Random path generation upon functional decomposition
AssigneeEcole Nationale De L'aviation Civile
InventorChristophe Hurter
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Abstract
A method of defining a path model from a set of realistic paths is provided, where each path in the set of realistic paths is expanded on piece-wise polynomial basis, and a respective centroid function and sequence of eigenfunctions calculated for each expanded representation. A set of principle paths representing the major variation of this set of paths is obtained describing the variations of the set of realistic paths with respect to the centroid. The path model thus comprises a linear combination of said principle paths. The path model may be used as the basis for the generation of new curves having similar characteristics to the original set of realistic paths.
Claims12
An apparatus for displaying a modified path based on a path model obtained by expanding each path in a set of realistic paths on piece-wise polynomial basis to obtain an expanded representation of each said path, calculating a respective centroid function and a sequence of eigenfunctions for each said expanded representation, and calculating a set of principle paths representing a major variation of said set of realistic paths, where said principle paths describe variations of said set of realistic paths with respect to the respective said centroid function, and wherein said path model comprises a linear combination of said principle paths, said apparatus comprising:
- at least one memory;
- one or more processor configured to:
- process and display said modified path for at least one of said paths in said set of realistic paths by multiplying each said coefficient of each said principle path by a respective random value to obtain a result, and to add the result to a corresponding vector of said centroid function, to generate the decomposition coefficients of a new path for display.
A method of displaying a modified path based on a path model, said method comprising:
- obtaining a set of realistic paths, and expanding each path in said set of realistic paths on piece-wise polynomial basis to obtain an expanded representation of each said path,
- calculating a respective centroid function and a sequence of eigenfunctions for each said expanded representation, and
- calculating a set of principle paths representing the major variation of said set of realistic paths,
- where said principle paths describe the variations of said set of realistic paths with respect to the respective said centroid function, and wherein said path model comprises a linear combination of said principle paths;
- and
- multiplying each said coefficient of each said principle path by a respective random value to obtain a result, and adding the result to a corresponding vector of said centroid function, to generate the decomposition coefficients of a new path for display.
Dependencies are inferred from the claim text.