US6688886B2 — System and method for separating three-dimensiona…

Claim 1

Independent Claim 45 words

A computer-implemented method for separating a three-dimensional polygonal structure, comprising: selecting two points on the structure; determining a piece-wise continuous curve on the surface of the structure based on the two points: and separating the structure into two objects based on the piece-wise continuous curve.

Claim 2

Dependent Claim 45 words

A computer-implemented method for separating a three-dimensional polygonal structure, comprising: selecting two points on the structure; determining a piece-wise continuous curve on the surface of the structure based on the two points: and separating the structure into two objects based on the piece-wise continuous curve.

Claim 3

Dependent Claim 54 words

The method of claim 1 , wherein the determining a piece-wise continuous curve on the surface of the structure comprises: calculating a local curvature for each edge of the structure; generating a cost function based on the local curvature and length of the edge; and determining the shortest path based on the cost function.

Claim 4

Dependent Claim 24 words

The method of claim 2 , further comprising generating a set of control points to create a fitting surface based on the shortest path.

Claim 5

Dependent Claim 18 words

The method of claim 3 further comprising applying the fitting surface to separate the structure into two portions.

Claim 6

Dependent Claim 13 words

The method of claim 4 , further comprising interactively highlighting a separated portion.

Claim 7

Dependent Claim 15 words

The method of claim 4 , further comprising interactively highlighting a border of the portion.

Claim 8

Dependent Claim 15 words

The method of claim 3 , wherein the fitting surface is expressed as a function.

Claim 9

Dependent Claim 16 words

The method of claim 3 , wherein the fitting surface is expressed as a spline function.

Claim 10

Dependent Claim 13 words

The method of claim 3 , wherein the fitting surface is interactively adjusted.

Claim 11

Dependent Claim 19 words

The method of claim 3 , further comprising determining a shortest path between the points and the fitting surface.

Claim 12

Dependent Claim 15 words

The method of claim 3 , further comprising minimizing the curvature along the fitting surface.

Claim 13

Dependent Claim 21 words

The method of claim 3 , wherein the fitting surface is adjusted by moving one or more points on the object.

Claim 14

Dependent Claim 18 words

The method of claim 3 , wherein the cutting surface is adjusted by moving one or more nodes.

Claim 15

Dependent Claim 33 words

The method of claim 3 , wherein the cutting surface is adjusted by: specifying a point on the cutting surface and between two nodes; and adjusting the point to vary the cutting surface.

Claim 16

Dependent Claim 14 words

The method of claim 1 , wherein the structure comprises one or more teeth.

Claim 17

Dependent Claim 19 words

The method of claim 1 , wherein the shortest path is used to segment the structure into two portions.

Claim 18

Dependent Claim 39 words

The method of claim 1 , further comprising: displaying a plane having a surface specified by a plurality of nodes; adjusting one or more nodes to modify the surface of the plane; and applying the plane to the structure.

Claim 19

Dependent Claim 18 words

The method of claim 17 , further comprising providing a handle to adjust each orientation of the plane.

Claim 20

Dependent Claim 22 words

The method of claim 18 , wherein adjusting one or more nodes further comprises dragging and dropping the one or more nodes.

Claim 21

Dependent Claim 22 words

The method of claim 18 , wherein the flexible plane surface is formed using a function applied over a two dimensional plane.

Claim 22

Dependent Claim 15 words

The method of claim 20 , wherein the function is represented as bicubic Bézier patches.

Claim 23

Dependent Claim 67 words

The method of claim 1 , wherein the object is two joined teeth to be separated, further comprising: receiving an initial digital data set representing the two joined teeth, representing the two joined teeth as a teeth mesh; applying a fitting surface to the teeth mesh; identifying an intersecting line between the teeth mesh and fitting surface; and generating two separated teeth based on the intersecting line.

Claim 24

Dependent Claim 18 words

The method of claim 22 , further comprising rendering a three-dimensional (3D) graphical representation of the separated teeth.

Claim 25

Dependent Claim 33 words

The method of claim 22 , further comprising receiving an instruction from a human user to modify the graphical representation of the teeth and modifying the graphical representation in response to the instruction.

Claim 26

Dependent Claim 70 words

A computer program, residing on a tangible storage medium, for use in determining a piece-wise continuous curve on the surface of a three-dimensional polygonal structure, the program comprising executable instructions operable to cause a computer to: compute a local curvature for each edge of the object; generate a cost function based on the local curvature and length of the edge; and determine the shortest path based on the cost function.

Claim 27

Dependent Claim 70 words

A computer program, residing on a tangible storage medium, for use in determining a piece-wise continuous curve on the surface of a three-dimensional polygonal structure, the program comprising executable instructions operable to cause a computer to: compute a local curvature for each edge of the object; generate a cost function based on the local curvature and length of the edge; and determine the shortest path based on the cost function.

Claim 28

Independent Claim 95 words

A method for use in separating a computer model of teeth, the method comprising performing the following steps on a computer having at least one processor and memory: receiving a data set that contains a 3D representation of one or more teeth, calculating a local curvature for each edge of the teeth; generating a cost function based on the local curvature and length of the edge; determining the shortest path by minimizing the cost function; determining a fitting surface for the shortest path; and applying the fitting surface to the teeth to separate the teeth.

Claim 29

Independent Claim 95 words

A method for use in separating a computer model of teeth, the method comprising performing the following steps on a computer having at least one processor and memory: receiving a data set that contains a 3D representation of one or more teeth, calculating a local curvature for each edge of the teeth; generating a cost function based on the local curvature and length of the edge; determining the shortest path by minimizing the cost function; determining a fitting surface for the shortest path; and applying the fitting surface to the teeth to separate the teeth.

Claim 30

Dependent Claim 45 words

A computer-implemented method to separate first and second portions of a tooth, comprising: defining a cutting surface intersecting the first and second portions by specifying two points on the tooth; and applying the cutting surface to the tooth to separate the tooth into two portions.

Claim 31

Dependent Claim 45 words

A computer-implemented method to separate first and second portions of a tooth, comprising: defining a cutting surface intersecting the first and second portions by specifying two points on the tooth; and applying the cutting surface to the tooth to separate the tooth into two portions.

Claim 32

Dependent Claim 56 words

The method of claim 27 , wherein defining a cutting surface further comprises: calculating a local curvature for each edge of the tooth; generating a cost function based on the local curvature and length of the edge; determining the shortest path by minimizing the cost function; and fitting the cutting surface based on the shortest path.

Claim 33

Dependent Claim 42 words

The method of claim 27 , further comprising: calculating a local curvature for each edge of the structure; generating a cost function based on the local curvature and length of the edge; and determining the shortest path based on the cost function.

Claim 34

Dependent Claim 24 words

The method of claim 29 , further comprising generating a set of control points to create a fitting surface based on the shortest path.

Claim 35

Dependent Claim 18 words

The method of claim 30 further comprising applying the fitting surface to separate the structure into two portions.

Claim 36

Dependent Claim 15 words

The method of claim 31 , wherein the fitting surface is expressed as a function.

Claim 37

Dependent Claim 16 words

The method of claim 31 , wherein the fitting surface is expressed as a spline function.

Claim 38

Dependent Claim 13 words

The method of claim 30 , wherein the fitting surface is interactively adjusted.

Claim 39

Dependent Claim 13 words

The method of claim 34 , further comprising interactively highlighting a separated portion.

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	2007-02-09	2007-08-11	2008-02-10	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	2011-02-09	2011-08-11	2012-02-10	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	2015-02-09	2015-08-11	2016-02-10	$7700.00	Window Closed / Lapsed

System and method for separating three-dimensional models

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