Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates

 The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of M?bius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex generated by the unknown point and the four known points. Substitution of M?bius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4. contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gau? (1842), A. Schreiber (1908) and A.␣Ansermet (1910). Received: 05 March 1996; Accepted: 15 October 1996     

Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution

Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same degree as that of the original spherical Poisson kernel. Received: 4 June 1996 / Accepted: 7 April 1997     

The spacetime gravitational field of a deformable body

The high-resolution analysis of orbit perturbations of terrestrial artificial satellites has documented that the eigengravitation of a massive body like the Earth changes in time, namely with periodic and aperiodic constituents. For the space-time variation of the gravitational field the action of internal and external volume as well as surface forces on a deformable massive body are responsible. Free of any assumption on the symmetry of the constitution of the deformable body we review the incremental spatial (“Eulerian”) and material (“Lagrangean”) gravitational field equations, in particular the source terms (two constituents: the divergence of the displacement field as well as the projection of the displacement field onto the gradient of the reference mass density function) and the `jump conditions' at the boundary surface of the body as well as at internal interfaces both in linear approximation. A spherical harmonic expansion in terms of multipoles of the incremental Eulerian gravitational potential is presented. Three types of spherical multipoles are identified, namely the dilatation multipoles, the transport displacement multipoles and those multipoles which are generated by mass condensation onto the boundary reference surface or internal interfaces. The degree-one term has been identified as non-zero, thus as a “dipole moment” being responsible for the varying position of the deformable body's mass centre. Finally, for those deformable bodies which enjoy a spherically symmetric constitution, emphasis is on the functional relation between Green functions, namely between Fourier-/ Laplace-transformed volume versus surface Love-Shida functions (h(r),l(r) versus h ^′(r),l ^′(r)) and Love functions k(r) versus k ^′(r). The functional relation is numerically tested for an active tidal force/potential and an active loading force/potential, proving an excellent agreement with experimental results. Received: December 1995 / Accepted: 1 February 1997     

Multiplotting With Images from the Kodak DCS420 Digital Camera

This paper explores the potential of a digital camera to produce multiple images suitable for plotting. The objective was to build a three dimensional database by linking triangulated images from a Kodak DCS420 digital camera with a computer aided measurement system. The system then supplied X, Y, Z data from x, y image co-ordinates captured off two or more images. Relative accuracy in object space was around 1;50 000.     

Internet teaching foundation for the Remote Sensing Core Curriculum program

The Remote Sensing Core Curriculum (RSCC) was initiated in 1993 to meet the demands for a college-level set of resources to enhance the quality of education across national and international campuses. The American Society of Photogrammetry and Remote Sensing adopted the RSCC in 1996 to sustain support of this educational initiative for its membership and collegiate community. A series of volumes, containing lectures, exercises, and data, is being created by expert contributors to address the different technical fields of remote sensing. The RSCC program is designed to operate on the Internet taking full advantage of the World Wide Web (WWW) technology for distance learning. The issues of curriculum development related to the educational setting, with demands on faculty, students, and facilities, is considered to understand the new paradigms for WW-influenced computer-aided learning. The WWW is shown to be especially appropriate for facilitating remote sensing education with requirements for addressing image data sets and multimedia learning tools. The RSCC is located at http://www.umbc.edu/rscc     

Modelling the short-term response of the Greenland ice-sheet to global warming

 A two-dimensional vertically integrated ice flow model has been developed to test the importance of various processes and concepts used for the prediction of the contribution of the Greenland ice-sheet to sea-level rise over the next 350 y (short-term response). The mass balance is modelled by the degree-day method and the energy-balance method. The lithosphere is considered to respond isostatically to a point load and the time evolution of the bedrock follows from a viscous asthenosphere. According to the IPCC-IS92a scenario (with constant aerosols after 1990) the Greenland ice-sheet is likely to cause a global sea level rise of 10.4 cm by 2100 AD. It is shown, however, that the result is sensitive to precise model formulations and that simplifications as used in the sea-level projection in the IPCC-96 report yield less accurate results. Our model results indicate that, on a time scale of a hundred years, including the dynamic response of the ice-sheet yields more mass loss than the fixed response in which changes in geometry are not incorporated. It appears to be important to consider sliding, as well as the fact that climate sensitivity increases for larger perturbations. Variations in predicted sea-level change on a time scale of hundred years depend mostly on the initial state of the ice-sheet. On a time scale of a few hundred years, however, the variability in the predicted melt is dominated by the variability in the climate scenarios. Received: 21 August 1996/Accepted: 12 May 1997     

Exhumed fault-bounded Alpine blocks along the Periadriatic lineament: the Eder unit (Carnic Alps, Austria)

The Eder unit in the Carnic Alps, which is situated immediately south of the Periadriatic lineament (PL), represents a fault-bounded block consisting of a low-grade (up to 400?°C, indicated by epizonal illite “crystallinity” values, recrystallized quartz, and non-recrystallized white mica) metamorphic Paleozoic metasedimentary sequence. Until now, it has been assumed to represent a separate Variscan nappe. The rocks of the Eder unit show a strong E- to W-oriented stretching lineation on steep foliation planes (D₁) subparallel to the PL. D₁ structures originated near the temperature peak of metamorphism, and shear sense indicators show dextral ductile shear parallel to the PL. Tight mesoscale D₂ folds formed on the cooling path. K–Ar and Ar–Ar ages from newly formed white mica cluster around 32–28 and 18–13 Ma and suggest a two-stage Tertiary history of the Eder unit. We interpret the Eder unit as a fault-bounded block formed during Oligocene large-scale dextral shearing along the PL (near T_max) and exhumed in mid-Miocene times during another phase of activity along the PL. Its nature as a separate Variscan nappe is questioned.     

Formation of silica oncoids around geysers and hot springs at El Tatio, northern Chile

Siliceous oncoids, up to 4 cm in diameter, are common on the laterally extensive sinter aprons that surround the spectacular geysers and hot springs at El Tatio in northern Chile. Many of these complex oncoids developed close to geyser and spring vents that discharge boiling water. Internally the oncoids, which are composed of precipitated amorphous silica, are formed of complex arrays of spicules and concentric laminae as well as detrital volcanic grains. Spicular growth is dominant in most examples. The formation and growth of the spicules and concentric laminae were mediated by a microbial community which included filamentous microbes, mucus, and possibly bacteria. The microbes and mucus were silicified by replacement and encrustation. In some laminae the filamentous microbes lay parallel to the growth surface; in other laminae most filaments forming the thin mats were suberect. Amorphous silica precipitated between the filaments occluded porosity and commonly disguised the microbial fabric. The oncoids grew on the proximal sinter aprons around the geyser vents and hot spring pools. Most growth took place subaerially with the silica delivered to the precipitation sites by splashing water from the geysers and/or periodic shallow flooding of the discharge aprons. Unlike silica oncoids at other geothermal sites, vertical growth of oncoids that formed in some rimstone pools was not limited by water depth.     

Spillover models for axial rivers in regions of continental extension: the Rio Mimbres and Rio Grande in the southern Rio Grande rift, USA

The Pliocene-early Pleistocene history of the ancestral Rio Grande and Quaternary history of the Rio Mimbres in the southern Rio Grande rift, New Mexico, illustrate how axial rivers may alternately spill into and subsequently abandon extensional basins. Three types of spillover basins are recognized, based on the angle at which the axial river enters the basin and whether it descends the hanging wall dip slope or footwall scarp to reach the basin floor. In the Mimbres basin type, the axial river enters and flows through the spillover basin nearly parallel to the footwall scarp, resulting in a narrow belt of basin-axis-parallel channel sand bodies located near the footwall scarp. In contrast, an axial river may enter a spillover basin at a high angle to its axis, either descending the hanging wall dip slope (Columbus basin type) or footwall scarp (Tularosa basin type), and construct a fluvial fan, consisting of radiating distributary channels orientated nearly perpendicular to the basin axis. Faulting exerts significant control on river spillover by creating the topographic gaps through which the axial river moves and by terminating spillover by subsequently uplifting or tilting the gap. Spillover may also be autocyclic in origin as a result of aggradation to the level of a pre-existing gap, headward erosion creating and/or intersecting a gap, or simple river avulsion upstream of a gap. Predicting facies architecture in the three types of spillover basins is critical to successful subsurface exploration for hydrocarbon reservoirs, groundwater aquifers or placer mineral deposits.