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US7033327B2
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Method of determining the long axis of an object
Assignee: 3M Innovative Properties Co
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Filing: 2002-09-13
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Granted: 2006-04-25
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Expires: 2022-09-13
Abstract
Abstract The long axis of an object that is complex in shape, such as a tooth, may be accurately determined using digital data representing the shape of the object. A polyhedron is defined such that the center of the polyhedron coincides with a point representing the centroid of the object. Axis lines are then determined by establishing reference lines through each face of the polyhedron and the point representing the centroid of the object. The moment of the object is calculated about each axis line, and the axis line that corresponds to the smallest calculated moment is selected. Additional iterations of the method are then carried out by recursively subdividing the corresponding face into smaller sections until a desired angular accuracy is achieved. The method is particularly useful for orthodontic diagnosis and treatment.
Inventors
- 👤 Richard E. Raby
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-08 21:27
CPC Classifications
A; A61; A61B; A61B5/00; A61B5/103; G; G06; G06T; G06T7/00; G06T7/70; G06T7/73; G06T7/60; G06T7/66; A61C; A61C7/00; A61C7/002; A61C2007/004; G06T2207/00; G06T2207/30; G06T2207/30004; G06T2207/30036
Claims Analysis
Total Claims: 68
Claim 1
Independent Claim
101 words
A method of determining the long axis of an object comprising: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment; controlling the object within a three-dimensional (3D) modeling environment based upon the determined long axis; and constructing an article in accordance with the selected axis lines.
Claim 2
Independent Claim
101 words
A method of determining the long axis of an object comprising: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment; controlling the object within a three-dimensional (3D) modeling environment based upon the determined long axis; and constructing an article in accordance with the selected axis lines.
Claim 3
Dependent Claim
42 words
A method of determining the long axis of an object according to claim 1 wherein the act of defining a polyhedron includes the act of defining a polyhedron having a center that coincides wit the point representing the centroid of the object.
Claim 4
Dependent Claim
67 words
A method of determining the long axis of an object according to claim 2 wherein the act of defining a polyhedron tat surrounds a point representing the centroid of the object includes the act of establishing a polyhedron that surrounds the point and the act of translating the data representing the object relative to the polyhedron so that the center of the polyhedron coincides with the point.
Claim 5
Dependent Claim
53 words
A method of determining the long axis of an object according to claim 1 wherein the act of defining, for at least some of the faces of the polyhedron, an axis line that passes through the face includes the act of defining an axis line that passes through the centroid of the face.
Claim 6
Dependent Claim
28 words
A method of determining the long axis of an object according to claim 1 wherein the act of defining a polyhedron comprises the act of defining an icosahedron.
Claim 7
Dependent Claim
58 words
A method of determining the long axis of an object according to claim 1 and including the acts of: defining a reference line that passes through a vertex of the face corresponding to the selected axis line; determining the angle between the reference line and the selected axis line; and comparing the determined angle to a pre-selected value.
Claim 8
Dependent Claim
102 words
A method of determining the long axis of an object according to claim 6 and including the acts of: subdividing into projected sections the face corresponding to the selected axis line if the determined angle is greater than the pre-selected value; defining, for at least some of the subdivided sections of the face, a subdivided section axis line that passes through the subdivided section and also passes through the point representing the centroid of the object; calculating the moment of the object about each subdivided section axis line; and selecting the subdivided section axis line that corresponds to the smallest calculated moment.
Claim 9
Dependent Claim
54 words
A method of determining the long axis of an object according to claim 7 wherein the act of defining, for at least some of the subdivided sections of the face, a subdivided section axis line includes the act of defining a subdivided section axis line that passes through the centroid of the subdivided section.
Claim 10
Dependent Claim
39 words
A method of determining the long axis of an object according to claim 7 wherein the act of subdividing into sections the face corresponding to the selected axis line comprises the act of subdividing the face into triangular sections.
Claim 11
Dependent Claim
37 words
A method of determining the long axis of an object according to claim 7 wherein the projected sections have vertices that are tangent to a reference sphere that is also tangent to the vertices of the polyhedron.
Claim 12
Dependent Claim
27 words
A method of determining the long axis of an object according to claim 10 wherein the polyhedron is an icosahedron and wherein the projected sections are triangles.
Claim 13
Dependent Claim
72 words
A method of determining the long axis of an object according to claim 7 and including the acts of: defining a reference line that passes through a vertex of the subdivided section corresponding to the selected axis line; determining the angle between the reference line and the selected subdivided section axis line; and comparing the determined angle between the reference line and the selected subdivided section axis line to a pre-selected value.
Claim 14
Dependent Claim
45 words
A method of determining the long axis of an object according to claim 12 and including the act of further subdividing the subdivided section if the determined angle between the reference line and the selected subdivision section axis line is greater than the pre-selected value.
Claim 15
Dependent Claim
20 words
A method of determining the long axis of an object according to claim 1 wherein the object is a tooth.
Claim 16
Dependent Claim
33 words
A method of determining the long axis of an object according to claim 14 and including the additional act of providing a set of data representing the shape of a patient's actual tooth.
Claim 17
Dependent Claim
35 words
A method of determining the long axis of an object according to claim 14 and including the additional act of providing a set of data representing the shape of a model of a patient's tooth.
Claim 18
Dependent Claim
33 words
A method of determining the long axis of an object according to claim 14 and including the additional ant of providing a set of data representing points on external surfaces of the tooth.
Claim 19
Dependent Claim
34 words
A method of determining the long axis of an object according to claim 14 and including the additional act of providing a set of data representing points distributed throughout the volume of the tooth.
Claim 20
Dependent Claim
35 words
A method of determining the long axis of an object according to claim 14 and including the additional act of using the selected axis line to determine the facial axis point of the clinical crown.
Claim 21
Dependent Claim
40 words
A method of determining the long axis of an object according to claim 14 and including the additional act of using the selected axis line to place an orthodontic appliance on the tooth or on a model of the tooth.
Claim 22
Dependent Claim
39 words
A method of determining the long axis of an object according to claim 14 and including the additional act of using die selected axis line to determine a desired orientation of the tooth at a stage of orthodontic treatment.
Claim 23
Dependent Claim
29 words
A method of determining the long axis of an object according to claim 14 and including the additional act of using the selected axis line to diagnose a malocclusion.
Claim 24
Dependent Claim
37 words
A method of determining the long axis of an object according to claim 14 and including the additional act of using the selected axis line to predict movement of the tooth during the course of orthodontic treatment.
Claim 25
Dependent Claim
22 words
A method of detennining the long axis of an object according to claim 1 wherein the moment is the moment of inertia.
Claim 26
Dependent Claim
22 words
A method of determining the long axis of an object according to claim 7 wherein the moment is the moment of inertia.
Claim 27
Dependent Claim
27 words
The method of claim 1 , wherein controlling the object comprises displaying the object within the 3D modeling environment using the determined Long axis as a reference.
Claim 28
Dependent Claim
19 words
The method of claim 1 , further comprising using the selected axis line for orthodontic treatment of a patient.
Claim 29
Dependent Claim
15 words
The method of claim 1 , wherein the orthodontic appliance comprises an indirect bonding tray.
Claim 30
Dependent Claim
13 words
The method of claim 1 , wherein the article comprises an orthodontic appliance.
Claim 31
Dependent Claim
19 words
The method of claim 1 , further comprising using the determined long axis for placement of an orthodontic appliance.
Claim 32
Dependent Claim
29 words
The method of claim 1 , further comprising predicting a path of movement of a tooth during the course of an orthodontic treatment based on the determined long axis.
Claim 33
Dependent Claim
30 words
The method of claim 1 , further comprising identifying a spatial relationship of a tooth to another tooth represented within the 3D modeling environment based on the determined long axis.
Claim 34
Independent Claim
115 words
A method comprising: defining a polyhedron that surrounds a point representing the centroid of a tooth; defining, for at least some of the faces of the polyhedron, an axis line that passes trough the face and also trough the point representing the centroid of the tooth; calculating the moment of the tooth about each axis line; selecting the axis line that corresponds to the smallest calculated moment; and predicting a path of movement of the tooth during the course of an orthodontic treatment based on the determined long axis; and using the selected axis line and the predicted path of movement to place an orthodontic appliance on the tooth or a model of the tooth.
Claim 35
Independent Claim
115 words
A method comprising: defining a polyhedron that surrounds a point representing the centroid of a tooth; defining, for at least some of the faces of the polyhedron, an axis line that passes trough the face and also trough the point representing the centroid of the tooth; calculating the moment of the tooth about each axis line; selecting the axis line that corresponds to the smallest calculated moment; and predicting a path of movement of the tooth during the course of an orthodontic treatment based on the determined long axis; and using the selected axis line and the predicted path of movement to place an orthodontic appliance on the tooth or a model of the tooth.
Claim 36
Independent Claim
86 words
A method of determining the long axis of an object comprising: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment; and constructing an article in accordance with the selected axis line.
Claim 37
Independent Claim
86 words
A method of determining the long axis of an object comprising: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment; and constructing an article in accordance with the selected axis line.
Claim 38
Dependent Claim
108 words
A computer-implemented system comprising: a computing device having software executing thereon that processes digital data to determine a long axis of an object by: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment; and using the selected axis line to place an orthodontic appliance on the tooth or a model of the tooth.
Claim 39
Dependent Claim
108 words
A computer-implemented system comprising: a computing device having software executing thereon that processes digital data to determine a long axis of an object by: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment; and using the selected axis line to place an orthodontic appliance on the tooth or a model of the tooth.
Claim 40
Independent Claim
101 words
A method comprising: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment as the long axis of the object; controlling the object within a three-dimensional (3D) modeling environment based upon the selected axis line; and using the selected axis line to fabricate an indirect bonding tray.
Claim 41
Independent Claim
101 words
A method comprising: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment as the long axis of the object; controlling the object within a three-dimensional (3D) modeling environment based upon the selected axis line; and using the selected axis line to fabricate an indirect bonding tray.
Claim 42
Dependent Claim
96 words
A computer-readable medium comprising a computer program that performs a method of: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment; placing an orthodontic appliance on a tooth or a model of a tooth in accordance with the selected axis line.
Claim 43
Dependent Claim
96 words
A computer-readable medium comprising a computer program that performs a method of: defining a polyhedron that surrounds a point representing the centroid of an object; defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; calculating the moment of the object about each axis line; selecting the axis line that corresponds to the smallest calculated moment; placing an orthodontic appliance on a tooth or a model of a tooth in accordance with the selected axis line.
Claim 44
Independent Claim
201 words
A method of determining the long axis of an object comprising: (a) providing a set of data representing the shape of an object in a multi-dimensional environment; (b) defining a polyhedron that surrounds a point representing the centroid of the object; (c) defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; (d) calculating the moment of the object about each axis line; (e) selecting the axis line that corresponds to the smallest calculated moment; (f) determining the angle between the selected axis line and a reference line defined by the point representing the centroid of the object and a vertex of the polyhedron face associated with the selected axis line; (g) comparing the determined angle to a pre-selected value; (h) recursively following, by subdividing into sections the face corresponding to the selected axis line, at least some of acts a–g if the determined angle is greater than the pre-selected value; (i) processing the data representing the object within the multi-dimensional environment in accordance with the determined long axis; and (j) constructing an article in accordance with the determined long axis.
Claim 45
Independent Claim
201 words
A method of determining the long axis of an object comprising: (a) providing a set of data representing the shape of an object in a multi-dimensional environment; (b) defining a polyhedron that surrounds a point representing the centroid of the object; (c) defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; (d) calculating the moment of the object about each axis line; (e) selecting the axis line that corresponds to the smallest calculated moment; (f) determining the angle between the selected axis line and a reference line defined by the point representing the centroid of the object and a vertex of the polyhedron face associated with the selected axis line; (g) comparing the determined angle to a pre-selected value; (h) recursively following, by subdividing into sections the face corresponding to the selected axis line, at least some of acts a–g if the determined angle is greater than the pre-selected value; (i) processing the data representing the object within the multi-dimensional environment in accordance with the determined long axis; and (j) constructing an article in accordance with the determined long axis.
Claim 46
Dependent Claim
53 words
A method of determining the long axis of an abject according to claim 38 and including the act of recursively following, by further subdivision of the subdivided face sections, at least some of acts a–g if the determined angle corresponding to the first subdivision of the face is greater than the pre-selected value.
Claim 47
Dependent Claim
53 words
A method of determining the long axis of an object according to claim 38 wherein the act of defining, for at least some of the faces of the polyhedron, an axis line that passes through the face includes the act of defining an axis line that passes trough the centroid of the face.
Claim 48
Dependent Claim
28 words
A method of determining the long axis of an object according to claim 38 wherein the act of defining a polyhedron comprises the act of defining an icosahedron.
Claim 49
Dependent Claim
22 words
A method of determining the long axis of an object according to claim 38 wherein the moment is the moment of inertia.
Claim 50
Dependent Claim
189 words
A computer-readable medium comprising computer program that performs a method of: (a) accessing a set of data representing the shape of an object; (b) defining a polyhedron that surrounds a point representing the centroid of the object; (c) defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; (d) calculating the moment of the object about each axis line; (e) selecting the axis line that corresponds to the smallest calculated moment; (f) determining the angle between the selected axis line and a reference line defined by the point representing the centroid of the object and a vertex of the polyhedron face associated with the selected axis line; (g) comparing the determined angle to a pre-selected value; (h) recursively following, by subdividing into sections the face corresponding to the selected axis line, at least some of acts a–g if the determined angle is greater than the pre-selected value; and (i) placing an orthodontic appliance on a tooth or a model of a tooth in accordance with the selected axis line.
Claim 51
Dependent Claim
189 words
A computer-readable medium comprising computer program that performs a method of: (a) accessing a set of data representing the shape of an object; (b) defining a polyhedron that surrounds a point representing the centroid of the object; (c) defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the centroid of the object; (d) calculating the moment of the object about each axis line; (e) selecting the axis line that corresponds to the smallest calculated moment; (f) determining the angle between the selected axis line and a reference line defined by the point representing the centroid of the object and a vertex of the polyhedron face associated with the selected axis line; (g) comparing the determined angle to a pre-selected value; (h) recursively following, by subdividing into sections the face corresponding to the selected axis line, at least some of acts a–g if the determined angle is greater than the pre-selected value; and (i) placing an orthodontic appliance on a tooth or a model of a tooth in accordance with the selected axis line.
Claim 52
Independent Claim
198 words
A method of determining the long axis of a tooth comprising: (a) accessing a set of data representing the shape of a tooth within a modeling environment; (b) defining a polyhedron that surrounds a point representing the centroid of the tooth; (c) defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the tooth centroid; (d) calculating the moment of the tooth about each axis line; (e) selecting the axis line that corresponds to the smallest calculated moment; (f) determining the angle between the selected axis line and a reference line defined by the point representing the centroid of the tooth and a vertex of the polyhedron face associated with the selected axis line; (g) comparing the determined angle to a pre-selected value; (h) recursively following, by subdividing into sections the face corresponding to the selected axis line, at least some of acts a–g if the determined angle is greater than the pre-selected value; and (i) processing the data representing the tooth in accordance with the determined long axis to place an orthodontic appliance on the tooth or a model of the tooth.
Claim 53
Independent Claim
198 words
A method of determining the long axis of a tooth comprising: (a) accessing a set of data representing the shape of a tooth within a modeling environment; (b) defining a polyhedron that surrounds a point representing the centroid of the tooth; (c) defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the tooth centroid; (d) calculating the moment of the tooth about each axis line; (e) selecting the axis line that corresponds to the smallest calculated moment; (f) determining the angle between the selected axis line and a reference line defined by the point representing the centroid of the tooth and a vertex of the polyhedron face associated with the selected axis line; (g) comparing the determined angle to a pre-selected value; (h) recursively following, by subdividing into sections the face corresponding to the selected axis line, at least some of acts a–g if the determined angle is greater than the pre-selected value; and (i) processing the data representing the tooth in accordance with the determined long axis to place an orthodontic appliance on the tooth or a model of the tooth.
Claim 54
Dependent Claim
53 words
A method of determining the long axis of a tooth according to claim 44 and including the act of recursively following, by further subdivision of the subdivided face sections, at least some of acts a–g if the determined angle corresponding to the first subdivision of the face is greater than the pre-selected value.
Claim 55
Dependent Claim
53 words
A method of determining the long axis of a tooth according to claim 44 wherein the act of defining, for at least some of the faces of the polyhedron, an axis line that passes through the face includes the act of defining an axis line that passes through the centroid of the face.
Claim 56
Dependent Claim
28 words
A method of determining the long axis of a tooth according to claim 44 wherein the act of defining a polyhedron comprises the act of defining an icosahedron.
Claim 57
Dependent Claim
33 words
A method of determining the long axis of a tooth according to claim 44 and including the additional act of providing a set of data representing the shape of a patient's actual tooth.
Claim 58
Dependent Claim
35 words
A method of determining the long axis of a tooth according to claim 44 and including the additional act of providing a set of data representing the shape of a model of a patient's tooth.
Claim 59
Dependent Claim
33 words
A method of determining the long axis of a tooth according to claim 44 and including the additional act of providing a set of data representing points on external surfaces of the tooth.
Claim 60
Dependent Claim
34 words
A method of determining the long axis of a tooth according to claim 44 and including the additional act of providing a set of data representing points distributed throughout the volume of the tooth.
Claim 61
Dependent Claim
35 words
A method of determining the long axis of a tooth according to claim 44 and including the additional act of using the selected axis line to determine the facial axis point of the clinical crown.
Claim 62
Dependent Claim
39 words
A method of determining the long axis of a tooth according to claim 44 and including the additional act of using the selected axis line to determine a desired orientation of the tooth at a stage of orthodontic treatment.
Claim 63
Dependent Claim
29 words
A method of detennining the long axis of a tooth according to claim 44 and including the additional act of using the selected axis line to diagnose a malocclusion.
Claim 64
Dependent Claim
37 words
A method of determining the long axis of a tooth according to claim 44 and including the additional act of using the selected axis line to predict movement of the tooth during the course of orthodontic treatment.
Claim 65
Dependent Claim
31 words
A method of determining the long axis of a tooth according to claim 44 and including the additional act of using the selected axis line to fabricate an indirect bonding tray.
Claim 66
Dependent Claim
22 words
A method of determining the long axis of a tooth according to claim 44 wherein the moment is the moment of inertia.
Claim 67
Dependent Claim
179 words
A computer-readable medium comprising a computer program that performs a method of: (a) providing a set of data representing the shape of a tooth; (b) defining a polyhedron that surrounds a point representing the centroid of the tooth; (c) defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the tooth centroid; (d) calculating the moment of the tooth about each axis line; (e) selecting the axis line that corresponds to the smallest calculated moment; (f) detennining the angle between the selected axis line and a reference line defined by the point representing the centroid of the tooth and a vertex of the polyhedron face associated with the selected axis line; (g) comparing the determined angle to a pre-selected value; (h) recursively following, by subdividing into sections the face corresponding to the selected axis line, at least some of acts a–g if the determined angle is greater than the pre-selected value; and (i) constructing an orthodontic appliance in accordance with the selected axis line.
Claim 68
Dependent Claim
179 words
A computer-readable medium comprising a computer program that performs a method of: (a) providing a set of data representing the shape of a tooth; (b) defining a polyhedron that surrounds a point representing the centroid of the tooth; (c) defining, for at least some of the faces of the polyhedron, an axis line that passes through the face and also through the point representing the tooth centroid; (d) calculating the moment of the tooth about each axis line; (e) selecting the axis line that corresponds to the smallest calculated moment; (f) detennining the angle between the selected axis line and a reference line defined by the point representing the centroid of the tooth and a vertex of the polyhedron face associated with the selected axis line; (g) comparing the determined angle to a pre-selected value; (h) recursively following, by subdividing into sections the face corresponding to the selected axis line, at least some of acts a–g if the determined angle is greater than the pre-selected value; and (i) constructing an orthodontic appliance in accordance with the selected axis line.
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USPTO Annuity & Maintenance Windows
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| 7.5 Years (Year 8) | 2013-04-24 | 2013-10-24 | 2014-04-25 | $3760.00 | Window Closed / Lapsed |
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