Abstract: A method for generating digital setups for an orthodontic treatment path. The method includes receiving a digital 3D model of teeth, performing interproximal reduction (IPR) on the model and, after performing the IPR, generating an initial treatment path with stages including an initial setup, a final setup, and a plurality of intermediate setups. The method also includes computing IPR accessibility for each tooth at each stage of the initial treatment path, applying IPR throughout the initial treatment path based upon the computed IPR accessibility, and dividing the initial treatment path into steps of feasible motion of the teeth resulting in a final treatment path with setups corresponding with the steps. The setups can be used to make orthodontic appliances, such as clear tray aligners, for each stage of the treatment path.

Abstract: An article includes a substrate with a physical surface, and a hierarchy of parent and child optical element sets embodied on the physical surface, such that a first encoded value represented by the parent optical element set is based at least in part on the visual appearance of a particular optical element in the child optical element set, and a second, different encoded value represented by the particular parent optical element is based at least in part on the visual appearance, and the second encoded value not being decodable from a distance greater than a threshold distance, the first encoded value being decodable from the distance greater than the threshold distance.

Abstract: In some examples, an article includes a substrate that having a physical surface; a multi-dimensional machine-readable code embodied on the physical surface, wherein the multi-dimensional machine-readable optical code comprises a static data (SD) optical element set and a dynamic lookup data (DLD) optical element set, each set embodied on the physical surface, wherein the DLD optical element set encodes a look-up value that references dynamically changeable data, wherein the SD optical element set encodes static data that does not reference other data, wherein the DLD optical element set is not decodable at the distance greater than the threshold distance.

Abstract: In some examples, an article includes a substrate, the substrate including a physical surface; a hierarchy of parent and child optical element sets embodied on the physical surface, wherein a first encoded value represented by the parent optical element set is based at least in part on a visual appearance of a particular optical element in the child optical element set, and a second encoded value represented by the particular optical element is based at least in part on the visual appearance, the first and second encoded values being different, and the second encoded value not being decodable from a distance greater than a threshold distance, the first encoded value being decodable from the distance greater than the threshold distance.

Abstract: In some examples, an article includes a substrate and a plurality of optical element sets embodied on the substrate, wherein each optical element set includes a plurality of optical elements, wherein each respective optical element represents an encoded value in a set of encoded values, wherein the set of encoded values are differentiable based on visual differentiability of the respective optical elements, wherein each respective optical element set represents at least a portion of a message or error correction data to decode the message if one or more of the plurality of optical element sets are visually occluded, and wherein the optical element sets for the message and error correction data are spatially configured at the physical surface in a matrix such that the message is decodable from the substrate without optical elements positioned within at least one complete edge of the matrix that is visually occluded.

Abstract: Methods for recognizing or identifying tooth types using digital 3D models of teeth. The methods include receiving a segmented digital 3D model of teeth and selecting a digital 3D model of a tooth from the segmented digital 3D model. An aggregation of the plurality of distinct features of the tooth is computed to generate a single feature describing the digital 3D model of the tooth. A type of the tooth is identified based upon the aggregation, which can include comparing the aggregation with features corresponding with known tooth types. The methods also include identifying a type of tooth, without segmenting it from an arch, based upon tooth widths and a location of the tooth within the arch.

Abstract: Methods for recognizing or identifying tooth types using digital 3D models of teeth. The methods include receiving a segmented digital 3D model of teeth and selecting a digital 3D model of a tooth from the segmented digital 3D model. An aggregation of the plurality of distinct features of the tooth is computed to generate a single feature describing the digital 3D model of the tooth. A type of the tooth is identified based upon the aggregation, which can include comparing the aggregation with features corresponding with known tooth types. The methods also include identifying a type of tooth, without segmenting it from an arch, based upon tooth widths and a location of the tooth within the arch.