Abstract: An optic has a freeform optical surface transforming incident light emitted by a zero-étendue light source to form an irradiation pattern including a caustic of light rays focused along a curve. The transverse thickness of the illuminated curve is determined by the diffraction limit of the wavelength of the incident light.

Abstract: An optic has a freeform optical surface transforming incident light emitted by a zero-étendue light source to form an irradiation pattern including a caustic of light rays focused along a curve. The transverse thickness of the illuminated curve is determined by the diffraction limit of the wavelength of the incident light.

Abstract: A battery pack is provided for a mobile communication device, comprising a casing defining a cavity that conforms, at least partially, to the outer shape of the mobile communication device and one or more rechargeable power cells housed within the thickness of the casing. An internal interface engages a corresponding interface on the mobile communication device to provide power from the one or more rechargeable cells to the mobile communication device. An external interface is electrically coupled to the internal interface in order to transmit signals from the mobile communication device to an external device and may further serve to recharge the one or more rechargeable power cells. The battery pack may also serve as an extendible platform by providing additional integrated communication interfaces and/or processors that can be utilized by the mobile communication device to extend its communication and/or processing capabilities.

Abstract: Disclosed is durable and water-resistant or water-proof communication accessory with a built-in battery for a mobile communication device capable of enclosing, powering, and protecting a mobile device and protecting it from dirt, water, weather, bumps, and scratches. The built-in battery can extend the battery operating time of mobile communication device while protecting the sensitive electronics, glass screen, and data.

Abstract: An optic has a freeform optical surface transforming incident light emitted by a spatially extended light source into a constellation of images of the spatially extended light source. The images in the constellation are mixed to form a target illumination pattern having a sharp-edge at least along a portion of a boundary. The images include a focused image, and an edge of the focused image participates in forming the sharp-edged boundary the target illumination pattern.

Abstract: An optic has a freeform optical surface transforming incident light emitted by a spatially extended light source into a constellation of images of the spatially extended light source. The images in the constellation are mixed to form a target illumination pattern having a sharp-edge at least along a portion of a boundary. The images include a focused image, and an edge of the focused image participates in forming the sharp-edged boundary the target illumination pattern.

Abstract: Embodiments of this disclosure relate to battery packs and/or holsters and, more particular, to an external battery pack and/or holster for mobile electronic devices.

Abstract: A method determines a sequence for drilling holes in a workpiece according to a pattern by first partitioning the holes in the pattern into packets. A global sequence of the packets is determined by solving a global traveling salesman problem (TSP), and a local sequence of the holes in each packet is determined by solving a local TSP for each packet. Then, the local sequences of the holes are joined according to the global sequence of the packets to determine a complete sequence for drilling the holes.

Abstract: A method controls an operation of a machine using a model predictive control (MPC). The method determine, in response to receiving a state of the operation of the machine, a dual solution of a dual parametric problem of a parametric form of the MPC using a parallel quadratic programming (PQP) rescaling iteratively a candidate dual solution of the dual parametric problem. The coefficients of the dual parametric problem include data representing dynamics of the machine and constraints on the operation of the machine. A parameter of the dual parametric problem includes the state of the operation of the machine. The method determines a primal solution of a primal problem of the MPC using the dual solution of the dual parametric problem.

Abstract: A method for generating a representation of a polyline formed by a sequence of points determines an overcomplete set of geometric primitives that redundantly fit overlapping sections of the polyline. The overcomplete fitting is performed such that the set includes one or more types of geometric primitives, each fitted to a section of the polyline formed by a subset of the sequence of points. The method determines a local cost of each geometric primitive based on a combination of a fitting error and an encoding cost of the geometric primitive, and determines a join cost of each successive pair of adjacent primitives. Next, the method determines a combination of the geometric primitives forming a connected path along a length of the polyline such that a sum of the local costs of the geometric primitives and the join costs of adjacent primitives in the combination is optimized.

Abstract: A method for generating a trajectory based on an input trajectory formed by points representing spatial coordinates for a numerically controlled (NC) process determines a plurality of sequences of the points and determines, for each sequence, local costs of each point in the input trajectory. Each sequence is formed by removing a unique combination of points from the input trajectory and the local cost of a point for a sequence is determined based on a spatial arrangement of the point with respect to at least some of points in the sequence. For each sequence, a sum of corresponding local costs of each point in the input trajectory is determines and the trajectory is determined based on an optimal sequence with an optimal value of the sum of the local costs.

Abstract: A battery pack is provided for a mobile communication device, comprising a casing defining a cavity that conforms, at least partially, to the outer shape of the mobile communication device and one or more rechargeable power cells housed within the thickness of the casing. An internal interface engages a corresponding interface on the mobile communication device to provide power from the one or more rechargeable cells to the mobile communication device. An external interface is electrically coupled to the internal interface in order to transmit signals from the mobile communication device to an external device and may further serve to recharge the one or more rechargeable power cells. The battery pack may also serve as an extendible platform by providing additional integrated communication interfaces and/or processors that can be utilized by the mobile communication device to extend its communication and/or processing capabilities.

Abstract: Locations in a pattern of a part are evaluated to determine if the locations are interior or exterior to a feature of the pattern. The pattern is used to cut the feature from a material by a laser cutting machine. A location in the feature is rendered into an array stored in a memory so that a value stored at an address in the array corresponding to coordinates of the location is either odd or even as determined by a counting process of the rendering. Then, the location is identified as being interior if the value is odd, and as being exterior if the value is even. The rendering can use modified forms of either rasterization or ray casting.

Abstract: A method for planning a radiation therapy treatment of a body represented by a volume of voxels determines a radiation dose matrix representing a spatial distribution of a radiation dose of beams of radiation irradiating the volume with homogeneous stopping power. The beams are collimated and are shifted copies of each other at each depth of the volume, and the spatial distribution is determined by calculating cumulative beam-axial doses in a single matrix-matrix multiplication and redistributing the cumulative beam-axial doses to all voxels in the volume using a convolution. Next, a set of correcting operations is applied to the radiation dose matrix to produce a cumulative voxel radiation dose of the volume. Each correcting operation is linear, independent from another correcting operation and has a transform.

Abstract: A method determines a sequence for drilling holes in a workpiece according to a pattern by first partitioning the holes in the pattern into packets. A global sequence of the packets is determined by solving a global traveling salesman problem (TSP), and a local sequence of the holes in each packet is determined by solving a local TSP for each packet. Then, the local sequences of the holes are joined according to the global sequence of the packets to determine a complete sequence for drilling the holes.

Abstract: A method for generating a representation of a polyline formed by a sequence of points determines an overcomplete set of geometric primitives that redundantly fit overlapping sections of the polyline. The overcomplete fitting is performed such that the set includes one or more types of geometric primitives, each fitted to a section of the polyline formed by a subset of the sequence of points. The method determines a local cost of each geometric primitive based on a combination of a fitting error and an encoding cost of the geometric primitive, and determines a join cost of each successive pair of adjacent primitives. Next, the method determines a combination of the geometric primitives forming a connected path along a length of the polyline such that a sum of the local costs of the geometric primitives and the join costs of adjacent primitives in the combination is optimized.

Abstract: A method for reconstructing—three-dimensional (3D) lines in a 3D world coordinate system from two-dimensional (2D) lines in a single image of scene detects and clusters the 2D lines using vanishing points. A constraint graph of vertices and edges is generated, wherein the vertices represent the 2D lines, and the edges represents constraints on the 2D lines, then identifying the 3D lines that satisfy the constraints and reconstructing the 3D lines using the identified constraints.

Abstract: A battery pack is provided for a mobile communication device, comprising a casing defining a cavity that conforms, at least partially, to the outer shape of the mobile communication device and one or more rechargeable power cells housed within the thickness of the casing. An internal interface engages a corresponding interface on the mobile communication device to provide power from the one or more rechargeable cells to the mobile communication device. An external interface is electrically coupled to the internal interface in order to transmit signals from the mobile communication device to an external device and may further serve to recharge the one or more rechargeable power cells. The battery pack may also serve as an extendible platform by providing additional integrated communication interfaces and/or processors that can be utilized by the mobile communication device to extend its communication and/or processing capabilities.

Abstract: A method determines trajectories of redundant actuators of a machine including a first actuator and a second actuator. The method determines a first trajectory of the first actuator tracking a reference trajectory with an error tolerance, wherein the error tolerance is a function of a constraint of the second actuator, and determines a second trajectory of the second actuator based on a difference between the reference trajectory and the first trajectory.

Abstract: A battery pack is provided for a mobile communication device, comprising a casing defining a cavity that conforms, at least partially, to the outer shape of the mobile communication device and one or more rechargeable power cells housed within the thickness of the casing. An internal interface engages a corresponding interface on the mobile communication device to provide power from the one or more rechargeable cells to the mobile communication device. An external interface is electrically coupled to the internal interface in order to transmit signals from the mobile communication device to an external device and may further serve to recharge the one or more rechargeable power cells. The battery pack may also serve as an extendible platform by providing additional integrated communication interfaces and/or processors that can be utilized by the mobile communication device to extend its communication and/or processing capabilities.