Abstract: A navigation system is configured to identify a current location and a destination location of an airborne platform, identify a current cell in which the current location is located; identify a plurality of current neighbors associated with the current cell; calculate, for a first path from the current location to the destination location through a first current neighbor of the plurality of current neighbors, a first value of an objective function, the first value depending on whether the first path includes a predetermined navigational node; calculate, for a second path from the current location to the destination location through a second current neighbor of the plurality of current neighbors, a second value of the objective function depending on whether the second path includes a predetermined navigational node; and output the current neighbor and/or path that satisfies an objective condition based on the values.

Abstract: In one general aspect, a drone control device includes a body, a motor that is configured to move the body, a network module, an input module, and a processor. The network module is configured to communicate with a security system that monitors a property and receive data associated with a location within the property. The input module is configured to receive user input. The processor is configured to perform operations that include: determine, from among the location within the property and other locations within the property, a target location within the property; move the body to the target location within the property by providing a signal to the motor; receive, from the input module, input data that is associated with an operation of the security system; and in response to receiving the input data, perform the operation of the security system.

Abstract: An aircraft including a wing system, a plurality of control surfaces, a camera mounted on a camera pod, and a control system. The camera pod is configured to vary the orientation of the camera field of view only in yaw, relative to the aircraft, between a directly forward-looking orientation and a side-looking orientation. The control system controls the control surfaces such that they induce a significant aircraft yaw causing an identified target to be within the field of view of the camera with the camera in the directly forward-looking orientation.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for an unmanned aerial system inspection system. One of the methods is performed by a UAV and includes obtaining, from a user device, flight operation information describing an inspection of a vertical structure to be performed, the flight operation information including locations of one or more safe locations for vertical inspection. A location of the UAV is determined to correspond to a first safe location for vertical inspection. A first inspection of the structure is performed is performed at the first safe location, the first inspection including activating cameras. A second safe location is traveled to, and a second inspection of the structure is performed. Information associated with the inspection is provided to the user device.

Abstract: A method and a system are provided herein for calculating whether or not a specific aerial vehicle at a specified point of time can maneuver over a given location in the terrain while complying with terrain clearance requirements. The system may include a computer memory configured to store a 3D model representing at least a portion of a terrain located in a vicinity of an aerial vehicle; a computer processor configured to map said portion of the terrain into at least two types: a first type indicative of a potential of the aerial vehicle to maneuver over a respective terrain while complying with terrain clearance, and a second type indicative of a non-potential of said aerial vehicle to maneuver over a respective terrain, wherein the mapping is carried out based on said parameters, the 3D model and given predefined performance of the aerial vehicle.

Abstract: A regulator device for regulating a speed of rotation, of a shaft of a gas generator of at least one turboshaft engine of a rotorcraft. The rotorcraft has at least one main rotor for regulating at least lift and/or propulsion for said rotorcraft in the air; a control member for controlling a collective pitch of the blades of said at least one main rotor, said control member serving to generate a control setpoint for said collective pitch; at least one turboshaft engine suitable for driving rotation of said at least one main rotor, said at least one engine producing, at least temporarily, a drive torque that is transmitted to said at least one main rotor; and measurement means for taking at each instant a measurement of said drive torque transmitted by said at least one engine to said at least one main rotor.

Abstract: An apparatus, system and method for managing airspace for unmanned aerial vehicles (UAVs). The apparatus, system and method may include a platform comprising at least records of certified administratively acceptable requestors of restricted use of the airspace for UAVs, a plurality of airspace management rules for UAVs, and a broadcaster for providing notifications over at least one telecommunications network; and a plurality of applications, each instantiated by a processor on one of a plurality of corresponded devices by non-transitory computing code, wherein the plurality of corresponded devices comprises at least a plurality of mobile devices. A first of the plurality of applications may be capable of receiving the restricted UAV use request from a requestor within a physical area of the restricted UAV use request, and of forwarding the restricted UAV use request and an identification of the requestor to the platform over the at least one telecommunications network.

Abstract: Moving device identification information, i.e., identification information for identifying moving device 20 and operation information for specifying an operation to be performed by moving device 20 is encoded into a two-dimensional code. Image analyzing unit 25 analyzes a captured image to obtain the moving device identification information and an address of operation information. Operation information requesting unit 26 requests actual operation information from operation information storage device 10 by designating the address of operation information. Operation information storage unit 11 stores the actual operation information. Operation information transmitting unit 22 transmits the actual operation information to moving device 20 in response to the request from operation information requesting unit 26.

Abstract: A system of pressure control for an environment to be pressurized includes a controller configured to calculate an environment leakage effective area CdALEAK according to: CdALEAK=f(Pc, Tc, Pa, WLEAK) wherein Pc is an environment pressure; Tc is an environment temperature; Pa is an ambient pressure outside of the environment; WLEAK=WECS?WOFV?WAPU; wherein WECS=air pressure inflow into the environment; WOFV=air pressure outflow to ambient that is outside of the environment; WAPU=f(Tin, Pin, APURPM, Flowfuel); wherein Tin=inlet temperature to a power source; Pin=inlet pressure to the power source; APURPM=rotational speed of the power source; Flowfuel=power source fuel flow. A processor is in communication with the controller and configured to compare a current CdALEAK value with a control limit; wherein the control limit is based on historical CdALEAK values.

Abstract: Methods and systems for data recording for an aircraft are provided. The method includes a ground station (GS) module external to the aircraft, and a trigger module onboard the aircraft. The GS module performs: creating a trigger library comprising multiple trigger logic modules based on a first user input and aircraft specific parameters; generating an aircraft-specific configuration file (CF) based on a second user input and the trigger logic library; and transmitting the CF to the trigger module. The trigger module performs: receiving the CF; receiving and processing the CF with various aircraft signals during aircraft operation to monitor for triggers; and, responsive to determining that the trigger occurred, (i) recording data bus activity for a duration of time associated with the trigger identity, (ii) generating a customized data report (CDR) including the record of data bus activity, and (iii) transmitting the CDR to the GS module.

Abstract: Provided is a signal processing device including a plurality of sound collection units that is arranged at given positions, and a detection unit configured to detect, from respective sounds that have occurred in accordance with a movement of a region to which attachment is performed and have been collected by the sound collection units, a direction of the movement of the region.

Abstract: A hybrid-electric propulsion system includes a propulsor, a turbomachine, and an electrical system, the electrical system including an electric machine coupled to the turbomachine. A method for operating the propulsion system includes operating, by one or more computing devices, the turbomachine in a steady-state flight operating condition, the turbomachine rotating the propulsor when operated in the steady-state flight operating condition; receiving, by the one or more computing devices, a command to accelerate the turbomachine while operating the turbomachine in the steady-state flight operating condition; and providing, by the one or more computing devices, electrical power to the electric machine to add power to the turbomachine, the propulsor, or both in response to the received command to accelerate the turbomachine.

Abstract: A unmanned aerial vehicle (UAV) includes a body with plurality of motors, a motor controlling circuit, a microprocessor for controlling the flight state of the UAV, a plurality of motion sensors, and a capacitive touch sensor incorporated into a battery. When the user grasps the UAV by the battery, the touch sensor is activated and the microprocessor alters the flight state of the UAV.

Abstract: Systems and techniques are described for cataloging objects in a property using a drone. In some implementations, a system monitors a property that includes a drone configured to survey the property. A control unit accesses data identifying items and provides instructions to the drone to locate the items. The control unit receives data identifying a location of a portion of the items, image data associated with each identified items, and data indicating remaining items not located. In response, the data identifying the remaining items and data indicating that the drone did not locate the remaining portion of the items are transmitted to a client device. The control unit receives data indicating a location within the property of a first group of the remaining portion of the items and data indicating that a second group of the remaining portion of the items are not located within the property.

Abstract: A direct-broadcast remote identification (RID) device attachable to an unmanned aircraft system (UAS) encodes identifier signals based on a unique identifier of the UAS and position data, e.g., the current and originating (launch) positions of the UAS, and transmits encoded data signals receivable and decodable by specially configured receiver devices in range. The encoded identifier signals may be transmitted at low power via radio-control frequencies, whitespace frequencies, ISM frequencies, DME frequencies, or ADS-B frequencies as needed. The receiver devices may decode identifier signals to display the relative positions of, and information about, nearby UAS even in internet-denied areas (standalone mode). The receiver devices may retrieve additional data, such as operator information and flight plans, from remote databases by establishing wireless connections when said connections are available (connected mode).

Abstract: Various methods for monitoring a target user by a drone include tracking the target user by the drone, detecting an object in the presence of the target user based on one or more detection criteria, determining whether the object is a potential threat to the target user based on one or more threat criteria, determining whether to notify the third party of the potential threat to the target user based on one or more notification criteria in response to determining that the object is a potential threat, notifying the third party of the potential threat to the target user in response to determining that the third party should be notified, receiving a response from the third party including a command, and performing an action based on the command.

Abstract: A control and monitoring module is provided for activating an actuator assigned to the control and monitoring module and for monitoring a signal line and/or a power supply line connected to the control and monitoring module and/or to the actuator. The control and monitoring module is configured to detect a fault in the signal line and/or the power supply line, if, during a simulation executed by a testing device, an actual voltage at the control and monitoring module and/or the actuator exceeds a specified upper voltage threshold value or drops below a specified lower voltage threshold value. A system including the control and monitoring module and a method for operating a control and monitoring module are also provided.

Abstract: In one example a management system for an autonomous vehicle, comprises a first image sensor to collect first image data in a first geographic region proximate the autonomous vehicle and a second image sensor to collect second image data in a second geographic region proximate the first geographic region and a controller communicatively coupled to the first image sensor and the second image sensor and comprising processing circuitry to collect the first image data from the first image sensor and second image data from the second image sensor, generate a first reliability index for the first image sensor and a second reliability index for the second image sensor, and determine a correlation between the first image data and the second image data. Other examples may be described.

Abstract: Described are techniques that use an autonomous mobile unmanned machine that includes at least one sensor device suitable to verify an alarm condition. Upon assertion of an alarm condition message asserted as a result of a potential alarm condition existing within a facility, the machine receives a location of the alarm condition and is programmed with a route from a current location of the autonomous mobile unmanned machine to the location of the alarm condition. The at least one sensor device carried by the autonomous mobile unmanned machine collects sensor data at least at the location of the alarm condition and the machine sends to a system a message pertaining to status of the alarm condition.

Abstract: A braking force control system includes a braking mechanism configured to generate a braking force for the vehicle, a first unit configured to supply a braking oil pressure to the braking mechanism, a second unit configured to supply a braking oil pressure to the braking mechanism by using a path other than a path used by the first unit, and an electronic control unit configured to execute braking control by alternatively operating the first unit or the second unit. The electronic control unit is configured to execute first braking control by operating the first unit in a case where the second unit is not operated when an execution request for the first braking control is received and execute the first braking control by continuously operating the second unit in a case where the second unit is operated when an execution request for the first braking control is received.

Abstract: The embodiments of the present invention disclose a target tracking method. The method includes: generating, by the unmanned aerial vehicle, an outer frame according to location information of the at least two targets. At least two targets that need to be tracked are located within the outer frame. The unmanned aerial vehicle adjusts a flight parameter, so that the outer frame falls within a vision angle range of the unmanned aerial vehicle. In this way, multiple targets are converted to a “single target”, to find an optimal location for observing all the multiple targets, and it is ensured that the multiple targets are tracked with robustness for maximum duration.

Abstract: Flying lane management systems and methods for Unmanned Aerial Vehicles (UAVs) include, in an air traffic control system configured to manage UAV flight in a geographic region, communicating to one or more UAVs over one or more wireless networks, wherein a plurality of flying lanes are defined and standardized in the geographic region each based on a specific purpose; determining an associated flying lane of the plurality of flying lanes for each of the one or more UAVs; communicating the associated flying lane to the one or more UAVs over the one or more wireless networks; receiving feedback from the one or more UAVs via the one or more wireless networks during flight in the associated flying lane; and providing a new instruction to the one or more UAVs based on the feedback.

Abstract: Various techniques are described to facilitate controlling an unmanned aerial vehicle (UAV) and viewing feedback received from a UAV. A graphical user interface (GUI) is provided that allows a user to view a display window. The display window may indicate structures or portions of structures in which additional image data is desired by highlighting these portions within the display window. Static imagery may be leveraged to provide smooth and consistent feedback transitions. When a delay exists between the time the UAV sends live video data and the time it may be displayed in the GUI, the static images may be shown in the display window initially until the live video data may be displayed. The opacity of structures included in an initial display window may also transition to a greater opacity over time, with the live video eventually being displayed.

Abstract: A self-adjusting flight control system is disclosed. In various embodiments, an input interface receives an input signal generated by an inceptor based at least in part on a position of an input device comprising the inceptor. A processor coupled to the input interface determines dynamically a mapping to be used to map input signals received from the inceptor to corresponding output signals associated with flight control and uses the determined mapping to map the input signal to a corresponding output signal. The processor determines the mapping at least in part by computing a running average of the output signal over an averaging period and adjusting the mapping at least in part to associate a neutral position of the input device comprising the inceptor with a corresponding output level that is determined at least in part by the computed running average.

Abstract: The present disclosure relates to the technical field of unmanned aerial vehicles, and in particular, to an unmanned aerial vehicle. The unmanned aerial vehicle includes at least a first dual-polarized antenna and a second dual-polarized antenna, wherein the first dual-polarized antenna is provided in a horizontal direction of the unmanned aerial vehicle, and the second dual-polarized antenna is provided in a vertical direction of the unmanned aerial vehicle. As the antenna designed in this structure is applied to the unmanned aerial vehicle of the present application, a weak signal in a vertical polarization direction is compensated by a strong electromagnetic signal in a horizontal polarization direction, and therefore an image transmission height of the unmanned aerial vehicle is increased in the vertical direction.

Abstract: Apparatus, methods and systems to associate a flight plan of an unmanned aerial vehicle (e.g., a drone) with a cryptographic signature are disclosed herein. Some disclosed examples include one or more non-transitory computer-readable media including computer-executable instructions. The computer readable instructions, when executed by one or more processors, cause the one or more processors to compare a flight path over a geographic area of an unmanned aerial vehicle to a geographically identified no-fly zone. The flight path is included in a flight plan. The instructions also cause the vehicle to determine whether the flight path enters the geographically identified no-fly zone, and based on whether the flight path is determined to enter the geographically identified no-fly zone, associate the flight plan with a cryptographic signature.

Abstract: A wireless engine monitoring system for an aircraft engine includes a housing and wireless transceiver that receives engine data, including engine data relating to environmental engine emissions. A processor processes the engine data and generates an alarm report when the environmental engine emissions exceed a threshold.

Abstract: A first embodiment relates to a shape-reconfigurable drone and, more specifically, to a shape-reconfigurable drone comprising unit module drones having a rectangular-parallelepiped body capable of applying a thrust in every direction, thereby being capable of flying horizontally without rotating the drone and of forming a drone assembly formed by the coupling of the unit module drones, and thus can fly solo or can fly in various shapes.

Abstract: A flight controller includes an altitude capture controller, an altitude profile predictor, and an alert generator. The altitude capture controller receives a first current altitude, a target altitude, and at least one energy state parameter; generates a flight control command, a first expected altitude, and a first predicted altitude. The altitude profile predictor generates a second predicted altitude. The alert generator calculates an expected altitude deviation by comparing a second current altitude of the platform to the first expected altitude; calculates a predicted altitude deviation by comparing the first predicted altitude to the second predicted altitude; and outputs an alert responsive to at least one of (i) an expected altitude threshold function indicating the expected altitude deviation exceeds an expected altitude deviation threshold or (ii) a predicted altitude threshold function indicating the predicted altitude deviation exceeds a predicted altitude deviation threshold.

Abstract: Systems and methods for unmanned aerial vehicle (UAV) course profiling are provided. A plurality of images may be captured by a UAV flying along a course at a first location. A profile may be constructed for the course based on the images captured by the UAV. The constructed course profile is transmitted over a communication network to a virtual reality system at a second location. The virtual reality system may generate a virtual environment corresponding to the course based on the constructed course profile, and a second UAV at the second location may fly along the virtual course.

Abstract: A flight route generating method includes accepting, by an input, input of a departure point and a waypoint that the unmanned aerial vehicle will pass, and displaying, on a display, a flight route passing through the departure point and the waypoint, an end time arrival point at which the unmanned aerial vehicle will arrive at an end time of a time zone in which flight of the unmanned aerial vehicle is permitted.

Abstract: A method for updating an electronic card in a vehicle based on a deviation between predicted states and actual states comprises calculating a predicted state of the vehicle, establishing an actual state of the vehicle, determining a deviation between the predicted state and the actual state, and storing information in the map if the predicted state and the actual state deviate from one another.

Abstract: A system for continued navigation of unmanned aerial vehicles beyond restricted boundaries. The system comprises a monitoring device to track a geolocation corresponding to an unmanned aerial vehicle and to compare the geolocation corresponding to the unmanned aerial vehicle with a geolocation corresponding to a restricted boundary to determine a location of the unmanned aerial vehicle with respect to a restricted environment, and a route generator to generate an alternative navigation method to navigate the restricted environment when the unmanned aerial vehicle is located within a predetermined distance of the restricted environment.

Abstract: According to an aspect, a system in an aircraft includes a vehicle management system (VMS) and a load control system (LCS). The LCS includes an LCS processor operable to receive and transmit a plurality of data and load management commands to one or more of: the VMS and a load control interface. The LCS processor is further operable to interact with one or more of: the VMS, one or more LCS sensors, and a load capturing interface of the aircraft to execute the load management commands as a sequence of one or more load management subcommands. The load capturing interface is operable to capture and release an external load relative to the aircraft using a load capture device. The LCS processor is also operable to report a status of execution of the load management commands to the VMS and the load control interface.

Abstract: A method and device for monitoring and controlling a path of a following aircraft (AC2) with respect to vortices (V1, V2) generated by a leading aircraft (AC1) while both aircraft (AC1, AC2) fly in a formation (F), wherein the device includes a unit for determining, using a vortex transport model, a safety position (PS) at which the following aircraft (AC2) is not subjected to effects of the vortices (V1, V2) generated by the leading aircraft (AC1), a unit for determining, using a vortex signature model, an optimum position (PO) at which the following aircraft (AC2) benefits from at least one (V1) of the vortices (V1, V2), and a control unit for bringing and keeping the following aircraft (AC2) in the safety position (PS) while a predetermined condition(s) is met and otherwise for bringing the following aircraft (AC2) and keeping it in the optimum position (PO).

Abstract: A method and apparatus for controlling photography of an unmanned aerial vehicle and a wearable device are disclosed.

Abstract: Embodiments for a module for scheduling sleep/wake intervals for a first one or more communication devices are disclosed. The module includes a computer readable medium having instructions thereon. The instructions, when executed by one or more processing devices, cause the one or more processing devices to obtain a coverage prediction for the first one or more communication devices. The coverage prediction indicates intervals during which a second one or more communication devices are predicted to be within range of the first one or more communication devices. The instructions also cause the one or more processing devices to generate sleep intervals and wake intervals for the first one or more communication devices based on the coverage predictions.

Abstract: Aircraft and associated methods, apparatus, system and storage devices for automatically positioning of lift control devices such as high lift devices including slats and flaps so an aircraft equipped with this technology will not need to count on the crew to command the lift control devices.

Abstract: A device can be configured to detect a physical connection with an unmanned aerial vehicle (UAV) flight controller through an interface. The device can identify a UAV identifier associated with the UAV flight controller and determine, based on the UAV identifier, an application programming interface (API) for communicating with the UAV flight controller. Using the API, the device can establish a communications link with the UAV flight controller and perform an action based on the communications link.

Abstract: An example method includes receiving a plurality of data streams acquired for a respective parameter of a plurality of parameters indicating an operating condition of the aircraft, selecting at least one data stream corresponding to at least one parameter of the respective plurality of parameters, selecting a portion of data from the at least one data stream, comparing the portion of data to a model determined for the at least one parameter based on historical data, determining that a failure has occurred or is likely to occur during operation of the aircraft based on the comparing, and transmitting aircraft health monitoring information indicative of occurrence or likelihood of occurrence of the failure.

Abstract: This invention proposes a new method and software to generate a path with good quality for aerial video shooting in large scale scenes. Using a coarse 2.5D model of a scene, this path generation method consists of several steps: first the user is expected to specify a set of landmarks and designate a superset of key-views for each landmark; our system then automatically generates and evaluates a variety of local camera moves for observing each landmark, which are smooth and collision-free; then automatically determines the optimal order in which the landmarks should be visited, chaining the local camera moves into a single continuous trajectory. Thus, users are able to focus on specifying the visual content that should be captured by the aerial video, rather than on the difficult lower level aspects of designing and specifying the precise drone and camera motions.

Abstract: Systems and methods are provided for managing air traffic and tolling for a plurality of unmanned aircraft system. Various embodiments include terrestrial and unmanned aircraft system based tracking modules for tracking a plurality of unmanned aircraft systems and reporting flight data to a tolling entity for collection from operators.

Abstract: Disclosed are examples of systems, apparatus, methods and computer program products for locating unmanned aerial vehicles (UAVs). A region of airspace may be scanned with two scanning apparatuses. Each scanning apparatus may include one or more directional Radio Frequency (RF) antennae. The two scanning apparatuses may have different locations. Radio frequency signals emitted by a UAV can be received at each of the two scanning apparatuses. The received radio frequency signals can be processed to determine a first location of the UAV.

Abstract: In some embodiments, a method for managing growing vine in a vineyard includes operating one or more unmanned aerial vehicles (UAV) to fly over a plurality of sections of a vineyard. The UAVs are fitted with a plurality of cameras equipped to generate images in a plurality of spectrums. The plurality of sections of the vineyard grow vines of a plurality of varietals. The method further includes taking a plurality of aerial images of the sections of the vineyard in the plurality of spectrums, using the plurality of cameras, while the UAVs are flying over the plurality of sections of the vineyard, and executing an analyzer on a computing system to machine analyze the plurality of aerial images for anomalies associated with growing the vines of the plurality of varietals. The machine analysis takes into consideration topological information of the vineyard, as well as current planting information of the vineyard.

Abstract: One embodiment is a method including defining a maximum deflection for a first axis of a control surface axis of an aircraft; defining a maximum deflection for a second axis of the control surface; and creating a graphical representation of the maximum deflection for the first and second control surface axes. The method further includes determining an angle of rotation of a structure on which the control surface is carried, wherein the angle of rotation is relative to a body of the aircraft; rotating the graphical representation in accordance with the determined angle of rotation; calculating a distance between a point representing a selected combination of roll moment and yaw moment and each edge of the graphical representation; and calculating a control surface deflection based on the calculated distances.

Abstract: A method of calculation, by a flight management system termed FMS, of a trajectory flown by an aircraft comprises the steps, calculated by the FMS, of: for at least one transition of the trajectory arising from the flight plan: 1) determining an initial transition comprising at least one arc exhibiting a single initial turning radius, 2) determining an initial trajectory incorporating the initial transition, 3) determining for each parameter a plurality of predicted values of the parameter in the course of the initial transition, 4) determining a plurality of ordered subdivisions of the arc of the initial transition according to a predetermined criterion, 5) determining, for each subdivision, an associated turning radius, 6) determining an improved transition on the basis of the ordered subdivisions and of the successive associated turning radii, 7) determining an improved trajectory incorporating the improved transition, 8) displaying the improved trajectory to a pilot of the aircraft.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for sending a flight plan for execution by a drone, where the flight plan is adapted to a flight controller of the drone. Receiving flight data from the drone while the drone is executing the flight plan. Determining a modification to the flight plan based on the flight data received from the drone. Sending the modification to the flight plan to the drone while the drone is executing the flight plan, such that the drone executes the flight plan as modified by the modification.

Abstract: Based on a detection information from a plurality of sensors detecting a surrounding object in different fashions, a vehicle control apparatus configured to perform vehicle control for avoiding or mitigating a collision with the object determines an occurrence of a detection capability impaired state in which a detection capability for detecting the object is impaired at any of sensors, based on the detection information about the sensor or the other sensors. The vehicle control apparatus shortens an actuation time until implementing the vehicle control, in comparison with a time when the sensor detects the object without causing the detection capability impaired state, if the object is detected by the sensor in which the detection capability impaired state has been eliminated within a predetermined time after determining that the detection capability impaired state has been eliminated.

Abstract: A method is provided. The method comprises: receiving thermal energy at a heat resistant container; converting all or a portion of the received thermal energy into electric energy; converting the electric energy into electromagnetic energy; and radiating the electromagnetic energy.

Abstract: An apparatus accesses terrain data describing a surface and comprising a plurality of positions located on the surface. The apparatus determines curvatures/second derivatives of the surface between adjacent positions along surface spanning lines along the surface. The apparatus defines vertices by determining an accumulated absolute curvature along the line spanning the surface based on the curvature between positions by adding the absolute value of the curvature to the accumulated absolute curvature, determining whether the accumulated absolute curvature is equal to or greater than a reset value, and when it is determined that the accumulated absolute curvature is equal to or greater than the reset value, defining a vertex at the position. When it is determined that the accumulated absolute curvature is not equal to or greater than the reset value, the absolute value of the next curvature is added to the accumulated absolute curvature.