Abstract: Task: To provide a high quality air conditioner with high efficiency and stability, preventing adverse effect of manufacturing variation on the refrigerant distribution. Solution: The air conditioner having an expansion valve for decompressing a refrigerant, and a heat exchanger for heat exchange between the refrigerant and air. The air conditioner includes a first linearly shaped piping that is connected to the expansion valve and vertically disposed, a branch pipe connected to the first piping for branching a refrigerant flow path into a plurality of sections, a plurality of second pipings connected to the branch pipe, and a plurality of distributors connected to the second piping for further branching the refrigerant flow path to the heat exchanger.

Abstract: A black rifle including a receiver with a bolt carrier movably located therein, a receiver extension tube connected to the receiver, the receiver extension tube including an aperture disposed at an end of the receiver extension tube, and a buffer assembly having an interface surface configured to interface with bolt carrier and being configured to reciprocate through the aperture within the receiver extension tube, the buffer assembly including an open fluid passage, through the buffer assembly, that is sized and shaped for enabling movement of the bolt carrier relative to the receiver and effect automatic or semi-automatic fire when the receiver extension is at least partially filled with water.

Abstract: Semi-automatic rifle including a free floating barrel with a muzzle located at a distal end and an engagement mechanism at a proximal end. The barrel has a length measured from the proximal end to the distal end. A receiver can be configured to couple the engagement mechanism of the barrel and a bolt at least partially rotatably mounted relative to the receiver. A gas cylinder system being coupled to the barrel substantially close to the muzzle and including an operating rod. A trigger assembly coupled to the receiver to receive at least a portion of the operating rod and a bridge coupled to the trigger assembly. A fire control located substantially within the trigger assembly and configured to actuate the bolt so as to eject a cartridge and load a subsequent cartridge from a clip.

Abstract: A firearm weapon loading system includes a handgun loading and cocking assistant device having a slidable alignment guide and a body holder. The slidable alignment guide is coupled with the body holder, and the handgun selectively engages the device when the magazine is ready to load into the handgun. The device is selectively positioned on the handgun to facilitate loading and cocking the handgun with one hand.

Abstract: A slide assembly quick release pin and arm that secure a recoil assembly within a slide. The pin is inserted through a pair of apertures in a front portion of the slide and through a bore in the nose portion of the recoil assembly aligned between the apertures. As the pin secures the recoil assembly within the slide an arm attached to the end of the pin rests in a recess, flush to the body of the slide in a locked orientation. The pin arm is rotated from a locked orientation within the recess in the assembled configuration to an unlocked orientation out of the recess before the firearm is disassembled. Additionally, the arm acts as a handle for grasping and rotating to provide a mechanical advantage when a user is removing or inserting the pin into the apertures and bore.

Abstract: A noise suppressor design is provided that improves reduction of muzzle blast without increasing the size or weight of the noise suppressor. In various embodiments, a noise suppressor for a firearm might comprise a central axis and a plurality of baffles that each nests within adjacent baffles along the central axis. A first baffle and a second baffle of the plurality of baffles might each comprise a proximal end having a first/second aperture oriented along the central axis and a plurality of notches in the proximal end adjacent to the first/second aperture and aligned in a first orientation. A third baffle of the plurality of baffles might comprise a proximal end having a third aperture oriented along the central axis and a single notch in the proximal end adjacent to the third aperture and aligned in a second orientation that is 90 degrees relative to the first orientation.

Abstract: A variety of apparatuses and associated methods are provided for providing a retractable suppressor system for gas generator systems such as a firearm. One embodiment includes a suppressor system that includes a retractable structure and housing, a fixed baffle, floating baffles, and springs to displace the floating baffles within the suppressor as the suppressor is extended from the housing along a gas generator system, e.g. a barrel of a firearm and thereby enclose the barrel within the suppressor. Embodiments of the invention permit full retraction, partial retraction/extension, or full extension of an exemplary suppressor with respect to an emission section of the gas generator e.g., firearm muzzle. Embodiments of the invention include an external latch which enables an operator to latch or unlatch the suppressor as it moves from one position to another and prevents accidental activation. Embodiments of the invention are configured to operate with accessory mounting systems.

Abstract: A suppressor for a firearm includes a casing having a front end and defining a longitudinal axis. Baffles are inside the casing, and a front cap is downstream from the baffles. A retainer is connected to the casing, disposed between the baffles and the front cap, and has upstream and downstream surfaces. The baffles, front cap, and retainer define a fluid pathway along the longitudinal axis. Apertures through the retainer and radially disposed from the fluid pathway provide fluid communication through the retainer. A contoured wall extends axially upstream from the upstream surface of the retainer and defines a plurality of damping wells in the upstream surface of the retainer radially disposed from the fluid pathway and circumferentially separated by the apertures. The downstream surface of the retainer is symmetrical with the upstream surface.

Abstract: A shock activated laser module for simulated shooting transmits a brief laser beam to mark a point of impact. The module includes a housing, an electro-optical member, a stored energy member and a retaining cap securing the electro-optical member and stored energy member in the housing. The laser module housing is selectively attached in combination to any one of a simulated firearm barrel, a simulated firearm gas reservoir, or to an actual firearm for dry-firing practice.

Abstract: A cocker mechanism for cocking a string of a crossbow is presented, the cocker mechanism comprising a rope, a pair of handles secured to respective ends of the rope and a pair of string connectors operatively secured by the rope between the pair of handles, the string connector comprising a body, a rope-connecting portion including a bearing member rotatably secured to the body about a axle and a bearing member rotation axis thereof for supporting pressure and translational movements of the rope thereon, a string-connecting portion for securing the string of the crossbow when cocking the crossbow. A kit thereof and a method of use thereof are concurrently presented.

Abstract: Apparatus for electromagnetic launching system for the linear acceleration of macro particles. The apparatus disclosed is autonomously-powered, compact, and lightweight. The apparatus disclosed has low recoil force, low acoustic report, and low visible and infra-red signature. The apparatus disclosed is capable of automatic operation and the maximum particle velocity can be adjusted. The apparatus disclosed includes a trigger, controller, component power source, particle container, particle loader, propellant container, propellant loader, igniter, combustion chamber, sound suppressor, linear electrical generator, linear electrical motor, and thermal barrier.

Abstract: A disrupter cannon is used to disrupt or destroy explosive devices. A disrupter cannon may launch a liquid (e.g., water) toward an explosive device to disrupt the explosive device. The liquid may be launched through a nozzle. The nozzle may include passages that spread the liquid to for a column of liquid with a cross-section. A nozzle that provides a column of liquid with an oval cross-section may be more effective at disrupting certain types of explosive devices.

Abstract: A toy gun with a two-stage safety includes a gun body, a trigger press member, a two-stage safety and a trigger assembly. The pull handle is placed inside the gun body and includes a first blocker and a second blocker. The trigger press member includes a press block movably engaged with the first blocker. The two-stage safety includes a movable block, a stopper and a swing block. The stopper is movably engaged with the second blocker or returns toward the pull handle. The stopper includes a protruding portion and a protruding pillar. A side edge or a distal end of the swing block is movably engaged with the protruding pillar. The trigger assembly includes a push block and a linkage rod.

Abstract: A blank-only machine non-firearm includes a replica shell and replica barrel from a non-firing replica machinegun, such as an airsoft replica machinegun. An insert that defines a receiver may be inserted into and contained within the interior volume of the replica shell. An exhaust gas barrel is attached to the receiver and extends within the replica barrel. The replica receiver and barrel are configured to fire blank cartridges and not to fire live rounds. Noise and flash from a firing blank cartridge is directed from a chamber defined by the receiver to the exhaust gas barrel and hence to the replica barrel.

Abstract: An insert for repair or increase durability of 1911-style firearms is disclosed. In addition, a grip modification particularly suited for concealed carry is disclosed.

Abstract: Grip sleeves for firearm grips are disclosed. The grip sleeve may include a hollow body formed of an elastic material. The hollow body may include an inner contact surface configured to be placed around a grip of the firearm, and an outer contact surface surrounding the inner contact surface. The grip sleeve for the firearm may also include a ridge portion extending from the inner contact surface into an interior space of the hollow body. The ridge portion may extend along a height of the hollow body.

Abstract: A detachable folding stock includes folding body sections and a folding butt that can be folded and assumes its operational orientation in either the extended or the folded positions of the stock. The detachable folding stock is removably mountable to a pistol, which is mounted thereon by means of a locking pistol frame stock rim to a pistol grip lock well, for instance using a catching locker. The detachable folding stock includes the lock well, which is attached to the body and into which the pistol grip fits. The detachable folding stock can assume its operational position in a magazine change operation without interrupting the pistol grip lock well during a magazine change operation.

Abstract: In one aspect, a retractable buttstock may include a buttpad that allows the user to rest the weapon on their shoulders; a pair of extension rods; a buffer tube that allows the buttstock to attach to the firearm; and a buffer tube housing to receive the buffer tube. In an exemplary embodiment, the extension rods are hollow and a resilient unit is received in each extension rod. The extension rods have a pair of first positioning grooves and a pair of second positioning grooves to engage with stoppers of the buffer tube housing. The buttstock can be fully-extended and collapsed depending on whether the stoppers engage with the first or second positioning grooves. It is noted that the user can operate the retractable buttstock with one hand.

Abstract: A multi-spectral weapon sight optical system, a multi-spectral weapon sight, and a multi-spectral weapon sight system are disclosed. The multi-spectral weapon sight optical system includes first and second catadioptric optical systems arranged along a common axis and have a common aperture. The first catadioptric optical system forms a first on-axis image from first radiation having a first wavelength band while substantially transmitting second radiation to the second catadioptric optical system wherein the second radiation has a second wavelength band. The second catadioptric optical system forms a second on-axis image using the second radiation. First and second image sensors respectively receive the first and second images and form respective first and second digital images, which are then electronically fused to form a fused image. The fused image is displayed on a display and viewed as a visible display image using a day sight.

Abstract: A handgun mounted accessory such as a laser sight is combined with a trigger-guard mounted flush profile switch to provide high reliability of operation. The switch is designed and located to provide passive user switching in use without separate movement or applied force of the user's hand or fingers.

Abstract: A self-correcting scope compares the original aim point of a projectile discharge device with the actual impact point and self-corrects the scope to account for the offset between these two points. The scope uses a typical optical lens which converts the incoming image to a digital image which is displayed by the invention on a digital display device which functions as the “eyepiece” of the scope. The invention also compresses the image either to the left or to the right or both of the field of interest in order to allow a shooter to be able to detect an intrusion into the field on interest from a point farther than can be achieved in a non-compressed image.

Abstract: An optical device housing has a post rotatably extending therefrom and a sleeve fixedly extending therefrom. The sleeve is disposed around the post. A knob is connected to the post. A clutch mechanism includes: a friction element movably engaged with the sleeve; a friction surface; and an adjustment element engaged with the friction element and rotatable relative to the optical device housing and the knob housing. Rotation of the adjustment element selectively engages the friction surface with the interior surface.

Abstract: A turret cover for a turret assembly. In one or more embodiments the turret cover includes an upper portion including a turret housing defining a battery recess and an illumination recess. An illumination assembly can be mounted in the illumination recess. In various embodiments, the illumination assembly includes a downwardly facing surface including a lighting element. In various embodiments, the turret cover includes a lower portion including an exterior sleeve portion of an at least partially transparent plastic material and a plurality of etched adjustment marks. In some embodiments, the lower portion is at least partially inserted into the illumination recess such that an upwardly facing edge of the exterior sleeve portion is positioned adjacent to the lighting element of the illumination assembly such that, in operation, the lighting element illuminates the plurality of etched adjustment marks via an edge lighting process.

Abstract: An effector launching system and method may be used on a moving ship deck. The launching system includes a plurality of effectors and a robot that is arranged on the moving platform. The robot includes a moveable robot arm having an end portion that is engageable with the effectors for firing the effectors during engagement. The system includes a sensor for detecting movement of the moving platform and a motion stabilization controller that is in communication with a processor and the robot arm for controlling movement of the robot arm. The motion stabilization controller adjusts the robot arm in response to the detected movement of the moving platform to maintain the end portion in a static position when the effector is fired.

Abstract: A mounting mechanism is disclosed. The mounting mechanism includes a base, a clamp and a lever. The base includes a lever keeper and a first rail-engaging surface. The clamp includes a second rail-engaging surface. The lever, which includes a lever tab, is connected to the clamp at a pivot to allow an operator to selectively place the clamp in an engaged position or a disengaged position. The lever is configured to move the clamp to the engaged position to allow a rail projection to be secured in a mounting cavity located between the first rail-engaging surface of the base and the second rail-engaging surface of the clamp. When in the engaged position, the lever tab located on the lever is configured to be engaged with the lever keeper located on the base in order to prevent the lever from swinging away from the clamp.

Abstract: The disclosed technology regards a de-coupled V-hull structure for use with an armored vehicle, and energy absorbing crush elements suitable for mounting the V-hull structure in a de-coupled manner to the vehicle. The energy absorbing V-hull structure includes a sloped armor structure forming a cavity having a v-shaped cross-section and a plurality of reinforcing elements, including a backbone, hull stiffeners and lateral supports. The elements are coupled together and supported by energy absorber mounts, extending along each side of the structure. Crush elements suitable for decoupling the V-hull structure are also disclosed, having a uniquely designed housing, a plurality of plates positioned within the housing, and affixation means for securing the crush element to the underside of the vehicle and to the top of the V-hull structure.

Abstract: The invention pertains to a method for threat handling of a ground based vehicle, comprising the steps of providing at least two kinds of systems for said threat handling, wherein said threat handling comprises determining information about said threat and determining actions for handling said threats based upon said information, and providing a control unit for controlling provided systems, providing a separate hardware safety configuration unit, and providing said separate hardware safety configuration unit with by means of provided means determined information about said threat so as to in an evaluation step deciding if said control unit should be given a go ahead for handling said threat or not. The invention also relates to a computer program product comprising program code for a computer implementing a method according to the invention. The invention also relates to a device and a ground based vehicle which is equipped with the device.

Abstract: An area denial system may be operationally placed with communication latency compensation. The area denial system may include a plurality of munitions, one or more sensor devices, and a command and control unit, networked together and having a command and control latency for communication between the command and control unit and the remainder of the area denial system. Latency compensation may include determining a first target position, determining a first predicted position area for the target using the command and control latency and the first target position, receiving an authorization to arm one or more of the munitions, determining a second target position, and determining that the second target position is outside a threshold distance from a first authorized munition of the one or more authorized munitions, and in response, de-authorizing the first authorized munition.

Abstract: A hand-held personal-protection shock device apparatus and method providing a safety-pin mechanism to prevent unauthorized use or use by an attacker who wrests the device away; a siren that sounds when unauthorized use is attempted; a hand-held configuration that is comfortable to grip securely, with the shocking elements positioned optimally; built-in recharging equipment; and a switch configuration which promotes safe, rapid, and efficient use in an attack by a person or animal.

Abstract: A device comprises a reactive semiconductor bridge including a conductive metal, a reactive material, and an overcoat. When a high current passes through the reactive semiconductor bridge, the conductive metal vaporizes into a high temperature plasma. The reactive material is coupled to the conductive metal such that the conductive metal experiences an exothermic reaction to the plasma. When the conductive metal turns to plasma, the overcoat material absorbs at least a part of the exothermic reaction of the reactive material and breaks into a plurality of particles that are propelled away from the bridge. A gap is disposed between the overcoat and a membrane, and an explosive material couples to the membrane. The plurality of particles crosses the gap and penetrates the membrane to ignite the explosive material in response to being propelled away from the bridge.

Abstract: An improved broadhead for an archery arrow includes a blade member having a rear portion, a tip opposite the rear portion with a chisel point, and a pair of opposing blades. The tip can be generally flat. Each of the opposing blades includes a cutting edge disposed between the blade member rear portion. Each cutting edge includes a concave curved portion, and can include a beveled portion. Each of the opposing blades has a surface that includes a radial curve and each of the cutting edges has a generally helical shape. The blade member can be formed from a single sheet of metal. The blade member can be fixed to a ferrule for mounting to an arrow.

Abstract: An application for a non-lethal arrow. The application may comprise a foam tip and may further comprise an elastic attachment mechanism and a base. The foam tip may comprise an impact end and a base connection end. The elastic attachment mechanism may comprise one or more elastic fingers. The base may comprise a shaft connection end and a flat supporting plate end. The ends of the finger or fingers of the elastic attachment mechanism may be secured to the base. The length of the finger or fingers may be elastically extended and wrapped around at least a portion of the foam tip, holding the foam tip against the flat support plate of the base.

Abstract: The present invention is an improved arrowhead for bowhunting. Furthermore, it is an arrowhead with improved blade strength and blade retention. A ferrule is included in the arrowhead and is used to connect the blades to the arrow shaft. The ferrule has an open slot and a closed slot perpendicular to each other which receive a primary blade and a secondary blade. The two blades interlock by the use of notches along the edges of the two blades that fit together within the open slot. The primary blade has an angle at the tip that is larger than the angle on the remainder of the primary blade improving the strength at the tip of the arrowhead.

Abstract: This disclosure relates to self-contained cartridges and launcher systems for discharging or launching payloads to downrange targets, and methods of attenuating or offsetting recoil when activating such cartridges. Examples of payloads that can be deployed with the disclosed launcher apparatus include chemical, biological, pyrotechnic, marker, tracer, signaling, non-lethal, explosive, smoke, and similar payloads.

Abstract: The missile comprises at least one separable propulsion stage and a terminal vehicle arranged to the front of the separable propulsion stage, said missile being provided at the front with a separable protective fairing comprising at least two individual shells and with a connecting part connected to the missile towards the rear beyond the position of the rear end of the terminal vehicle. The protective fairing is configured such that, when mounted on the missile, it surrounds all of the terminal vehicle and it is connected at the rear end to the connecting part by means of articulated connecting elements.

Abstract: A mechanism including: a toggle link rotatably connected to a base structure; a first element associated with the toggle link; a second element associated with the base structure; a biasing element having a first end attached to the base structure and a second end attached to the toggle link such that the first element moves towards the second element; and a blocking element movably disposed between a first position blocking movement of the toggle link and a second position allowing to first element of the toggle link to move towards the second element when the base structure undergoes an acceleration event greater than a predetermined threshold.

Abstract: The present invention provides a polymeric ammunition comprising: a three piece primer insert; a substantially cylindrical polymeric middle body extending about the three piece primer insert, wherein the substantially cylindrical polymeric middle body comprises: a substantially cylindrical polymeric bullet-end coupling element at a first end of the substantially cylindrical polymeric middle body opposite a substantially cylindrical polymeric coupling end connected by a powder chamber, wherein the substantially cylindrical polymeric coupling end extends over the substantially cylindrical coupling element and covers an circumferential surface of the primer flash hole aperture; and a substantially cylindrical polymeric bullet-end upper portion comprising a bullet-end coupling element connected to the substantially cylindrical polymeric bullet-end coupling element opposite a projectile aperture adapted to engage a bullet.

Abstract: Generally, embodiments of the invention can include a linear shaped charge (LSC) end cap coupling structure adapted for holding an initiator structure adapted to initiate a booster explosive material, the booster explosive material, and the LSC in abutting contact with each other. One embodiment includes a rubber body formed with cavities adapted to receive the LSC, booster, and initiator structure (e.g., detonation cord). One internal cavity can be formed with a plurality of flexible protrusions or fins which are oriented towards a center axis of the preferred embodiment of three cavities configured to impart an interference fit with the initiator structure. Methods related to the invention are also provided.

Abstract: A tape measure including a housing defining an interior and an exterior, where the housing has an opening. A spool is rotatable within the interior of the housing. A tape is at least partially coiled around the spool and extends through the opening of the housing. The tape is movable between an extended position and a retracted position. A biasing member is disposed within the interior of the housing, and the biasing member biases the tape towards the retracted position. The tape measure further includes a bumper disposed at least partially within the housing and having a channel that receives the tape such that the tape extends through the channel. The bumper is movable relative to the housing and is configured to move in response to movement of the tape.

Abstract: A tool for controlling an offset between two stops, includes: a body which includes an extension with an end configured to abut against one of the stops, a sliding rule that is configured to slide in a longitudinal direction in relation to the body and which has an end configured to bear against the other stop, the sliding rule being shifted in a transversal direction in relation to the extension, and a system configured to control the displacement of the sliding rule in relation to the body.

Abstract: In addition to other aspects disclosed, a caliper is configured to measure at least one physical dimension. The caliper has a display configured to present a first representation and a second representation of a measurement provided by the caliper. The format of the first representation is different from the format of the second representation, and the first representation is approximately simultaneously displayed with the second representation.

Abstract: An apparatus for determining the thickness of passing mail items M conveyed on a conveying deck (12) of a mail processing machine (10) comprising a deflecting element (18) which is positioned to successively contact without active compression each conveyed mail item, measures a parameter that indicates a change in a resistivity of the deflecting element, and generates a signal indicative of the measured parameter; and a processing unit (24) which receives the signal from the deflecting element and determines a thickness value for each conveyed mail item based on the measured parameter.

Abstract: A method for high dynamic range and high accuracy interferometry measurements is described. The method uses a broadband light source for generating light, an interferometer, a phase shifting device, an imaging optical system and a detector array for collecting and measuring the reflected light from an object. The detected light is processed by a processor unit to obtain the object's surface.

Abstract: An optical interrogation system, e.g., an OFDR-based system, measures local changes of index of refraction of a sensing light guide subjected to a time-varying disturbance. Interferometric measurement signals detected for a length of the sensing light guide are transformed into the spectral domain. A time varying signal is determined from the transformed interferometric measurement data set. A compensating signal is determined from the time varying signal which is used to compensate the interferometric measurement data set for the time-varying disturbance. The compensation technique may be applied along the length of the light guide.

Abstract: A position measuring apparatus detects, from respective first and second imaging planes of first and second captured images, first and second corresponding points estimated to represent a common three-dimensional position. The apparatus calculates first to fourth projected points. Each of the first and second projected points represents a projected point of the first corresponding point on a corresponding one of the first and second common planes. Each of the third and fourth projected points represents a projected point of the second corresponding point on a corresponding one of the first and second common planes. The apparatus calculates a first beam connecting the first and second projected points, a second beam connecting the third and fourth projected points, and a point having a minimum square distance relative to each of the first and second beams as a restored point representing the three-dimensional position of the first and second corresponding points.

Abstract: Some embodiments of the invention include a coordinate measuring device, in particular a laser tracker, for capturing the position and alignment of a measuring aid, which is movable in space and comprises a retroreflector. In some embodiments, the coordinate measuring device may include at least a support fastened on a base so it is rotatable about a first axis of rotation; a beam deflection unit fastened on the support so it is rotatable about a second axis of rotation, which is essentially orthogonal to the first axis of rotation, a first bearing for the rotatable mounting of the beam deflection unit on the support, and a second bearing for the rotatable mounting of the support on the base.

Abstract: Method and system for measuring one or more parameters of a patterned structure, using light source producing an input beam of at least partially coherent light in spatial and temporal domains, a detection system comprising a position sensitive detector for receiving light and generating measured data indicative thereof, an optical system configured for focusing the input light beam onto a diffraction limited spot on a sample's surface, collecting an output light returned from the illuminated spot, and imaging the collected output light onto a light sensitive surface of the position sensitive detector, where an image being indicative of coherent summation of output light portions propagating from the structure in different directions.

Abstract: Measuring device for measuring test objects includes a transmitter-receiver unit and a corresponding mirror arrangement. Mirror arrangement has a first mirror forming a first focal point and a second focal point in an x-y plane, and first mirror is, at least sectionally, elliptically curved for deflecting radiation between the focal points. Mirror arrangement includes a second mirror arranged in region of first focal point, second mirror is used for deflecting radiation between a z-direction extending transversely to the x-y plane and between the x-y plane. Test object to be measured is arranged in region of second focal point by a test object holder. Radiation reflected on test object is evaluated by a control unit. Measuring device allows measuring of test object in simple and flexible way, in particular measurement over the entire circumference of test objects in form of plastic pipes having circular cross sections.

Abstract: Methods and systems for efficient and accurate inspection of tubular goods are disclosed. Inner and outer diameter measurements of a tubular good along the entire length are obtained using laser or other light measurement systems. Discrete sections of a tubular good can be identified. For each section, at least one measurement of an outer diameter of an outside surface of the discrete section, and at least one measurement of an inner diameter of an inside surface of the discrete section are obtained. In addition, a geometric center coordinate for each discrete section of the tubular good is obtained. The measurements defining the outside surface, inside surface, and geometric center in association with the longitudinal position of each discrete section are recorded.

Abstract: One aspect of the present invention relates to a mask inspection system for inspecting lithography masks, including a placement table for placing a lithography mask to be inspected, a first optical unit with a first beam path for examining structures of the lithography mask, and a second optical unit with a second beam path for establishing a position of at least one edge of the lithography mask. Here, the second beam path of the second optical unit passes at least once through a plane defined by the placement table.