Cartesian to polar coordinate transformation
First Claim
1. A method for converting a Cartesian system of discrete data elements to a polar system of discrete data elements, each Cartesian element having a corresponding data value, comprising:
- dividing each Cartesian element into subelements;
designating one of the subelements as a polar system origin;
defining a polar system about said origin comprising an intersecting plurality of radial sector lines and a plurality of confocal arcs formed of said subelements, said sector lines and arcs defining boundaries of polar elements;
for each subelement within the boundaries of a polar element, determining a subelement data value derived from the data value of the Cartesian element from which the subelement was divided; and
calculating a data value for each polar element based on the data values of the subelements within the boundaries of the polar element.
1 Assignment
0 Petitions
Accused Products
Abstract
In an improved Cartesian to polar coordinate transformation, a Cartesian system of discrete data elements is converted to a polar system of discrete data elements. Each Cartesian element is divided into subelements and one of the subelements is designated as the polar system origin. A polar system comprising an intersecting plurality of radial sector lines and a plurality of confocal arcs formed of the subelements is defined about the origin. The lines and arcs define boundaries of polar data elements. The subelements lying within the polar element boundaries are identified and their respective data values are derived from the data values of corresponding Cartesian elements. Polar element data values are calculated based on the data values of the subelements contributing to the polar element. The present transformation technique offers the advantage of few floating point operations and provides a computationally efficient conversion system readily adaptive to changes in system parameters.
46 Citations
23 Claims
-
1. A method for converting a Cartesian system of discrete data elements to a polar system of discrete data elements, each Cartesian element having a corresponding data value, comprising:
-
dividing each Cartesian element into subelements; designating one of the subelements as a polar system origin; defining a polar system about said origin comprising an intersecting plurality of radial sector lines and a plurality of confocal arcs formed of said subelements, said sector lines and arcs defining boundaries of polar elements; for each subelement within the boundaries of a polar element, determining a subelement data value derived from the data value of the Cartesian element from which the subelement was divided; and calculating a data value for each polar element based on the data values of the subelements within the boundaries of the polar element. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
-
-
13. An image-processing system for converting a Cartesian system of discrete data elements to a polar system of discrete data elements comprising:
-
an input that receives a source array of discrete data elements indexed by Cartesian coordinates, each Cartesian element having a corresponding data value; and a processing subsystem comprising a processor and a memory, the processor operating under the control of a program stored in the memory to; divide each Cartesian element into subelements, each subelement indexed by its own Cartesian coordinates; designate one of the subelements as a polar system origin; define a polar system about said origin including an intersecting plurality of radial sector lines and a plurality of confocal arcs formed of said subelements, said sector lines and arcs defining boundaries of polar elements; for each subelement within the boundaries of a polar element, determine a subelement data value derived from the data value of the Cartesian element from which the subelement was divided; calculate a data value for each polar element based on the data values of the subelements within the boundaries of the polar element; and store each polar element data value in memory. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20, 21, 22)
-
-
23. A method for converting a pixel image array arranged as a Cartesian system of discrete data elements to an image array arranged as a polar system of discrete data elements, each Cartesian element having a corresponding data value, comprising:
-
sensing an image at a sensor comprising an array of pixels; storing said image in a memory as an array of discrete data elements indexed by Cartesian coordinates; dividing each Cartesian element into subelements; designating one of the subelements as a polar system origin; defining a polar system about said origin comprising an intersecting plurality of radial sector lines and a plurality of confocal arcs formed of said subelements, said sector lines and arcs defining boundaries of polar elements; for each subelement within the boundaries of a polar element, determining a subelement data value derived from the data value of the Cartesian element from which the subelement was divided; calculating a data value for each polar element based on the data values of the subelements within the boundaries of the polar element; and storing the polar element data values in memory.
-
Specification