A method to automatically eliminate collisions between digital mesh objects and smoothly move mesh objects between spatial arrangements.

Abstract

This provides an automated method for eliminating collisions between digital mesh objects and smoothly moving digital mesh objects between different spatial arrangements. [Solution] Collisions are removed from a set of digital mesh objects using a perturbation method or a mesh deformation method. After collision removal, the digital mesh objects are output in a state where there are no collisions between them. The digital mesh objects can be moved between an initial state and a final state based on the movement constraints of the mesh objects and the interpolated state between the initial state and the final state. Based on the constraints and the interpolated state, the number of states for the movement of the set of digital mesh objects is determined collectively for the set or individually for each mesh object.

Description

Background Art

[0001] The purpose of the orthodontic treatment planning process is to create a set of effective states in which teeth can move between them in order to achieve a final setup that is orthodontically correct. Using those states, a clear tray aligner or other orthodontic appliance can then be designed. Constraint-based movement between states is the first step necessary in the planning process because it creates an approximate path that teeth will take between an initial setup and a final setup. Also, constraint-based movement between states can be used in an interactive software system by a dental technician to design a treatment plan, or used in a doctor's examination room to show a patient an approximation of tooth movement during treatment. However, subsequent refinement is likely to be necessary to remove collisions between teeth within the interpolated path. There is a need to automatically remove collisions between states and create a smooth movement path between states for orthodontic treatment planning or other purposes.

Summary of the Invention

[0002] A first method for automatically removing collisions between digital mesh objects includes receiving a set of digital mesh objects in a first state with one or more collisions between the digital mesh objects, removing the collisions using a perturbation method, and outputting a set of transformation equations that describe the movement of teeth between the first state and a second state, or the positions of the teeth in the second state. A second method for automatically removing collisions between digital mesh objects includes receiving a set of digital mesh objects in a first state with one or more collisions between the digital mesh objects, removing the collisions using a mesh deformation method, and outputting a set of digital mesh objects in a second state without collisions between the digital mesh objects.

[0003]

[0004] A method for moving digital mesh objects between spatial arrangements includes the steps of receiving an initial set of digital mesh objects and receiving a final state for that set of digital mesh objects. The method also includes the steps of identifying movement constraints between the digital mesh objects, estimating the number (n) of interpolated states of the digital mesh objects between the initial and final states based on those constraints, and creating n interpolated states for the movement of the set of digital mesh objects between the initial and final states.

[0005] The state of the digital mesh object can be used as a digital setup for dental treatment planning or orthodontic treatment planning. [Brief explanation of the drawing]

[0006] The accompanying drawings are incorporated herein and constitute part of this specification, illustrating the advantages and principles of the present invention together with the description. The drawings are as follows: [Figure 1] This is a diagram of system 10 for eliminating collisions between digital mesh objects and for smoothly moving digital mesh objects between spatial arrangements for dental treatment planning or orthodontic treatment planning. [Figure 2] This is a flowchart showing how to automatically eliminate collisions between mesh objects. [Figure 3] This is a diagram of the data model used by the genetic algorithm. [Figure 4] This figure shows an example of the initial setup, as well as the corresponding intermediate and final setups. [Figure 5] This is a flowchart of a method for iterative collision removal of mesh objects. [Figure 6] This diagram shows a colliding mesh object with multiple collision points. [Figure 7]This is a flowchart showing how to achieve tooth movement using a set of constraints on tooth movement. [Figure 8] This figure shows that by changing the interpolation between states of a single set of constraints, it is possible to incorporate multiple different sets of constraints. [Modes for carrying out the invention]

[0007] The embodiments include automated methods for eliminating collisions between digital mesh objects and for smoothly moving digital mesh objects between different spatial arrangements. These methods can be used to generate digital setups for use, for example, in dental treatment planning or orthodontic treatment planning. These methods can also be used with other collections of digital mesh objects in their other applications.

[0008] A method for automatically generating digital setups for orthodontic appliances is described in U.S. Provisional Patent Application No. 62 / 569081, filed on October 6, 2017, entitled "Automated Process for Intermediate Orthodontic Digital Setup Generation," which is incorporated herein by reference as being fully described.

[0009] Figure 1 shows a diagram of system 10 for eliminating collisions between digital mesh objects and for smoothly moving digital mesh objects between spatial arrangements for dental treatment planning or orthodontic treatment planning. System 10 includes a processor 20 that receives a digital 3D model (12) of a tooth from an intraoral 3D scan or a scan of a tooth mold, and in other embodiments, the system receives manual input from a user. System 10 may also include an electronic display device 16, such as a liquid crystal display (LCD) device, and an input device 18 that receives user commands or other information. Systems that generate digital 3D images or models based on a set of images from multiple viewpoints are disclosed in U.S. Patents 7,956,862 and 7,605,817, both of which are incorporated herein by reference as if they were fully described. These systems may use an intraoral scanner to obtain digital images from multiple views of a tooth or other intraoral structure, and process these digital images to generate a digital 3D model representing the scanned tooth and gum. System 10 may be implemented using, for example, a desktop, notebook, or tablet computer. System 10 may receive 3D scans locally or remotely over a network.

[0010] The 3D scans discussed herein are represented as triangular meshes. A triangular mesh is a common representation of a 3D surface and has two components. The first component, called the vertices of the mesh, is simply the coordinates of the 3D points reconstructed on the surface, i.e., the coordinates of the point cloud. The second component, the mesh faces, is an efficient way to encode the connections between points on an object and interpolate between discrete sample points on a continuous surface. Each face is a triangle defined by three vertices, and a surface can be obtained that can be represented as a set of small triangular face patches.

[0011] The methods and algorithms described herein can be implemented in software or firmware for execution by a processor, such as processor 20.

[0012] Automatic collision removal between mesh objects Methods described herein can be used to eliminate collisions between sets of digital mesh objects by either perturbing the objects in a direction that may eliminate collisions, or by deforming the shape of the mesh objects. The term "digital mesh object" includes mesh objects. A list of the methods described and a brief description of each method are shown in Tables 1 and 2 below.

[0013] [Table 1]

[0014] [Table 2]

[0015] Furthermore, this specification also describes interactive tools that can be used in setting up orthodontic treatment plans to automatically eliminate collisions between teeth using these methods.

[0016] The description of these methods is divided into two sections. In the first section, a set of intelligent perturbation functions that can be used to shift one or more of those mesh objects in order to remove collisions without changing the shape of the one or more mesh objects is presented. These functions can be applied to remove collisions between sets of teeth without changing the shape of the tooth mesh. In the second section, techniques that can be used to deform the shape of the mesh objects themselves to remove collisions without shifting the locations of those collisions are presented. This can be applied to remove collisions between teeth that are colliding erroneously due to scanner artifacts. Each approach may be required for different parts of the treatment planning process. For example, perturbation may be desirable when trying to find a collision-free trajectory between states, but mesh deformation may be desirable when collisions are caused by artifacts in the mesh that do not exist in the actual tooth anatomy.

[0017] Section 1: Methods for Automatically Removing Collisions Using Intelligent Perturbation Functions I. Directed Perturbation In this approach, a favorable direction in which the mesh or collection of mesh objects is perturbed is identified, and one or more of those objects are perturbed in this general direction. A flowchart of this approach is shown in Figure 2.

[0018] First, for each object, a favorable direction is identified, defined as a vector in three-dimensional space (Step 22). This information can be input by the user or calculated based on information such as a vector opposite to the intrusion between objects (Method A), a vector perpendicular to the intrusion between objects (Method B), or a vector of movement toward an ideal state with no or few collisions (Method C). In the next optional selection step, for each object, a vector with an angle of theta or less from the identified direction is randomly selected (Step 24). This optional selection step introduces an element of randomness to the technique, allowing the algorithm to search the space near the selected direction in search of the optimal solution. Next, the magnitude of the perturbation is identified for each object (Step 26). The magnitude(s) can be selected completely randomly, via user input, using some information that defines the amount of perturbation (e.g., intrusion depth), or as a scaling factor for the amount of perturbation. In the final step, the perturbation is applied to the mesh object by shifting the object(s)(s)(s) along their respective vectors by a specified magnitude(s)(s)(s)(s) (Step 28).

[0019] Method A: Calculate the direction (and depth) of entry between two objects. Aspects of this method are also mentioned in Section 2 of Method 1. First, principal component analysis (PCA) is used to fit the contact points between the two colliding objects to a plane. Other methods for plane fitting, such as support vector regression, can also be used. The direction of penetration is identified as a direction perpendicular to the plane (e.g., a vector associated with the smallest principal component), or alternatively, as the average of the vertex normal directions for all contact points. The depth of penetration can also be calculated by identifying the vertices that lie within the boundary formed by the contact points (see Section 2 of Method 1), and then calculating the maximum point-to-plane distance when the vertices are projected onto the plane along the direction of penetration. The sum of the maximum point-to-plane distances for the two colliding objects is the depth of penetration.

[0020] Method B: Calculate the direction perpendicular to the direction of entry between two objects. Directions perpendicular to the direction of entry may also be calculated by PCA, or by using the equation of the plane after calculating the plane. Specifically, the vectors associated with the two largest principal components are the two directions perpendicular to the direction of entry. More generally, the vectors perpendicular to the direction of entry lie on the plane, and any of those vectors can be selected as the perpendicular direction.

[0021] Method C: Calculate the direction toward the ideal state. If an ideal state is available with no collisions or only a few collisions, the perturbation direction vector of each object moving towards this ideal state can be calculated as follows:

number

[0022] II. Propagating Directional Perturbations In addition to the colliding object, neighboring objects may also be moved using the perturbation function described above. Perturbing non-collisioning objects near a colliding object has the advantage of creating space for the colliding object to move into without creating a new collision. The method for perturbing a colliding mesh object and its neighboring objects is the same as the method described above. First, a set of mesh objects in the local vicinity of the colliding object is identified. Next, one of the methods described above (method A, B, or C) is used to determine the direction of perturbation for each object. To minimize unnecessary movement, it may be desirable to set the magnitude of the perturbation for each object to a value less than or equal to the magnitude identified for the colliding object. One option to achieve this result is to scale the magnitude of the perturbation according to the distance between the colliding object and the neighboring objects, such that objects closer to the colliding object have a larger magnitude, while objects further away from the colliding object have a smaller magnitude.

[0023] III. Gradient Descent The effectiveness of each point in the trajectory is evaluated using a scoring function that penalizes tooth collisions. Whenever there are no collisions between teeth, this scoring function returns zero, and the score increases with collisions. Gradient descent finds the optimal tooth movement by perturbing the corresponding states to reduce the collision score.

[0024] Finding the optimal perturbation to reduce the score function is a complex nonlinear optimization problem. While there is no guarantee of finding a global solution, the deepest descent method can be used to find the optimal direction for perturbation states that reduce the collision score to a minimum.

[0025] Since calculating collision points between complex geometric shapes such as teeth cannot be expressed in a closed mathematical form, the gradient of the score function with respect to object movement needs to be numerically approximated. To compute this gradient approximation, each state can be perturbed multiple times so that the rate of change of the score for each state can be calculated. Using the rate of change of the score (i.e., the gradient of the objective function), the direction vector for ultimately moving the object is derived.

[0026] First, a subset of objects in the state is identified by selecting the colliding objects and adjacent objects. For each degree of freedom in each object's free vector (or each degree of freedom corresponding to translation), the change in the objective function is recorded by adding and subtracting a small delta to that degree of freedom. The resulting change vector is normalized and treated as an estimate of the direction of the objective function's gradient. To generate random perturbations of the state, the negative value of the gradient is multiplied by a scaling factor and added to the state's degree of freedom vector along with a small random component. The scaling factor is a random number from 0 to the maximum value estimated using the penetration depth of the state.

[0027] IV. Simultaneous Perturbation Probability Approximation (SPSA) An alternative method for approximating gradients is called Simultaneous Perturation Stochation Approximation (SPSA). To approximate the direction of the deepest descent using SPSA, a random direction can be selected to perturb the current state, and the rate of change of the score along that random direction can be calculated. The main advantage of the SPSA method is that only two function calls of the score function are sufficient to have an approximation of the perturbation direction. In comparison, numerical gradient approximation requires 2n function calls, where n is the dimension of the state vector. If the number of score function calls is computationally expensive, SPSA can result in faster convergence times because a rough approximation of the direction of the deepest descent allows for faster optimization towards a better region. Furthermore, by extending SPSA with momentum techniques, it is possible to track the history of the estimated direction to obtain more accurate deepest descent results. The following sections describe the SPSA method in more detail.

[0028] Approximation of the steepest descent direction using SPSA: Let f() be the scoring function, and x = [x1, x2, ... x n If we consider ] as the current state, then the random direction Δ = [Δ1, Δ2, ... Δ n Using ] and a fixed perturbation size c, the SPSA of the gradient of f(x) can be calculated, which is expressed by g(x):

number

[0029] To avoid numerical instability in the g(x) calculation, each element of Δ follows a uniform Bernoulli distribution.

number

[0030] Gradient descent optimization using SPSA: If the initial state is represented by x(0), the approximate value of the steepest descent method using the SPSA method is g(x(0)). Therefore, the intelligent perturbation to reduce the score can be calculated by the following equation. x(1) = x(0) - μg(x(0)), In the formula, μ is the step size of the steepest descent. The local minimum of the score function can be found using the successive steepest descent update method. Generally, at any step x(i), the updated state x(i+1) can be calculated as follows: x(i+1)=x(t)-μ i g(x(i)), μ in the formula i , is the step size in the i-th iteration. The step size μ during the successive steepest descent. i Making μ smaller results in a more stable solution, for example, μ i =μ / n is obtained, where μ is the initial step size.

[0031] Aggregation of SPSA steepest descent history using the momentum method: SPSA steepest descent encodes the rate of change of the score function in a random direction at each time point, which can result in very noisy paths towards local minima. Momentum is a common method for smoothing the steepest descent direction by preserving the history of more recent steepest descent directions. The momentum direction is a weighted sum of previously calculated directions, with older directions receiving lower weights compared to more recent ones. The following equality is calculated using the momentum method for the i-th iteration.

number

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[0032] V-Grid Search Perturbation This method performs perturbation by using the approach evaluation unit to identify the mesh object that needs to be perturbed first, as previously described in the target perturbation method. Furthermore, neighboring objects can also be added to this list of objects that may be perturbed.

[0033] The perturbation itself is performed by sequentially changing the state of a set of objects in order to move the objects toward a higher scoring state. For each object, a spatial grid of possible locations is constructed around the object's position with a given spatial resolution (e.g., 1 mm). Optionally, the search can be accelerated by excluding some locations using an entry evaluation unit. The collision score can then be evaluated by moving each object to one of its own grid locations. If there are three objects and nine locations for each object, there are 729 configurations to evaluate. The best scoring configuration is selected, and this process can then be repeated over several iterations, so that it is computationally acceptable to reduce the spatial resolution of the grid by a given percentage, e.g., 0.5 each time. The spatial grid can be constructed in Cartesian coordinates or (in the case of tooth data) dental arch coordinates. Table 3 provides exemplary pseudocode for implementing this method.

[0034] [Table 3]

[0035] VI. Mode-based behavioral perturbations Some perturbation methods can derive higher-order information about the placement of mesh objects in order to select a mode of behavior. For example, if a perturbation function detects that an object is colliding with both neighboring objects, it can attempt to create space by spreading those objects outward through movement perpendicular to the direction of entry. While these perturbation methods may not immediately produce states that improve the value of the objective function, such states may be important for generating paths around the problem domain.

[0036] VII. Genetic Algorithms A genetic algorithm (GA) for resolving conflicts for each state (set of teeth) is described herein. Figure 3 is a diagram of the data model used by the GA. The GA starts over from the beginning for each state 34. The GA evolves a population of N chromosomes 36 (solutions) over many iterations (generations), maintaining chromosomes with high fitness (called parents) and removing chromosomes with low fitness (inferior). Parents replicate themselves and, through mutation and crossover operations, produce offspring that pass on successful attributes to the next generation. Evolution proceeds until a criterion is met. In this case, the method terminates the evolution of an intermediate setup when it finds a state that resolves all conflicts in that intermediate setup.

[0037] Table 4 contains exemplary pseudocode for implementing GA using the following definitions: A chromosome is a vector of tuples 38, one for each tooth 40, where each tuple 38 consists of a position modifier 42 and a direction modifier 44.

[0038] [Table 4]

[0039] Simple example Figure 4 shows a simple example, illustrating an initial setup 46 (malocclusion) for a simplified dental arch consisting of four teeth, an example of one intermediate setup 48, and a final setup 50. To resolve collisions, the algorithm runs on this intermediate state (see the two intermediate ellipses in setup 48). In this case, the algorithm may create a population of N=100 chromosomes, where each chromosome contains a vector of tuples, where each tuple contains small displacements and small directional changes (e.g., <0.04 mm, 0.09 mm, 0.01 mm>; 1.5 degrees along a given axis). The algorithm repeats the following over the required number of generations to generate chromosomes without collisions: A) measure the fitness of each chromosome (e.g., as collision count), B) shuffle the population into groups of four, flag two lowest fitness chromosomes to remove, and C) replace the crossovered and mutated inferior chromosomes with parental copies. Iterate until complete. Ultimately, over several generations, the teeth in the intermediate state were moved to prevent collisions. Then, the process restarts, using the next intermediate setup as input.

[0040] An interactive tool for orthodontic treatment planning using perturbation methods. In addition to applying algorithms that automatically eliminate collisions in a series of oral states, methods for perturbing teeth toward more effective states have many potential applications in interactive tools, including the interactive generation of intermediate and final setups for orthodontic treatment planning, and for dental treatment planning, including the planning of optimal implant placement.

[0041] When adjusting the specific placement of teeth for orthodontic treatment, dental technicians may strive to achieve certain quality standards, such as aesthetic appearance, or instructions from the orthodontist. However, it can be difficult to manually manipulate teeth on a small scale to achieve these goals without causing collisions between them. Even when treatment planning software prevents tooth collisions, additional work may be required to manipulate the teeth (either one at a time or in groups) to the desired position without causing collisions.

[0042] An interactive tool that allows for the application of perturbation functions to reduce or eliminate minor collisions enables dental technicians to focus more on other objectives than collisions. A technician can place a tooth in a state where it satisfies its higher-order objectives but has collisions, and then use this tool to find a very similar state without collisions.

[0043] Many of the perturbation functions described above depend on a scaling factor that limits the distance from the original state to the perturbed state. These scaling factors can be linked to sliders or other control units in a graphical user interface, allowing the dental technician to control how extreme the tooth movement becomes when the collision is resolved.

[0044] Embodiments of the present invention can also be applied to dental settings to enable automated or semi-automated planning of the placement of crowns, bridges, or implants. In this application, a dentist can roughly position implants in a digital dental arch format to achieve general aesthetic goals. Then, using an intelligent perturbation function, both collisions between teeth in one dental arch and collisions between teeth in opposing dental arches can be automatically minimized or eliminated. Mesh deformation (described in the next section) can also be applied to the implant to design an implant that fits correctly in the patient's mouth. As an alternative to collisions, another score, such as the depth of entry or the number of collision points, can also be used.

[0045] Section 2: How to automatically remove collisions using mesh deformation Various parts of the digital orthodontic workflow may generate effective tooth placements that include collisions. There are two main causes of these collisions. Firstly, teeth in a malocclusion state do not contain collisions, but related geometric shapes (such as tooth roots) that do contain collisions may be automatically generated. Secondly, dental technicians may intentionally create tooth placements with small collisions between teeth or between tooth roots. The theoretical interpretation of these is that these collisions should be ignored because they are between parts of the mesh that may represent scanning problems or segmentation errors.

[0046] In various processes for optimizing tooth placement, effectiveness is evaluated by checking for collisions between teeth, so such collisions (especially in the final setup) are problematic. However, collisions can be eliminated by modifying the geometric shape using automated methods. These methods can also be applied interactively, allowing the dental technician to ensure that the changes to the geometric shape are not too extreme or that they are applied only to areas or objects selected by the technician.

[0047] Method 1: Automatic removal of inter-mesh collisions by local mesh deformation An iterative collision removal technique is described herein, which involves identifying the parts of a colliding mesh object and shifting them until the collision is removed.

[0048] The process for iterative collision removal is shown in the flowchart of Figure 5. First, the contact points between two colliding objects are identified (step 52). Colliding objects may have multiple collision points, as shown in Figure 6, which illustrates collision points 64. Therefore, in the next step, minimal linkage clustering is used to identify the contact points associated with each collision point (step 54). For each collision point, PCA is used to fit the contact points to a plane (step 56). The entry direction can be defined as either a vector perpendicular to the fitted plane (i.e., a vector associated with the smallest principal component) or the average of the vertex normal directions at the contact point (step 58). Two methods are possible to identify colliding mesh vertices (step 60). In the first method, the mesh objects are cut along the plane identified by PCA, and only the submeshes closest to each other are retained. Then, the vertices of both submeshes are projected onto the plane, and vertices within the convex hull of the contact point are identified as colliding. In the second method, vertices of opposing meshes that are within a short distance d from each other when projected onto the plane are identified as colliding. Next, the colliding vertices on each mesh object are shifted by a small amount d in the opposite direction of the collision (step 62). This process is repeated iteratively until there is no more collision between the two objects.

[0049] Method 2: Global Mesh Reduction Table 5 provides example pseudocode for implementing a global mesh reduction method.

[0050] [Table 5]

[0051] The advantage of this method is that it preserves the overall shape of the modified mesh and avoids introducing sharp edges to previously smooth areas. However, it can introduce a significant amount of error if large reductions are required to eliminate collisions.

[0052] This method may be better suited to automatically generated geometric shapes, such as tooth roots, where it is necessary to maintain a smooth surface while avoiding collisions with each other or with the crown mesh.

[0053] Smooth movement of mesh objects between spatial arrangements A method for smoothly moving a set of digital 3D mesh objects between two spatial arrangements is described herein. This method incorporates movement constraints for each object's movement per state, allowing multiple objects to be moved at different speeds according to these constraints. In orthodontic treatment planning processes, this constraint-based method can be used to model tooth movement between states according to the amount of force applied to each tooth.

[0054] In orthodontic treatment planning, it is necessary to move the teeth from one stage to the next until the final setup is achieved. The basic method for achieving this goal is to move the teeth between stages using linear interpolation. However, basic interpolation assumes that all teeth move at a uniform speed, which is not the case. Rather, the amount of movement of each tooth is based on the amount of force applied to that tooth (determined by the treatment instrument) and the anatomical structure (tooth shape, root length, jaw thickness, etc.).

[0055] To achieve realistic tooth movement, one approach is to use a set of constraints on tooth movement, as shown in the flowchart in Figure 7, to reflect the amount of achievable movement per tooth.

[0056] First, identify the movement constraints for each tooth (step 66). These constraints may be manually provided by the clinician, established heuristically, or calculated using biomechanical modeling. The constraints may also be communicated by other modalities such as radiography or computed tomography (CT), which can be used to determine the root shape, root length, and jaw thickness. This information is then combined with the treatment appliance information to determine the constraints on tooth movement. Once the constraints are established, estimate the total number of interpolated states by subdividing the entire tooth movement by the constraints (step 68). To subdivide with a higher resolution than the constraints, the constraints may be multiplied by a scale factor. Table 6 provides exemplary pseudocode for implementing steps 66 and 68.

[0057] [Table 6]

[0058] Tooth movement can be subdivided into n states using two methods. In the first method ("simultaneous completion"), tooth movement is planned so that all teeth complete their movement simultaneously (step 70). This means that teeth with the same constraints but different total movement amounts move at different speeds so that they complete their movement at the same time. Using the simultaneous completion method, patient discomfort during treatment can be minimized. In the second method ("fast completion"), tooth movement is planned so that each tooth completes its movement at the same speed as allowed by the constraints (step 72). This means that teeth with the same constraints but different total movement amounts required move at the same speed and complete their movement at different times. Using the fast completion method, the aesthetic appearance during treatment can be improved more quickly.

[0059] Simultaneous completion: The translation of the teeth is subdivided into n states by equally distributing the total translation amount across states. The rotation is subdivided into n states using quaternion spherical linear interpolation (SLERP). SLERP has several advantages over linear interpolation, including the guarantee of the shortest path between two angles and the fact that the object's velocity remains constant during rotation.

[0060] Fast turnaround: The number of tooth-specific states, ni, is calculated for each tooth. For each tooth, the tooth's translation is subdivided into the number of states, ni, by equally dividing the total translation amount among the states. The rotation is subdivided into the number of states, ni, using SLERP. Then, the interpolation for each tooth is zero-padded so that the total number of states becomes n.

[0061] Enabling more orthodontists to control and / or enable hybrid treatment options. By controlling the constraints (and thus the resolution) in the interpolation parameters and / or the stepped thresholds, either coarse or fine orthodontic correction can be achieved. These constraints can be defined by the amount of control the orthodontist desires to have in the treatment process. High resolution (small constraints) allows the orthodontist to control and monitor the treatment more as it progresses, because higher resolution leads to finer orthodontic correction, which may result in more visits to the orthodontic clinic and smaller, more precise movements by the clear tray aligner (CTA). Low resolution (large constraints) results in less control, which may be desired for less complex cases and to keep costs low. This variety of options can also lead to a hybrid treatment process. During phases of larger movements, traditional brackets and wires may be involved, resulting in a stage where the CTA can take over.

[0062] The method described above can be adjusted to account for forces that change throughout the treatment process, as shown in Figure 8, and allows for treatment planning using multiple sets of different appliances (e.g., brackets and wires, followed by clear tray aligners). To change the forces, first, an intermediate state is defined in which the treatment modality will be switched. Next, constraints are defined on tooth movement from the initial state to the intermediate state (c1), and from the intermediate state to the final state (c2), and interpolation is performed.

[0063] Figure 8 shows that, for example, changes in the corresponding therapeutic device can alter the interpolation between states of a single set of constraints 74, thereby incorporating multiple different sets of constraints 76.

[0064] This process can also be applied to CTAs made from various materials, each with different inherent forces and costs. This allows orthodontists to communicate a variety of treatment options to patients based on cost (materials + time cost + visits), treatment duration, aesthetics (CTA duration), and other factors.

[0065] Note (Note 1) A computer implementation method for automatically eliminating collisions between digital mesh objects, The steps include receiving a set of digital mesh objects in a first state, which involves one or more collisions between the digital mesh objects, The steps include eliminating the collision using a perturbation method, The process includes the step of outputting a set of transformation formulas that describe the movement of teeth between the first state and the second state, or the position of teeth in the second state, The movement or position of the teeth is represented by the digital mesh object. method. (Note 2) The removal step is the method described in Appendix 1, which includes using a directional perturbation method. (Note 3) The method according to Appendix 1, wherein the removal step includes using a propagating directional perturbation method. (Note 4) The removal step is the method described in Appendix 1, which includes using a gradient descent method. (Note 5) The method according to Appendix 1, wherein the removal step includes using a simultaneous perturbation probability approximation method. (Note 6) The method described in Appendix 1, wherein the removal step includes using a grid search method. (Note 7) The method according to Appendix 1, wherein the removal step includes using a behavior mode-based perturbation method. (Note 8) The method described in Appendix 1, wherein the removal step includes using a genetic algorithm. (Note 9) The method according to Appendix 1, wherein the output step includes outputting the set of digital mesh objects in the second state as a digital setup for a dental treatment plan or an orthodontic treatment plan. (Note 10) The method according to Appendix 1, wherein the output step includes outputting a set of conversion formulas necessary to move the teeth from the first state to the second state. (Note 11) The method according to Appendix 1, wherein the output step includes outputting a set of the digital mesh objects in the second state without collisions between the digital mesh objects. (Note 12) A computer implementation method for automatically eliminating collisions between digital mesh objects, The steps include receiving a set of digital mesh objects in a first state, which involves one or more collisions between the digital mesh objects, The steps include removing the collision using a mesh deformation method, The steps include outputting a set of digital mesh objects in a second state where there are no collisions between the digital mesh objects, Methods that include... (Note 13) The method according to Appendix 12, wherein the removal step includes using a local mesh deformation method at the impact surface. (Note 14) The removal step is the method described in Appendix 12, which includes using a global mesh reduction method. (Note 15) The method according to Appendix 12, wherein the output step includes outputting the set of digital mesh objects in the second state as a digital setup for a dental treatment plan or orthodontic treatment plan. (Note 16) A computer implementation method for moving digital mesh objects between spatial arrangements, The steps include receiving a set of initial digital mesh objects, A step of receiving the final state for the set of digital mesh objects, The steps include identifying movement constraints between the digital mesh objects, Based on the aforementioned constraints, the steps include: estimating the number n of interpolated states of the digital mesh object between the initial state and the final state; The steps include creating n interpolated states for the movement of the set of digital mesh objects between the initial state and the final state, Methods that include... (Note 17) The method according to Appendix 16, wherein the step of creating the digital mesh objects comprises equally dividing the translation of the set of digital mesh objects among the interpolated states. (Note 18) The method according to Appendix 16, wherein the step of creating the set of digital mesh objects is further subdivided into the interpolated states using a quaternion spherical linear interpolation method. (Note 19) The method according to Appendix 16, wherein the step of creating the digital mesh object includes dividing each translation or rotation amount of the digital mesh object according to the constraints of translation or rotation for each state. (Note 20) The method according to Appendix 16, further comprising outputting the interpolated state as a digital setup for a dental treatment plan or orthodontic treatment plan. (Note 21) The aforementioned identifying step is the method described in Appendix 16, which includes receiving constraints entered by the user. (Note 22) The aforementioned movement constraints vary between states, as described in Appendix 16. (Note 23) The steps described above are according to the method described in Appendix 16, which reflects treatment using multiple orthotic devices with different mobility constraints for each condition.

Claims

1. A computer operation method for automatically eliminating collisions between digital mesh objects, The steps include: the computer receiving a set of digital mesh objects in a first state, which involves one or more collisions between the digital mesh objects; A step of determining one or more objects that are in a collision state, A step of determining one or more objects in the vicinity of one or more objects that are not in a collision state but are in a collision state, The steps include: performing a perturbation method on one or more neighboring objects with a first perturbation magnitude of one or more; The steps include: performing a perturbation method with a second perturbation magnitude on one or more objects in the aforementioned collision state; The computer outputs a set of conversion formulas that describe the movement of teeth between the first state and the second state, or the position of teeth in the second state. Includes, The movement or position of the teeth is represented by the digital mesh object. method.

2. The method according to claim 1, wherein the output step includes outputting the set of digital mesh objects in the second state as a digital setup for a dental treatment plan or an orthodontic treatment plan.

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