1,277 research outputs found
Solutions of the Bogomolny Equation on R^3 with Certain Type of Knot Singularity
This paper studies the moduli space of solutions to the Bogomolny equation on
R^3 with a certain type of knot singularity. For technical reasons, I have to
assume the monodromy along the meridian of the knot lies in (0, 1/8) or in
(3/8, 1/2) and I don't know how to resolve this constraint. The main result of
this paper is: a neighbourhood of a solution to the Bogomolny equations on R^3
with such knot singularity in the moduli space has an analytical structure.
Moreover, certain solutions (that come from gluing a model solution with the
knot singularity and classical regular solutions) have a neighbourhood in the
moduli space that has a manifold structure.Comment: Some small errors and typos are correcte
Systems and Methods for Graphical Rendering.
A method of rendering a graphical scene includes determining a plurality of functions that contribute to a light transport model of the scene, projecting each function of the plurality of functions into the wavelet domain, encoding basis coefficients of each function in a wavelet tree, each function being encoded in at least one wavelet tree such that the plurality of functions are represented in the wavelet domain by a plurality of wavelet trees, traversing direct paths through the plurality of wavelet trees, along which direct paths an integral coefficient may be nonzero, to determine the radiance of a point in the scene, and rendering the scene
Systems and Methods for Graphical Rendering.
A computer readable medium configured to approximate the integral of the product of a plurality of functions includes logic configured to factor the plurality of functions into a set of fixed functions and one varying function, logic configured to determine a first vector that represents the product of the fixed functions in the wavelet domain, logic configured to determine a second vector that represents the one varying function in the wavelet domain, and logic configured to determine an inner product of the first vector and the second vector
Systems and Methods for Graphical Rendering
A computer readable medium configured to determine the integral of the product of a plurality of functions. The computer readable medium includes logic configured to project each function of the plurality of functions into the wavelet domain, logic configured to encode basis coefficients of each function in a wavelet tree, each function being encoded in at least one wavelet tree such that the plurality of functions are represented in the wavelet domain by a plurality of wavelet trees, and logic configured to traverse direct paths through the plurality of wavelet trees to determine the integral of the product of the function represented by the wavelet trees, along which direct paths an integral coefficient may be nonzero
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