Applications of Surface Networks to Sampling Problems in Computer Graphics

This thesis develops the theory, algorithms and data structures for adaptive sampling of parametric functions, which can represent the shapes and motions of physical objects. For the first time, ensured methods are derived for determining collisions and other interactions for a broad class of parametric functions. A new data structure, called a surface network, is developed for the collision algorithm and for other sampling problems in computer graphics. A surface network organizes a set of parametric samples into a hierarchy. Surface networks are shown to be good for rendering images, for approximating surfaces, and for modeling physical environments. The basic notion of a surface network is generalized to higher-dimensional problems such as collision detection. We may think of a two-dimensional network covering a three-dimensional solid, or an n-dimensional network embedded in a higher-dimensional space. Surface networks are applied to the problems of adaptive sampling of static parametric surfaces, to adaptive sampling of time-dependent parametric surfaces, and to a variety of applications in computer graphics, robotics, and aviation. First we develop the theory for adaptive sampling of static surfaces. We explore bounding volumes that enclose static surfaces, subdivision mechanisms that adjust the sampling density, and subdivision criteria that determine where samples should be placed. A new method is developed for creating bounding ellipsoids of parametric surfaces using a Lipschitz condition to place bounds on the derivatives of parametric functions. The bounding volumes are arranged in a hierarchy based on the hierarchy of the surface network. The method ensures that the bounding volume hierarchy contains the parametric surface completely. The bounding volumes are useful for computing surface intersections. They are potentially useful for ray tracing of parametric surfaces. We develop and examine a variety of subdivision mechanisms to control the sampling process for parametric functions. Some of the methods are shown to improve the robustness of adaptive sampling. Algorithms for one mechanism, using bintrees of right parametric triangles, are particularly simple and robust. A set of empirical subdivision criteria determine where to sample a surface, when we have no additional information about the surface. Parametric samples are concentrated in regions of high curvature, and along intersection boundaries. Once the foundations of adaptive sampling for static surfaces are described, we examine time-dependent surfaces. Based on results with the empirical subdivision criteria for static surfaces, we derive ensured criteria for collision determination. We develop a new set of rectangular bounding volumes, apply a standard L-dimensional subdivision mechanism called k-d trees, and develop criteria for ensuring that we detect collisions between parametric surfaces. We produce rectangular bounding boxes using a "Jacobian''-style matrix of Lipschitz conditions on the parametric function. The rectangular method produces even tighter bounds on the surface than the ellipsoidal method, and is effective for computing collisions between parametric surfaces. A new collision determination technique is developed that can detect collisions of parametric functions, based on surface network hierarchies. The technique guarantees that the first collision is found, to within the temporal accuracy of the computation, for surfaces with bounded parametric derivatives. Alternatively, it is possible to guarantee that no collisions occur for the same class of surfaces. When a collision is found, the technique reports the location and parameters of the collision as well as the time of first collision. Finally, we examine several applications of the sampling methods. Surface networks are applied to the problem of converting a two-dimensional image, or texture map, into a set of triangles that tile the plane. Many polygon-rendering systems do not provide the capability of rendering surfaces with textures. The technique converts textures to triangles that can be rendered directly by a polygon system. In addition, potential applications of the collision determination techniques are discussed, including robotics and air-traffic control problems

Heat flow at the spreading centers of the Guaymas Basin, Gulf of California

Fifty-four new heat flow measurements in the central troughs of the Guaymas basin support the hypothesis that they are sites of active intrusion. In the northern trough a distinct pattern of hydrothermal cooling is revealed, with venting along the western boundary fault of the trough. In the southern trough an analogous pattern is apparently superimposed upon a conductive cooling anomaly associated with a recent central intrusion. The discharge of thermal waters occurs along the boundary faults and through other faults associated with a possible horst block located in the north central floor of the southern trough. The heat flow patterns suggest that the intrusions are episodic and do not occur simultaneously along the length (15–40 km) of a spreading segment. A review of all available heat flow measurements for the Guaymas basin suggests that most of the recharge for a pervasive regional hydrothermal system is limited to the central depressions, with perhaps some contribution from pore water. The discharge of thermal waters occurs predominantly in the central depressions and possibly along the boundary transform faults and fracture zones. The regions of the basin more than a few kilometers in distance from the spreading axis, although presumably underlain by a hydrothermal system, are probably not the location of numerous vents or recharge zones

Sampling Deformed, Intersecting Surfaces with Quadtrees

A quadtree algorithm is developed to render deformed, intersecting parametric surfaces with inside-outside functions. The task of adaptively sampling a surface may be broken into two parts: a subdivision mechanism for recursively subdividing a surface, and a set of subdivision criteria for determining where to subdivide. A surface quadtree is a collection of parametric samples arranged in a quadtree. A restricted quadtree is a quadtree whose neighboring elements must be the same size within a factor of two. Restricted surface quadtrees are shown to be an effective recursive subdivision mechanism. The quadtree samples are concentrated along silhouette and intersection boundaries, and in regions of high curvature, using several subdivision criteria. The recursive subdivision algorithm that finds the sample points is proven to have a complexity of O(n) along boundary curves, where n is the linear resolution of the boundary in parameter space. A new proximity subdivision criterion concentrates samples where two surfaces potentially intersect. An extended modeling hierarchy that includes deformations is demonstrated with several examples. The initial implementation using surface quadtrees is moderately more efficient and substantially more robust than uniform Sampling techniques; surface quadtrees are potentially much more efficient and robust than uniform sampling at rendering deformed, intersecting surfaces

Estimate of heat flux and its temporal variation at the TAG hydrothermal mound, Mid-Atlantic Ridge 26°N

Author Posting. © American Geophysical Union, 2003. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 108, B9 (2003): 2434, doi:10.1029/2001JB000703.From August 1994 to March 1995, three 50-m-high vertical thermistor arrays designated “Giant Kelps” (GKs) were deployed around the central black smoker complex (CBC) at the TAG hydrothermal mound, Mid-Atlantic Ridge (26°08primeN, 44°49primeW). These were designed to monitor the temporal variability of the vertical temperature distribution in the hydrothermal plume. One small high-temperature probe “Hobo” was also deployed in one of the black smoker vents of CBC. Over the observation period, two typical characteristics are recognized in plume temperatures measured with GKs: (1) the amplitudes of temperature anomalies decrease with increasing height above the top of CBC; (2) maximum temperature anomalies on the upper thermistors occurred periodically and nearly simultaneously across the array about every 6 hours. Conversely, maximum temperature anomalies on the lower thermistors occurred periodically every 12 hours, indicating that the location of the plume discharged from CBC was forcibly moved by the change in direction of tidally modulated current flow. The heat flux from CBC was estimated from temperatures measured by GKs based on a model of buoyant hydrothermal fluid rising in a stable, stratified density environment. The estimated heat flux from CBC gradually decreases from about 86 to 55 MW over the ~7 months of measurement, with a mean rate of decrease of 0.17 MW d-1. Since the black smoker effluent temperature measured with Hobo was almost stable over the measurement period, a plausible cause of the decrease is a reduction in the volume of hydrothermal fluid provided to the CBC (in which case the estimated mean rate of decrease in volume flux of CBC is 8.9 m3 d-1). Estimated heat flux, temperature anomalies observed by Hobo, and diffuse flow and subbottom temperature anomalies recorded by other long-term monitoring instruments before, during, and after ODP Leg 158 indicate that the drilling probably affected the fluid flow pattern within the mound but had little effect on the total heat flux from CBC.This study was supported by the Ridge Flux project of the Science and Technology Agency, Japan, the US NSF, and the UK NERC BRIDGE program. GK instrumentation development and deployments were supported in large part by NSF grant OCE-9324542

Models of hydrothermal circulation within 106 Ma seafloor : constraints on the vigor of fluid circulation and crustal properties, below the Madeira Abyssal Plain

Author Posting. © American Geophysical Union, 2005. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 6 (2005): Q11001, doi:10.1029/2005GC001013.Heat flow measurements colocated with seismic data across 106 Ma seafloor of the Madeira Abyssal Plain (MAP) reveal variations in seafloor heat flow of ±10–20% that are positively correlated with basement relief buried below thick sediments. Conductive finite element models of sediments and upper basement using reasonable thermal properties are capable of generating the observed positive correlation between basement relief and seafloor heat flow, but with variability of just ±4–8%. Conductive simulations using a high Nusselt number (Nu) proxy for vigorous local convection suggest that Nu = 2–10 within the upper 600–100 m of basement, respectively, is sufficient to achieve a reasonable match to observations. These Nu values are much lower than those inferred on younger ridge flanks where greater thermal homogeneity is achieved in upper basement. Fully coupled simulations suggest that permeability below the MAP is on the order of 10−12–10−10 m2 within the upper 300–600 m of basement. This permeability range is broadly consistent with values determined by single-hole experiments and from modeling studies at other (mostly younger) sites. We infer that the reduction in basement permeability with age that is thought to occur within younger seafloor may slow considerably within older seafloor, helping hydrothermal convection to continue as plates age.Funding in support of this work was provided by the U.S. National Science Foundation (OCE-0001892), the U.S. Science Support Program for IODP (T301A7), and the Institute for Geophysics and Planetary Physics/Los Alamos National Laboratory (1317)

A miniature deep sea temperature data recorder : design, construction, and use

A miniature temperature recorder has been developed to be used with the hydraulic piston sediment corer <HPC) on the Deep Sea Drilling Project <DSDP). The instrumentation fits into pressure-sealed slots in the wall of the HPC, allowing temperature measurements to be made simultaneously with coring operations. Temperatures from -2 to 70°C are measured to a resolution of about 0.01°C. Up to 1300 13-bit measurements are recorded in random access memory (RAM), at a sampling rate ranging between 0.1 s to over 100 min., as specified by the operator in a program loaded into a microprocessor of the instrument. During recording the instrumentation uses about 3.5 mamp at 7.5 volts, which can be supplied for about 20 hours of operation by a custom-made pack of silver-oxide batteries. The corer is normally left motionless in the sediment for about 10 min. to allow extrapolation of the measured temperatures to equilibrium in-situ temperature. Examples of data from DSDP Leg 86 are given.Funding was provided by the National Science Foundation under grant Nos. OCE 82-14658 and OCE 83-00073. Additional support was provided by U.S. Geological Survey of Woods Hole to begin development of instrumentation; and to the Ocean Industry Program of the Woods Hole Oceanographic Institution to complete the development

Heat flow from the Southeast Indian Ridge flanks between 80°E and 140°E: Data review and analysis

International audienceWe analyze available heat flow data from the flanks of the Southeast Indian Ridge adjacent to or within the Australian-Antarctic Discordance (AAD), an area with patchy sediment cover and highly fractured seafloor as dissected by ridge- and fracture-parallel faults. The data set includes 23 new data points collected along a 14-Ma old isochron and 19 existing measurements from the 20- to 24-Ma old crust. Most sites of measurements exhibit low heat flux (from 2 to 50 mW m−2) with near-linear temperature-depth profiles except at a few sites, where recent bottom water temperature change may have caused nonlinearity toward the sediment surface. Because the igneous basement is expected to outcrop a short distance away from any measurement site, we hypothesize that horizontally channelized water circulation within the uppermost crust is the primary process for the widespread low heat flow values. The process may be further influenced by vertical fluid flow along numerous fault zones that crisscross the AAD seafloor. Systematic measurements along and across the fault zones of interest as well as seismic profiling for sediment distribution are required to confirm this possible, suspected effect

Lake Kivu expedition : geophysics, hydrography, sedimentology (preliminary report)

In March 1971, seven members of the Woods Hole Oceanographic Institution were engaged in a multidisciplinary study of Lake Kivu. This expedition represents part of a long-range program concerned with the structural and hydrographical settings of the East African Rift Lakes and their relationships to the Red Sea and the Gulf of Aden Rifts. The program started in May 1963 with a geophysical study on Lake Malawi (von Herzen and Vacquier, 1967). Several expeditions of our Institution into the Red Sea and Gulf of Aden area in 1964, 1965 and 1966 (Degens and Ross, 1969) provided detailed geological information on the "northern" extension of the East African Rift. And finally our study of last year on Lake Tanganyika c1osed a major gap in the program; it allowed us to out1ine a model on the evolution of a rift which starts with (i) bulging of the earth's crust, (ii) block-faulting, (iii) volcanism and hydrothermal activity, and which has its final stage in (iv) sea floor spreading (Degens et al. 1971). In the case of Lake Tanganyika, only the second stage of this evolution series has been reached, i.e. block-faulting. In contrast, the Red Sea and the Gulf of Aden had already evolved to active sea floor spreading, almost 25 million years ago. Somewhere along the line between Lake Tanganyika and the Gulf of Aden must lie the "missing link" of this evolution series. Lake Kivu, almost 100 miles to the north of Lake Tanganyika is situated at the highest point of the Rift Valley and is surrounded by active volcanoes and geothermal springs. As recently as 1944, lava flows reached the lake shore. This lake was therefore, a natural choice to test our hypothesis on the origin and development of rifts. Furthermore, the occurrence of large quantities of dissolved gases, e.g., CO2 and methane, represented an interesting geochemical phenomenon worthwhile to investigate.Supported by the National Science Foundation with Grants GA 19262, GB 20956, and GU 3927; grants from the Petroleum Research Fund of the American Chemical Society PRF#1943A2; and by private research funds of the Woods Hole Oceanographic Institution

Deep-sea corehead camera photography and piston coring

Cameras were mounted in a newly designed corehead of a piston corer and used to photograph coring operations during 36 stations on CHAIN cruise 75 and 28 stations on ATLANTIS II cruise 42. Through the analysis of these photographs, the deep-water operation of a piston corer during its descent, tripping, impact with the bottom, and ascent has been studied, providing information on the corer's stability, effectiveness in obtaining a bottom sample, and influence on the nearby sea-floor. Accurate determinations of the amount of penetration were possible, allowing comparisons to be made with the more indirect methods of determining penetration and with the length of core recovered. Sediment clouds produced by bottom currents were noticed in many of the bottom photographs. A number of suggestions are made for future piston coring operations. The corer descends with little rotation and swinging. Free-fall and penetration generally take place in less than 5 seconds, with a rotation of 20-60° and an increase of about 6° in vertical deviation. During penetration, the corer disturbs the surrounding sea floor, producing both mounds and depressions around the core barrels. While resting in the bottom, the corer is very stable although some wobbling does occur. Considerable rotation takes place during both pull-out and ascent; frequent sediment discharges from the piston corer occur. No consistent relationship was found between the amount of penetration and the length of core recovered, and thus with the degree of core shortening. Comparisons between piston and pilot cores indicate that the piston cores have been shortened and disturbed relative to the pilot cores, and that as much as a meter of the upper portion of the piston core has been lost. The position of the mud-mark appears to be a reliable indicator of the amount of penetration; estimates by extrapolation of the thermal gradient to the surface are less reliable. The vertical deviation of the corer in the bottom does not influence the amount of penetration. Stratigraphic dips in the recovered cores correspond poorly to this vertical deviation in the bottom.The National Science Foundation Grants GA-1077 and GA-1209 and submitted to the Office of Naval Research under Contract Nonr-4029(00); NR 260-101, and N00014-66-C0241; NR 083- 004