Patent ID: 8029277

Claim:
A method of measuring displacement of a virtual three-dimensional tooth for treatment planning using a workstation, comprising the steps of: (a) obtaining a virtual three-dimensional model of each tooth in a jaw of a patient in an initial state; (b) selecting a tooth origin for said each tooth; wherein said tooth origin for said each tooth is selected based upon anatomical structure of said each tooth; wherein said tooth origin for said each tooth remains fixed on said each tooth; (c) finding a reference virtual arch based upon location of said tooth origin for said each tooth; wherein said reference virtual arch is contained in an arbitrary plane; wherein said arbitrary plane is located based upon location of said tooth origin for said each tooth; wherein said reference virtual arch is shaped in a monotonous curve; (d) finding a tooth axes system for said each tooth; wherein said tooth axes system comprises said tooth origin for said tooth, a tooth x-axis in mesial and distal directions of said tooth, a tooth y-axis in buccal and lingual directions of said tooth and a tooth z-axis in occlusal and gingival directions of said tooth; wherein said tooth axes system for said each tooth is connected to said each tooth via said tooth origin for said each tooth; (e) finding a reference orthogonal curvilinear coordinate system for said each tooth; wherein said reference orthogonal curvilinear coordinate system comprises a reference origin for said tooth, a reference x-axis for said tooth, a reference y-axis for said tooth, and a reference z-axis for said tooth; wherein said reference origin for said tooth resides at a point on said reference virtual arch where an orthogonal projection from an orthogonal projection point meets said reference virtual arch; wherein said orthogonal projection point is located on said arbitrary plane where an orthogonal projection from said tooth origin of said tooth meets said arbitrary plane; wherein said reference x-axis for said tooth coincides with a tangent to said reference virtual arch at said reference origin; wherein said reference y-axis for said tooth is normal to said reference x-axis and passes through said reference origin; wherein said reference z-axis for said tooth is orthogonal to a plane formed by said reference x-axis for said tooth and said reference y-axis for said tooth and passes through said reference origin; (f) moving a tooth from said initial position to a desired position; and (g) measuring displacement for said tooth from said initial position to said desired position using said reference virtual arch, said reference orthogonal curvilinear coordinate system for said tooth, and said tooth axes system for said tooth.