System for encoding and manipulating models of objects
OwnerAlyn Rockwood, Hongbo Li +1inventors
InventorsAlyn Rockwood, Hongbo Li, David Hestenes
Life of this patent
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Abstract
A method models an object composed of one or more components. Data are input to a memory of a computer system for each component of the object. The data include Cartesian coordinates expressed in Euclidean space of a plurality of points x of each component. Each component point x is encoded as a vector x in a general homogeneous space by x=(x+½x2e+e*)E=xE−½x2e+e*, where e and e* are basis null vectors of a Minkowski space E. General homogeneous operators are associated with each data point to generate a model of the object. The general homogeneous operators are applied to each encoded point of the associated component for each component to manipulate the model of the object.
Claims14
A method for modeling a moving object composed of one or more components, comprising:
- inputting data for each component of the object, the data including coordinates expressed in Euclidean space for a plurality of points x of each component;
- encoding, for each component, each point x as a null vector x in a homogeneous space by x=(x+½x2e+e*)E=xE−½x2e+e*, where e and e* are null vectors of with unit bivector E=ee;
- associating a plurality of general homogeneous operators with each component to generate a model of the object;
- and
- determining a motion of the object by a time dependent displacement versor D=D(t) satisfying a differential equation D=½VD, with “screw velocity” V given by V=−Iω+eν, where ω is a velocity and ν is a rotational translational velocity of the object, wherein the object is a rigid body.
Dependencies are inferred from the claim text.