
pp. 93
Author(s):  
I Gede Aditya Nugraha ◽  
I Ketut Gede Darma Putra ◽  
I Made Sukarsa
Keyword(s):  
Augmented Reality ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Museum Collections ◽  
3D Object ◽  
The Real ◽  
Virtual Objects ◽  
The People ◽  
Augmented Reality Application ◽  
Augmented Reality Technology

Museum Bali is one of the museum which is located in Denpasar City that established since 1910. The Museum collections consist of items such as living equipment, art, religion, handwriting, and other things that show the situation and the development of the Balinese culture. Augmented Reality is a technology which combines two-dimensional virtual objects or three-dimensional virtual objects into the real environment. Museum Bali has decreased the amount of visitors in recent years and requires an innovation to promote Museum Bali. One innovation that is expected to promote the Museum Bali is to create an augmented reality application that called Augmented Reality Museum Bali in Android platform. Utilizing augmented reality technology that works by detecting the marker then it show up the 3D object and the information from one of the objectsin Museum Bali. Markerless method used in detection marker that make this application moreattractive and expected to be a new experience for the people who want to know more about Museum Bali.

scholarly journals Chemical Etching of {hk0} Silicon Plates in EDP Part I: Experiments and Comparison with TMAH

2000 ◽  
Vol 23 (1) ◽  
pp. 37-51
Author(s):  
C. R. Tellier ◽  
T. G. Leblois ◽  
A. Charbonnieras
Keyword(s):  
Experimental Study ◽  
Chemical Etching ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Slowness Surface ◽  
The Real ◽  
Geometrical Features ◽  
Etched Surface ◽  
Dissolution Slowness

This paper deals with the anisotropic chemical etching of various silicon plates etched in EDP. Changes with orientation in geometrical features of etched surface and in the etching shape of starting circular sections are systematically investigated. These etching shapes are compared with shapes produced by etching in KOH and TMAH solutions; This experimental study allows us to determine the dissolution slowness surface for the EDP solution and to investigate the real influence of the etchant on two dimensional and three dimensional etching shapes.

scholarly journals Powers of Elliptic Scator Numbers

2021 ◽  
Author(s):  
Manuel Fernandez-Guasti
Keyword(s):  
Rational Number ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Interpretation ◽  
Two Dimensional ◽  
Closed Curves ◽  
Complex Algebra ◽  
The Real ◽  
Polar Representation ◽  
Three Dimensional Space

Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1+1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1+2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1+2 dimensions.

IMPLEMENTASI AR DENGAN METODE MARKER SEBAGAI KATALOG PADA TOKO MEBEL BERBASIS WEB-AR.pdf

2019 ◽  
Vol 3 (1) ◽  
pp. 1-9
Author(s):  
Aulia Sari Prihatini ◽  
Mahrizal Masri ◽  
Mhd. Zulfansyuri Siambaton
Keyword(s):  
Augmented Reality ◽  
Real Time ◽  
Real World ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Web Browser ◽  
Web Based ◽  
The Real ◽  
Real Objects

Reality Increasing or often also called AR (Augmented Reality) in English, is a technology that can add two-dimensional or three-dimensional illusions of objects together into a 3D into the real world then project illusion objects into real time. Unlike the illusion of reality where in the real world is completely replaced, reality only adds to or completes reality. Augmented Reality unites real objects and illusions into real circles, works interactively in real time and found integration between objects in 3D and good integration requires effective investigation. Web AR provides Web-based access using Augmented Reality through a web browser using a combination of technologies including WebRTC, WebGL, WebVR, and Modern APLs sensors. Catalogs are publicity tools used by companies as a way to promote their products and services. Examples of companies that use catalogs are Furniture stores that promote products. Here it will be visualized into 3D until it looks more clear and attractive to consumers. So, based on the description above, the author takes the title "Implementation of Augmented Reality with Marker Method as Media Catalog in AR-Based Furniture Stores. Keywords: Augmented Reality, WEB AR, catalog

scholarly journals Magnetotelluric analysis using Mohr circles

Geophysics ◽  
1993 ◽  
Vol 58 (10) ◽  
pp. 1498-1506 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Mechanical Stress ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Impedance Tensor ◽  
Two Dimensional ◽  
Skew Angle ◽  
The Real ◽  
Mohr Circle ◽  
Quantitative Expression

The Mohr circle, most commonly met in the analysis of mechanical stress, is used to depict magnetotelluric impedance information, taking the real and quadrature parts of magnetotelluric tensors separately. The magnetotelluric concepts of two‐dimensionality, three‐dimensionality, skew and anisotropy are then all given quantitative expression on a diagram, as are various magnetotelluric invariants. In particular, a new invariant, the “central impedance,” becomes evident in a discussion of effective impedances. Some insight is gained into impedance rotations, and an anisotropy angle is defined, analogous to skew angle. Mohr circles are also tested to depict the effects of the shear and twist operations on a regionally two‐dimensional structure. Generally, the application of shear or twist results in an impedance tensor with a Mohr circle of typical three‐dimensional form.

STM OBSERVATION OF GRATING SURFACES

1990 ◽  
Vol 04 (03) ◽  
pp. 181-193 ◽  
Author(s):  
TAKANORI OSHIO ◽  
YOSHIYUKI SAKAI ◽  
SHAW EHARA ◽  
KŌSHI TAKASHIMA
Keyword(s):  
Three Dimensional ◽  
Apex Angle ◽  
Radius Of Curvature ◽  
Real Surface ◽  
Finite Radius ◽  
The Real ◽  
Optical Grating ◽  
Stm Image

Three dimensional topographic images of optical grating surfaces have been obtained by the use of an STM. The STM can measure the grating surfaces in detail in air without touching the surfaces. The shape of an STM image is deformed from that of the real surface in some respects due to the finite radius of curvature, R, of the pointed probe tip. Reference figures, each of which shows the resultant STM shape of the image corresponding to a real surface having a certain set of values of blaze angle, θ, and apex angle, ϕ, have been prepared. With the aid of these figures, we could estimate, conversely, values of θ and ϕ, in addition to R of the tip used, from the STM image obtained. The possible ambiguities in the estimation were also discussed. Thus, θ and ϕ values of gratings with line densities of 1,200 ~ 18,000 line/mm have been measured with errors of less than 10%. This conducting method with the use of an STM and reference figures may be very effective in the inspection of surfaces fabricated by submicron machining in general.

Caustics of the harmonic double cusp near an E 6 point

1982 ◽  
Vol 382 (1783) ◽  
pp. 319-334 ◽  
Keyword(s):  
Three Dimensional ◽  
Large Family ◽  
Two Dimensional ◽  
Liquid Drops ◽  
The Real ◽  
Bifurcation Set ◽  
High Codimension ◽  
Viewing Screen ◽  
Real Singularity

The harmonic double cusp is the real singularity x 4 – 6 x 2 y 2 + y 4 . Its unfolding is eight-dimensional and contains a stratum of codimension five corresponding to the E 6 singularity x 3 + y 4 . A complete description of the bifurcation set in a neighbourhood of the E 6 stratum is given by means of a tableau of two-dimensional sections over the three-dimensional base. The tableau also gives information about the bifurcation set near other strata of high codimension, notably D – 6 : x 2 y – y 5 and A * 7 : x 2 – y 8 , and it shows how these strata fit together. In optics, the harmonic double cusp organizes a large family of caustics produced by generic thin lenses. Some predictions made by the tableau have already been confirmed by observations of caustics from liquid drops: points in the tableau base correspond to experimental set-ups, and the fibre corresponds to the viewing screen.

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