Abstract: Systems and methods are provided for optimizing a parametrization scheme in accordance with information about the surface signal. A surface parametrization is created to store a given surface signal into a texture image. The signal-specialized metric of the invention minimizes signal approximation error, i.e., the difference between the original surface signal and its reconstruction from the sampled texture. A signal-stretch parametrization metric is derived based on a Taylor expansion of signal error. For fast evaluation, the metric of the invention is pre-integrated over the surface as a metric tensor. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail. Compared to traditional geometric parametrizations, the number of texture samples can often be reduced by a significant factor for a desired signal accuracy.

Abstract: Systems and methods are provided for providing a fine-to-coarse look ahead in connection with parametrization in a graphics system. The use of a variety of parametrization metrics may be supplemented and improved by the fine-to-coarse look ahead techniques of the invention. First, the metric of a parametrization is minimized using a coarse-to-fine hierarchical solver, and then accelerated with a fine-to-coarse propagation. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail at all levels of detail in the progressive mesh sequence.

Abstract: Systems and methods are provided for optimizing the geometric stretch of a parametrization scheme. Given an arbitrary mesh, the systems and methods construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. The systems and methods minimize geometric stretch, i.e., small texture distances mapped onto large surface distances, to balance sampling rates over all locations and directions on the surface. The systems and methods also minimize texture deviation, i.e., “slippage” error based on parametric correspondence, to obtain accurate textured mesh approximations. The technique(s) begin by partitioning the mesh into charts using planarity and compactness heuristics. Then, the technique(s) proceed by creating a stretch-minimizing parametrization within each chart, and by resizing the charts based on the resulting stretch. Then, the technique(s) simplify the mesh while respecting the chart boundaries.

Abstract: An optical waveguide including: a dielectric core region extending along a waveguide axis; and a dielectric confinement region surrounding the core about the waveguide axis, the confinement region comprising a photonic crystal structure having a photonic band gap, wherein during operation the confinement region guides EM radiation in at least a first range of frequencies to propagate along the waveguide axis, wherein the core has an average refractive index smaller than about 1.3 for a frequency in the first range of frequencies, and wherein the core a diameter in a range between about 4 &lgr; and 80 &lgr;, wherein &lgr; is a wavelength corresponding to a central frequency in the first frequency range.

Abstract: Valve boxes of this invention comprise a housing including an inner chamber that extends axially through the housing from a housing base. The housing chamber includes a diameter that is defined by a housing sidewall surface that extends outwardly from the base, forming a chamber opening. The chamber opening includes a seal surface that is positioned radially inwardly towards the chamber. The valve box further includes a lid that is positioned over the housing chamber opening. The lid includes a concave center section and a seal surface disposed radially therearound. The lid seal surface is positioned radially towards the chamber, and is placed opposite the chamber opening seal surface. An annular seal is interposed between the housing chamber and lid seal surfaces.

Abstract: This invention provides a novel coffee blend and a process for making said novel coffee. This novel coffee contains both a “faster-roast fraction” and a “slower-roast fraction”. The “faster-roast fraction” contributes no less than 20% and no more than 80% to the 100% coffee blend, preferably no less than 30% and no more than 70% to the coffee blend, and more preferably, no less than 40% and no more than 60% to the coffee blend. Similarly, the “slower-roast fraction” contributes no less than 20% and no more than 80% to the 100% coffee blend, preferably no less than 30% and no more than 70% of the coffee blend, and more preferably, no less than 40% and no more than 60% of the coffee blend. Any 100% coffee blend where the “faster-roast fraction” and the “slower-roast fraction” in combination contribute a minimum of 70% of the 100% total is covered herein.

Abstract: An optical waveguide having a working mode with a tailored dispersion profile, the waveguide including: (i) a dielectric confinement region surrounding a waveguide axis, the confinement region comprising a photonic crystal having at least one photonic bandgap, wherein during operation the confinement region guides EM radiation in a first range of frequencies to propagate along the waveguide axis; (ii) a dielectric core region extending along the waveguide axis and surrounded by the confinement region about the waveguide axis, wherein the core supports at least one guided mode in the first frequency range; and (iii) a dielectric dispersion tailoring region surrounded by the confinement region about the waveguide axis, wherein the dispersion tailoring region introduces one or more additional modes in the first range of frequencies that interact with the guided mode to produce the working mode.

Abstract: An optical waveguide including: a dielectric core region extending along a waveguide axis; and a dielectric confinement region surrounding the core about the waveguide axis, the confinement region comprising a photonic crystal structure having a photonic band gap, wherein during operation the confinement region guides EM radiation in at least a first range of frequencies to propagate along the waveguide axis, wherein the core has an average refractive index smaller than about 1.3 for a frequency in the first range of frequencies, and wherein the core a diameter in a range between about 4&lgr; and 80&lgr;, wherein &lgr; is a wavelength corresponding to a central frequency in the first frequency range.

Abstract: Valveboxes of this invention comprise a housing including an inner chamber that extends axially through the housing from a housing base. The housing chamber includes a diameter that is defined by a housing sidewall surface that extends outwardly from the base, forming a chamber opening. The chamber opening includes a seal surface that is positioned radially inwardly towards the chamber. The valve box further includes a lid that is positioned over the housing chamber opening. The lid includes a concave center section and a seal surface disposed radially therearound. The lid seal surface is positioned radially towards the chamber, and is placed opposite the chamber opening seal surface. An annular seal is interposed between the housing chamber and lid seal surfaces.

Abstract: The present invention provides a composition comprising a) a laxative selected from the group consisting of bisacodyl and enteric coated vanilloid compounds; and b) simethicone in an amount effective to enhance the efficacy of the laxative. The simethicone enhances the transit of the laxatives through the small bowel.

Abstract: Roast and ground or flaked coffee products which provide more brew strength and cup color at lower levels of brews solids. These coffee products include darker fasted roasted coffee that is predominantly high acidity-type coffee that provide, when brewed appropriate conditions, a consumable coffee beverage having:(1) a brew solids level of from about 0.4 to about 0.6%;(2) a Titratable Acidity of at least about 1.52;(3) a brew absorbance of at least about 1.25, provided that when the Titratable Acidity is in the range of from about 1.52 to about 2.0, the brew absorbance is equal to or greater than the value defined by the equation:1.25+?0.625.times.(2.0-TA)!where TA is the Titratable Acidity.

Abstract: Apparatus for supporting fabric such as a net curtain 5 over an aperture such as a window comprises first and second members 4 and 2 respectively which have exposed faces which are mutually magnetically attractive, the sacond member 2 being L-shaped to provide below its exposed face a ledge for supporting the first member 4.

Abstract: Roast and ground or flaked coffee products which provide more brew strength and cup color at lower levels of brews solids. These coffee products contain darker fasted roasted coffee that is predominantly high acidity-type coffee that provide, when brewed appropriate conditions, a consumable coffee beverage having:(1) a brew solids level of from about 0.4 to about 0.6%;(2) a Titratable Acidity of at least about 1.52;(3) a brew absorbance of at least about 1.25, provided that when the Titratable Acidity is in the range of from about 1.52 to about 2.0, the brew absorbance is equal to or greater than the value defined by the equation:1.25+?0.625.times.(2.0-TA)!where TA is the Titratable Acidity.

Abstract: An apparatus for determining an area of a surface which is traversed and treated by an object during a unit of time is configured for use with a moveable object that has a first axis of a known length. The object is capable of movement along a second axis and the first and second axes define an angle between them which is other than 0.degree.. A signalling means includes a sensor which may be mounted in a motion-sensing relationship to the object for providing a motion signal when the object moves a distance along the second axis. The motion signal has a predetermined relationship to that distance. A timing means repetitively provides a plurality of timing signals, each sequential pair of which defines an interval of time of known duration. A computing means is coupled to the timing means and to the signalling means for receiving at least one sequential pair of timing signals and at least one motion signal.