Method and apparatus for propagating a piecewise linear function to a line
First Claim
1. For a multi-state space, a method of propagating a first piecewise linear function (PLF), which is defined over a first state, to a second state, wherein the second state is a line, wherein the PLF has a plurality of inflection points, the method comprising:
- a) projecting vectors from points on the first state that are locations of inflection points in the first PLF;
b) at each intersection of the line and one of the vectors, computing a cost;
c) at each endpoint of the line that does not intersect one of the vectors, computing a cost; and
d) based on the computed costs, specifying a second PLF that is defined over the second state, wherein the second PLF contains information regarding each computed cost.
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Accused Products
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 line. 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 any intersection of the line and one of the vectors, the method computes a cost. The method also computes a cost at any endpoint of the line that does not intersect one of the vectors. Based on the computed costs, the method then specifies a second PLF that is defined over the second state.
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Citations
23 Claims
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1. For a multi-state space, a method of propagating a first piecewise linear function (PLF), which is defined over a first state, to a second state, wherein the second state is a line, wherein the PLF has a plurality of inflection points, the method comprising:
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a) projecting vectors from points on the first state that are locations of inflection points in the first PLF;
b) at each intersection of the line and one of the vectors, computing a cost;
c) at each endpoint of the line that does not intersect one of the vectors, computing a cost; and
d) based on the computed costs, specifying a second PLF that is defined over the second state, wherein the second PLF contains information regarding each computed cost. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
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12. A computer readable medium that stores a computer program that, in a multi-state space, propagates a first piecewise linear function (PLF), which is defined over a first state, to a second state, wherein the second state is a line, wherein the PLF has a plurality of inflection points, the computer program comprising instructions for:
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a) projecting vectors from points on the first state that are locations of inflection points in the first PLF;
b) at each intersection of the line and one of the vectors, computing a cost;
c) at each endpoint of the line that does not intersect one of the vectors, computing a cost; and
d) based on the computed costs, specifying a second PLF that is defined over the second state, wherein the second PLF contains information regarding each computed cost. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20, 21, 22)
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23. For a multi-state space, a method of propagating a first piecewise linear function (PLF), which is defined over a first state, to a second state, wherein the second state is a line, wherein the PLF has a plurality of inflection points, the method comprising:
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a) projecting vectors from points on the first state that are locations of inflection points in the first PLF;
b) at each intersection of the line and one of the vectors, computing a cost;
c) at each endpoint of the line that does not intersect one of the vectors, computing a cost; and
d) based on the computed costs, specifying a second PLF that is defined over the second state, wherein the second PLF is a function that reflects the cost of a path expansion from the first state to the second state.
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Specification