Method and apparatus for propagating a piecewise linear function to a surface
First Claim
1. For a multi-state space comprising plurality of states, a method of propagating a first piecewise linear function (PLF), which represents costs associated with a first state, to represent costs associated with a second state, wherein the second state is a surface, wherein the first PLF has plurality of inflection points, the method comprising:
- a) projecting vectors from points on the first state that correspond to locations of inflection points in the first PLF;
b) at each intersection of the boundary of the surface and one of the vectors, computing a cost; and
c) based on the computed costs, specifying a second PLF that represent costs associated with the second state.
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Abstract
Some embodiments of the invention provide a method for propagating a first piecewise linear function (PLF), which is defined over a first state, to a second state, which is a surface. In some embodiments, the space includes a set of states and a transition map that specifies a set of states that can be reached from each particular state. For instance, in some embodiments, the space is a graph that includes points, lines, and surfaces. The method projects vectors from points on the first state that are locations of inflection points in the first PLF. At each intersection of the boundary of the surface and one of the vectors, the method computes a cost. Based on the computed costs, the method specifying a second PLF that is defined over the second state.
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Citations
20 Claims
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1. For a multi-state space comprising plurality of states, a method of propagating a first piecewise linear function (PLF), which represents costs associated with a first state, to represent costs associated with a second state, wherein the second state is a surface, wherein the first PLF has plurality of inflection points, the method comprising:
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a) projecting vectors from points on the first state that correspond to locations of inflection points in the first PLF; b) at each intersection of the boundary of the surface and one of the vectors, computing a cost; and c) based on the computed costs, specifying a second PLF that represent costs associated with the second state. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A computer readable medium that stores a computer program that, in a multi-state space comprising plurality of states, propagates a first piecewise linear function (PLF), which represents costs associated with a first state, to represent costs associated with a second state, wherein the second state is a surface, wherein the first PLF has plurality of inflection points, the computer program comprising set of instructions for:
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a) projecting vectors from points on the first state that correspond to locations of inflection points in the first PLF; b) at each intersection of the boundary of the surface and one of the vectors, computing a cost; and c) based on the computed costs, specifying a second PLF that represent costs associated with the second state. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20)
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Specification