Abstract: The present invention relates to the secure configuration of electronic devices, such as for example network-connected “smart” devices and appliances, collectively referred to as “IoT devices”. A computer-implemented method of secure configuration of at least one electronic device is provided. According to the method, the electronic device connects to a blockchain database; determines from said blockchain database a configuration block comprising block identification data, where the block identification data corresponds to device identification data, stored with the electronic device; obtains configuration information from said configuration block; and using the configuration information, conducts configuration of the electronic device.

Abstract: Provided is a control device for a machine tool that exchanges a tool and machines a work piece on the basis of a machining program, said control device being provided with a machining program analysis unit that analyzes a machining program and extracts, from the machining program, measurement-related information relating to a dimensional measurement of a tool, and with a measurement program generation unit that, on the basis of the measurement-related information and basic tool information input in advance, generates a measurement program for measuring the dimensions of the tool.

Abstract: Loads that act on all the bearings that support a main spindle are derived from a variation in the state of the main spindle and, in addition, raceway surface contact pressures of the respective bearings are analyzed, so it is possible to accurately keep track of the state of each bearing. Then, when the raceway surface contact pressure exceeds a corresponding threshold, a machining condition is changed to execute control such that the raceway surface contact pressure does not exceed the corresponding threshold, and, furthermore, when the raceway surface contact pressure exceeds the corresponding threshold even when the machining condition is changed, the main spindle is controlled to stop, so it is possible to prevent a seizure of each bearing. Thus, it is possible to improve machining accuracy by controlling the main spindle with high accuracy.

Abstract: A programming device receives a number of local coordinate systems from a user. Each local coordinate system is referenced directly or via at least one other local coordinate system to a global machine coordinate system of a motion-controlled machine. The programming device receives from the user, in each case with reference to one of the local coordinate systems, a number of positions to be approached by the end effector and/or a number of obstacles to be bypassed by the end effector. The programming device determines, with reference to the positions to be approached received from the user and the obstacles received from the user in the global machine coordinate system, the path to be traveled by the end effector The programming device stores the path to be traveled by the end effector as a first file so that it can be retrieved again at a later time.

Abstract: A three-dimensional (3-D) printer and a method for adjusting a working coordinate of a platform thereof are provided. The 3-D printer includes a platform, a printing head and a control unit. The platform includes a carrying surface and adjustment points located on the carrying surface. The printing head disposed above the platform for moving along a datum plane and a normal direction of the datum plane. The control unit controls the printing head to move from the datum plane toward the platform to contact each of the adjustment points for obtaining a coordinate offset of the carrying surface corresponding to the datum plane, and adjusts a model coordinate of a digital 3-D model information according to the coordinate offset. The control unit moves the printing head according to the adjusted model coordinate to print a 3-D object related to the digital 3-D model information on the carrying surface.

Abstract: A CPU 41 reads a next block (S1), and then determines whether the read block is a TCP (tool center point) control finish command “G49” or not (S2). If it is determined to be the TCP control finish command “G49”, the TCP control is finished. If it is determined not to be the TCP control finish command “G49”, whether the read block is a coordinate-system transformation command “P1” or not is determined (S3). Next, if it is determined not to be the coordinate-system transformation command “P1”, the TCP control is performed, without transforming the coordinate system, in accordance with a command of the block (S11). Next, the process returns to S1, and then the process after S1 is executed.

Abstract: An operation position locating system locates a position on a product where an operation is performed in a manufacturing process of the product including one or more operations to be performed. The system includes an operation completion coordinates detection unit and an operation position locating unit. The operation completion coordinates detection unit processes a plurality of images obtained by capturing from a plurality of viewpoints a range including an operation completion position where an operation is completed when the operation is completed, thereby detecting a set of operation completion coordinates representing the operation completion position.

Abstract: An electronic system for compensating the dimensional accuracy of a 4-axis CNC machining system includes a CNC machining system configured to machine a plurality of features into a part, a dimensional measuring device configured to measure a plurality of dimensions of the part, and to provide an output corresponding to the measured dimensions and a compensation processor in communication with the CNC machining system and dimensional measuring device. The CNC machining system includes a global coordinate system, and at least one feature being defined relative to a local coordinate system that is translated from the machine coordinate system. Additionally, the compensation processor is configured to receive the output from the dimensional measuring device, to calculate a plurality of CNC offsets, including at least one local offset, and to provide the offsets to the CNC machining system.

Abstract: A numerical control apparatus controls a machine tool including an X axis for moving a turret to which a plurality of tools are attached, a H axis for rotating the turret, and a C axis for rotating a work and not including a Y axis orthogonal to the X axis. The numerical control apparatus includes a unit configured to independently rotate the H axis according to an independent rotation command for the H axis and perform tool replacement during an imaginary Y-axis control mode, the imaginary Y-axis control mode being a mode for converting an X-Y axes movement command in a machining program into a command in an X-H-C coordinate system and for driving the X axis, the H axis, and the C axis in association with one another according to the converted command.

Abstract: A system for controlling a numerical control machine tool with movable component parts carrying tools (5) and/or mechanical component parts to be checked includes a control unit (7) and a sensor device (9) having an associated interface unit (15). A digital channel (20), through which there are transmitted measuring signals from the interface unit to the control unit, is used, at different moments and as an alternative to the measuring process, for transmitting confirmation pulse signals (ACK) consequent to request/instruction messages that the control unit sends to the interface unit. A method for controlling the machine tool includes the sending of request/instruction messages (M) from the control unit to the interface unit, for example for checking the efficiency and the operativeness of the measuring chain, and the reception of confirmation pulse signals through the transmission channel which is a component part of the measuring chain.

Abstract: A numerical control device according to the present invention includes a display part for displaying a program coordinate and a command coordinate such that they can be compared with each other. The display part may be adapted to further display an actual coordinate. The display part may also be adapted to further display a program trajectory, a command trajectory and an actual trajectory, which are obtained from a machining program and the program coordinate, the command coordinate and the actual coordinate, respectively.

Abstract: A work apparatus sets a virtual target point on an image plane in an imaging apparatus, and obtains a plurality of coordinate values of a moving unit at which a work reference point of a work unit and the virtual target point are caused to match in an image captured by the imaging apparatus. Further, the work apparatus obtains, in the image, coordinate values of the moving unit at which a position of light projection by a distance information obtaining unit and the virtual target point are caused to match, and a plurality of pieces of distance information obtained from the distance information obtaining unit at those coordinate positions. Then, the work apparatus calculates, based on the plurality of coordinate values and the plurality of pieces of distance information obtained through the above processing, a calibration parameter for the moving unit and the distance information obtaining unit.

Abstract: An electronic system for compensating the dimensional accuracy of a 4-axis CNC machining system includes a CNC machining system configured to machine a feature into a part, a dimensional measuring device configured to measure a dimension of the part, and to provide an output corresponding to the measured dimension, and a compensation processor in communication with the CNC machining system and dimensional measuring device. The compensation processor is configured to receive the output from the dimensional measuring device, to calculate a plurality of CNC offsets, and to provide the offsets to the CNC machining system.

Abstract: Embodiments of the invention disclose a method for optimizing a simulation of a machining of a workpiece performed by removing a set of swept volumes from a volume of the workpiece, wherein the volume is partitioned into a set of cells, comprising the steps of: associating with each cell a subset of distance fields representing a subset of swept volumes intersecting with the cell, wherein at least part of the subset of swept volumes forms a composite surface of the cell; subjecting the cell with a set of rays incident to the cell from at least one direction; and selecting a distance field of the subset of distance fields into an optimal subset associated with the cell, wherein a boundary of the swept volume represented by the distance field intersects with at least one ray at a point of intersection lying on the composite surface.

Abstract: A main control process is made common to all machine tools by describing in a NC program a tool trajectory including a change in posture in a coordinate system (30) fixed to a machining object (W), fixedly arranging a preparatory reference coordinate system (20) on a machine table (2), representing an installation position of the machining object (W) and a position of a spindle (91) on which a tool (11) is mounted in the preparatory reference coordinate system (20), and containing portions relating to a configuration of axes in a conversion function group of correlation between the position (q) of the spindle (91) and an axis coordinate (r). Thus, the processes of reading the NC program, correction of the tool trajectory and conversion into the trajectory of a spindle position based on the installation position of the machining object, the tool shape, and tool dimensions are made completely common.

Abstract: The present invention provides a method for machining a part from a workpiece. The workpiece is divided into a plurality of sectors and a plurality of fiducials are disposed within each sector. The separation distance between each fiducial is then calibrated to a workpiece distance unit. The present invention then includes the steps of a) positioning the workpiece into the desired position relative to a cutting machine; b) calibrating the cutting machine to the workpiece distance units of one sector; c) cutting one sector with the calibrated cutting machine; d) repeating steps a-c until the part is completed.

Abstract: Methods for generating supports (30) for parts (50) produced by solid freeform fabrication (“SFF”) are disclosed. The method includes defining a plurality of layers (L) that make up the part, and for each layer, determining those regions (R) that require support. The method also includes merging the regions for the different layers (L) into one or more common regions that require support, and providing at least one support for each of the one or more common regions. The result is that fewer supports are used as compared to conventional SFF fabrication methods.

Abstract: Device and method for positioning a precision part on a turntable (130). The device (100) comprises at least two distance sensors (121.1, 121.2, 121.3), which operate in a contactless manner and are situated in a previously known configuration to a rotational axis (A1) of the turntable (130). The measurement axes (124.1, 124.2, 124.3) of the distance sensors (121.1, 121.2, 121.3) are radially oriented in the direction of the rotational axis (A1) so that the measurement axes (124.1, 124.2, 124.3) of the distance sensors (121.1, 121.2, 121.3) meet in a virtual measuring point (MV). The distance sensors (121.1, 121.2, 121.3) are connected to analysis electronics (200). Output signals (a.1, a.2, a.3) of the distance sensors (121.1, 121.2, 121.3) may be processed on the basis of the analysis electronics (200), in order to allow coaxial centering of the precision part (11) in relation to the rotational axis (A1) upon placement of the precision part (11) on the turntable (130).

Abstract: A method and a device for position-dependent compliance compensation in a machine tool is disclosed. The compliance of the machine tool is derived at a position of a tool of the machine tool from machine data stored in memory, a machining force acting on the tool during a machining process at this position is determined, and at least one machining parameter that has an influence on the machining process is derived at this position in dependence on the derived compliance and the machining force so as to counteract a displacement of the tool with respect to a desired position caused by the compliance of the machine tool and the machining force. This optimizes the machining time and/or contour fidelity when machining a workpiece with a machine tool.

Abstract: The present invention provides a system and method for the on-machine 2-D contour measurement, employing the contour measurement, coordinate system transformation, error identification, and image matching theory in image processing field to develop the on-machine measurement of X-Y-plan manufacturing error of a micro device manufactured by a high-precision micro-device machine tool, contour error, and trace error.

Abstract: A process for accurately determining a workpiece position in relation to a reference coordinate system is provided. The process includes providing a machine having a table and a machine coordinate system, determining locations of three reference geometric aspects of the table, providing a workpiece, and attaching the workpiece to the table. Thereafter, locations of three geometrical aspects of the workpiece are determined using photogrammetry followed by calculation of any offset between the three reference geometrical aspects of the table and the three geometrical aspects of the workpiece. Any offset that has been determined can then be used to accurately determine the workpiece position in relation to the reference coordinate system.

Abstract: Methods for generating supports (30) for parts (50) produced by solid freeform fabrication (“SFF”) are disclosed. The method includes defining a plurality of layers (L) that make up the part, and for each layer, determining those regions (R) that require support. The method also includes merging the regions for the different layers (L) into one or more common regions that require support, and providing at least one support for each of the one or more common regions. The result is that fewer supports are used as compared to conventional SFF fabrication methods.

Abstract: A method for constructing a distance histogram for nearest neighbor classification. A training sample is determined for each of two classes. For each defect, a distance is measured in the feature space between the defect and the training sample for each of the classes. All of the distances for a given defect are normalized by dividing each distance for the given defect by the sum of all of the distances for the given defect. A histogram is constructed by plotting a chart of the normalized distances versus the number of defects having the distances. A threshold bar is placed on the center of the histogram to construct a normal nearest neighbor classifier. The threshold bar can be adjusted to the left or to the right to construct a weighted nearest neighbor classifier.

Abstract: A machining apparatus in which the machining efficiency can be improved even if characters are machined in a printed circuit board. A coordinate transformation unit is provided for transforming central coordinates of each dot d of each character of a character string into coordinates in a machining coordinate system with which the holes will be machined. Prior to machining, based on a character string and position information of the character string described in a machining program, central coordinates of each dot of each character of the character string are transformed into coordinates in the machining coordinate system with which the holes will be machined. Each dot d is regarded as a hole and machined. The number of times of movement of a table can be thus minimized so that the machining efficiency can be improved.

Abstract: Apparatus and method for fitting a workpiece to geometric design data of a workpiece. Nominal data points are selected from the geometric design data. Command codes are created to generate measured data points. The measurement data points have associated nominal measurement points which are used to fit the workpiece to the geometric design data. The apparatus and method may also be used to determine whether a workpiece is within tolerance and for process control.

Abstract: A method of self calibrating a positioning system, by positioning a reference device provided with reference markings at different calibration locations, and sensing the positions of the reference markings at each calibration location, is provided. The calibration parameters are selected such that differences in relative positions of the sensed locations, expressed in actual coordinates for different calibration locations are reduced or preferably minimized.

Abstract: According to embodiments, techniques for extracting a signal parameter from a selected region of a generally repetitive signal are disclosed. A pulse oximetry system including a sensor or probe may be used to obtain an original photoplethysmograph (PPG) signal from a subject. A filter transformation may be applied to the original PPG signal to produce a baseline PPG signal. The baseline PPG signal may contain artifacts and/or noise, and a region of the baseline PPG signal suitable for extracting the signal parameter may be selected. A suitable region of the baseline PPG signal may be selected by applying one or more thresholds to the baseline PPG signal, where the values of the thresholds may be set based on derivative values, amplitude-based percentiles, and/or local minima and maxima of the baseline PPG signal. A portion of the original PPG signal corresponding to the selected region may be processed, and the signal parameter may be extracted from the processed region.

Abstract: A method is disclosed for controlling movement of machine tool systems by providing a conversational programming interface that permits a user to create a universal program for execution by various machine tool systems for machining a part, each system having at least four movable axes. The user defines program blocks including geometry definitions which are independent of any axis kinematics configuration. A first tool path relative to a first Cartesian coordinate system is generated for forming the geometry, then mapped to a second Cartesian coordinate system corresponding to the part. The mapped path is transformed to a third Cartesian coordinate system corresponding to an orientation and location of the part relative to an axis kinematics configuration of a current machine tool system. The transformed path is processed to generate positions for the movable axes of the current system.

Abstract: A method is disclosed for eliminating sources of error in the system correction of a coordinate measuring machine. Herein, a number j of reference structures 33 on a rigid reference object 30 are measured in a starting orientation k=0, and the starting coordinates and the reference coordinates of the reference structures 33 on the reference object 30 are determined in a number k?3 of mutually different orientations.

Abstract: A method and an apparatus to analyze two measured signals that are modeled as containing desired and undesired portions such as noise, FM and AM modulation. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, a transformation is used to evaluate a ratio of the two measured signals in order to find appropriate coefficients. The measured signals are then fed into a signal scrubber which uses the coefficients to remove the unwanted portions. The signal scrubbing is performed in either the time domain or in the frequency domain. The method and apparatus are particularly advantageous to blood oximetry and pulserate measurements. In another embodiment, an estimate of the pulserate is obtained by applying a set of rules to a spectral transform of the scrubbed signal. In another embodiment, an estimate of the pulserate is obtained by transforming the scrubbed signal from a first spectral domain into a second spectral domain.

Abstract: Apparatus and method for fitting a workpiece to geometric design data of a workpiece. Nominal data points are selected from the geometric design data. Command codes are created to generate measured data points. The measurement data points have associated nominal measurement points which are used to fit the workpiece to the geometric design data. The apparatus and method may also be used to determine whether a workpiece is within tolerance and for process control.

Abstract: A signal processor which acquires a first signal, including a first primary signal portion and a first secondary signal portion, and a second signal, including a second primary signal portion and a second secondary signal portion, wherein the first and second primary signal portions are correlated. The signals may be acquired by propagating energy through a medium and measuring an attenuated signal after transmission or reflection. Alternatively, the signals may be acquired by measuring energy generated by the medium. A processor of the present invention generates a primary or secondary reference signal which is a combination, respectively, of only the primary or secondary signal portions. The secondary reference signal is then used to remove the secondary portion of each of the first and second measured signals via a correlation canceler, such as an adaptive noise canceler, preferably of the joint process estimator type.

Abstract: A method for determining a deviation of at least one regulating variable on chip removal machines with a mechanical drive for a tool and/or a workpiece, regulated by a control system, wherein the regulation comprises a plurality of values of at least three spatial axes for the control system and for the drive, and the values have a functional relation with the axes. A protocol is prepared from a plurality of control system actual values detected by measuring devices and/or selected drive actual values and a control system nominal value and/or a drive nominal value is calculated at least in relation to an axis, and a control system differential value and/or a drive differential value is calculated at least in relation to the axis. A chip removal machine which implements such a method is disclosed.

Abstract: A raster cutting apparatus and method for producing accurately formed, aspheric ophthalmic lenses having a good quality surface finish. The accurate form and good surface finish are obtained by using a substantially spherically shaped cutting tool having a large radius. The methods include utilizing a cutting path which provides substantially constant cutting-force, such as a constant surface-cutting-speed raster pattern.

Abstract: In a method for smoothing polylines in NC programs, the coordinates of points which, connected by linear segments, represent an original polyline, are shifted in a geometrical filter unit such that a resulting polyline, made up of coordinates of points, is smoothed as compared to the original polyline.

Abstract: A method and system for building one or more three-dimensional objects, where the method includes providing a computer-aided design model of a three-dimensional object having an initial spatial orientation in a coordinate system, and determining an optimal spatial orientation of the computer-aided design model in the coordinate system based on one or more criteria.

Abstract: A method and tool arrangement for producing straight bevel gears and the like on a multi-axis computer controlled machine wherein a single tool is utilized in the machining process.

Abstract: A method and tool arrangement for producing straight bevel gears and the like on a multi-axis computer controlled machine wherein a single tool is utilized in the machining process.

Abstract: A method and tooling for inspecting a contour of an edge of a cutout formed in a disk, each cutout fixedly receiving a turbine blade. A first device receives the disk containing the cutouts. A second device has a sensor associated with the movement of an instrument, the first device securing the disk at a predetermined orientation to the sensor. The disk is secured to the first device, the instrument being directed along the cutout defining a path substantially parallel to a surface of the contour, the instrument remaining in physical contact with the surface of the contour. The sensor transmits a signal associated with instrument movement to an algorithm to convert the signal to two-dimensional positions along the tangent path along the surface of the contour. The acceptability of the edge contour of the cutout is determined by comparing the two-dimensional positions to predetermined ranges of values.

Abstract: A method and a system for programming an industrial robot to move relative to defined positions on an object. The system includes a geometrical model of the object, the real object, and an industrial robot. A plurality of measuring points are generated corresponding to different points on the surface of the real object expressed in a coordinate system associated with the robot. The system further includes a calibration module arranged to determine orientation and position of the geometrical model of the object relative to the coordinate system associated with the robot, a calculating module arranged to calculate the deviation between the measuring points and corresponding points on the geometrical model, and an adjusting module arranged to adjust the defined positions based on the calculated deviations.

Abstract: A method and system can align a robot arm with a payload station. A probe and a contact detector may be positioned on the robot arm and three pins may be placed on the payload station. A controller may move the robot arm in a pattern over the payload station until contact may be made between the probe and one of the pins. A search about the contact location may be performed to obtain additional contacts. The search may be interrupted when contact is made between the probe and one of the pins. The position of the pin may be calculated from three such contacts on the spherical portion of the pin. The location of the probe at the time of contact may be stored and a localized search about the pin location may be performed. If the position of the pin cannot be resolved from three contacts, additional contacts may be made until a combination of three contacts does provide a solution.

Abstract: A machine readable medium and a method are disclosed that determine whether a pattern of manufactured or simulated features violates a feature relating tolerance and determines acceptability of the pattern. Allowable tolerance may include feature relating tolerances and material conditions. Manufactured centers are drawn relative to a one true position. A circle drawn through or outside the manufactured centers is used to determine if there is feature relating tolerance violation. Material condition may also be used.

Abstract: A machining data generator generates NC machining data specifying machining operations for shaping the external shape of a piston. The machining data generator uses a machining data sheet (provided by a spreadsheet software) describing noncircular part shape data on the shape of a noncircular part and condition data (machining condition data and shape data on shapes of parts other than the noncircular part necessary for shaping the overall shape of the piston). The machining data sheet is prepared beforehand. A machining data generation program reads the machining data sheet in step S4, recognizes directives “start cell” and “end cell” defining a cell region and described in the machining data sheet and fetches matrix data from the cell region in step S5, and fetches condition data other than the noncircular part shape data from the machining data sheet, and calculates NC machining data to be given to a NC machine tool on the basis of the condition data and the noncircular part shape data in step S6.

Abstract: The invention relates to especially simple, rapid and multidimensional surface reproduction. According to the inventive method for reconstructing a surface of a structure which is described by 3D data points in chronological order, 3D data points are processed using a linear interpolation in such a way that chronologically directly adjacent 3D data points remain unchanged.

Abstract: A controller that eliminates an error caused by acceleration/deceleration control, and controls the velocity of drive axes which is not represented by a rectangular coordinate system such that maximum allowable values of velocity, acceleration, and jerk of the drive axes are not exceeded. A program is analyzed in a command analysis section, and an interpolated position on a motion path in the rectangular coordinate system is determined in a first interpolation section, and then converted by means of a transformation section into drive axes' positions not in the rectangular coordinate system. In a tangential acceleration calculating section, a tangential acceleration is determined. In a velocity limit calculating section, a velocity limit at the time of each position being reached is determined which does not exceed maximum allowable values of velocity, acceleration, and jerk of the drive axes.

Abstract: A numerical control apparatus for machine tool, includes: an NC program storage portion for storing an NC program; a block skip command detection portion for detecting whether a block skip command for skipping execution of blocks after a position where the block skip command is described is present in the NC program stored in the NC program storage portion or not; a block skip end command detection portion for detecting whether a block skip end command provided in connection with the block skip command to permit execution of blocks after a position where the block skip end command is described is present in the NC program or not; and a coordinate comparison portion for performing comparison concerning a difference between coordinates on at least one control axis in the block skip command and the block skip end command.

Abstract: In a separate process from a boring process, the prealignment is performed beforehand on the circuit board, employing an alignment device, to create the positional data indicating the position of boring the hole in a pattern within the circuit board. In the boring process, the circuit board is carried into the working apparatus. The panel alignment is made on the circuit board. The positional data for positioning the circuit board on a table of the working apparatus is created. The synthesis of the positional data created by the prealignment and the positional data created by the panel alignment is performed to calculate the boring position of the circuit board on the table. The hole is bored at the calculated position in the circuit board, employing a boring machine of the working apparatus. Thereafter, the circuit board is carried out from the working apparatus.

Abstract: The invention relates to a device for controlling the position for work devices (41) of mobile machines (40). The inventive device comprises a measuring device (1,2) for measuring an angle (?) which is formed between a level (42) that is determined by the position of the work device (41) and the direction of the gravitational force (g). The inventive device also comprises an angle transmitter (5) for predetermining an angle (??) which is formed between a level (42) that is determined by the position of the work device (41) and the direction of the gravitational force (g). The inventive device further comprises a controller (3, 4, 6–16) for controlling the angle (?) between the level (42) of the work device (41) and the direction of the gravitational force (g) in such a way that the measured angle (?) matches the predetermined angle (??).

Abstract: In a method for the wireless transmission of a control command from a transmitting element to a measuring probe using electromagnetic signals, the control command includes at least one bit sequence which is made up of high bits and at least one low bit. The high bits are produced by the enveloping curve of a plurality of electromagnetic signals which recur with a carrier frequency. Within one bit sequence, at least one low bit is transmitted at least once between two high bits.

Abstract: A numerically controlled curved-surface machining unit comprises a component converting matrix·angle-addition value forming function of converting CL (cutter location) data into components on a normal coordinate system on the basis of the machine configuration of the simultaneous multiple-axis control NC machine, a component converting function of converting from the workpiece coordinate system to the normal coordinate system, a function of forming second angles of a second rotary axis on the normal coordinate system, a compensating function of forming a continuous angle distribution from a distribution of the second angles, a function of forming first angles of a first rotary axis on a coordinate system rotated by the second angles at the second rotary axis, a compensating function of forming a continuous angle distribution from a distribution of the first angles, a machine coordinate transformation matrix forming function of obtaining a matrix for converting the tool control point vectors on the workpiece c