Abstract: A computer-implemented method of processing a digital dental impression includes determining one or more first digital surface regions visible from a first side of the digital dental impression along an occlusion axis and one or more second digital surface regions visible from a second side of the digital dental impression along the occlusion axis, segmenting the digital dental impression into one or more digital segments and determining the one or more digital segments as a first digital segment or a second digital segment based on the majority of digital surface regions in the one or more digital segments.

Abstract: An oral appliance (100) comprising a sensing arrangement (101) disposed in proximity to at least one part of a facial muscle complex of a user. A method of controlling the oral appliance (100) comprising sensing, with the sensing arrangement (101), the at least one part of the facial muscle complex being brought towards the sensing arrangement; and in response to sensing the at least one part of the facial muscle complex being brought towards the sensing arrangement (101), controlling the oral appliance (100) to perform an action. An external processing unit (200) is arranged to interact with the oral appliance (100) in response to the oral appliance (100) performing the action.

Abstract: A dental appliance including a dielectric substrate with one or more electric areas having one or more integrated circuits, one or more electric lines, and optionally one or more shielding lines. The dental appliance further includes one or more ground areas including one or more ground pads, one or more sensing areas including one or more sensing pads, and optionally one or more shielding pads. The dental appliance is configured to monitor dental contact, dental forces, and/or for detecting teeth clenching and/or grinding.

Abstract: The present disclosure includes method, system, apparatus, and indicator embodiments. One apparatus includes an appliance for placement over one or more teeth and a release agent receptacle including an outer portion provided on appliance surface, an inner portion provided within the outer portion, and one or more apertures formed in the outer portion.

Abstract: A bite registration device including a scan post configured to attach to a dental implant, a bite pillar configured to be attached at a coronal end of the scan post, and a mechanism for attaching the bite pillar to the scan post, wherein the mechanism enables adjustment of a distance from a coronal end of the bite pillar to an apical end of the scan post. A bite pillar including a wide coronal end and an elongate shape configured to attach to an object in a mouth of a patient. A scan post including a screw thread for attaching a bite pillar thereto. A reference pillar configured as an elongate shape to be attached at a first end to an object in a mouth of a patient. Related apparatus and methods are also described.

Abstract: Disclosed is a method for determining the relative arrangement of patient's jaws in a bite position when the patient's occlusion is not defined by natural teeth alone, where the method includes a step of obtaining a digital 3D representation including both surface data relating to dental tissue in one of the patient's jaws and surface data relating to a scan appliance arranged in relation to the jaw, where the scan appliance is configured for at least partly defining the patient's occlusion.

Abstract: A steerable illumination fixtures include an emitting source and a refractive optical system that steers an emitted beam by relative translation of the emitting source against the optical system. The light emitting source may be placed along an optical axis of one or more lenses to produce an output beam along that axis, or translated in-plane (orthogonal to the optical axis) relative to the lenses to produce a steered beam. The optical system may include refractive lenses and in some embodiments mixing channels and/or one or more baffles with apertures. The design is typically optimized to produce a round, uniform beam that retains approximately the same power level and beam width as it is steered. It is beneficial, but not required, that a second lens have a diameter equal to or larger than a first lens. The lenses may be configured so that the effective focal plane of the two lenses together is located approximately at the plane of the light emitting source.

Abstract: An interconnect structure for a semiconductor device includes a plurality of unit cells. Each unit cell is formed of interconnected conducting segments. The plurality of unit cells forms a conducting lattice.

Abstract: A safety device for monitoring a technical installation with a pressure-sensitive sensor. The pressure sensitive sensor having a plurality of first and second electrodes, wherein each first electrode overlaps each second electrode in an associated coupling site. Furthermore, each first electrode is spaced apart from the associated second electrode in the associated coupling site by a pressure sensitive material. Upon application of a force at the coupling site, an electrical resistance between the associated first and second electrode changes. A measuring circuitry coupled to said plurality of first and second electrodes successively determines the electrical resistance at associated coupling sites. For determining the electrical resistance at a coupling site via the associated first and second electrode, the measuring circuitry connects the further first and second electrodes to a terminal for receiving a defined potential to enable isolated measurement of the electrical resistance at the coupling site.

Abstract: Technologies for merging three-dimensional models of dental impressions include a computing device that generates multiple three-dimensional models that are each indicative of a dental impression of a user's dental arch. The models may be generated by scanning the dental impressions. The computing device determines whether a model is indicative of the complete anatomy of the user's arch and, if not, merges multiple models with a merge strategy to generate a merged model. The models may be merged by aligning geometry of the models, selecting geometry from one of the models using the merge strategy, and generating the merged model that includes the selected geometry. The merge strategy may include selecting from the model associated with the dental impression that includes the most detail of the user's anatomy or selecting from the model with the greatest depth.

Abstract: A steerable illumination fixtures include an emitting source and a refractive optical system that steers an emitted beam by relative translation of the emitting source against the optical system. The light emitting source may be placed along an optical axis of one or more lenses to produce an output beam along that axis, or translated in-plane (orthogonal to the optical axis) relative to the lenses to produce a steered beam. The optical system may include refractive lenses and in some embodiments mixing channels and/or one or more baffles with apertures. The design is typically optimized to produce a round, uniform beam that retains approximately the same power level and beam width as it is steered. It is beneficial, but not required, that a second lens have a diameter equal to or larger than a first lens. The lenses may be configured so that the effective focal plane of the two lenses together is located approximately at the plane of the light emitting source.

Abstract: A method and system are provided for providing patient data useful for dental procedures, including scanning a dental structure of a patient when coupled to a geometric structure to provide a virtual model representative of the coupling and the dental structure, and relating the virtual model to a body reference of the patient.

Abstract: A method for taking an impression for producing a dental prosthesis involves: A) generating an impression of regions of the upper jaw and lower jaw of a patient using an at least two-part tray, whereby the tray is inserted into the oral cavity of the patient; B) fixing the at least two tray parts to each other or against each other; C) determining the position and orientation of the at least two tray parts with respect to each other; and D) taking the tray parts out of the oral cavity of the patient. Also disclosed is the tray for implementing the method, whereby at least one marking is arranged on the surface of each tray part, and a device for intra-oral determination of the orientation and position of the marking and, thus, the at least two tray parts, is provided, whereby the device comprises a computer and a recording facility.

Abstract: A method of evaluating the quality of a surface on a component comprises the steps of (a) contacting a surface of a component with a media and imprinting qualities of the surface with the media; and (b) evaluating the imprint to determine the quality of the surface of the component.

Abstract: A dental method and associated apparatus is disclosed in which a navigation body, comprising a plurality of navigation elements, is scanned using a scanner. Relative locations of the navigation elements are determined and, based on the relative locations, a scanner coordinate system is determined. A dental model is also scanned using the scanner to obtain three-dimensional virtual image data of the dental model and the scanner coordinate system is associated with the image data. A three-dimensional virtual image of the dental model is positioned, based on the three-dimensional virtual image data, within a three-dimensional virtual scene.

Abstract: Various examples are provided for a smart mouth guard for diagnosis, quantification, and/or management of e.g., bruxism. In one example, among others, a diagnostic mouth guard includes a plurality of pressure sensors and processing circuitry configured to provide pressure sensor data to an external processing unit when located in an oral cavity. The diagnostic mouth guard may also include temperature, pH and/or inertia sensors. In another example, a system includes the diagnostic mouth guard and the external processing unit such as, e.g., a smart phone, table or computer. The diagnostic mouth guard can communicate with the external processing unit over a wireless channel.

Abstract: An information processing device (104) performs integration processing for each intersection point for raw data outputted from an occlusal force detecting device having a sensor sheet (102) which uses an organic piezoelectric film (201), to create occlusal force data, wherein the raw data includes address information of each intersection point and data obtained based on a signal indicating a change in occlusion force.

Abstract: The present disclosure includes method, system, apparatus, and indicator embodiments. One apparatus includes an appliance for placement over one or more teeth and a release agent receptacle including an outer portion provided on appliance surface, an inner portion provided within the outer portion, and one or more apertures formed in the outer portion.

Abstract: Technologies for merging three-dimensional models of dental impressions include a computing device that generates multiple three-dimensional models that are each indicative of a dental impression of a user's dental arch. The models may be generated by scanning the dental impressions. The computing device determines whether a model is indicative of the complete anatomy of the user's arch and, if not, merges multiple models with a merge strategy to generate a merged model. The models may be merged by aligning geometry of the models, selecting geometry from one of the models using the merge strategy, and generating the merged model that includes the selected geometry. The merge strategy may include selecting from the model associated with the dental impression that includes the most detail of the user's anatomy or selecting from the model with the greatest depth.

Abstract: The invention could be a process for creating a dental anatomical representation comprising the following steps, seating radiopaque elastomer material between an upper jaw and a lower jaw of a mouth of a patient, the patient then fully biting down upon the radiopaque elastomer material to form the radiopaque elastomer material into a physical record of at least a portion of each of the two jaws and each jaw's position relative to the other jaw; taking a first scan of the patient's mouth with the formed radiopaque elastomer material in place between the jaws; and creating a virtual representation of the formed radiopaque elastomer material from data presented in the first scan, then using the virtual representation to align and correlate data obtained from the first scan and any other scans of a patient's anatomy.

Abstract: Supplemental reference surface devices are provided for use in three-dimensional modeling of intra-oral scenes using identifiable positional characteristics from structured illumination or other techniques. Reference surface devices having at least one substantially plane smooth non-polished face are disclosed for locating the positions of intra-oral features, and for stitching together separate 3D tiles according to the identifiable positional characteristics. Reference can be attached to an intra-oral feature in or adjacent to the imaged intra-oral scene. Disclosed are reference surface devices having orientation and position indicia, as well as reference surface devices having a multiplicity of faces distributed in spatial position and angular orientation to facilitate correlation of 2D images obtained by imaging systems in different positions.

Abstract: An electronic 3D model of at least a portion of a maxillary arch of a patient is displayed. Inputs indicating a peak of a mesiobuccal cusp of a maxillary first molar are received for both the patient's right and left sides. In addition, an electronic 3D model of at least a portion of a mandibular arch of a patient is displayed. Inputs indicating relevant points on the mandibular first molar are received for both the patient's right and left sides. Side scores are generated for the patient's right and left sides based on the indicated points. A final occlusion score for the patient is displayed. The final occlusion score is based on the side score for the right side and the side score for the left side.

Abstract: An apparatus and method for creating dental prosthetics is provided. The apparatus includes a base, an ear mount portion for making contact with a patient's head such that the patient's temporomandibular joints are maintained in a fixed level position relative to the base, a chin mount portion for making contact with the patient's chin and nose bridge such that the chin mount portion maintains the patient's head in a perpendicular orientation relative to the base, a bite fork portion including a bite fork which may be inserted into the patient's mouth for the purpose of obtaining the patient's bite registration information, and a camera mount portion including a camera oriented toward the patient's face.

Abstract: An anti-obstructive airway dental orthotic is described. The orthotic includes a maxillary retainer and a mandibular retainer releasably attaching to a plurality of teeth of a wearer. The retainers are attached by at least one strut, either variable in length or of a plurality of lengths, which exert a forward force on the lower jaw, tending to advance the mandible relative to the maxilla. This advancement of the lower jaw promotes a less obstructed airway in the wearer, while fenestrations in the retainers may allow for greater comfort and tongue movement.

Abstract: An intra-oral mandibular advancement appliance to be inserted in the mouth of a patient so as to maintain an open airway to the patient's throat and thereby improve breathing during sleep. The mandibular advancement appliance has particular application for use by those wishing to reduce the effects of snoring and/or sleep apnea. The appliance includes an upper tray assembly against which is seated the patient's teeth carried by his upper jaw and a lower tray assembly against which the patient's teeth carried by his lower jaw are seated. The lower tray assembly is mated to and slidably adjustable by the patient relative to the upper tray assembly. By virtue of the foregoing, the position of the patient's lower jaw can be selectively and continuously moved forward with respect to the position of the upper jaw to prevent an occlusion of the airway as the patient's condition changes over time.

Abstract: A system and method for modeling bite function. A top pantograph is fixed to a patient via clutches to the top teeth of the patient, a bottom pantograph is fixed to a patient via clutches to the bottom teeth of the patient and the actual bite of the patient is optically monitored by monitoring the relation of the top pantograph to the bottom pantograph during a bite cycle and storing a hinge axis. Data is stored relating to the actual bite and the top teeth are scanned to create a top teeth model while the bottom teeth are scanned to create a bottom teeth model. A digital representation of the top pantograph is digitally fitted to the top teeth, a digital representation of the bottom pantograph bottom pantograph is digitally fitted to the bottom teeth, and the relationship of the top teeth model and the bottom teeth model to the hinge axis is recorded.

Abstract: The invention concerns methods and a device for the determination of the centric position of a human set of teeth with improved precision. This is needed for the adjustment of an articulator in the production of dentures. For this purpose a plurality of successive bite movements or displacement movements of the lower jaw are recorded in form of electronic signal data and evaluated for the determination of the centric position.

Abstract: A method for generating a radiologic three-dimensional digital volume tomography image of a patient's body part includes fixing a marker support to the patient's body part. The marker support is provided with a non-radioopaque support body in which a plurality of radioopaque marker elements are affixed. A nominal size S and/or a nominal distance D of the radioopaque marker elements to each other is known. The body part is image recorded with a digital volume tomography device so as to generate a three-dimensional raw image of the patient's body part. A size S? and/or a distance D? of the radioopaque marker elements in the three-dimensional raw image is measured. An aberration value is generated by comparing the size S? and/or the distance D? with the respective nominal size S and/or the nominal distance D of the radiopaque marker elements. The three-dimensional raw image is corrected with the aberration value.

Abstract: A combination tool for defining and measuring anatomical features of a patient for the fabrication of dentures. The tool includes components for preparing a double arch impression, for determining the vertical spacing of the patient's mouth, for measuring the lip, mid line and smile lines of the patient, and for determining the occlusal plane of the patient. This single tool replaces the need for a multitude of tools typically used in preparing for the fabrication of dentures.

Abstract: A device for measuring anatomical dimensions of animals, and particularly the angle of inclination between the occlusal plane of an animal, defined by the contact surface between its upper and lower dental arches, and the alternative reference planes passing either through the anterior sagittal point and the temporomandibular joints, or through the anterior sagittal point and the eyes of the animal includes an element of contact with the animal, at least one first movable member attached revolvingly to the contact element around a first axis of rotation, and at least one graduated scale situated on the contact element, or on the first movable element to enable the measurement of their relative rotation. The contact element also includes a locator plate sized to fit inside the animal's mouth between its upper and lower dental arches, and to be aligned with the occlusal plane.

Abstract: In a method according to an embodiment of the present invention, a plurality of microsphere targets is applied to a surface of a tooth on the upper dentition of a person and a tooth surface of the lower dentition of the person. At least two sets of stereoscopic images are obtained, where the microsphere targets are visible in the field of view of each image. The center position of the beads is photogrammetrically determined in three dimensions for each set using the images taken from perspective positions. The change in bead positions in the sets of stereoscopic images is analyzed to mathematically characterize the jaw motion of the person.

Abstract: A method and system for evaluating images, such as x-ray image, to provide feedback that can be used for subsequent image acquisition. The feedback may be used to adjust the positioning of a patient with respect to an image capture device, or a setting of the image capture device. The image capture device may be part of a dental x-ray imaging system that generates an x-ray image of the patent and provides the image to a collector service. The image is evaluated by the collector service for positioning errors and other operator correctable issues that may have had an impact on the image quality. A report that includes feedback regarding the operator correctable issues, as well as suggested corrective action, is generated and provided to the imaging system operator.

Abstract: A system and method for modeling bite function. A top pantograph is fixed to a patient via clutches to the top teeth of the patient, a bottom pantograph is fixed to a patient via clutches to the bottom teeth of the patient and the actual bite of the patient is optically monitored by monitoring the relation of the top pantograph to the bottom pantograph during a bite cycle and storing a hinge axis. Data is stored relating to the actual bite and the top teeth are scanned to create a top teeth model while the bottom teeth are scanned to create a bottom teeth model. A digital representation of the top pantograph is digitally fitted to the top teeth, a digital representation of the bottom pantograph bottom pantograph is digitally fitted to the bottom teeth, and the relationship of the top teeth model and the bottom teeth model to the hinge axis is recorded.

Abstract: A TemporoMandibular Joint (TMJ) balancing appliance and a method for using the same are provided, in which a first base portion accommodates incisor teeth, a second base portion is extended from a left side of the first base portion and accommodates left molar teeth, and a third base portion is extended from a right side of the first base portion and accommodates right molar teeth. The first base portion includes an upper part for accommodating upper incisor teeth and a lower part for accommodating lower incisor teeth and has a center for accommodating the upper and lower incisor teeth higher than the left and right sides.

Abstract: A denture grinding machine includes: a denture-holding table for holding dentures; a grinding tool for grinding the dentures held on the denture-holding table; a main body for holding the grinding tool; a moving mechanism for causing relative movement between the denture-holding table and the main body; and a driving mechanism for relatively driving the main body and the denture-holding table. The moving mechanism moves relatively the denture-holding table and the main body in three-dimensional coordinate directions based on grinding portion data, and the grinding tool performs grinding of the denture occlusal surface from a direction perpendicular to the occlusal surface.

Abstract: Methods, devices, and storage media provide for receiving a selection of parameters pertaining to an animal; receiving a selection of parameters pertaining to an animal interaction with a cable; simulating the animal interaction based on the selection of parameters pertaining to the animal and the animal interaction; collecting test data during the simulating; and storing the test data.

Abstract: One embodiments of the present subject matter include a method that includes fixing a top pantograph to a patient via clutches to the top teeth of the patient, fixing a bottom pantograph to a patient via clutches to the bottom teeth of the patient, optically monitoring the bite of the patient by monitoring the relation of the top pantograph to the bottom pantograph during a bite cycle, storing data relating to the actual bite storing patient data including a three-dimensional model including a top teeth model and a bottom teeth model, storing a digital top pantograph model associated with the top pantograph, storing a digital bottom pantograph model associated with the bottom pantograph, digitally pairing the bite data, the top pantograph model and the bottom pantograph model to the patient data, and digitally modeling the bite.

Abstract: The occlusal position of a patient is measured by means of light transmission through a layer of a polysiloxane which is not cross-linked. This material forms an exceptionally accurate impression of a patient's bite essentially instantaneously and enables subsequent recording and analysis of the bite in a matter of minutes.

Abstract: An apparatus for registering occlusal dimensions, comprising a support surface sized and configured for providing areal support to a registration rim; and at least one connector adapted to releasably connect to a dental implant extension.

Abstract: An occlusion evaluation apparatus capable of evaluating a masticatory ability depending on an occlusal geometry of teeth without actually used by a human subject, reads three dimensional data of geometries of maxillary molar teeth 1, 2, 3, 4 and mandibular molar teeth 5, 6, 7, 8, and specifies a geometry of a fluxion space Va defined by a plane Sa which includes two adjacent contact points Pa between the maxillary molar teeth 1, 2, 3, 4 and mandibular molar teeth 5, 6, 7, 8 and which is perpendicular to the occlusal plane, the occlusal surfaces of the maxillary molar teeth 1, 2, 3, 4, and the occlusal surfaces of the mandibular molar teeth 5, 6, 7, 8.

Abstract: A bite registration post (10) includes a circular shank portion (12) that terminates at a lower threaded stem (14). The post includes an upper fixed diameter portion (20) and a lowered tapered portion (18) that tapers in diameter in the direction towards the threaded stem (14). A pair of spaced-apart, enlarged circular flanges are positioned along the shank at a location distal from the threaded stem (14).

Abstract: One embodiments of the present subject matter include a method that includes fixing a top pantograph to a patient via clutches to the top teeth of the patient, fixing a bottom pantograph to a patient via clutches to the bottom teeth of the patient, optically monitoring the bite of the patient by monitoring the relation of the top pantograph to the bottom pantograph during a bite cycle, storing data relating to the actual bite storing patient data including a three-dimensional model including a top teeth model and a bottom teeth model, storing a digital top pantograph model associated with the top pantograph, storing a digital bottom pantograph model associated with the bottom pantograph, digitally pairing the bite data, the top pantograph model and the bottom pantograph model to the patient data, and digitally modeling the bite.

Abstract: An apparatus for measuring mandibular position is disclosed. In one embodiment, the apparatus includes a first slide operable to adjustably couple to a second slide, such that the second slide is operable to travel in a direction substantially parallel to a long axis of the first slide, and an indicator configured to indicate a location of the second slide relative to the first slide in the direction substantially parallel to the long axis of the first slide. The apparatus further includes an adjustment mechanism coupled to the first slide and the second slide, the adjustment mechanism configured to adjust the distance between the first slide and the second slide in a direction substantially orthogonal to the long axis of the first slide.

Abstract: A jaw-relation reproduction condition is determined by measuring a jaw movement of a patient, and reproducing a jaw state of the patient on an occlusion-state reproducing apparatus in accordance with the jaw-relation reproduction condition. Dentures are arranged on the apparatus in accordance with the jaw-relation reproduction condition to prepare pre-grinding dentures. Denture data with reference points which is three-dimensional image data containing reference points that represents a positional relationship between the jaw-relation reproduction condition and the dentures and an occlusal surface of the dentures. An occlusion state of the denture data with the reference points is reproduced by using the jaw-relation reproduction condition on a three-dimensional image. Grinding data of a grinding portion is determined under a dynamic condition or set condition from a portion surrounded by an image of upper and lower jaws on the three dimensional image in a reproduced occlusal state.

Abstract: A system for generating an electronic model having a common coordinate system includes a scanning device; a first plate module; and a second plate module. Each of the plate modules is configured to separately couple to the scanning device. The plate modules also can be moveably coupled together using an articulation device. Each of the plate modules includes alignment structures (e.g., spheres) to facilitate determining a position and orientation of the plate modules within a coordinate system of the scanning device.

Abstract: A method for testing a coating for blade roots, includes: providing a disk test piece including at least one bearing surface and a blade test piece including at least one bearing surface coated with the coating to be tested, the blade test piece including two test piece halves adapted to be engaged on either side of the disk test piece, and subjecting the blade test piece engaged with the disk test piece to tensile cycles during which the test pieces undergo tensile stress with respect to each other in a tensile direction, the tensile strain being transmitted via the bearing surfaces contacting the blade test piece and the disk test piece. The method allows for very faithful reproduction of the behavior and ageing of the coating and thus allows for accurate evaluation of the quality of the coatings.

Abstract: An occlusion evaluation apparatus capable of evaluating a masticatory ability depending on an occlusal geometry of teeth without actually used by a human subject, reads three dimensional data of geometries of maxillary molar teeth 1, 2, 3, 4 and mandibular molar teeth 5, 6, 7, 8, and specifies a geometry of a fluxion space Va defined by a plane Sa which includes two adjacent contact points Pa between the maxillary molar teeth 1, 2, 3, 4 and mandibular molar teeth 5, 6, 7, 8 and which is perpendicular to the occlusal plane, the occlusal surfaces of the maxillary molar teeth 1, 2, 3, 4, and the occlusal surfaces of the mandibular molar teeth 5, 6, 7, 8.

Abstract: The invention relates to a simplified fronto-sagittal and two-dimensional ultrasound apparatus exclusively intended for the exploration of the two right and left temporo-mandibular articulations (ATM) at rest or during mandibular movement, in the case of stomatology and traumatology exams. The calculation and the adjustment of the parameters for obtaining a displayed image of the region of the temporo-mandibular articulations is already done during the design step. Accordingly, the invention provides an apparatus with small dimensions and a lower cost relative to traditional ultrasound apparatuses, which will promote its use in medical practices both from a logistic and financial point of view. This exploration method has a low cost, does not require any particular preparation or hospitalisation for the patient, does not include any risks due to X-rays, and has no known side effects. The apparatus includes a quadruple hinged ultrasound probe (right and left) (FIG.

Abstract: One embodiments of the present subject matter include a method that includes fixing a top pantograph to a patient via clutches to the top teeth of the patient, fixing a bottom pantograph to a patient via clutches to the bottom teeth of the patient, optically monitoring the bite of the patient by monitoring the relation of the top pantograph to the bottom pantograph during a bite cycle, storing data relating to the actual bite, fitting the top pantograph and bottom pantograph to casts that are fixed to an automatically adjustable articulator and replicating the bite by moving the automatically adjustable articulator and optically monitoring said movement to replicate the monitored bite using feedback by comparing optical data relating to the replicated bite to the data relating to the actual bite.

Abstract: An apparatus for measuring a dental occlusion includes: a position sensor (30) for detecting a position and posture of a lower jaw (12) relative to an upper jaw (11) and; an arithmetic circuit (31) for computing a posture relative to a translation distance in a state of occlusal contact. The computation is derived from the position and posture of the lower jaw (12) relative to the upper jaw (11) detected by the position sensor (30). The apparatus also includes a display monitor (32) for displaying the posture relative to the translation distance computed by the arithmetic circuit (31).