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Design of arbitrary linear and non-linear maps

  • US 7,649,534 B2
  • Filed: 02/01/2006
  • Issued: 01/19/2010
  • Est. Priority Date: 02/01/2006
  • Status: Expired due to Fees
First Claim
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1. A system for distortionless conversion between a first space and a second space, comprising:

  • a processor, wherein the processor is adapted to;

    (a) receive the first space and the second space, wherein the first space and second space each respectively comprises one of a linear and non-linear mapping of a plurality of points in a coordinate system;

    (b) determine a mapping from points in the first space to points in the second space by;

    (c) determining at least one first triangular region of the first mapping, wherein each first triangular region is defined by a first set of three vertices (A1, B1, C1);

    (d) determining each of a plurality of corresponding second triangular regions in the second mapping corresponding respectively to each of the first triangular regions of the first mapping, wherein each triangular region in the second mapping is defined by a second set of three vertices (A2, B2, C2), wherein each of the second set of three vertices respectively corresponds identically in location to the first set of three vertices (A1, B1, C1);

    (e) for each first triangular region, determining a first point (P1) associated with the region;

    (f) determining a first vector associated with the first point (VA1P1), wherein the first vector is defined by the first point (P1) and a vertex (A1) of the associated triangular region;

    (g) determining a second vector (V′

    A1P1) from the first point to a side of the triangular region opposite the vertex, the second vector intersecting the side of the triangular region at a second point (P′

    ) so as to subdivide the side into a first segment (B1P′

    ) and a second segment (C1P′

    );

    (h) determining a first ratio of a length of the first vector (VA1P1) to a length of the second vector (V′

    A1P1);

    (i) determining a second ratio of a length of the first segment (B1P′

    ) to a length of the second segment (C1P′

    );

    (j) determining a third point (P2

    ) on a side of the second triangular region opposing the vertex (A2) using the second ratio;

    (k) determining a third vector (VA2P2) in the second triangular region using the first ratio, wherein the third vector is defined by the vertex (A2) and the third point (P2

    ); and

    (l) determining a fourth point in the second triangular region (P2) using the point (P2

    ) and the third vector corresponding respectively to the first point in the first triangular region.

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