System and method for finding the distance from a moving query point to the closest point on one or more convex or non-convex shapes
First Claim
1. A system for determining a closest point on a shape to a query point comprising:
- one or more memories for storing one or more geometric model portions, the geometric model portions having a plurality of line segments, each of the line segments being between a first and a second endpoint, wherein the line segments and end points are connected to form a shape including one or more parameters; and
one or more central processing units (CPU'"'"'s) for executing;
a multiresolution process that creates one or more models of the shape, the one or more models having a hierarchy of resolutions, wherein each model comprises one or more model line segments approximating one or more of the line segments and wherein each model line segment is associated with an error;
a distance process that for every model line segment determines a distance between a closest point on one or more of the model line segments and a query point, the distance representing one or more of the parameters, the distance process further determining an upper bound and a lower bound of an envelope enclosing the segment, the closest point being within the envelope, the upper bound representing an upper limit of the parameter in the envelope determined by an upper error of the respective model containing the model line segment and the lower bound representing a lower limit of the parameter in the envelope determined by a lower error of the respective model, wherein the upper bound and the lower bound of the envelope are parallel to each other or converging to each other; and
a priority process that orders the model line segments according to their respective lower bounds if a maximum error for every one of the model line segments is less than a threshold, the priority process selecting a smallest distance as a minimum distance between the query point and the shape.
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Abstract
The present invention is a computer system and method for determining the closest point on a shape (2 dimensional or 3 dimensional surface) to any general query point. The system has one or more central processing units (CPUs), one or more memories, and one or more geometric model portions stored in one or more of the memories. The geometric model portions have a plurality of line segments (polygons), each of the line segments (polygons) being between a first and a second endpoint (having a polygon boundary). The line segments and end points (polygons and polygon boundaries) are connected to form a shape (in 3 dimensions, a surface) with one or more parameters. Parameters can include geometric position, time, temperature, pressure, flow, color, texture, or any other descriptive value. A multiresolution process that creates one or more models of the shape (surface). The models having a hierarchy of resolutions. Each model has one or more model line segments (model polygons) that approximate one or more of the line segments (polygons). Each model line segment (model polygons) is associated with an error. A distance process, for every model line segment (polygon), determines a distance between a closest point on one or more of the model line segments and a query point. The distance represents one or a combination of two or more of the parameters. The process further determines a confidence level in terms of an upper bound and a lower bound of an envelope enclosing the segment (polygon). The closest point is within the envelope—the upper bound representing an upper limit of the parameter in the envelope determined by an upper error of the respective model containing the model line segment and the lower bound representing a lower limit of the parameter in the envelope determined by a lower error of the respective model. A priority process orders the model line segments (polygons) according to their respective lower bounds and if a maximum error for every one of the model line segments is less than a threshold. The priority process also selects the smallest distance as the minimum distance between the query point and the shape.
63 Citations
30 Claims
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1. A system for determining a closest point on a shape to a query point comprising:
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one or more memories for storing one or more geometric model portions, the geometric model portions having a plurality of line segments, each of the line segments being between a first and a second endpoint, wherein the line segments and end points are connected to form a shape including one or more parameters; and
one or more central processing units (CPU'"'"'s) for executing;
a multiresolution process that creates one or more models of the shape, the one or more models having a hierarchy of resolutions, wherein each model comprises one or more model line segments approximating one or more of the line segments and wherein each model line segment is associated with an error;
a distance process that for every model line segment determines a distance between a closest point on one or more of the model line segments and a query point, the distance representing one or more of the parameters, the distance process further determining an upper bound and a lower bound of an envelope enclosing the segment, the closest point being within the envelope, the upper bound representing an upper limit of the parameter in the envelope determined by an upper error of the respective model containing the model line segment and the lower bound representing a lower limit of the parameter in the envelope determined by a lower error of the respective model, wherein the upper bound and the lower bound of the envelope are parallel to each other or converging to each other; and
a priority process that orders the model line segments according to their respective lower bounds if a maximum error for every one of the model line segments is less than a threshold, the priority process selecting a smallest distance as a minimum distance between the query point and the shape. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A system for determining a closest point on a surface to a query point comprising:
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on or more memories for restoring one or more geometric model portions, the geometric model portions having a plurality of polygons, each of the polygons having a polygon boundary, wherein the polygons and polygon boundaries are connected to form a surface including one or more parameters;
one or more central processing units (CPU'"'"'s) for executing;
a multiresolution process that creates one or more models of the surface, the models having a hierarchy of resolutions, wherein each model includes one or more model polygons approximately one or more of the polygons and wherein each model polygon is associated with an error;
a distance process that for every model polygon determines a distance between a closest point on one or more of the model polygons and a query point, the distance representing one or more of the parameters, the distance process further determining an upper bound and a lower bound of an envelope enclosing the polygons, the closest point being within the envelope, the upper bound representing an upper limit of the parameter in the envelope determined by an upper error of the respective model containing the model line segment and the lower bound representing a lower limit of the parameter in the envelope determined by a lower error of the respective model, wherein the upper bound and the lower bound of the envelope are parallel to each other or convergent to each other; and
a priority process that orders the model polygons according to their respective lower bounds if a maximum error for every one of the model polygons is less than a threshold, the priority process selecting a smallest distance as a minimum distance between the query point and the surface. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28)
a robotic manipulator with a controller for moving the robotic manipulator;
one or more input devices for selecting one or more query points; and
one or more imaging devices for creating the geometric model portion.
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29. A method for finding a minimum distance between one or more query points and a shape in one or more geometric model portions, the geometric model portions having a plurality of line segments, each of the line segments being between a first and a second endpoint, wherein the line segments and end points are connected to form the shape, the shape including one or more parameters, the method further comprising the steps of:
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creating one or more models of the shape, the models having a hierarchy of resolutions, wherein each model has one or more model line segments approximating one or more of the line segments and wherein each of the model line segments is associated with an error;
determining a distance between a closest point on one or more of the model line segments and a query point, the distance representing one or more of the parameters;
determining an upper bound and a lower bound of an envelope enclosing the model line segment, the closest point being within the envelope, the upper bound representing an upper limit of the parameter in the envelope determined by an upper error of the respective model containing the model line segment and the lower bound representing a lower limit of the parameter in the envelope determined by a lower error of the respective model, wherein the upper bound and the lower bound of the envelope are parallel to each other or convergent to each other; and
ordering the model line segments according to their respective lower bounds using a priority process if a minimum error for every one of the model line segments is less than a threshold, the priority process selecting a smallest distance as the minimum distance between the query point and the shape.
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30. A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps for finding a minimum distance between one or more query points and a shape in one or more geometric model portions, the geometric model portions having a plurality of line segments, each of the line segments being between a first and a second endpoint, wherein the line segments and end points are connected to form the shape including one or more parameters, the method further comprising the steps of:
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creating one or more models of the shape, the models having a hierarchy of resolutions, wherein each model comprises one or more model line segments approximating one or more of the line segments and wherein each of the model line segments is associated with an error;
determining a distance between a closest point on one or more of the model line segments and a query point, the distance representing one or more of the parameters;
determining an upper bound and a lower bound of an envelope enclosing the model line segment, the closest point being within the envelope, the upper bound representing an upper limit of the parameter in the envelope determined by an upper error of the respective model containing the model line segment and the lower bound representing a lower limit of the parameter in the envelope determined by a lower error of the respective model, wherein the upper bound and the lower bound of the envelope are parallel to each other or convergent to each other; and
ordering the model line segments according to their respective lower bounds if a maximum error for every one of the model line segments is less than a threshold, the priority process selecting a smallest distance as the minimum distance between the query point and the shape.
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Specification