N-Dimensional Coordinates Conversion
AssigneeMicrosoft Corporation
InventorsBrian C. Beckman, Henricus Johannes Maria Meijer
Life of this patent
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Abstract
Aspects of the subject matter described herein relate to converting between polar and rectangular coordinates. In aspects, the Nth polar angle is measured upward from the sine-projection of the Nth component in the (N−1)th dimension. The last polar coordinate is zero if and only if the corresponding last rectangular coordinate is zero. The conversion may be applied in any number of dimensions without re-writing the conversion logic.
Claims20
A method implemented at least in part by a computer, the method comprising:
- obtaining an angle of an N-dimensional polar representation of a point, the N-dimensional polar representation having one distance component and N−1 angle components, the angle corresponding to that of the last dimension of the representation, N being greater than two;
- and
- calculating a rectangular coordinate of the point by at least causing the angle to be operated on by function that returns a value corresponding to a value returned by a sine function operating on the angle.
At least one computer-readable medium containing instructions which when executed by a computer, perform actions, comprising:
- at an interface, receiving an angle partially defining a point in a polar coordinate system that has N dimensions, N>2, the angle definable by a first vector and a second vector, the first vector having a component in the ith dimension of the polar coordinate system, the second vector corresponding to a sine-projection of the first vector in the (i−1)th dimension of the polar coordinate system;
- and
- providing, at the interface, a rectangular coordinate corresponding to the angle.
In a computing environment, an apparatus, comprising:
- an interface operable to receive a first value corresponding to a first coordinate system and to return a second value in a second coordinate system, one of the coordinate systems being a polar coordinate system having an angle definable by a first vector and a second vector, the first vector having a component in the ith dimension of the polar coordinate system, the second vector corresponding to a sine-projection of the first vector in the (i−1)th dimension of the polar coordinate system;
- and
- conversion logic to compute the second value using the first value.
Dependencies are inferred from the claim text.