94 results about "Rotational transformation" patented technology

The focal length estimation method and apparatus claimed in this application aligns plural overlapping images with one another for constructing an image mosaic. This is accomplished by computing a planar perspective transformation between each overlapping pair of the images, computing from the planar perspective transformation a focal length of each image of the pair, computing from the focal length of each image a focal length transformation, computing a rotational transformation for each of the pair of images whereby a combination of the rotational transformation and the focal length transformation relates the respective image to a three-dimensional coordinate system. Registration errors between the pair of images are reduced by incrementally deforming the rotational transformation of one of the pair of images. The planar perspective transform is a matrix of warp elements, and the focal length is computed as a function of the warp elements, the function being derivable by constraining a first two rows or the first two columns of the matrix to have the same norm and to be orthogonal. The focal length of one image of a pair of images is found by applying the constraint on the matrix columns, while the focal length of the other image of the pair is found by applying the constraint on the matrix rows

A kit comprising rotating element sheet material and a gradient field stylus, where the sheet material comprises a plurality of rotatable elements disposed in a substrate and in contact with an enabling fluid; where the substrate comprises a plurality of sheet latching components; where one of the rotatable elements comprises first and second rotatable latching components and a core configured to present a first aspect in a first orientation and a second aspect in a second orientation, related by a rotational transformation about an axis of the rotatable element; and where one of the sheet latching components is proximal to the first rotatable latching component in the first orientation and proximal to the second rotatable latching component in the second orientation; and where the rotatable and sheet latching components exhibit an attractive force based on a first gradient field; and where a distal end of the gradient field stylus exhibits an attractive force with the rotatable latching components based on a second gradient field.

The marker has thereon one three-dimensional indicator 3. Based on the location and height of the three-dimensional indicator 3 relative to the plane indicator 2 as well as the estimated position of the camera relative to the marker, the center positions of the upper face and the lower face of the three-dimensional indicator 3 on the image of the camera are estimated. The estimated center position of the upper face of the three-dimensional indicator 3 is compared with that detected from the image. When the error between them has a value equal to or higher than a predetermined value, based on the posture estimated, a rotational transformation is carried out.

A trackball rotates a three-dimensional image displayed by a computer. Displacement data is generated for designated first and second non-antipodal points on the surface of the trackball's roller ball, for displacement of the designated first and second points during a time interval between a starting time and an ending time. The displacement data is used to generate a rotational transformation that is representative of a change in rotational orientation of the roller ball occurring during the time interval. The generated transformation is then applied to the displayed computer image to cause the image to be rotated around an image pivot point in correspondence with the rotation of the roller ball around its center.

The invention discloses a computer-aided design method for fracture reduction. The present invention determines the length and short principal axis of the broken section of the fracture, establishes a three-dimensional rectangular coordinate system, determines the quaternion representation of the vector on the central principal axis and its direction in the three-dimensional coordinate system, and selects the easy-to-operate fractured end as the distal end The fracture ends are rotated, rotated, and translated separately to obtain the coaxial optimal path point of the fracture ends, so as to realize the anastomosis of the fracture sections and complete the fracture reduction; the invention uses quaternion to represent the direction of the central axis of the two fracture ends. Vector, and then obtain the rotation axis and the rotation angle of each rotation, the quaternion is faster to solve when describing the rotation transformation, and can effectively avoid the occurrence of problems such as universal locks; the present invention rotates and spins the broken end of the fracture and translation operations to obtain the optimal coaxial trajectory point of the fracture end, which can provide effective information for doctors to diagnose and operate.

Rotating element sheet material comprising a plurality of rotatable elements disposed in a substrate and in contact with an enabling fluid; where one of the plurality of rotatable elements comprises a core configured to present a first aspect in a first orientation and a second aspect in a second orientation, and where the first orientation and the second orientation are related by a rotational transformation about an axis of the rotatable element, and where the rotatable element in contact with the enabling fluid is further configured to exhibit a first addressing dipole configured to couple with a first vector field and a second addressing dipole configured to couple with a second vector field, and where the rotatable element exhibits the first aspect in the first vector field in a first direction and the second aspect in the second vector field in the first direction.

A diode laser beam combining apparatus for producing a high combined beam power density in the far field at reduced levels of power consumption and heat dissipation includes an array of semiconductor laser emitters arranged in a collinear manner with respect to each other and having an emitter pitch between about 0.7 mm and 2.5 mm. The apparatus also includes a cylindrical lens for collimating emitter beams generated by the array of laser emitters in a direction perpendicular to a junction plane of the laser emitters. The apparatus further includes a micro-optic array and a long focal length cylindrical lens. The micro-optic array is configured to perform a rotational transformation of the collimated emitter beams. The micro-optic array has a lateral spacing in a direction parallel to the junction plane of the laser emitters that matches the emitter pitch. The long focal length cylindrical lens collimates emitter beams in the direction perpendicular to the junction plane after passing through the micro-optic array.

The invention discloses a high-precision five-axis ion beam machining device with high dynamic performance and a control method thereof. The high-precision five-axis ion beam machining device with high dynamic performance comprises a digital control system, a machine frame component, an X-axis linear motion component, a Y-axis linear motion component, a Z-axis linear motion component, an A-axis direct driving component, a B-axis direct driving component, a workpiece conveying component and an ion source; and the accurate movement of the ion source is realized through the driving action in five directions. The control method comprises the following steps: when the machining along the normal direction of an optical mirror surface is carried out, the pose position of an optical mirror surface point in the coordinate system of a workpiece is converted into a coordinate point in the coordinate system of a machine tool through rotational transformation, the equal target range machining along the normal direction is carried out, and the motion pose position of each axis of the machine tool is calculated; and S-type speed machining mode is then adopted, and the speed of each axis of the machine tool at each working point is calculated. The invention has the advantages that the motion is stable, the rigidity is good, the precision is high, and the dynamic performance is high.

The invention relates to a 3D printing path generation method employing parallel modeling and slicing. The method comprises the following steps of: 1) drawing a sweeping path; 2) carrying out discretization to form ordered path points and storing coordinates of various path points; 3) establishing a vector and representing the axis direction from a Pi section to a Pi+1 section through the vector vi; 4) constructing a Rodrigues rotation matrix R, and obtaining a rotation axis k and a rotation angle thetai of spatial rotation change of the Rodrigues rotation matrix R; 5) acquiring section contours of a starting layer and a stop layer; 6) solving point sets of the sections of intermediate layers; 7) repeating the calculation in the step 6), and sequentially solving the point sets of the sections of the intermediate layers; 8) carrying out translation and rotation transformation on the point sets of various layers according to a rotation formula to obtain a space coordinate set M of a final model; and 9) realizing 3D printing employing parallel modeling and slicing according to the corresponding transformation between double-cradle five-axis coordinates and a direct coordinate system.Compared with the prior art, the method has the advantages that slicing and modeling are carried out simultaneously, and the method is suitable for various models.

The invention provides a thin-walled tubular model slicing method and system of a five-axis 3D printer and a printing method. The thin-walled tubular model slicing method comprises the steps that a coordinate system is established, and a three-dimensional model of a to-be-printed workpiece is read; the gravity center of each height cross section of the three-dimensional model is extracted, and all gravity centers are sequentially connecting to obtain a gravity center curve; rotation transformation is performed on a working turntable to enable the projection of a curvature vector of the gravity center curve of the current height layer of the three-dimensional model on the horizontal plane to be zero, the rotating posture information of the working turntable corresponding to the current height layer of the three-dimensional model is obtained, and the slicing information of the current height layer of the three-dimensional model is obtained through calculation; and the current height layer of the three-dimensional model is updated, and the steps are repeated until hierarchical slicing is completed, and the hierarchical slicing information of the to-be-printed workpiece is obtained; According to the thin-walled tubular model slicing method, the projection of the curvature vector of the gravity center curve of the current height layer of the three-dimensional model on the horizontal plane is enabled to be zero through rotation transformation of the table top of the turntable, the posture of the three-dimensional model is adjusted to be vertically upward, support-free printing is realized, the printing effect is good, and the surface precision of a formed part is high.

The invention provides a pre-coding method and device according to a complex matrix, belonging to the field of singular value decomposition, wherein the method comprises the following steps: a step of constructing a real matrix: constructing the real matrix shown in the specification corresponding to the complex matrix H=A+Bi; a step of diagonalizing: diagonalizing the real matrix X through Jacobi iteration so as to obtain a diagonalizable matrix of the real matrix, wherein all non-diagonal elements in the diagonalizable matrix are not more than a pre-set threshold value; a step of calculating the matrix: calculating a singular value diagonalizable matrix D and a right singular matrix V of the complex matrix according to a Jacobi rotational transformation matrix used in the diagonalizable matrix; and a step of pre-coding: pre-coding a signal to be transmitted by an MIMO transmitter utilizing the right singular matrix V by taking the right singular matrix V as a filter matrix. By means of the technical scheme provided by the invention, the SVD processing time of the complex matrix can be reduced; and increasingly high real-time requests can be satisfied.

An accelerometer located within a mobile device is used to estimate a gravity vector on a target plane in a world coordinate system. The accelerometer makes multiple measurements, each measurement being taken when the mobile device is held stationary on the target plane and a surface of the mobile device faces and is in contact with a planar portion of the target plane. An average of the measurements is calculated. A rotational transformation between an accelerometer coordinate system and a mobile device's coordinate system is retrieved from a memory in the mobile device, where the mobile device's coordinate system is aligned with the surface of the mobile device. The rotational transformation is applied to the averaged measurements to obtain an estimated gravity vector in a world coordinate system defined by the target plane.

The invention relates to a method for sensing a large-deformation space pose of a flexible body. The method comprises the following steps of: step 1, arranging three first fiber gratings on the outerperipheral surface of a flexible carrier along a spiral line, connecting two ends of the flexible carrier with a moving end and a fixed end of a to-be-detected flexible body respectively, enabling thethree first fiber gratings to distribute on the same section of the flexible carrier uniformly along the circumference of the section, dividing the flexible carrier into a plurality of sections, andsetting a grid point at each section of the first fiber gratings; step 2, calculating tensile strain, a deflection angle, curvature and a bending angle of each section of the flexible carrier; step 3,substituting the deflection angle, the curvature and the bending angle obtained in the step 2 into a rotation transformation matrix and a translation transformation matrix, acquiring a transformationmatrix between a flexible carrier fixed end coordinate system and a flexible carrier moving end coordinate system according to the rotation transformation matrix and the translation transformation matrix, and acquiring space coordinates of the moving end center and an Euler angle of the moving end surface of the flexible carrier. The sensing method is accurate, efficient and sensitive in response.

A method and an apparatus for encoding and decoding an orientation interpolator indicating the locations of keyframes on a temporal axis and the rotation of an object in each of the keyframes are provided. The apparatus for encoding an orientation interpolator includes an break point extractor which extracts, from a first animation path constituted by an orientation interpolator input thereinto, a minimum number of break points, which can bring about an error of no greater than a predetermined error limit between the first animation path and a second animation to be generated by the extracted break points, a key data encoder which encodes key data input from the break point extractor, and a key value data encoder which encodes key value data input from the break point extractor by generating rotational differential data, by which the object is rotationally transformed by as much as a difference between a rotational transformation value of a current keyframe and a rotational transformation value of a previous keyframe.

The invention provides a method for obtaining a harmonic gear transmission conjugate profile based on rotation transformation. According to the method, a track expression of any point on a center lineof a deformation end of the flexible gear is solved by utilizing coordinate transformation. According to a kinematics principle, a meshing equation of harmonic gear transmission is constructed. And the calculation flow chart of the method is completely drawn. The method is characterized in that the motion trails of points on the center line of the deformation end of the flexible gear are accurately described through coordinate transformation, that is, the center line of the deformation end of the flexible gear is calculated strictly according to the equidistant curve of the outer contour of the wave generator, and the rotation angle can be accurately calculated. When the profile curve of the wave generator and the profile of any gear are known, the theoretical profile of the other gear can be solved by using the method. The method has important guiding significance for optimization design of the contour shape of the harmonic tooth.

The invention discloses a method for calculating a deflection angle corresponding to maximum coil mutual inductance on a spatial scale, and belongs to the technical field of wireless power transmission. According to the method, a spiral coil with a circular section is used as an analysis object, model space parameters are reduced in a coordinate rotation transformation mode, and directional pitching analysis is carried out on a secondary coil in a space range. In the aspect of mutual inductance formula calculation, a mutual inductance calculation formula of a coupling coil at a spatial position is derived by adopting an optimization method of a Taylor series expansion formula according to a Neumann electromagnetic theory. An analysis result shows that when a transmitting coil is fixed at an original point and a receiving coil is located at any spatial position, a unique pitching deflection angle can be always found such that the mutual inductance between the coupling coils is in a maximum state. Moreover, under the condition that the parameters of the coil are known, a specific equation relation exists between a pitching rotation angle and the spatial position of the primary centerof the secondary coil. According to the method, the deflection angle corresponding to the optimal mutual inductance of a model can be effectively calculated through the formula.

The invention relates to a method and apparatus for quantifying dimensional variations and process capability independently of datum points, and, more specifically, relates to a measurement system which receives design values specifying measurement points of a first design and values corresponding to measurement points of a first part manufactured according to the first design using a first process. The system calculates a reference point of the first part and translates the received values based on a difference between reference points of the first part the first design. The system includes a rotation module that applies a rotational transformation with a first angle to the translated values. The system includes an error minimization module that determines a first value for the first angle that minimizes deviations between the transformed values and the specified design values. The system includes an error determination module that computes deviations between the transformed values and the specified design values. The system includes an analysis module that calculates a process metric of the first process based on the computed deviations.

The invention discloses a three-dimensional character loop animation automatic accumulation method. The method includes the steps of calculating relative location Qk of a controller Ck corresponding to every portion of a character with an abdomen center point of the character as the origin of a coordinate for a three-dimensional character model completing frame binding; performing spaced sampling along a character movement path S, and calculating the normal Nn and the tangent Tn of a path curve of every sampling point; calculating a rotational transformation matrix Mn between two consecutive sampling points according to the normal Nn and the tangent Tn; calculating a step conversion factor Stepn of the controller Ck corresponding to every portion of the three-dimensional character; calculating displacement and rotation animation data of the controller Ck corresponding to every portion of the character during the movement along the movement path S after taking step accumulation into consideration according to the step conversion factor Stepn. The three-dimensional character loop animation automatic accumulation method provides a quick automatic generation method for common animation of characters moving along paths of three-dimensional animation.

A method and an apparatus for encoding key value data of an orientation interpolator representing the rotation of an object in a keyframe image are provided. The apparatus includes a rotational differential data generator which generates, using a rotational transformation value of a current keyframe and a restored rotational transformation value of a previous keyframe, a rotational differential value used to rotate the object by as much as a difference between rotational transformation applied to the object in the current keyframe by key value data and rotational transformation applied to the object in the previous keyframe by key value data, and outputs rotational differential data by quantizing the rotational differential value, a circular DPCM operator which selectively performs a linear DPCM operation or a circular DPCM operation on rotational differential data, and an entropy encoder which entropy-encodes the rotational differential data.

A method and an apparatus for encoding key value data of an orientation interpolator representing the rotation of an object in a keyframe image are provided. The apparatus includes a rotational differential data generator which generates, using a rotational transformation value of a current keyframe and a restored rotational transformation value of a previous keyframe, a rotational differential value used to rotate the object by as much as a difference between rotational transformation applied to the object in the current keyframe by key value data and rotational transformation applied to the object in the previous keyframe by key value data, and outputs rotational differential data by quantizing the rotational differential value, a circular DPCM operator which selectively performs a linear DPCM operation or a circular DPCM operation on rotational differential data, and an entropy encoder which entropy-encodes the rotational differential data.

The invention relates to a control method, system and equipment for a surgical field center of a reconstruction instrument and a readable storage medium, and the method comprises the steps: obtaining a current pose of a movable platform under a mechanical coordinate system after reconstructing the instrument surgical field center, and obtaining a target pose of a static platform under the mechanical coordinate system after reconstructing the instrument surgical field center according to the current pose of the movable platform; performing pose transformation on the static platform according to the current pose of the movable platform and the target pose of the static platform; obtaining the torsion angle between the movable platform and the static platform on the central axis according to the current pose of the movable platform and the target pose of the static platform, performing rotation transformation on the movable platform according to the torsion angle so that the parallel platform can return to the zero position, and the problem that in the prior art, it is difficult to achieve pose zero returning of a parallel robot is solved; the control accuracy of reconstruction of instrument surgical field center is improved, and the motion performance of the parallel platform is guaranteed.

The invention belongs to the technical field of infrared, and particularly relates to a thermal rotation device suitable for conduction, convection and radiation at the same time. The thermal rotationdevice of the present invention is obtained by performing rotation conversion on a specific region by coordinate conversion. For example, the thermal rotation device is obtained by rotating an angleof an annular area through coordinate transformation, material parameters of the thermal rotation device are determined, direction regulation and control of local heat flow are achieved, the local heat flow in the thermal rotation device is made to rotate, and meanwhile temperature distribution of the background is not affected. The method is not only suitable for a steady state condition, but also suitable for a transient state condition. The feasibility of the rotator device is verified through finite element simulation. Due to the fact that conduction, convection and radiation can be seen everywhere in the nature, the device has wide application value, for example, the heat flow direction can be changed to achieve recycling of waste heat.

The invention relates to an iron shell and tooth permanent magnet spherical motor cogging torque analysis method. The cogging torque generated when one magnetic pole is obtained through a finite element, then the cogging torque generated by other magnetic poles is obtained through space coordinate rotation transformation, all the cogging torques are superposed to obtain the total cogging torque, and therefore the corresponding relations between the rotor space position and the cogging torque are obtained.

The invention provides a multi-axis mechanical arm and a manipulator. The multi-axis mechanical arm comprises a base, a first rotating piece rotationally connected with the base, a first connecting rod rotationally connected with the first rotating piece, a second connecting rod rotationally connected with the first connecting rod, a second rotating piece rotationally connected to one end of the second connecting rod, a third connecting rod rotationally connected to one end of the second rotating piece and a third rotating piece rotationally connected to the third connecting rod, and the multi-axis mechanical arm further comprises a driving assembly used for driving the first rotating piece, the first connecting rod, the second connecting rod, the second rotating piece, the third connecting rod and the third rotating piece to move. The multi-axis mechanical arm is provided with six rotating shafts, can freely rotate in a three-dimensional space, is provided with three rotating pieces,and can change the position of the end part of the multi-axis mechanical arm through the rotation of each rotating piece, so that the fine action of an end effector of the mechanical arm is realized.

A new gaming tool and method of game play including an unconventional deck of playing-cards not employing symbolic relations, but rather employing actual relations between rectilinear geometric regions. The playing-cards preferably employ geometric interactions of reflection, complementarity, contrariety, and identity. Geometric card properties that further enhance game play include figure-ground reversibility, handedness, rotational transformation, and perpendicular association. Indexing indicia are optionally provided so that the user can easily visualize the rectilinear geometric regions on a playing card by looking at only the corner of the card.