Method for modelling a surface and device for implementing same
First Claim
1. A process for modeling a surface representing an interface between two areas with different properties in a three-dimensional body, comprising the steps of:
- measuring to obtain a set of geometrical data, from said interface of said three-dimensional body, relating to the surface and associated with respective points on said surface;
meshing the surface so that all said points are a subset of nodes of a mesh;
storing at a specific memory address for each node of the mesh, the following data;
first, second, and third coordinates,a number of satellite nodes,satellite node address data providing access to specific coordinates of said satellite nodes and consequently to satellite node related data relating thereto, andgeometrical data associated with said each node of the mesh;
for each node of the mesh, defining a local roughness index derived from a weighted sum of the coordinates of the node and of its satellites;
defining a global roughness index obtained by summing the local roughness indices associated with the nodes, and a global violation index of said geometrical data, to thereby generate a sum of said global roughness index and said global violation index;
fitting fitted coordinates of each node processed by an iterative method in which for each step of an iteration there is added a weighted combination of the coordinates of the node and of the satellites of said node and a combination of the geometrical data associated with said node, to thereby minimize said sum of the global roughness index and the global violation index; and
creating a representation of the surface from the fitted coordinates of each node.
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Abstract
A method for obtaining a model of a surface including the steps of obtaining measurements of geometrical data concerning specific points on the surface, making a grid of the surface, with the grid passing through said points, memorizing, at an address which is specific to each node of the grid, the coordinates of the node, the number of satellites of the node, information for access to the addresses of said satellites and thereafter to information which relates to them, and geometrical data which may be associated with said node; for each node, defining a local roughness index obtained from a weighted sum of the current coordinates of the node and its satellites, defining the sum of an overall roughness index representing the sum of all the local roughness indices, and of an overall index of the infringement of said geometrical data, iteratively adjusting the coordinates of indefinite nodes, by using at each adjustment the sum of a weighted combination of current node neighbor coordinates and of a combination of geometrical data associated with the node, in order to minimize said sum, and creating a model of the surface on the basis of the adjusted coordinates.
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Citations
16 Claims
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1. A process for modeling a surface representing an interface between two areas with different properties in a three-dimensional body, comprising the steps of:
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measuring to obtain a set of geometrical data, from said interface of said three-dimensional body, relating to the surface and associated with respective points on said surface; meshing the surface so that all said points are a subset of nodes of a mesh; storing at a specific memory address for each node of the mesh, the following data; first, second, and third coordinates, a number of satellite nodes, satellite node address data providing access to specific coordinates of said satellite nodes and consequently to satellite node related data relating thereto, and geometrical data associated with said each node of the mesh; for each node of the mesh, defining a local roughness index derived from a weighted sum of the coordinates of the node and of its satellites; defining a global roughness index obtained by summing the local roughness indices associated with the nodes, and a global violation index of said geometrical data, to thereby generate a sum of said global roughness index and said global violation index; fitting fitted coordinates of each node processed by an iterative method in which for each step of an iteration there is added a weighted combination of the coordinates of the node and of the satellites of said node and a combination of the geometrical data associated with said node, to thereby minimize said sum of the global roughness index and the global violation index; and creating a representation of the surface from the fitted coordinates of each node. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A device for modeling a surface representing an interface between two areas with different properties in a three-dimensional body, comprising:
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means for measuring to obtain a set of geometrical data, from said interface of said three-dimensional body, relating to the surface and associated with respective points on said surface; means for meshing the surface so that all said points are a subset of nodes of a mesh; means for storing at a specific memory address for each node of the mesh, the following data; first, second, and third coordinates, a number of satellite nodes, satellite node address data providing access to specific coordinates of said satellite nodes and consequently to satellite node related data relating thereto, and geometrical data associated with said each node of the mesh; calculation means for fitting fitted coordinates of each node processed by an iterative method in which for each step of an iteration there is added a weighted combination of the coordinates of the node and of the satellites of said node and a combination of the geometrical data associated with said node, to thereby minimize a sum of a global roughness index obtained by summing local roughness indices associated with the nodes, each local roughness index derived from a weighted sum of the coordinates of the node and the coordinates of its satellites, and of a global violation index of said geometrical data; and means for creating a representation of the surface from the fitted coordinates of each node.
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Specification