Virtual articulation model for dental treatment

Abstract

A method for determining whether a tooth is correctly shaped and oriented to avoid interfering with another tooth using virtual articulation. The method includes a) receiving, by a computing device, data indicative of a virtual dentition of an oral cavity of a patient, the data indicative of the virtual dentition including data indicative of at least one of a virtual mandibular arch representing a mandibular arch of the patient or a virtual maxillary arch representing a maxillary arch of the patient; b) receiving data indicative of a selected point on the virtual dentition of the oral cavity; and c) determining a tangent vector indicative of a direction of motion of the selected point, and determining whether an orientation of a tooth of the virtual dentition or a shape of the tooth is correctly shaped and oriented based on the determined tangent vector, wherein the tangent vector is based on an axis of rotation of the virtual mandibular arch.

Description

Technical Field

[0001] This disclosure relates to dental treatment plans using virtual joint movements. Background Technology

[0002] Digital dentistry is on the rise as more dentists use digital impression systems. These systems use intraoral scanning cameras or traditional physical impressions, along with associated processing systems, to generate digital three-dimensional (3D) models of the patient's teeth (e.g., the patient's maxillary and mandibular arches). These digital 3D models can then be used to create physical models for dental restorations or orthodontic treatment plans.

[0003] Orthodontists or dentists can use physical models of a patient's teeth to determine how to reorient and / or reshape them so that they fit together when the patient's mouth is closed. Typically, the physical model is cast in artificial stone from the physical impression. Simple occlusal alignment is accomplished using a wax occlusal plate or a monolithic impression material that captures both the upper and lower occlusal surfaces simultaneously, spatially associating one arch with the other. Dental articulation is achieved by further capturing the relationship between the occlusal alignment material and points at or near the condyle using a face bow, and then transferring this relationship to the corresponding stone model of the arch mounted in a mechanical articulator. Face bows may not accurately capture the actual condylar axis because the ear canal is partially displaced from the condyle. They cause discomfort to the patient, pose a challenge to the capture manipulation by clinical practitioners, and require physical transfer of the mechanical instrument to the dental laboratory, where it is used to align the stone casting in the mechanical articulator. This process can take several days to complete, or at least a few hours. Facebows and dental articulation devices are expensive, and disputes can arise between clinics and laboratories regarding who owns them and when they should be returned to their rightful owners after use. Because model teeth are completely opaque and obscure certain contact points, making them impossible to see, it is also difficult to visualize and identify contact points on the tooth surfaces when using such devices to test occlusion. Furthermore, without using a computer to manipulate the 3D digital scan data, it is difficult to measure distances, angles, orientations, areas, and changes over time. Summary of the Invention

[0004] Generally, this disclosure describes techniques for using virtual joint motion to determine whether teeth are properly shaped and oriented to avoid interfering with other teeth. Virtual joint motion can refer to the measurement and / or visualization of temporomandibular dynamics of a virtual dentition based on a three-dimensional scan of a patient's teeth. The virtual dentition may include a virtual representation of the patient's mandibular arch and / or maxillary arch. Temporomandibular dynamics can refer to the rotation of the virtual dentition about one or more axes of rotation. A computing device can utilize the virtual joint motion model to determine tangent vectors indicating the movement of a portion of the virtual dentition about one of the axes of rotation. The computing device can utilize the tangent vectors to determine whether the user's teeth are properly shaped and / or oriented to reduce or eliminate interference between teeth. Additionally or alternatively, the techniques of this disclosure can enable a computing device to determine whether the roots of the user's teeth are properly aligned with axial loads (e.g., to distribute the load through the teeth and roots to the mandible and maxilla). Furthermore, the computing device can output a graphical user interface that provides a dental treatment provider with information about the shape, orientation, and movement of teeth during virtual joint motion.

[0005] The techniques and systems disclosed herein can provide one or more advantages. For example, the techniques disclosed herein can enable computing devices and / or dental treatment providers to determine the correct position, orientation, and shape of any tooth in a patient's oral cavity based on the patient's own mandibular dynamics, which can reduce or eliminate interference between teeth, thereby improving the health and function of the patient's teeth. In another instance, the techniques disclosed herein can enable computing devices and / or dental treatment providers to determine the correct position, orientation, and shape of any tooth in an arch (e.g., the mandibular arch) (in the absence of information about the dentition of the opposing arch (e.g., the maxillary arch), which can make it easier for computing devices and / or dental providers to reconstruct the dentition (e.g., orthognathic surgery, dentures, dental restorations, etc.).

[0006] In one example, this disclosure describes a method comprising: receiving, via a computing device, data indicating a virtual dentition of a patient's oral cavity, the data indicating the virtual dentition including data indicating at least one of a virtual mandibular arch representing the patient's mandibular arch or a virtual maxillary arch representing the patient's maxillary arch; receiving, via the computing device, data indicating selected points on the virtual dentition of the oral cavity; determining, via the computing device, a tangent vector indicating a direction of movement of the selected points based on a rotation axis of the virtual mandibular arch; and performing an action via the computing device based on the determined tangent vector.

[0007] For example, this disclosure describes a system including a storage device and a processor in communication with the storage device, the processor being configured to receive data indicating a virtual dentition of a patient's oral cavity, the data indicating the virtual dentition including data indicating at least one of a virtual mandibular arch representing the patient's mandibular arch or a virtual maxillary arch representing the patient's maxillary arch; receive data indicating a selected point on the virtual dentition of the oral cavity; determine a tangent vector indicating the direction of movement of the selected point based on the axis of rotation of the virtual mandibular arch; and perform an action based on the determined tangent vector.

[0008] For example, this disclosure describes a non-transitory computer-readable storage medium storing instructions that, when executed, cause at least one processor to receive data indicating a virtual dentition of a patient's oral cavity, the data indicating the virtual dentition including data indicating at least one of a virtual mandibular arch representing the patient's mandibular arch or a virtual maxillary arch representing the patient's maxillary arch; receive data indicating a selected point on the virtual dentition of the oral cavity; determine a tangent vector indicating the direction of movement of the selected point based on the axis of rotation of the virtual mandibular arch; and perform an action based on the determined tangent vector.

[0009] Details of one or more aspects of this disclosure are shown in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will become apparent from the detailed description, the drawings, and the claims. Attached Figure Description

[0010] Figure 1 This is a block diagram illustrating an exemplary system for virtual joint motion according to an example of this disclosure.

[0011] Figure 2 An example of a digital 3D model of a patient's teeth is shown according to this disclosure.

[0012] Figure 3 A front view of an exemplary digital 3D model of a dental arch in a maximally cusped position, according to an example of this disclosure, is shown.

[0013] Figure 4 A left-side view of a digital 3D model of a dental arch in a maximally cusped pose, according to an example of this disclosure, is shown.

[0014] Figure 5 An exemplary axis of rotation and an exemplary tangent vector or ray are shown as an example according to this disclosure.

[0015] Figure 6 An example of a rotation axis and tangent vector or ray according to this disclosure is shown.

[0016] Figure 7An exemplary dental arch and multiple tangential vectors or rays are shown as an example according to this disclosure.

[0017] Figure 8 An exemplary user interface showing an occlusal view of teeth and multiple tangential vectors or rays according to an example of this disclosure is illustrated.

[0018] Figure 9 An example of a occlusal view of teeth and an exemplary user interface of a tangential vector or ray is shown according to this disclosure.

[0019] Figure 10A and 10B An exemplary user interface showing a tooth and multiple tangent vectors or rays according to an example of this disclosure is illustrated.

[0020] Figure 11A and 11B An exemplary user interface showing a distal view of a tooth and multiple tangent vectors or rays according to an example of this disclosure is illustrated.

[0021] Figure 12A and 12B An exemplary user interface showing a distal view of a tooth and multiple tangent vectors or rays according to an example of this disclosure is illustrated.

[0022] Figures 13A to 13B An exemplary user interface showing a portion of a dental arch and multiple tangential vectors or rays according to an example of this disclosure is illustrated.

[0023] Figure 14 This is a flowchart illustrating an exemplary process using the techniques disclosed herein.

[0024] Figure 15 An exemplary 3D digital model of a dental arch including the root is shown as an example according to this disclosure.

[0025] Figures 16A to 16C A digital 3D model of a dental arch according to an example of this disclosure is shown.

[0026] Figure 17 This is a flowchart illustrating an exemplary process using the techniques disclosed herein.

[0027] Figure 18 This is a flowchart illustrating an exemplary process using the techniques disclosed herein.

[0028] Figure 19 This is a flowchart illustrating an exemplary process using the techniques disclosed herein.

[0029] Figure 20 This is a flowchart illustrating an exemplary process using the techniques disclosed herein. Detailed Implementation

[0030] Figure 1 This is a diagram of an example system 10 used to perform virtual joint movements and determine whether a patient's teeth are correctly positioned, oriented, or shaped. System 10 includes a computing system 14. The computing system 14 may include a desktop computer, laptop computer, tablet computer, or any type of computing device.

[0031] System 10 may also include an electronic display device 16 for displaying a digital 3D model of the intraorific structure. In some examples, the display device 16 is part of the computing system 14, and in other examples, the display device 16 may be separate from the computing system 14. The display device 16 may be implemented using any electronic display, such as a cathode ray tube (CRT), liquid crystal display (LCD), light-emitting diode (LED) display, or organic light-emitting diode (OLED) display.

[0032] System 10 may also include an input device 18 for receiving user commands or other information. In some examples, the input device 18 is part of the computing system 14, and in other examples, the input device 18 may be separate from the computing system 14. The input device 18 can be implemented using any device for inputting information or commands, such as a keyboard, microphone, cursor control device (e.g., mouse), or touchscreen. Components of system 10 can also be combined; for example, a tablet computer may combine a processor, display, and touchscreen input device into a single unit.

[0033] The computing system 14 includes one or more processors 20 and one or more storage devices 22. The storage device 22 may be configured to provide short-term storage of information as volatile memory, and therefore not retain the stored contents upon deactivation. Examples of volatile memory include random access memory (RAM), dynamic random access memory (DRAM), static random access memory (SRAM), and other forms of volatile memory known in the art. In some examples, the storage device 22 may also include one or more computer-readable storage media. The storage device 22 may be configured to store a larger amount of information compared to volatile memory. The storage device 22 may also be configured to provide long-term storage of information as non-volatile memory, and retain the information after an activation / deactivation cycle. Examples of non-volatile memory include flash memory or electrically programmable memory (EPROM) or electrically erasable programmable memory (EEPROM).

[0034] In various examples, processor 20 may include or may be programmable processing circuitry, fixed-function circuitry, digital signal processor (DSP), general-purpose microprocessor, application-specific integrated circuit (ASIC), field-programmable gate array (FPGA) or other equivalent integrated or discrete logic circuitry, and any combination of such components, or a portion thereof. Figure 1 In one example, processor 20 is configured to execute code for virtual joint motion module 24 to perform the techniques of this disclosure. The techniques described herein can be implemented in software or firmware modules, for example, for execution by processor 20 or other computing devices. In other examples, the techniques of this disclosure can be implemented in hardware modules or a combination of software and hardware.

[0035] In some examples, according to the technology of this disclosure, processor 20 can execute virtual joint motion module 24 to determine the correct position, orientation, and shape (also referred to as morphology) of any tooth in the oral cavity based on the patient's own mandibular dynamics. As another example, virtual joint motion module 24 can modify, restore, or form virtual dental anatomy for the patient based on the patient's mandibular dynamics. Thus, virtual joint motion module 24 enables dental treatment providers (e.g., orthodontists, dentists, technicians, etc.) to form a functional occlusion that is undisturbed and avoids tooth wear, and to reduce or minimize stress on the patient's temporomandibular joint (TMJ) by improving dynamic cusp occlusion. In some examples, forming a undisturbed functional occlusion can also contribute to the long-term stability of the occlusion. The technology of this disclosure enables dental treatment providers to use computational system 14 to diagnose and treat orthodontic malocclusion, biting habits, tooth wear, and TMJ disorders. As another example, the technology of this disclosure enables virtual joint motion module 24 to form or assist dental treatment providers in forming orthodontic settings, dental prosthesis designs, prosthesis designs, dental implant placements, and orthognathic surgery plans.

[0036] The computing system 14 receives data indicating the patient's oral cavity. The patient's oral cavity may include the dentition, more typically the human dentition such as individual teeth, quadrants, complete dental arches, paired dental arches that may be single or in various types of occlusion, soft tissues (e.g., the gingival and mucosal surfaces of the oral cavity or perioral structures such as lips, nose, cheeks, and chin), as well as bones and any other supporting or surrounding structures. The oral cavity may include natural and artificial structures within the oral cavity such as dental objects (e.g., prostheses, implants, appliances, restorations, prosthetic components, or abutments).

[0037] The computing system 14 can directly receive data indicating a patient's oral cavity within the body using an intraoral scanner, cone-beam computed tomography (CBCT) scan (i.e., 3D X-ray), optical coherence tomography (OCT), magnetic resonance imaging (MRI), or any other 3D image capture system. In other examples, the computing system 14 can indirectly receive data indicating a patient's oral cavity by scanning an impression of a tooth or a casting made from an impression of a tooth. Some examples of indirect data acquisition methods include, but are not limited to, industrial computed tomography (CT) scans (i.e., 3D X-ray), laser scanning, and patterned light scanning. For example, the computing system 14 can acquire digital images from multiple views of teeth or other intraoral structures and process the digital images to generate a digital 3D model or scan representing the scanned teeth or other intraoral structures. The 3D model or scan can be implemented as, for example, a polygonal mesh or a point cloud representing the surface or intraoral structure of the scanned object.

[0038] In some examples, the computing system 14 stores data indicative of the patient's oral cavity as oral cavity model data 26 within storage device 22. Oral cavity model data 26 may include digital 3D models of the dentition or other intraoral structures from intraoral 3D scans or scans of dental impressions or castings. For example, oral cavity model data 26 may include 3D models or scans representing the patient's dentition, such as 3D models or scans representing the patient's mandibular arch (e.g., mandible and teeth) and / or 3D models or scans representing the patient's maxillary arch (e.g., maxillary and teeth). The 3D models representing the dentition, mandibular arch, and maxillary arch are referred to herein as virtual dentition, virtual mandibular arch, and virtual maxillary arch, respectively. In some examples, oral cavity model data 26 includes scans of the patient's oral cavity for different occlusal poses, such as closed (e.g., central / maximal cusp occlusion) scans, open scans, forward or protruding scans, lateral-left scans, and lateral-right scans.

[0039] Oral model data 26 may include a 3D virtual articular motion model of the patient's oral cavity based on scans of the virtual mandibular arch, virtual maxillary arch, and / or occlusal pose. In some examples, the computing system 14 determines the virtual articular motion model according to the techniques described in U.S. Patent Application No. 15 / 196631, filed June 29, 2016, entitled "Virtual Model of Articular Motion from Intraoral Scans," which is incorporated herein by reference in its entirety. The 3D virtual articular motion model can characterize TMJ motion. For example, the 3D virtual articular motion module can indicate the pure rotational axis of the virtual mandibular arch relative to the virtual maxillary arch.

[0040] The virtual joint motion module 24 can use oral model data 26 to perform various actions, such as treatment planning, crown and implant preparation, oral restoration, orthodontic setup design, orthodontic appliance design, and diagnostic intraoral aids, to, for example, assess or visually visualize tooth wear. As will be explained in more detail below, the virtual joint motion module 24 can use oral model data 26 to determine whether a patient's teeth are correctly oriented or aligned (e.g., to avoid interfering with another tooth or to provide appropriate axial load) or whether the morphology (i.e., shape) of a patient's teeth is correct (e.g., to avoid interfering with another tooth). In one example, the virtual joint motion module 24 determines whether a tooth is correctly oriented, positioned, or shaped based on tooth movement, such that when a tooth is correctly oriented, positioned, and / or shaped, it avoids interfering with another tooth. Similarly, correctly positioning, oriented, and / or shaped teeth can minimize tooth wear, end clenching habits, reduce pain or discomfort, improve chewing, improve speech, improve aesthetics, improve occlusal stability (e.g., by reducing contact forces and thus keeping the pressure on the periodontal ligament below the threshold required to cause tooth movement), or combinations thereof. The virtual joint motion module 24 can determine whether teeth are correctly oriented or correctly shaped, at least in part, based on a 3D virtual joint motion model of the oral cavity model data 26. The 3D virtual joint motion model can define one or more axes of rotation of the virtual mandibular arch. In some examples, the 3D virtual joint motion model defines four axes of rotation (also called pure axes of rotation) that are associated with movement (e.g., opening, left, right, forward) of the virtual mandibular arch from one of four different locations. For example, each of the four axes of rotation can indicate a protrusion offset, a leftward offset, a rightward offset, or an opening offset of the virtual mandibular arch. The axes of rotation indicating protrusion offset, leftward offset, rightward offset, or opening offset can be referred to as the protrusion guide axis, left guide axis, right guide axis, and opening axis, respectively.

[0041] In some examples, the virtual joint motion module 24 receives data indicating selected points in a virtual dental arch of the patient's mouth. In one example, the virtual joint motion module 24 outputs a graphical user interface (GUI) that includes a graphical representation of at least a portion of the patient's mouth, such as images of a virtual mandibular arch and / or a virtual maxillary arch. The computing system 14 can detect user input via an input device 18 (e.g., touch input, mouse input, etc.) that selects a specific point within the patient's mouth. The input device 18 can generate data indicating the user input (e.g., indicating the GUI location where the user input was received), selecting a point on or within the patient's dental arch, and can output the data indicating the selected point to the virtual joint motion module 24.

[0042] In some instances, the virtual joint motion module 24 selects points within or on the dentition. For example, the virtual joint motion module 24 can identify one or more points on the surface (e.g., occlusal surface) of one or more teeth, within one or more teeth, within the corresponding root of one or more teeth, within the gingiva, or in a combination thereof. As an example, the virtual joint motion module 24 can select one or more contact points by causing the 3D virtual joint motion model to perform virtual joint motion (e.g., performing various offsets) and detecting points where tooth collisions occur. In some examples, the virtual joint motion module 24 causes the 3D model to perform virtual joint motion in response to receiving user input. As another example, the virtual joint motion module 24 can automatically cause the 3D model to perform virtual joint motion, for example, by performing a predefined set of offsets. In some scenarios, the virtual joint motion module 24 detects one or more wear facets by identifying flat or curved surfaces in the expected contact area and selecting points within the wear facets as points on the dentition.

[0043] In response to receiving data indicating a selected point of the virtual dental arch, the virtual joint motion module 24 can determine one or more tangent vectors for the selected point. Each corresponding tangent vector indicates the direction of motion of the selected point. In some examples, each tangent vector is tangent to an arc of alignment on the corresponding axis of rotation. In other words, as... Figure 5 As further illustrated, each axis of rotation defines the center of a circle or arc, and a selected point defines the radius of that circle or arc such that each tangent vector is tangent to the circle or arc at the selected point. The selected point and the tangent vector together define a ray with a defined position and orientation in space. Without a base point, the position of the tangent vector is ambiguous. It should be noted that at a given distance along the axis of rotation, if defined by a plane perpendicular to the axis, each point in the plane defines a different tangent vector. However, each point along a line parallel to the axis of rotation will have the same tangent vector but a different base point. Therefore, each point in the space of the virtual dentition will define a unique ray. These rays can be used to determine whether a point in the virtual dentition will intersect a portion of the virtual dentition residing in the opposing arch due to performing any of the various mandibular offsets.

[0044] The virtual joint motion module 24 performs one or more actions in response to determining the tangent vector. Figure 1 In the example, the virtual joint motion module 24 can perform actions by outputting a GUI 30, which includes a graphical representation of at least a portion of the dental arch (e.g., at least a portion of the virtual mandibular arch and / or the virtual maxillary arch) and tangent vectors, to the display device 16. Figure 1 In the example, GUI 30 includes visual representations of teeth 32 and tangent vectors 34A-34D (collectively referred to as tangent vectors 34).

[0045] For example, the virtual joint motion module 24 performs actions by determining whether a particular tooth is correctly oriented and / or shaped. The virtual joint motion module 24 may determine whether a particular tooth is correctly oriented and / or shaped based on a tangent vector, for example, using that tangent vector as a reference. For instance, the virtual joint motion module 24 may determine whether a particular tooth is correctly oriented or shaped by determining whether one or more rays defined by a selected point and tangent vector 34 intersect a surface (e.g., occlusal surface) of the particular tooth. In some examples, a ray defined by a selected point intersecting the surface of a particular tooth and tangent vector 34 may indicate that a portion of the particular tooth will obstruct a portion of the opposing tooth. Therefore, the virtual joint motion module 24 may determine that a particular tooth is not correctly oriented, not correctly shaped, or both. In other words, the virtual joint motion module 24 may determine whether a particular tooth is properly oriented and shaped to reduce or prevent obstruction of another tooth (e.g., the opposing tooth) by determining whether one of the rays partially defined by tangent vector 34 intersects a surface (e.g., occlusal surface) of the particular tooth.

[0046] In yet another example, the virtual joint motion module 24 can perform actions by determining whether a particular tooth is correctly oriented for axial loads on that tooth. For example, the selected point may be located on the surface of the root of a particular tooth, or within the root, and the virtual joint motion module 24 can determine whether the root is properly oriented to transmit loads or forces to the bone. As an example, the virtual joint motion module 24 determines whether the root is properly oriented by determining whether the tangent vector is substantially parallel to the root of the tooth. In some instances, when the root of a tooth is not properly oriented, forces on the tooth may cause tooth movement (e.g., over time), which may impede occlusion and may cause wear on the tooth or its opposing occluder.

[0047] In some examples, the virtual joint motion module 24 updates or modifies the oral cavity model data 26. For example, the virtual joint motion module 24 can modify the dentition by updating the orientation, position, and / or shape of one or more teeth. For example, the virtual joint motion module 24 can modify the orientation of one or more teeth by changing the torque angle of the corresponding teeth. In another instance, the virtual joint motion module 24 can modify the shape of one or more teeth by adding material to and / or removing material from the corresponding teeth. In yet another instance, the virtual joint motion module 24 can modify the position of teeth, for example, by translating teeth in the mesial-distal direction to achieve a Class I molar relationship, or by translating teeth in the buccal-lingual direction to resolve posterior crossbite. Furthermore, the virtual joint motion module 24 can update or modify the oral cavity model data 26 in response to receiving user input from a dental processing provider via input device 18 to modify the orientation, shape, or both of one or more teeth.

[0048] In response to modification of the oral model data 26, the virtual joint motion module 24 can determine, based on the modified oral model data 26, whether one or more teeth are correctly oriented and / or shaped in the arrangement of the virtual dentition in the modified oral model data 26. For example, the virtual joint motion module 24 can determine one or more tangent vectors at one or more points on the updated dentition. In such an example, the virtual joint motion module 24 can determine whether one or more modified virtual teeth in the modified dentition are correctly oriented and / or shaped by determining whether any of the rays defined by the selected point and the associated tangent vector intersects a modified virtual tooth or the occlusal surface of a tooth. As another example, the virtual joint motion module 24 can determine whether a modified virtual tooth is correctly oriented by determining whether the tangent vector is aligned (e.g., substantially parallel) with the virtual root of a particular virtual tooth.

[0049] In this way, the computing device can determine the correct orientation and / or shape of any teeth in a patient's mouth based on the patient's own mandibular dynamics. For example, using the patient's own mandibular dynamics, the computing device can determine the correct orientation and / or shape of one or more teeth in a single arch, regardless of the shape or orientation of one or more teeth in a relative arch. Determining the correct position, orientation, and shape of teeth allows the computing device or dental treatment provider to formulate a treatment plan that reduces or eliminates interference between the patient's teeth. Reducing or eliminating interference between teeth can prolong dental health and improve the patient's quality of life.

[0050] Figure 2 An example of a digital 3D model of a patient's teeth according to this disclosure is shown. Figure 2 As shown, the oral model data 26 includes a virtual mandibular arch 38 representing the patient's mandibular arch. The oral model data 26 may also include a virtual maxillary arch representing the patient's maxillary arch.

[0051] Figure 3 A front view of an exemplary digital 3D model of a dental arch in a maximally cusped position, according to an example of this disclosure, is shown. Figure 3 refer to Figure 1 The system 10 is used to describe this. The digital 3D model 40 includes a virtual maxillary arch 42 and a virtual mandibular arch 44. Each of the rotation axes 46A-46C (collectively referred to as rotation axes 46) is associated with the movement of the virtual mandibular arch 44 in a corresponding direction among several different directions. Figure 3In the examples, rotation axis 46A may indicate the right guidance of the virtual mandibular arch 44, rotation axis 46B may indicate the left guidance of the virtual mandibular arch 44, and rotation axis 46C may indicate the opening of the virtual mandibular arch 44. In some examples, rotation axes 46A and 46B (e.g., lateral guidance axes) do not necessarily pass through specific anatomical features of the virtual dentition. For example, rotation axes 46A and 46B may include two rotations, such as one rotation for lateral deviation and one rotation for opening.

[0052] Figure 4 A left-side view of an exemplary digital 3D model of a dental arch in a maximally cusped position, according to an example of this disclosure, is shown.

[0053] Figure 5 An exemplary axis of rotation and an exemplary tangent vector or ray are shown as an example according to this disclosure. Figure 5 refer to Figure 1 The system 10 is used to describe this. The virtual joint motion module 24 can calculate one or more tangent vectors 521-52. N (Collectively referred to as tangent vector 52). Tangent vector 521 indicates the initial direction of motion of the selected point at position L1. Tangent vector 52 is tangent to a circle 54 (or a portion of a circle, such as an arc) centered on the axis of rotation 56. The plane of circle 54 is perpendicular to the axis of rotation 56. Thus, the axis of rotation 56 defines the center of circle 54 (or arc), and position L1 defines the radius R of the circle or arc, such that tangent vector 52 is tangent to circle 54 or arc at position L1. Each selected point L... i and its associated tangent vector 52 i A ray that is confined in space and has a definite position and direction. Without a base point, the tangent vector is 52. i The location is ambiguous. It should be noted that at a given distance along the axis of rotation, each point in the plane, defined by a plane perpendicular to the axis, determines a different tangent vector. However, each point along a line parallel to the axis of rotation will have the same tangent vector but a different base point. Therefore, each point in the space of the virtual dentition will define a unique ray. These rays can be used to determine whether a point in the virtual dentition will intersect a portion of the virtual dentition residing in the opposing arch due to performing any of the various mandibular offsets. The virtual joint motion module 24 can recalculate the tangent vectors (also called guide paths) at multiple locations along the arc 54. For example, the virtual joint motion module 24 can calculate the tangent vector 521 at point L1 and recalculate positions L2-L... N The new tangent vector at point 522-52 N .

[0054] Figure 6An exemplary axis of rotation and tangent vector or ray according to one example of this disclosure are shown. Figure 6 refer to Figure 1 The system 10 is described as follows. The virtual joint motion module 24 can define multiple rotation axes 62A-62C (collectively referred to as rotation axes 62) and multiple tangent vectors 64A-64D (collectively referred to as tangent vectors 64). It should be noted that each of the point 66 and tangent vectors 64 is defined as a ray with a defined position and orientation in the space of the virtual tooth row. Figure 6 In the example, rotation axis 62A can be a right-guided axis, rotation axis 62B can be a left-guided axis, and rotation axis 62C can be an opening axis. Each tangent vector in tangent vector 64 indicates the initial direction of movement of the corresponding offset point 66. For example, tangent vectors 64A, 64B, 64C, and 64D respectively indicate the initial direction of the rightward offset, forward offset, opening offset, and leftward offset point 66.

[0055] Figure 7 An exemplary dental arch and multiple tangential vectors or rays are shown as an example according to this disclosure. Figure 7 refer to Figure 1 The system 10 is used to describe this. The virtual maxillary arch 71 includes teeth 72.

[0056] The virtual joint motion module 24 can receive user input instructions to select point 76, or it can select point 76 on the surface of tooth 72. Figure 7 In the example, point 76 is associated with the wear facet of tooth 72. The virtual joint motion module 24 can determine multiple tangent vectors 74A-74D (collectively referred to as tangent vectors 74) associated with point 76. Each of point 76 and tangent vectors 74 defines a ray with a defined position and orientation in the space of the virtual dental arch. Tangent vectors 74A, 74B, 74C, and 74D can indicate the initial orientation of point 76 for rightward offset, forward offset, leftward offset, and opening offset, respectively.

[0057] Figure 8 An exemplary user interface according to one example of this disclosure is shown. Figure 8 refer to Figure 1 The system 10 is described in this way. The virtual joint motion module 24 can output a GUI 80 for display via a display device 16. In some examples, the GUI 80 includes a graphical representation of at least a portion of a virtual dental arch, such as a graphical representation of a specific tooth 82.

[0058] The virtual joint motion module 24 can receive user input instructions to select point 86, or point 86 can be selected on the surface of tooth 82. Figure 8In the example, point 86 is associated with the wear facet of tooth 82. The virtual joint motion module 24 can determine multiple tangent vectors 84A-84D (collectively referred to as tangent vector 84) associated with point 86. Similarly, the virtual joint motion module 24 can determine multiple rays defined by tangent vector 84 and point 86. The GUI 80 output by the virtual joint motion module 24 can include a graphical representation of each of the tangent vector 84, point 86, or the rays defined thereby. Tangent vectors 84A, 84B, 84C, and 84D can respectively indicate the initial direction of point 86 for rightward offset, forward offset, leftward offset, and opening offset.

[0059] Figure 9 An exemplary user interface according to one example of this disclosure is shown. Figure 9 refer to Figure 1 The system 10 is described in this way. The virtual joint motion module 24 can output a GUI 90 for display via a display device 19. In some examples, the GUI 90 includes a graphical representation of at least a portion of a virtual dental arch, such as a graphical representation of a specific tooth 92.

[0060] The virtual joint motion module 24 can receive user input instructions to select point 96, or it can select point 96 on the surface of tooth 92. Figure 9 In the example, point 96 is associated with the worn facet 91 of tooth 92. Figure 9 In the example, the wear facet 91 is located on the lingual side of the buccal cusp of tooth 92. The wear facet 91 can be located anywhere on tooth 92 where it contacts the opposing tooth. The virtual joint motion module 24 can determine one or more tangent vectors 94 associated with a selected point 96 within the wear facet 91. Figure 9 In the example, the tangent vector 94 can indicate the initial direction of the point 96 offset to the left.

[0061] In some examples, the virtual joint motion module 24 identifies the direction of motion causing the wear facet 91 based on the tangent vector (e.g., tangent vector 94) associated with it. For example, the virtual joint motion module 24 may determine one or more tangent vectors associated with a point 96 within the wear facet 91. Figure 9In the example, GUI 90 includes a tangent vector 94 associated with point 96. Virtual joint motion module 24 can determine the direction of movement causing wear facet 91 by determining whether any of the tangent vectors associated with point 96 is substantially parallel to the surface of wear facet 91. For example, when tangent vector 94 associated with point 96 is substantially parallel to the plane of wear facet 91, this can indicate that movement in the direction of tangent vector 94 (e.g., leftward offset) causes premature contact between wear facet 91 of tooth 92 and the opposing tooth in the relative arch, thus causing wear facet 91 over an extended period of time. In one scenario, virtual joint motion module 24 determines that tangent vector 94 is substantially parallel to the plane of wear facet 91. In response to determining that tangent vector 94 is substantially parallel to the plane of wear facet 91, virtual joint motion module 24 can determine that the direction of movement associated with tangent vector 94 is the direction of movement causing wear facet 91. In such a scenario, virtual joint motion module 24 determines that wear facet 91 is caused by leftward offset.

[0062] In one example, the virtual joint motion module 24 can determine whether the wear facet 91 is an active wear facet based on the tangent vector 94. An active wear facet can refer to a wear facet that continues to wear during the patient's TMJ movement. An inactive wear facet can refer to a previously formed wear facet that no longer wears during the patient's TMJ movement (e.g., a wear facet formed before receiving dental treatment, such as orthodontic braces). In some examples, the virtual joint motion module 24 can determine that a wear facet is an active wear facet in response to determining that the tangent vector 94 is substantially parallel to the plane of the wear facet 91.

[0063] For example, the virtual joint motion module 24 can determine that the wear facet 91 is an inactive wear facet in response to the determination that the plane of the wear facet 91 is substantially not parallel to the tangent vector 94. For instance, wear may have occurred before orthodontic treatment while a patient has malocclusion. After orthodontic treatment, the wear facets on the teeth may have a different orientation relative to the tangent vector that initially caused their movement. In such cases, the virtual joint motion module 24 can determine that the wear facet 91 is an inactive wear facet, which can indicate that the problem causing the facet has been resolved.

[0064] Figure 10A An exemplary user interface 1002A according to one example of this disclosure is shown. Figure 10B An exemplary user interface 1002B according to one example of this disclosure is shown. Figure 10A and 10B (Referred to collectively as Figure 10) Reference Figure 1The system 10 is described. GUI 1002A and 1002B (collectively referred to as GUI 1000) show a top view (e.g., occlusal surface) and a side view (e.g., distal surface) of tooth 1004, respectively.

[0065] like Figure 10A As shown, GUI 1002A includes graphical representations of points 1010, 1020, and 1030. (As...) Figure 10A and 10B As shown, GUI 1002 includes graphical representations of tangent vectors 1012 and 1014 associated with point 1010. Similarly, GUI 1002 may include graphical representations of tangent vectors 1022 and 1024 associated with point 1020, which, together with the point, define rays with defined positions and orientations in the space of the virtual dental arch. In some instances, points 1010 and 1020 are selected by the user. In another instance, the virtual joint motion module 24 can select points 1010 and 1020 located within the socket of tooth 1004. In the example of Figure 10, tangent vectors 1012 and 1022 are associated with a rightward offset, and tangent vectors 1014 and 1024 are associated with a leftward offset.

[0066] The virtual joint motion module 24 can determine whether the orientation and / or shape of the tooth 1004 is correct, at least in part, based on one or more of the tangent vectors 1012, 1014, 1022, or 1024.

[0067] According to one example, the virtual joint motion module 24 determines the orientation (e.g., torque angle) of tooth 104 by determining whether one of the rays defined by tangent vectors 1012, 1022 and points 1010, 1020 intersects the surface of the lingual cusp 1042, or whether one of the rays defined by tangent vectors 1014, 1024 and the same points 1010, 1020 intersects the surface of the buccal cusp 1044 of tooth 1004. Figure 10B In the example, the virtual joint motion module 24 determines that tooth 1004 is not properly oriented (e.g., the current torque angle would cause tooth 1004 to obstruct the occlusion) in response to determining whether one or both rays partially defined by tangent vectors 1014, 1024 intersect the surface of buccal cusp 1044.

[0068] When tooth 1004 is not oriented correctly, such as Figure 10B As the example shows, lateral leftward displacement can lead to premature contact between the buccal cusp 1044 and the surface of the opposing tooth, as can be seen from the ray associated with the left tangent vector intersecting this area of ​​the tooth and the presence of the worn facet 1031. Figure 10BIn the example, because the right-hand tangent vectors 1012 and 1022 are inclined away from the cusp 1042, the right-hand offset will avoid contact along the lingual cusp 1042. In such examples, the virtual joint motion module 24 can determine the torque angle of the tooth, as described below. Figure 11A and 11B Further description.

[0069] Figure 11A An exemplary user interface 1102A according to one example of this disclosure is shown. Figure 11B An exemplary user interface 1102B according to one example of this disclosure is shown. Figure 11A and 11B (Collectively referred to as Figure 11) Reference Figure 1 The system 11 is described. GUI 1102A and 1102B (collectively referred to as GUI 1100) show side views (e.g., distal surfaces) of tooth 1104.

[0070] As shown in Figure 11, the GUI 1102 each includes a point 1110 and graphical representations of tangent vectors 1112 and 1114 associated with the point 1110. The point and the tangent vectors together define rays with defined positions and orientations within the space of the virtual dental arch. In some examples, the virtual joint motion module 24 can select the point 1110 within the socket of the tooth 1104. In the example of Figure 11, tangent vector 1112 is associated with a rightward offset, and tangent vector 1114 is associated with a leftward offset.

[0071] The virtual joint motion module 24 can determine whether the orientation and / or shape of tooth 1104 is correct, at least in part, based on one or more of tangent vectors 1112 and / or 1114. In some examples, the virtual joint motion module 24 can determine whether the orientation of tooth 1104 is correct by determining whether a ray defined by tangent vector 1112 and point 1110 intersects the surface of lingual cusp 1142 or whether a ray defined by tangent vector 1114 and point 1110 intersects the surface of buccal cusp 1144. Figure 11A In the example, the virtual joint motion module 24 can determine that the tooth 1104 is incorrectly oriented in response to determining that a ray partially defined by the tangent vector 1114 intersects the surface of the tooth cusp 1144.

[0072] like Figure 11BAs shown, the virtual joint motion module 24 can modify or adjust the virtual dentition in response to determining that the current orientation and / or shape of the tooth 1104 is incorrect. For example, the virtual joint motion module 24 can determine the correct and appropriate orientation (e.g., torque angle) of one or more teeth by virtually rotating the tooth 1104 about a mesial-distal axis. In one example, the virtual joint motion module 24 rotates the tooth 1104 about the mesial-distal axis in predetermined increments (e.g., 1 degree). Alternatively, the virtual joint motion module 24 can rotate the tooth 1104 in adjustable increments (e.g., based on user input to rotate the tooth 1104).

[0073] In yet another example, the virtual joint motion module 24 can determine a rotation angle to correct the orientation of tooth 1104. For example, the virtual joint motion module 24 can determine the angular difference between the orientation of a tooth surface (e.g., the surface of the cusp 1142) and the associated tangent vector (e.g., tangent vector 1112). In one example, the virtual joint motion module 24 rotates tooth 1104 about a mesial-distal axis by this angular difference.

[0074] In some scenarios, a particular tooth (e.g., a premolar or molar, such as tooth 1104) comprises multiple cusps. In such scenarios, the virtual joint motion module 24 can determine the rotation angle based on multiple tangent vectors and associated tooth surfaces. For example, the virtual joint motion module 24 can calculate the average vector between tangent vectors 1112 and 1114, calculate the average surface plane between the surfaces of cusps 1142 and 1144, and calculate the angular difference in orientation between the average tangent vector and the average surface plane. The virtual joint motion module 24 is able to rotate tooth 1104 by this angular difference.

[0075] The virtual joint motion module 24 can determine whether the updated or modified orientation of tooth 1104 is correct by determining whether any ray defined by tangent vectors 1112 or 1114 and point 1110 intersects the surfaces of cusps 1142, 1144 after virtually rotating tooth 1104 about its mesial-distal axis. In some examples, the virtual joint motion module 24 determines that the updated orientation of tooth 1104 is correct in response to determining that a ray partially defined by tangent vectors 1112, 1114 does not intersect the surfaces of cusps 1142, 1144. In some examples, the virtual joint motion module 24 outputs GUI 1102B to indicate the correct orientation of tooth 1104.

[0076] In some examples, the paths traced by these reference points on the posterior teeth are geometrically similar to those traced by the canines or anterior guides. For example, as one of the reference points (e.g., point 1110) gets closer to the axis of rotation, the magnitude of the path scales proportionally to the distance from the axis of rotation. In some examples, the virtual joint motion module 24 can receive user input to correct the orientation of tooth 1104. As another example, the virtual joint motion module 24 can receive user input to adjust one or more guide teeth. The virtual joint motion module 24 can be referenced as... Figure 20 The described GUI recalculates the axis of rotation and outputs updated tangent vectors or rays and updated orientations of tooth 1104.

[0077] The virtual joint motion module 24 can determine one or more treatment plans. In one example, the virtual joint motion module 24 can determine the correct orientation (and / or shape) of multiple teeth within a virtual dentition. For example, the virtual joint motion module 24 can determine an orthodontic treatment plan (e.g., orthodontic appliances, such as braces or retainers) to correct the orientation of one or more teeth in the maxillary and / or mandibular arches. In some examples, the orthodontic treatment plan can indicate the final correct orientation of one or more teeth and the intermediate orientation of the corresponding teeth to achieve the correct orientation. In one example, the treatment plan may include a virtual model of one or more dental arches (e.g., to form a denture or dental implant). Furthermore, while the virtual joint motion module 24 is described as modifying a virtual dentition by adjusting the orientation or shape of teeth, it can also determine a treatment plan to adjust the shape and / or orientation of teeth, bones, or roots via orthognathic surgery or by cutting the maxilla or mandible and changing the position of the entire dental arch segment.

[0078] While the example of Figure 11 is described with reference to tangent vectors associated with leftward and rightward offsets to determine proper tooth orientation (e.g., appropriate or correct torque angle), in some examples, the virtual joint motion module 24 may utilize tangent vectors associated with mandibular protrusion movements along the anterior guidance to determine whether the posterior teeth are correctly oriented or shaped (e.g., assuming proper anterior guidance). Similarly, the virtual joint motion module 24 may utilize tangent vectors to determine whether the shape and / or orientation of the canines or incisors is correct (or determine which shape / or orientation is correct). Furthermore, the shape of the canines or incisors can be modified to achieve proper guidance and thus protect the posterior teeth to reduce or eliminate interference between teeth.

[0079] Thus, the technology disclosed herein enables a computing system to determine whether the current orientation and / or shape of one or more teeth in a patient's teeth is correct. Additionally or alternatively, the computing system can determine the correct orientation and / or shape of the patient's teeth and output information (e.g., to a dental treatment provider) to enable the dental treatment provider to develop a treatment plan. In some examples, the computing system determines the appropriate torque and tip angle of premolars and molars, aspects of appropriate canine relationships, and aspects of appropriate incisor relationships (e.g., including anterior tilt angle).

[0080] Figure 12A An exemplary user interface 1202A according to one example of this disclosure is shown. Figure 12B An exemplary user interface 1202B according to one example of this disclosure is shown. Figure 12A and 12B (Referred to collectively as Figure 12) Reference Figure 1 The system 12 is described. GUI 1202A and 1202B (collectively referred to as GUI 1200) show side views (e.g., distal surfaces) of tooth 1204.

[0081] As shown in Figure 12, GUI 1202 includes a graphical representation of point 1210. Also shown in Figure 12, GUI 1202 includes graphical representations of tangent vectors 1212 and 1214 associated with point 1210. Tangent vectors 1212 and 1214, together with point 1210, define rays with defined positions and orientations in the space of the virtual dental arch. In some examples, the virtual joint motion module 24 can select point 1210 within the socket of tooth 1204. In the example of Figure 12, tangent vector 1212 is associated with a rightward offset, and tangent vector 1214 is associated with a leftward offset.

[0082] The virtual joint motion module 24 can determine whether the orientation and / or shape of the tooth 1204 is correct, at least in part, based on one or more of tangent vectors 1212 and / or 1214. In some examples, the virtual joint motion module 24 can determine whether the shape of the tooth 1204 is correct, at least in part, based on tangent vectors associated with lateral offset (e.g., one of tangent vectors 1212 or 1214). For example, the virtual joint motion module 24 can determine that the shape of the tooth 1204 is incorrect in response to determining that a ray defined by tangent vector 1212 and point 1210 intersects the surface of the lingual cusp 1242 or a ray defined by tangent vector 1214 and point 1210 intersects the surface of the buccal cusp 1244. As another example, the virtual joint motion module 24 can determine that the shape of the tooth 1204 is incorrect in response to determining that the surfaces of the cusps 1242, 1244 are not centered within a ray partially defined by tangent vectors 1212, 1214.

[0083] According to some examples, the virtual joint motion module 24 can modify or adjust the virtual dentition in response to determining that the current orientation and / or shape of tooth 1204 is incorrect. For example, the virtual joint motion module 24 can adjust the shape of tooth 1204 by adding material to tooth 1204 and / or removing material from tooth 1204. For example, the virtual joint motion module 24 can add material to one part of tooth 1204 and remove material from another part of tooth 1204. The virtual joint motion module 24 can determine whether the shape of the updated or modified tooth 1204 is correct by determining whether a ray defined by tangent vector 1212 and point 1210 intersects the surface of lingual cusp 1242 or whether a ray defined by tangent vector 1214 and point 1210 intersects the surface of buccal cusp 1244. In some examples, the virtual joint motion module 24 outputs GUI 1202B to indicate the correct shape of tooth 1204.

[0084] The virtual joint motion module 24 can determine one or more treatment plans. In one example, the virtual joint motion module 24 can determine the correct shape (and / or orientation) of multiple teeth within a virtual dentition. For example, the virtual joint motion module 24 can determine an orthodontic treatment plan (e.g., orthodontic appliances, such as braces or retainers) to correct the orientation of one or more teeth in the maxillary and / or mandibular arches. In some examples, the orthodontic treatment plan can indicate the final correct orientation of one or more teeth and the intermediate orientation of the corresponding teeth to achieve the correct orientation. In one example, the treatment plan may include a virtual model of one or more dental arches (e.g., to form a denture or dental implant).

[0085] While the examples of Figures 11 and 12 are described with reference to tangent vectors associated with leftward and rightward offsets to determine appropriate tooth orientation (e.g., appropriate or correct torque angle), in some examples, the virtual joint motion module 24 may utilize tangent vectors associated with mandibular protrusion movements along the anterior guide to determine whether the posterior teeth are correctly oriented or shaped (e.g., assuming appropriate anterior guide). Similarly, the virtual joint motion module 24 may utilize tangent vectors to determine whether the shape and / or orientation of the canines or incisors is correct (or to determine which shape / or orientation is correct). For example, the virtual joint motion module 24 may determine correct canine orientation in response to determining that the guiding tangent vectors (left for the left canine, right for the right canine) are orthogonal to the distal-buccal region in the lower canines and orthogonal to the mesial-palatal region in the upper canines. Furthermore, the virtual joint motion module 24 may determine the correct torque angle of the lower canines based on open and / or closed tangent vectors. Additionally, the shape of the canines or incisors can be modified to achieve appropriate guide, and thus protect the posterior teeth to reduce or eliminate interference between teeth.

[0086] Thus, the technology disclosed herein enables a computing system to determine whether the current orientation and / or shape of one or more teeth in a patient's teeth is correct. Additionally or alternatively, the computing system can determine the correct orientation and / or shape of the patient's teeth and output information (e.g., to a dental treatment provider) to enable the dental treatment provider to develop a treatment plan. In some examples, the computing system determines the appropriate torque and tip angle of premolars and molars, aspects of appropriate canine relationships, and aspects of appropriate incisor relationships (e.g., including anterior tilt angle).

[0087] In some examples, the computing device automatically determines the orientation and / or shape of teeth based on such analysis and makes necessary modifications to the dentition without outputting a GUI or receiving user input. The computing device can output data indicating the correct shape and / or orientation of dental anatomy to other systems for further analysis and adjustment of the dentition, or to a digital design module that automatically or with user input designs devices such as 3D printed models for forming clear aligners, 3D printed aligner designs, custom framework designs, custom archwire designs, dental restoration mold designs (for additive methods), and custom grinding tool designs (for subtractive methods). The computing device can output graphical or human-readable instructions or directives for tooth movement or modification. The computing device can output partial guidance for tooth movement or dental anatomy modification constraints used by other systems to further optimize tooth position or shape. These outputs can take the form of positioning and / or orientation ranges or constrained values ​​for certain points or vector components of one or more axes. In some instances, the output may include data indicating relative changes in the position of the tooth surface, such as the amount of material to be added or subtracted or the thickness of the coating, or the radius of curvature of the surface, cusp, or pit, and the boundaries of the modified area.

[0088] Figure 13A An exemplary user interface 1302A according to one example of this disclosure is shown. Figure 13B An exemplary user interface 1302B according to an example of this disclosure is shown. Figures 13A to 13B (Collectively referred to as Figure 13) Reference Figure 1 The system 12 is used to describe this. GUI 1302A and 1302B (collectively referred to as GUI 1300) show the top and side views of tooth 1304, respectively.

[0089] As shown in Figure 13, GUI 1302 includes graphical representations of multiple points 1310A-1310N (collectively referred to as points 1310) within the socket of tooth 1304. As shown in Figure 13, GUI 1302 includes graphical representations of tangent vectors 1312A-1312N (collectively referred to as tangent vectors 1312) and tangent vectors 1314A-1314N (collectively referred to as tangent vectors 1314) associated with point 1310. Tangent vector 1314 and its corresponding base point 1310 together define rays with defined positions and orientations in the space of the virtual dental anatomy. In the example of Figure 13, tangent vector 1312 is associated with a rightward offset, and tangent vector 1314 is associated with a leftward offset.

[0090] The virtual articulation module 24 can determine whether the orientation and / or shape of the tooth 1304 is correct, at least in part, based on one or more of the tangent vectors 1312 and / or 1314, as described above with reference to Figures 11 and / or 12. For example, the virtual articulation module 24 can determine that the orientation of the tooth 1304 is correct in response to determining that a ray defined by the tangent vectors 1312 and / or 1314 and the corresponding base point 1310 does not intersect the surface of the lingual cusp 1322 or the buccal cusp 1324. In one example, the virtual articulation module 24 determines that the orientation of the tooth 1304 is incorrect in response to determining that one or more of the rays defined by the tangent vector 1314 and the corresponding base point 1310 intersect the surface of the buccal cusp 1324.

[0091] Figure 14 This is a flowchart illustrating an exemplary process using the techniques disclosed herein. Figure 14 refer to Figure 1 The system is described in this way.

[0092] The computing system 14 can receive data (1402) indicating a virtual dentition in the patient's oral cavity. For example, the data indicating a virtual dentition may include data indicating a virtual mandibular arch representing the patient's mandibular arch or a virtual maxillary arch representing the patient's maxillary arch. In some examples, the computing system 14 receives the data indicating a virtual dentition directly in vivo using an intraoral scanner, cone-beam computed tomography (CBCT) scan (i.e., 3D X-ray), or magnetic resonance imaging (MRI). In other examples, the computing system 14 may receive the data indicating a dentition indirectly by scanning an impression of the teeth or a casting made from an impression of the teeth. In yet another example, the computing system 14 may receive the data indicating a patient's dentition from another computing device, for example, via a network.

[0093] In some examples, the computing system 14 receives data (1404) indicating selected points of a virtual dentition in the patient's oral cavity. For example, the computing system 14 may output a graphical user interface (GUI) including a graphical representation of at least a portion of the patient's oral cavity, such as images of a virtual mandibular arch and / or a virtual maxillary arch. The computing system 14 may receive data indicating user input (e.g., via input device 18) that selects one or more points within the patient's oral cavity. Alternatively, the computing system 14 may select one or more points on the dentition. For example, the computing system 14 may select one or more points in the sockets of one or more teeth or one or more points on the surface of one or more teeth (e.g., within worn facets).

[0094] In some examples, the calculation system 14 determines one or more tangent vectors (1406) at a selected point. In some examples, each tangent vector is tangent to an arc centered on the corresponding axis of rotation and indicates the direction of motion of the selected point. In some examples, the calculation system 14 determines a ray (1406) defined by one or more tangent vectors and the selected point.

[0095] The computing system 14 performs one or more actions (1408) in response to determining the tangent vector. In one example, the computing system 14 performs an action by outputting a GUI 30 indicating the tooth row and the tangent vector to a display device 16. In some examples, the computing system 14 can perform an action by determining whether a particular tooth is correctly oriented and / or shaped. In yet another example, the computing system 14 can perform an action by determining whether a particular tooth is correctly oriented for axial loads on that tooth.

[0096] In some scenarios, the computing system 14 performs actions by updating or modifying a virtual dentition, for example by updating the orientation and / or shape of one or more teeth. In another scenario, the computing system 14 performs actions by determining one or more treatment plans for the patient's teeth.

[0097] Figure 15 An exemplary 3D digital model of a dental arch including the root is shown as an example according to this disclosure. Figure 15 refer to Figure 1 The system 10 is described as follows. The virtual joint motion module 24 can determine multiple tangent vectors 1502A-1502C (collectively referred to as tangent vectors 1502) associated with different roots of dental anatomy. Tangent vectors 1502 can indicate the initial orientation of the roots used for orifice offset. The calculation system 14 can determine that a given tooth is not correctly oriented in response to determining that the root of a given tooth is not parallel to the corresponding tangent vector 1502. In such an example, the calculation system 14 can rotate the tooth until the root is parallel to the tangent vector 1502.

[0098] Figures 16A to 16B A digital 3D model of a dental arch according to an example of this disclosure is shown. Figure 16 (reference) Figure 1 The system is described as system 10.

[0099] The digital 3D model 40 includes a virtual maxillary arch 42 and a virtual mandibular arch 44. Figure 16A Exemplary rotation axes 1646A, 1647A, and 1648A are shown before the modification of the guide canine. Figure 16B Exemplary rotation axes 1646B, 1647B, and 1648B are shown after modification of the guide canine (e.g., by increasing the height of the canine).

[0100] In the example of Figure 16, rotation axes 1646A and 1646B indicate the right guidance of the virtual mandibular arch 44, rotation axes 1647A and 1647B indicate the opening of the virtual mandibular arch 44, and rotation axes 1648A and 1648B indicate the left guidance of the virtual mandibular arch 44.

[0101] Figure 16C The effect of modifying the shape of the guiding canine by the tangent vector at point 1610 based on tooth 1604 is shown. Tangent vector 1612 shows the initial movement of point 1610 towards the right, and tangent vector 1614 shows the initial movement of point 1610 towards the left before modifying the guiding canine. Tangent vector 1622 shows the initial movement of point 1610 towards the right, and tangent vector 1624 shows the initial movement of point 1610 towards the left after modifying the guiding canine. Figure 16C As shown, the angle between tangent vectors 1622 and 1624 is smaller than the angle between tangent vectors 1612 and 1614, which provides additional tolerance to adjust the torque / orientation of tooth 1604.

[0102] Figure 17 This is a flowchart illustrating an exemplary process using the techniques disclosed herein. Figure 17 refer to Figure 1 System 10 is used to describe it. Figure 17 In the example, Figure 1 The computational system 14 can determine whether a tooth is correctly oriented, at least in part, based on one or more tangent vectors.

[0103] The computing system 14 receives data (1702) indicating a virtual dentition in the patient's oral cavity. In one example, the virtual dentition includes cusps (e.g., incisors, canines, or premolars with vestigial lingual cusps) or cusps (e.g., premolars or molars).

[0104] In some examples, the computing system 14 receives data (1704) indicating fossae on virtual teeth (e.g., molars or premolars) of a virtual dentition. For example, the computing system 14 may receive user input selecting a point in a fossa of a tooth. Alternatively, the computing system 14 may select a point in a fossa.

[0105] The calculation system 14 determines the ray (1706) based on the burrow and the tangent vector indicating the movement of the burrow. The tangent vector indicates the specific direction of movement of the selected burrow.

[0106] In some examples, the computing system 14 determines whether a ray defined by a tangent vector and a pit intersects the surface of a tooth (1708). For example, the computing device 15 can determine whether a ray intersects the crown of a virtual tooth or where the ray intersects the crown of a virtual tooth. The computing system 14 can determine the size of the intersection by determining the distance between the point where the ray enters the tooth and the point where the ray leaves the tooth.

[0107] The calculation system 14 rotates the tooth toward the intersection point (1710) in response to determining that the ray intersects the tooth surface ("yes" branch of 1708). The calculation system 14 is capable of rotating the tooth in fixed or variable angular increments. For example, the calculation system 14 is capable of rotating the tooth in relatively small fixed increments (e.g., 1 degree).

[0108] In response to determining that the ray does not intersect the surface of the tooth (the "No" branch of 1708), the computational system 14 can determine that the tooth is correctly oriented (1710). In such an example, the computational system 14 can stop rotating the tooth in response to determining that the tooth is correctly oriented.

[0109] In some instances, the computational system 14 rotates the tooth in variable increments. For example, the computational system 14 may perform a first rotation by rotating the tooth by a relatively large angle, and a subsequent rotation by rotating the tooth in decreasing increments (e.g., half the angle of the previous rotation). In such instances, the computational system 14 may change the direction of rotation in response to determining that the ray defined by the tangent vector and the fovea does not intersect the surface of the tooth. When the magnitude of the rotation increment meets (e.g., less than or equal to) a threshold size, the computational system 14 may stop rotating the tooth. In such examples, the computational system 14 may converge at the optimal torque angle of the tooth faster and / or more accurately than rotating the tooth in fixed increments.

[0110] Figure 18 This is a flowchart illustrating an exemplary process using the techniques disclosed herein. Figure 18 refer to Figure 1 System 10 is used to describe it. Figure 18 In the example, Figure 1The computational system 14 can determine whether a tooth is correctly oriented, at least in part, based on one or more tangent vectors.

[0111] The computing system 14 receives data indicating a virtual dentition in the patient's oral cavity (1802). In some examples, the computing system 14 receives data indicating one or more fossae on virtual teeth (e.g., molars or premolars) of the virtual dentition (1804). For example, the computing system 14 may receive user input selecting a point in a fossa of a tooth. Alternatively, the computing system 14 may select a point in a fossa.

[0112] The calculation system 14 determines the ray (1806) based on the left-side offset tangent vector and the right-side offset tangent vector for each fowl. The tangent vector indicates the specific direction of movement for the corresponding fowl.

[0113] In some examples, the calculation system 14 calculates the intersection points (if any) for each ray defined by the tangent vector and its corresponding fovea (1808). For example, the calculation system 14 determines the intersection point between one ray, which is partially defined by a laterally offset tangent vector, and a buccal cusp of a tooth (e.g., a molar or premolar), and the intersection point between another ray, which is partially defined by a laterally offset tangent vector, and a lingual cusp of a tooth. Additionally or alternatively, the calculation system 14 may determine the intersection points (if any) between a ray, which is partially defined by an anterior or posterior offset tangent vector, and a mesial or distal cusp of the same tooth.

[0114] exist Figure 18 In the example, for each tangent vector intersecting the surface of the tooth, the calculation system 14 can calculate the distance between the entry intersection (e.g., the point where the ray enters the tooth) and the exit intersection (e.g., the point where the ray leaves the tooth) (1810). The line segment between the entry and exit intersections is called the intersection segment. For example, the calculation system 14 can determine the distance of the intersection segment associated with the left-biased tangent vector by calculating the distance between the entry and exit intersections of a ray partially defined by a left-biased tangent vector. Similarly, the calculation system 14 can determine the distance of the intersection segment associated with a right-biased tangent vector by calculating the distance between the entry and exit intersections of a ray partially defined by a right-biased tangent vector.

[0115] In an example where multiple tangent vectors intersect a single cusp of a tooth, the calculation system 14 can determine the approximate distances of the intersection segments associated with the corresponding left-biased tangent vectors and the approximate distances of the intersection segments associated with the corresponding right-biased tangent vectors. The calculation system 14 can determine the approximate distances by calculating the maximum distance between the entry and exit points, the average distance between the entry and exit points, or a combination of distances (e.g., the total distance) between the entry and exit points of rays intersecting a given cusp. In other words, in the calculation system 14, the approximate distance associated with the left-biased tangent vector is the maximum distance, average distance, or total distance of the intersection segments of the left-biased tangent vectors, and the approximate distance associated with the right-biased tangent vector is the maximum distance, average distance, or total distance of the intersection segments of the right-biased tangent vectors.

[0116] The calculation system 14 can determine the difference (1812) between the distance associated with the right ray (e.g., associated with the right-side offset tangent vector) and the distance associated with the left ray (e.g., associated with the left-side offset tangent vector). For example, the calculation system 14 can determine the difference between the distance of the intersection segment of the left-side offset tangent vector and the distance of the intersection segment of the right-side offset tangent vector. In other words, the calculation system 14 subtracts the distance of the intersection segment associated with the left-side offset tangent vector from the distance of the intersection segment associated with the right-side offset tangent vector (or vice versa). In an example with multiple left and right-side offset tangent vectors, the calculation system 14 determines the difference between the approximate distance of the intersection segment associated with the left-side offset tangent vector and the approximate distance of the intersection segment associated with the right-side offset tangent vector.

[0117] In some examples, the calculation system 14 determines whether the difference is within tolerance (1814). When the difference between the distance of the intersection segment associated with the left offset vector and the distance of the intersection segment associated with the right offset vector is within tolerance or a threshold, this can indicate that the cusp of the tooth is approximately centered between the tangent vectors at the selected point. Therefore, the calculation system 14 can determine the correct tooth orientation (1818) in response to determining that the difference between the distance associated with the left offset vector and the distance associated with the right offset vector is within tolerance or a threshold (the "yes" branch of 1814).

[0118] Calculation system 14 rotates the tooth (1816) in response to determining that the difference is not within tolerance (the "No" branch of 1814). Calculation system 14 can rotate the tooth around the fossa toward the longer of the intersection segment associated with the left-side offset vector and the intersection segment associated with the right-side offset vector. In other words, if the intersection segment associated with the left-side offset tangent vector is longer than the intersection segment associated with the right-side offset tangent vector, calculation system 14 rotates the tooth toward the cusp associated with the left-side offset tangent vector. Again, if the left-side offset tangent vector intersects the tooth more than the right-side offset tangent vector, calculation system 14 rotates the tooth toward the cusp associated with the left-side offset tangent vector. Similarly, calculation system 14 can rotate the tooth around the buccal-lingual axis passing through the fossa, rather than around the mesial-distal axis passing through the fossa. In this way, calculation system 14 can balance or center the orientation of the dental anatomy relative to the tangent vectors.

[0119] The calculation system 14 is capable of rotating the teeth in fixed or variable angular increments. For example, the calculation system 14 is capable of rotating the teeth in relatively small fixed increments (e.g., 1 degree). In some instances, the calculation system 14 rotates the teeth in variable increments. For example, the calculation system 14 may perform a first rotation by rotating the teeth by a relatively large angle and a subsequent rotation by rotating the teeth in decreasing increments (e.g., half the angle of the previous rotation). In such instances, the calculation system 14 may change the direction of rotation in response to determining that the teeth have been overrotated. For example, the calculation system 14 may determine that the teeth have been overrotated in response to determining that the difference between the distance associated with the right-side offset tangent vector and the distance associated with the left-side offset tangent vector has changed sign (e.g., the difference has changed from a positive value to a negative value or from a negative value to a positive value).

[0120] In some cases, the calculation system 14 may not completely remove the intersection of the tangent vector and the tooth (e.g., because at least a portion of the dental anatomy will remain in the path of the tangent vector). In such examples, the calculation system 14 may also correct the dental anatomy by other means, such as by increasing the length of one or two canines appropriately to increase the slope of the opening angle according to the lateral offset angle.

[0121] Figure 19 This is a flowchart illustrating an exemplary process using the techniques disclosed herein. Figure 19 refer to Figure 1 System 10 is used to describe it. Figure 19 In the example, Figure 1 The computational system 14 can determine whether a tooth is correctly oriented, at least in part, based on one or more tangent vectors.

[0122] The computing system 14 receives data indicating a virtual dentition in the patient's oral cavity (1902). In some examples, the computing system 14 receives data indicating one or more fossae on virtual teeth (e.g., molars or premolars) of the virtual dentition (1904). For example, the computing system 14 may receive user input selecting a point in a fossa of a tooth. Alternatively, the computing system 14 may select a point in a fossa.

[0123] The calculation system 14 determines rays based on the left-side offset tangent vector, the right-side offset tangent vector, and the fovea (1906). The tangent vector indicates the specific direction of motion of the selected point.

[0124] In some examples, the calculation system 14 calculates the intersection point (if any) of each ray with a tooth (1908). For example, the calculation system 14 determines the intersection point between one ray, partially defined by a laterally offset tangent vector, and a buccal cusp of a tooth (e.g., a molar or premolar), and the intersection point between another ray, partially defined by a laterally offset tangent vector, and a lingual cusp of a tooth. Additionally or alternatively, the calculation system 14 may determine the intersection point (if any) between a ray, partially defined by an anterior or posteriorly offset tangent vector, and a mesial or distal cusp of the same tooth.

[0125] exist Figure 19 In the example, the computational system 14 can define polygons based on the intersection points of the corresponding rays with the tooth surface. For example, the computational system 14 can calculate a first polygon associated with a left-biased tangent vector (whose corresponding ray intersects the tooth), and a second polygon associated with a right-biased tangent vector (whose corresponding ray intersects the tooth). In other words, the rays form a non-planar sheet that can intersect a portion of the dental anatomy. The intersecting boundary can be discretely defined as a polygon comprising a finite number of points, where the corresponding finite number of rays intersect a portion of the dental anatomy (where the associated rays enter and exit the anatomy).

[0126] The calculation system 14 determines the magnitude of each polygon within the polygonal structure. In some examples, the calculation system 14 determines the magnitude by calculating the perimeter of the polygon. Alternatively, the calculation system 14 can calculate the magnitude by projecting the 3D polygon onto a plane and determining the region enclosed by the projected 3D polygon, or by summing the polygonal regions defined by adjacent line segments (where corresponding rays enter and exit the dental anatomy). In yet another example, the calculation system 14 can determine the magnitude by calculating the volume of the space defined on one side by a polygonal region on a ray sheet intersecting the dental anatomy and on the other side by the surface of the penetrating sheet of the dental anatomy. In yet another example, the calculation system 14 can determine the magnitude by calculating the maximum distance between any point on the penetrating dental anatomy and a corresponding point on a ray sheet perpendicular to the projection of the ray sheet. Thus, the calculation system 14 determines the magnitude of a first polygon associated with a left-biased tangent vector (intersecting the tooth) and the intersection magnitude of a second polygon associated with a right-biased tangent vector.

[0127] The calculation system 14 determines the difference between the magnitude of the first polygon and the magnitude of the second polygon (1912).

[0128] The calculation system 14 determines whether the difference in the magnitudes of the polygons is within tolerance or a threshold (1914). When the difference in the magnitudes of the polygons is within tolerance, this indicates that the cusp of the tooth is approximately centered between the tangent vectors at the selected point. Therefore, the calculation system 14 can determine the correct orientation of the tooth in response to determining that the difference between the distance associated with the left offset vector and the distance associated with the right offset vector is within tolerance or a threshold (the "yes" branch of 1914) (1918).

[0129] Calculation system 14 rotates the tooth (1916) in response to determining that the difference is not within tolerance (the "No" branch of 1914). Calculation system 14 can rotate the tooth about the fossa towards a larger polygon (e.g., a polygon with a larger value) (1916). In other words, if the polygon defined by the left-side offset tangent vector is larger than the polygon defined by the right-side offset tangent vector, calculation system 14 rotates the tooth towards the cusp associated with the left-side offset tangent vector. Similarly, calculation system 14 can rotate the tooth about the buccal-lingual axis passing through the fossa, rather than about the mesial-distal axis passing through the fossa. In this way, calculation system 14 can balance or center the orientation of the dental anatomy relative to the tangent vectors.

[0130] The calculation system 14 is capable of rotating the tooth in fixed or variable angular increments. For example, the calculation system 14 is capable of rotating the tooth in relatively small fixed increments (e.g., 1 degree). In some instances, the calculation system 14 rotates the tooth in variable increments. For example, the calculation system 14 may perform a first rotation by rotating the tooth by a relatively large angle and a subsequent rotation by rotating the tooth in a decreasing increment (e.g., half the angle of the previous rotation). In such instances, the calculation system 14 may change the direction of rotation in response to determining that the tooth has been overrotated. For example, the calculation system 14 may determine that the tooth has been overrotated in response to determining that the difference between the magnitude of the polygon associated with the right-side offset tangent vector and the magnitude of the polygon associated with the left-side offset tangent vector has changed sign (e.g., the difference has changed from positive to negative or from negative to positive).

[0131] In some cases, the calculation system 14 may not completely remove the intersection of the tangent vector and the tooth (e.g., because at least a portion of the dental anatomy will remain in the path of the tangent vector). In such examples, the calculation system 14 may also correct the dental anatomy by other means, such as by increasing the length of one or two canines appropriately to increase the slope of the opening angle according to the lateral offset angle.

[0132] Figure 20 This is a flowchart illustrating an exemplary process using the techniques disclosed herein. Figure 20 refer to Figure 1 The system is described as system 10.

[0133] The calculation system 14 performs virtual articulation movements on a 3D model of the patient's dentition to define four rotational axes associated with movement of the virtual mandibular arch (2002). The calculation system 14 sets a flag indicating whether the current set of calculations is the first set of calculations (2004). The first set of calculations refers to the first set of calculations to determine a set of rotational axes. In other words, the flag indicates whether the calculation system 14 has previously calculated all four rotational axes (e.g., flag = false when the calculation system has previously calculated all four rotational axes) or whether the calculation system 14 has not yet calculated all four rotational axes (e.g., flag = true).

[0134] The computational system 14 moves or performs virtual articulation of the virtual mandibular arch to the position of maximum cusp occlusion (2006). Then, the computational system 14 moves the virtual mandibular arch to the central open position (2008). The computational system 14 calculates a transformation matrix that defines the movement of the virtual mandibular arch from the position of maximum cusp occlusion to the central open position (2010). The computational system 14 calculates the open rotation axis, which may also be referred to as the central open rotation axis (2012). The computational system 14 calculates and plots the open ray for each target point (2014). In some examples, each open ray indicates the direction of movement for each corresponding target point used for open offset.

[0135] In one example, the computational system 14 moves or performs virtual articulation of the virtual mandibular arch to the maximum cusp occlusion position (2016). Then, the computational system 14 moves the virtual mandibular arch to the right maximum guide position (2018). The computational system 14 calculates a transformation matrix that defines the movement of the virtual mandibular arch from the maximum cusp occlusion position to the right maximum guide position (2020). The computational system 14 calculates a lateral right rotation axis, which may also be referred to as the lateral right maximum guide rotation axis (2022). The computational system 14 calculates and plots a lateral right ray for each target point (2024). In some examples, each lateral right ray indicates the direction of movement for each corresponding target point for rightward offset.

[0136] Calculation system 14 determines whether there have been any changes to the upper right or lower right canine (2026). If there have been any changes to the right canine (the "Yes" branch of 2026), calculation system 14 repositions the virtual mandibular arch to the position of maximum cusp anastomosis (2016). If there have been no changes to the right canine (the "No" branch of 2026), calculation system 14 determines whether the current group calculation is still the first group calculation (e.g., whether calculation system 14 has not yet calculated all four rotation axes such that the marker = true) (2028). If the current group calculation is not the first group calculation (the "No" branch of 2028), calculation system 14 determines whether the lower left canine has been changed (2040).

[0137] In one example, if the current group calculation is still the first group calculation (the "yes" branch of 2028), the calculation system 14 moves or performs virtual joint movement to the maximum cusp anastomosis position (2030). Then, the calculation system 14 moves the virtual mandibular arch to the left maximum guide position (2032). The calculation system 14 calculates a transformation matrix that defines the movement from the maximum cusp anastomosis position to the left maximum guide position (2034). The calculation system 14 calculates a lateral left rotation axis, which may also be referred to as the lateral left maximum guide rotation axis (2036). The calculation system 14 calculates and plots a lateral left ray for each target point (2038). In some examples, each lateral left ray indicates the direction of movement for each corresponding target point for leftward offset.

[0138] The calculation system 14 determines whether there have been any changes to the left upper or left lower canine (2040). If there have been any changes to the left canine (the "yes" branch of 2040), the calculation system 14 repositions the virtual mandibular arch to the position of maximum cusp anastomosis (2030). If there have been no changes to the left canine (the "no" branch of 2030), the calculation system 14 determines whether the current group calculation is still the first group calculation (e.g., whether the calculation system 14 has not yet calculated all four rotational axes such that the mark = true) (2042). If the current group calculation is not the first group calculation (the "no" branch of 2042), the calculation system 14 determines whether there have been changes to the upper or lower anterior teeth (2056).

[0139] In one example, if the current group calculation is still the first group calculation (the "yes" branch of 2042), the calculation system 14 moves or performs virtual joint movement to the maximum cusp occlusion position (2044). Then, the calculation system 14 moves the virtual mandibular arch to the maximum protrusion guide position (2046). The calculation system 14 calculates a transformation matrix that defines the movement of the virtual mandibular arch from the maximum cusp occlusion position to the maximum protrusion guide position (2048). The calculation system 14 calculates the protrusion rotation axis, which may also be referred to as the maximum protrusion guide rotation axis (2050). The calculation system 14 calculates and plots the protrusion ray for each target point (2052). In some examples, each protrusion ray indicates the direction of movement for each corresponding target point used for protrusion offset.

[0140] After the computation center opens the rotation axis, the lateral right rotation axis, the lateral left rotation axis, and the forward rotation axis, the computation system 14 updates the markers (e.g., by setting the markers to false) to indicate that all four rotation axes (2054) have been computed.

[0141] The calculation system 14 determines whether there have been any changes to the upper or lower anterior teeth (2056). If there have been any changes to the anterior teeth (the "yes" branch of 2056), the calculation system 14 repositions the virtual mandibular arch to the position of maximum cusp anastomosis (2044).

[0142] If there are no changes to the anterior teeth (the "No" branch of 2056), the calculation system 14 determines whether dynamic settings are enabled (2058). If dynamic settings are enabled (the "Yes" branch of 2058), the calculation system 14 re-determines whether there have been any changes to the teeth (2026). If dynamic settings are not yet enabled (the "No" branch of 2058), the calculation system 14 terminates the process.

[0143] Various examples have been described. These examples, as well as others, are all within the scope of the following claims.

Claims

1. A method for dental treatment, the method comprising: receiving, by a computing device, data indicative of a virtual dentition of an oral cavity of a patient, the data indicative of the virtual dentition including data indicative of at least one of a virtual mandibular arch representing a mandibular arch of the patient or a virtual maxillary arch representing a maxillary arch of the patient; receiving, by the computing device, data indicative of a selected point on the virtual dentition of the oral cavity; determining, by the computing device, a tangent vector indicative of a direction of motion of the selected point based on an axis of rotation of the virtual mandibular arch, wherein the axis of rotation defines a center of an arc that defines a plane that is perpendicular to the axis of rotation; and performing, by the computing device, an action based on the tangent vector.

2. The method of claim 1, wherein performing the action comprises: determining, by the computing device, whether an orientation of a tooth of the virtual dentition or a shape of the tooth is correct based on the tangent vector.

3. The method of claim 2, wherein determining whether the orientation or shape of the tooth is correct comprises: determining whether a ray defined by the selected point and the tangent vector intersects a surface of the tooth.

4. The method of claim 3, further comprising: in response to determining that the ray intersects the surface of the tooth, determining that the orientation of the tooth is incorrect.

5. The method of claim 3, further comprising: in response to determining that the ray does not intersect the surface of the tooth, determining that the orientation or shape of the tooth is correct.

6. The method of claim 1, the method further comprising: modifying, by the computing device, the virtual dentition to form an updated shape or an updated orientation of a tooth of the virtual dentition; and determining, by the computing device, whether the updated shape or a torque angle of the tooth is correct based on the tangent vector and the modified virtual dentition.

7. The method of claim 6, wherein modifying the virtual dentition comprises at least one of: adjusting a torque angle of the tooth, adjusting a shape of the tooth by adding material to the tooth or subtracting material from the tooth, or adjusting a guide tooth.

8. The method of claim 1, wherein performing the action comprises: outputting, by the computing device, for display, a graphical user interface indicative of at least one of the virtual dentition and a portion of the tangent vector.

9. The method of claim 1, wherein performing the action comprises: determining, by the computing device, one or more treatment plans for the patient based at least in part on the tangent vector.

10. The method of claim 1, wherein determining the tangent vector comprises: determining, by the computing device, an axis of rotation of the virtual mandibular arch, wherein the selected point defines a radius of the arc; and determining, by the computing device, the tangent vector as a tangent to the arc.

11. The method of claim 1, the method further comprising: determining, by the computing device, a plurality of axes of rotation, wherein each axis of rotation of the plurality of axes of rotation is associated with a motion of the virtual mandibular arch in a respective direction of a plurality of directions; and determining, by the computing device, a plurality of tangent vectors based on the plurality of axes of rotation, the plurality of tangent vectors each indicative of a respective direction of a plurality of directions of motion of the selected point; and determine, by the computing device, whether a tooth of the virtual dentition will interfere with a counter-bite tooth on an opposing arch based on at least one tangent vector of the plurality of tangent vectors.

12. The method of claim 11, wherein the selected point is associated with a wear facet on the tooth, and wherein performing the action comprises: identifying, by the computing device, at least one movement direction from a plurality of movement directions that caused the wear facet.

13. The method of claim 12, wherein identifying the at least one movement direction comprises: determining, by the computing device, a tangent vector of the plurality of tangent vectors that is parallel to a plane of the wear facet; and determining the at least one movement direction based on the tangent vector that is parallel to the plane of the wear facet.

14. The method of claim 1, wherein the tangent vector indicates movement of at least one of: a lateral excursion, a protrusive excursion, a retrusive excursion, or an opening excursion.

15. The method of claim 1, wherein performing the action comprises: determine, by the computing device, whether a root orientation of a tooth of the virtual dentition is correct for an axial load on the tooth.

16. A computing system comprising: at least one processor; and memory comprising instructions that, when executed by the at least one processor, cause the at least one processor to: receive data indicative of a virtual dentition of an oral cavity of a patient, the data indicative of a virtual dentition comprising data indicative of at least one of a virtual mandibular arch representing a mandibular arch of the patient or a virtual maxillary arch representing a maxillary arch of the patient; receive data indicative of a selected point on the virtual dentition of the oral cavity; determine, based on an axis of rotation of the virtual mandibular arch, a tangent vector indicative of a movement direction of the selected point, wherein the axis of rotation defines a center of a circular arc that defines a plane that is perpendicular to the axis of rotation; and perform an action based on the tangent vector to adjust the virtual dentition.

17. The computing system of claim 16, wherein execution of the instructions causes the at least one processor to perform the action that at least causes the at least one processor to determine, based on the tangent vector, whether an orientation of a tooth of the virtual dentition or a shape of the tooth is correct.

18. The computing system of claim 17, wherein execution of the instructions causes the at least one processor to determine whether the orientation or shape of the tooth is correct by determining whether a ray defined by the selected point and the tangent vector intersects a surface of the tooth.

19. The computing system of claim 18, wherein execution of the instructions causes the at least one processor to determine that the orientation of the tooth is incorrect in response to determining that the ray intersects the surface of the tooth.

20. A non-transitory computer-readable storage medium storing instructions that, when executed, cause at least one processor of a computing system to perform the method of any one of claims 1-15.

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