Patent Publication Number: US-2023146452-A1

Title: Method and apparatus for modeling and forming fiber-reinforced composite objects

Description:
FIELD 
     The present invention relates to systems and methods for modeling and forming fiber-reinforced plastic composite objects comprising one or more fiber tows. 
     BACKGROUND 
     Fiber-reinforced plastics (FRP), also called fiber-reinforced polymers, for example carbon fiber-reinforced plastics (CFRP) are widely used materials for lightweight structures, ranging from sports equipment, to automotive components, to aircraft structures. A method for manufacturing of FRP&#39;s comprises depositing fiber tows, for example preimpregnated fiber tows. 
     Forming of fiber-reinforced plastic composite objects is, for example, accomplished with robots to deposit layers of fiber material. Given a design, for example a three-dimensional model of an object to manufacture, raises the problem of how to manufacture the object using a plurality of layers of fiber material, for example using a robotic system. There is therefore a need for a system to assist a user with the analysis of an object to be manufactured using a plurality of fiber layers, to decompose the object into manufacturable components, to plan the paths of a robot that will deposit a plurality of fiber layers to form the components, and to prepare commands for guiding a robot to deposit the fiber layers. Although solutions exist for manufacturing of objects using flat fiber tapes, there is a need for solutions for analyzing, segmenting, and manufacturing objects using fiber tows which are substantially narrower and thicker than fiber tapes. There is also a need for systems and methods to to plan the application of fiber tows onto a surface to form an object. There is also a need to lay fiber tows over trajectories that comprise curves with small radii of curvature, and with improved and diversified fiber layout patterning capabilities. There is also a need for systems and methods to forecast and adjust a design for a compression molding step that, for example, introduces distortions in an object and the paths of the fiber material from which the object is made. 
     SUMMARY 
     This disclosure presents methods and systems for designing, segmenting, planning, and forming fiber-reinforced plastic composite objects. For example, the fiber-reinforced plastic composite objects comprise elongate fiber tows, for example elongate carbon fiber tows. For example, the fiber tows, because they are narrow, can be formed into tight curves. A method for forming tight curves using an elongate fiber tow comprises, for example, one or more of depositing the tow onto the surface of an object using a pressure foot device and forming a twist in the tow. For example, the pressure foot device is rotatable around an axis, for example an axis orthogonal to the surface of the object. The method for forming tight curves comprises, for example, rotating the pressure foot device that comprises a groove for one or more of guiding and rotating the tow onto the surface of an object. 
       FIG.  5    is a block diagram of a method for modeling and forming fiber-reinforced objects. The method is, for example, a computer-implemented method. The computer-implemented method is, for example, stored as computer-readable instructions on a non-transitory computer-readable storage medium. For example, the computer-implemented method, comprises, under the control of one or more computer systems configured with executable instructions: acquiring a digital model comprising two or more spatial dimensions of an object to be manufactured; forming a three-dimensional model decomposition of the object to be manufactured, wherein forming the three-dimensional model decomposition comprises segmenting at least a portion of the digital model comprising two or more spatial dimensions into one or more surface-based component models; and forming, on one or more surfaces of the one or more surface-based component models, one or more paths comprising one or more elongate fiber tow models. 
     For example, an embodiment of a surface-based component is planar. For example, an embodiment of a surface-based component is an isotropic deformation of a planar sheet, for example curved into one or more of a cylinder, a cylinder sector, a U, a V, a parabola, a wave. For example, the surface-based component is an isotropic deformation a planar sheet having undergone further anisotropic deformation that comprises one or more of stretching, compressing, and double-curvature bending in an additional range of, for example, up to 20% of the isotropic deformation of the planar sheet. 
     For example, one or more of the one or more elongate fiber tow models is formed of one or more longitudinally-folded fiber tape models. For example, one or more of the one or more elongate fiber tow models comprises a rectangular cross-section. For example, one or more of the one or more elongate fiber tow models comprises a width  100 W comprised in a range from 0.2 mm to 4 mm, for example from 0.4 mm to 2 mm. For example, one or more of the one or more elongate fiber tow models further comprises a height comprised in a range from 0.03 mm to 0.5 mm, for example from 0.12 mm to 0.25 mm. 
     For example, forming one or more paths comprises forming one or more concentric paths that are concentrically adjacent to each other. For example, forming one or more paths comprises forming one or more contour paths that follow at least a portion of a contour of one or more of the one or more surface-based component models; and forming a first layer comprising a first plurality of parallel paths and forming a second layer comprising a second plurality of parallel paths, wherein the second layer overlaps the first layer and the paths in the second layer are orthogonal to the paths in the first layer; and wherein the area covered by the first layer and the second layer is at least partially bounded by the one or more contour paths. 
     For example, forming one or more paths comprises acquiring a value for a number of layers of paths to form. For example, forming one or more paths comprises acquiring a value for a number of coplanar adjacent paths to form. For example, forming one or more paths comprises adjusting a spread of two or more coplanar adjacent paths to form. For example, forming one or more paths comprises acquiring a value for adjusting a spread of two or more coplanar adjacent paths to form over a selected region comprising one or more dimensions. For example, forming one or more paths comprises acquiring a value for a minimum longitudinal tow extremity offset from a surface-based component&#39;s contour. 
     For example, forming one or more paths comprises actuating a tow cutter as a function of one or more of a minimum tow extremity longitudinal offset from a surface-based component&#39;s contour, a path extremity longitudinal distance from a surface-based component&#39;s contour, and a lower limit on the tow length. 
     For example, forming one or more paths comprises forming one or more adjacently concentric spiral paths. For example, an adjacently concentric spiral comprises a spiral path comprising one or more tows that are adjacent along their longitudinal side. For example, a tow in a spiral path is longitudinally adjacent to itself upon completing one or more loops. In some embodiments, a filler, for example comprising a thermoplastic material, is formed between the tows forming the loops of the spiral path. 
     For example, forming one or more paths comprises forming one or more concentric contour paths that follow at least a portion of a contour of one or more of the one or more surface-based component models. For example, forming one or more paths comprises forming one or more contour paths at one or more offsets from a contour of one or more of the one or more surface-based component models. 
     For example, the method comprises acquiring path instructions comprised in a path pattern library. For example, the path pattern library comprises forming one or more of: a rectangular path pattern; a rounded rectangular path pattern; a circular path pattern; and a figure of eight path pattern. For example, forming one or more paths comprises forming one or more path patterns selected from a path pattern library. 
     For example, forming one or more paths comprises defining one or more regions of interest  16108  comprising one or more dimensions X, Y, Z and wherein the one or more regions of interest are highlighted on a computer display presenting one or more views of the surface-based components. For example, forming one or more paths comprises forming one or more path patterns selected from a path pattern library at one or more offsets from the one or more regions of interest. 
     For example, the method comprises acquiring a digital model of the object to be manufactured comprises storing in computer memory forbidden regions wherein the forming of paths comprising one or more elongate fiber tow models is excluded. For example, the method comprises highlighting, on a computer display presenting one or more views of the surface-based components, one or more of the forbidden regions. For example, the acquired digital model of the object to be manufactured comprises designated forbidden regions wherein the forming of paths comprising one or more elongate fiber tow models is excluded. 
     For example, forming of one or more paths comprising one or more elongate fiber tow models comprises a lower limit on the tow length. For example, forming one or more paths comprising one or more elongate fiber tow models comprises instructions to read from memory a lower limit on the tow length. For example, the method comprises highlighting, on a computer display presenting one or more views of: one or more of the surface-based components; one or more of the paths; and one or more of the elongate fiber tow models; wherein one or more of the elongate fiber tows the length of which is less than the lower limit on the tow length. 
     For example, forming one or more path comprising one or more elongate fiber tow model comprises reading from a computer memory a lower limit on the radius of curvature of the paths wherein a fiber tow follows the path continuously. For example, the method comprises highlighting, on a computer display presenting one or more view of the surface-based components, one or more of the tow path wherein the radius of curvature is lower than the radius of curvature lower limit stored in memory. 
     For example, forming one or more paths comprising one or more elongate fiber tow models comprises instructions to store in memory the tow twist at one or more locations along the path. For example, the method comprises highlighting, on a computer display presenting one or more views of the surface-based components, one or more of the tow paths wherein the tow twist is greater than a tow twist threshold stored in memory. 
     For example, forming of one or more paths comprising one or more elongate fiber tow models comprises a lower limit on the radius of curvature of the paths wherein a fiber tow follows the path continuously. For example, forming of one or more paths comprising one or more elongate fiber tow models comprises recording the tow twist at one or more locations along the path. For example, forming of one or more paths comprising one or more elongate fiber tow models comprises forming a discontinuity in the fiber tow at one or more locations in the path comprising a radius of curvature that is less than a lower limit. For example, forming of one or more paths comprises actuating a tow cutter  2300 . 
     For example, forming of one or more path comprising one or more elongate fiber tow model comprises forming one or more dimensional value of tow-free space enclosed by one or more path. For example, the one or more dimensional value of tow-free space is estimated, for example using a computation on a processor, in 2 or 3 spatial dimensions. For example, an alarm is raised, for example visually on a display, for example as a highlight projected onto the model, if one or more tow-free space value is greater than a predefined threshold, for example stored in memory. For example, if a value of tow-free space is greater than a tow-free space threshold value, one or more reinforcing path is formed within the tow-free space. 
     For example, forming of one or more path comprising one or more elongate fiber tow model comprises forming along the path one or more value of tow-free distance to one or more path around one or more of the path&#39;s centerline and the path&#39;s edge. For example, if a value of tow-free distance is greater than a tow-free distance threshold value, one or more waypoint defining the one or more path is adjusted to decrease the tow-free distance of the one or more path. For example, if a value of tow-free distance is greater than a tow-free distance threshold value, adjusting one or more waypoint defining the one or more path to decrease the tow-free distance of the one or more path. For example, the method comprises highlighting, on a computer display presenting one or more view of the surface-based components, one or more of the tow path wherein the tow-free distance is greater than a tow-free distance threshold stored in a computer memory. 
     For example, forming of one or more path comprising one or more elongate fiber tow model comprises forming a plurality of parallel paths that are spaced apart by a distribution profile specified by one or more distribution component. For example, the distribution profile comprises one or more of a ramp, an ellipse, a parabola, a hyperbola, and a curve specified using a user-edited function. 
     For example, segmenting the digital model comprises forming a first surface-based component comprising a first half-joint comprising one or more of a tenon and a mortise and forming a second surface-based component comprising a second half-joint matching the first half-joint and comprising one or more of a mortise and a tenon. For example, segmenting the digital model comprises: forming a first surface-based component and forming a second surface-based component that forms a joining between the first surface-based component, wherein one or more of the first surface-based component and the second surface-based component comprises one or more fillet at the joining between the first surface-based component and the second surface-based component. For example, segmenting the digital model comprises forming a first surface-based component and forming a second surface-based component that forms a joining between the first surface-based component at a joining region, and wherein the forming one or more path model comprises forming on the second surface-based component, at the joining region, one or more path that forms an angle of at most 80°, for example at most 60°, with a normal to the first surface-based component at the joining region. 
     For example, the method comprises acquiring one or more axis of symmetry in one or more of the surface-based components and dividing the one or more of the surface-based components at the one or more axes of symmetry into a plurality of component regions; and wherein the forming one or more path models comprises forming one or more first path model into a first component region of the plurality of component regions and mirroring the first path model into one or more of the other component regions of the plurality of component regions. 
     For example, the method comprises highlighting, on a computer display presenting one or more view of the surface-based component, one or more of the component region. For example, the method comprises highlighting, on a computer display presenting one or more view of the surface-based component, one or more axis of symmetry in one or more of the surface-based component. 
     For example, forming a three-dimensional model decomposition comprises enlarging one or more of the one or more surface-based component in one or more direction. For example, the method comprises a step of simulating a step comprising one or more of heating and compressing an assembly comprising one or more surface-based component models comprising one or more elongate fiber tow. For example, the simulating step comprises simulating a compression molding step. For example, the simulating step comprises forming one or more of a heating simulation and a compression simulation and rendering its results on a computer display. For example, the simulating step comprises estimating a decrease in size in one or more direction of one or more of the one or more surface-based components. For example, the simulating step comprises deforming one or more of the one or more surface-based components in one or more three-dimensional direction at one or more surface location. For example, the simulating step comprises forming instructions to adjust a computer-controlled compression molding process. For example, the simulating step comprises simulating a flow of infill material. For example, the simulating step comprises estimating a decrease in size in one or more dimension of one or more region comprising infill material. For example, the simulating step comprises estimating the displacement in one or more dimension of one or more path. For example, the simulating step comprises estimating the displacement in one or more dimensions of one or more elongate tow. For example, the simulating step comprises highlighting, on a computer display presenting one or more view of the surface-based components, one or more region wherein a displacement of infill material is greater than an an infill displacement threshold stored in memory. 
     For example, forming one or more path comprises forming one or more command to rotate a pressure foot device. For example, forming one or more path comprises forming one or more command to rotate a pressure foot device to an orientation angle with respect to a local tangent to the path being formed. For example, forming one or more path comprises actuating one or more pinch roller. 
     The disclosure also presents a system comprising: one or more computer processor; and memory with executable instructions that, when executed by the one or more processor, cause the system to: receive a digital model comprising two or more spatial dimensions of an object to be manufactured; form a three-dimensional model decomposition of the object to be manufactured, wherein forming the three-dimensional model decomposition comprises segmenting at least a portion of the digital model comprising two or more spatial dimensions into one or more surface-based component; and form, on a surface of the one or more surface-based component model, one or more path comprising one or more elongate fiber tow model. For example, one or more of the one or more elongate fiber tow model is formed of one or more longitudinally-folded fiber tape model. 
     For example, the system comprises an apparatus comprising a pressure foot device comprising a channel for guiding an elongate fiber tow onto an object surface. For example, the channel comprises a groove. For example, the pressure foot device is coupled to a pressure foot device rotation actuator. For example, the pressure foot device is comprised in a foot shaft housing  2100 , characterized by a pressure foot device&#39;s axis of rotation Z, defining a Z-axis, wherein the pressure foot device&#39;s axis of rotation Z is collinear with the channel for guiding an elongate fiber tow onto an object surface. 
     For example, the system comprises a computer display. For example, the system comprises a communication network connected to a system for applying an elongate fiber tow. For example, the system comprises a communication network connected to a computer server comprising a non-volatile storage medium comprising instructions describing one or more of: one or more digital model comprising two or more spatial dimensions of one or more object to be manufactured; one or more plane-based component; and one or more path. For example, one or more of the system and the computer server one or more of receive and transmit data indicating the status of the system and the state of an object being manufactured. 
     The disclosure also presents a non-transitory computer-readable storage medium comprising executable instructions that, when executed by one or more processor of a computer system, cause the computer system to at least: acquire a digital model comprising two or more spatial dimensions of an object to be manufactured; form a three-dimensional model decomposition of the object to be manufactured, wherein forming the three-dimensional model decomposition comprises segmenting at least a portion of the digital model comprising two or more spatial dimensions into one or more surface-based component; and form, on a surface of the one or more surface-based component model, one or more paths comprising one or more elongate fiber tow model. 
     For example, the instructions to form one or more path further comprise instructions to execute one or more of forming, loading, and storing into memory one or more elongate fiber tow model formed of one or more longitudinally-folded fiber tape model. For example, the elongate fiber tow model is a digital model, for example comprised in a digital library, for example stored on a non-transitory computer-readable storage medium. For example, one or more of the one or more elongate fiber tow model comprises a rectangular cross-section. For example, one or more of the one or more elongate fiber tow model comprises a width comprised in a range from 0.2 mm to 4 mm, for example from 0.4 mm to 2 mm. For example, one or more of the one or more elongate fiber tow models further comprises a height comprised in a range from 0.03 mm to 0.5 mm, for example from 0.12 mm to 0.25 mm. 
     For example, the instructions to form one or more path comprises instructions to form one or more set of concentric paths that are concentrically adjacent to each other. For example, the instructions to form one or more paths comprise instructions to: form one or more contour paths that follow at least a portion of a contour of one or more of the one or more surface-based component model; and form a first layer comprising a first plurality of parallel paths and form a second layer comprising a second plurality of parallel paths, wherein the second layer overlaps the first layer and the paths in the second layer are orthogonal to the paths in the first layer; and wherein the area covered by the first layer and the second layer is at least partially bounded by the one or more contour path. For example, the instructions to form one or more path comprise instructions to acquire a value for a number of layers of paths to form. For example, the instructions to form one or more path comprise instructions to acquire a value for a number of coplanar adjacent paths to form. For example, the instructions to form one or more path comprise instructions for adjusting a spread of two or more coplanar adjacent paths to form. 
     For example, the instructions to form one or more paths comprise instructions to acquire a value for adjusting a spread of two or more coplanar adjacent paths to form over a selected region comprising one or more spatial dimensions. For example, the instructions to form one or more paths comprise instructions to acquire a value for a minimum longitudinal tow extremity offset from a surface-based component&#39;s contour. 
     For example, the instructions to form one or more paths comprise instructions to actuate a tow cutter as a function of one or more of a minimum tow extremity longitudinal offset from a surface-based component&#39;s contour, a path extremity longitudinal distance from a surface-based component&#39;s contour, and a lower limit on the tow length. 
     For example, the instructions to form one or more paths comprise instructions to form one or more adjacently concentric spiral paths. For example, the instructions to form one or more paths comprise instructions to form one or more concentric contour paths that follow at least a portion of a contour of one or more of the one or more surface-based component models. For example, the instructions to form one or more paths comprise instructions to form one or more contour paths at one or more offsets specified in one or more directions from a contour of one or more of the one or more surface-based component models. 
     For example, the instructions further comprise instructions to acquire path instructions comprised in a path pattern library. For example the path pattern library is stored on a non-volatile storage medium. For example, the instructions comprised in the path pattern library comprise instructions to form one or more of: a rectangular path; a rounded rectangular path; a circular path; and a figure of eight path  7801 . For example, the instructions to form one or more paths comprise instructions to form one or more path patterns selected from a path pattern library. 
     For example, the instructions to form one or more paths comprise instructions to define one or more regions of interest comprising one or more dimensions and wherein the one or more regions of interest are highlighted on a computer display presenting one or more views of the surface-based components. For example, the instructions to form one or more paths comprise instructions to form one or more path patterns selected from a path pattern library at one or more offsets from the one or more regions of interest. 
     For example, the instructions to acquire a digital model of the object to be manufactured comprise instructions to store in memory one or more forbidden region wherein the forming of paths comprising one or more elongate fiber tow models is excluded. For example, the instructions to acquire a digital model of the object to be manufactured comprise instructions to highlight, on a computer display presenting one or more views of the surface-based components, one or more of the forbidden region. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to read from memory a lower limit on the tow length. For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of: one or more of the surface-based components; one or more of the paths; and one or more of the elongate fiber tow models; wherein one or more of the elongate fiber tows the length of which is less than the lower limit on the tow length. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to read from memory a lower limit on the radius of curvature of the paths wherein a fiber tow follows the path continuously. For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more of the tow paths wherein the radius of curvature is lower than the radius of curvature lower limit stored in memory. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to store in memory the tow twist at one or more location along the path. For example the instructions comprise instructions to highlight, on a computer display presenting one or more views of the surface-based components, one or more of the tow paths wherein the tow twist is greater than a tow twist threshold stored in memory. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to form a discontinuity in the fiber tow at one or more location in the path comprising a radius of curvature that is less than a lower limit. For example, the instructions to form one or more paths comprise instructions to actuate a tow cutter. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to form one or more dimensional value of tow-free space enclosed by one or more path. For example, the instructions comprise instructions wherein if a value of tow-free space is greater than a tow-free space threshold value, instructions are provided to form one or more reinforcing path within the tow-free space. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to form along the path and store in memory one or more value of tow-free distance to one or more path around one or more of the path&#39;s centerline and the path&#39;s edge. For example, the instructions comprise instructions wherein if a value of tow-free distance is greater than a tow-free distance threshold value, instructions are provided to adjust one or more waypoint defining the one or more path to decrease the tow-free distance of the one or more path. For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more of the tow paths wherein the tow-free distance is greater than a tow-free distance threshold stored in memory. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to form a plurality of parallel paths that are spaced apart by a distribution profile specified by reading from memory one or more distribution component. 
     For example, the instructions to segment the digital model comprise instructions to form a first surface-based component comprising a first half-joint comprising one or more of a tenon and a mortise and to form a second surface-based component comprising a second half-joint matching the first half-joint and comprising one or more of a mortise and a tenon. For example, instructions to segment the digital model comprise instructions to form a first surface-based component and to form a second surface-based component that forms a joining between the first surface-based component, wherein one or more of the first surface-based component and the second surface-based component comprises one or more fillets at the joining between the first surface-based component and the second surface-based component. For example, the instructions to segment the digital model comprise instructions to form a first surface-based component and form a second surface-based component that forms a joining between the first surface-based component and the second surface-based component at a joining region  17000 J, and wherein the instructions to form one or more path models  7001 ,  7002 ,  7003 ,  100 PC,  10201 ,  10202 ,  10203 ,  10204 ,  10205  comprise instructions to form on the second surface-based component, at the joining region, paths that form an angle of at most 80°, for example at most 60°, with a normal to the first surface-based component at the joining region. 
     For example, the instructions comprise instructions to acquire one or more axis of symmetry in one or more of the surface-based component and to divide the one or more of the surface-based component at the one or more axis of symmetry into a plurality of component regions; and wherein the instructions to form one or more path model comprises instructions to form one or more first path model into a first component region of the plurality of component regions and instructions to mirror the first path model into one or more of the other component regions of the plurality of component regions. For example the instructions comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more of the component region. 
     For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more axis of symmetry in one or more of the surface-based components. 
     For example, the instructions to form a three-dimensional model decomposition comprise instruction to enlarge one or more of the one or more surface-based components in one or more direction. 
     For example, the instructions comprise instructions to simulate a step comprising one or more of heating and compressing an assembly comprising one or more surface-based component model comprising one or more elongate fiber tow. For example, the instructions for the simulation step comprise instructions to estimate a decrease in size in one or more direction of one or more of the one or more surface-based components. For example, the instructions for the simulation step comprise instructions to deform one or more of the one or more surface-based components in one or more three-dimensional direction at one or more surface location. For example, the instructions for the simulation step comprise forming instructions to adjust a computer-controlled compression molding process. For example, the instructions to adjust a computer-controlled compression molding process comprise instructions to adjust one or more of compression rate and compression temperature. For example, the instructions for the simulation step comprise instructions to simulate a flow of infill material. For example, the instructions for the simulation step comprise instructions to estimate a decrease in size in one or more dimension of one or more region comprising infill material. For example, the instructions for the simulation step comprise instructions to estimate the displacement in one or more dimensions of one or more path. For example, the instructions for the simulation step comprise instructions to estimate the displacement in one or more dimension of one or more elongate tow. For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more region wherein a displacement of infill material is greater than an an infill displacement threshold stored in memory. 
     For example, the instructions to form one or more path comprise instructions to form one or more command to rotate a pressure foot device. For example, the instructions to form one or more path comprise instructions to form one or more command to rotate a pressure foot device to an orientation angle with respect to a local tangent to the path being formed. For example, the instructions to form one or more path comprise instructions to actuate one or more pinch roller. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a block diagram for an apparatus for modeling and forming fiber-reinforced objects. 
         FIG.  2 A  is a perspective view of a system for applying an elongate fiber tow for forming fiber-reinforced objects. 
         FIG.  2 B  is a perspective view of a pressure foot device. 
       FIG.  3 A 1  is a perspective view of tow paths of a first surface-based component model for forming a first fiber-reinforced object component. 
       FIG.  3 A 2  is a perspective view of tow paths of a first fiber-reinforced object component. 
       FIG.  3 B 1  is a perspective view of tow paths of a second surface-based component model for forming a second fiber-reinforced object component. 
       FIG.  3 B 2  is a perspective view of tow paths of a second fiber-reinforced object component. 
         FIG.  3 C  is a perspective view of an assembly sequence to form a joining by tenon into mortise insertion of a first fiber-reinforced object component into a second fiber-reinforced object component. 
         FIG.  3 D  is a perspective view of a fiber-reinforced object comprising a first fiber-reinforced object component and a second fiber-reinforced object component. 
         FIGS.  4 A,  4 B,  4 C  present different embodiments of elongate fiber to models. 
         FIG.  5    is a block diagram of a method for modeling and forming fiber-reinforced objects. 
         FIG.  6    is a graphical user interface for a system for modeling and forming fiber-reinforced objects. 
         FIG.  7    is an embodiment of surface-based component model for forming a fiber-reinforced object component. 
         FIG.  8 A  is an exploded perspective view of a fiber-reinforced object comprising a plurality of surface-based components that comprise a tenon and mortise joining and a plurality of fillets. 
         FIG.  8 B  is a perspective view of a fiber-reinforced object comprising a tenon and mortise joining and a plurality of fillets. 
         FIG.  9 A  is top view of a path for a figure of eight. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     This disclosure presents methods and systems for designing, segmenting, planning, and forming fiber-reinforced plastic composite objects. For example, the fiber-reinforced plastic composite objects comprise elongate fiber tows, for example elongate carbon fiber tows. For example, the fiber tows, because they are narrow, can be formed into tight curves. A method for forming tight curves using an elongate fiber tow comprises, for example, one or more of depositing the tow onto the surface of an object using a pressure foot device and forming a twist in the tow. For example, the pressure foot device is rotatable around an axis, for example an axis orthogonal to the surface of the object. The method for forming tight curves comprises, for example, rotating the pressure foot device that comprises a groove for one or more of guiding and rotating the tow onto the surface of an object. 
       FIG.  5    is a block diagram of a method for modeling and forming fiber-reinforced objects. The method is, for example, a computer implemented method  15000 . The computer implement method  15000  is, for example, stored as computer-readable instructions on a non-transitory computer-readable storage medium  4120 . For example, the computer-implemented method  15000 , comprises, under the control of one or more computer systems  4000  configured with executable instructions: acquiring  15010  a digital model comprising two or more spatial dimensions of an object  10000  to be manufactured; forming  15020  a three-dimensional model decomposition of the object to be manufactured, wherein forming the three-dimensional model decomposition comprises segmenting  15030  at least a portion of the digital model comprising two or more spatial dimensions into one or more surface-based component models  10100 ,  10200 ; and forming  15040 , on one or more surfaces of the one or more surface-based component models, one or more paths  100 P,  100 PC,  10101 ,  10102 ,  10103 ,  10104 ,  10201 ,  10202 ,  10203 ,  10204 ,  10205  comprising one or more elongate fiber tow models  100 ,  100 R,  100 F,  100 F 2 . 
     For example, an embodiment of a surface-based component is planar. For example, an embodiment of a surface-based component is an isotropic deformation of a planar sheet, for example curved into one or more of a cylinder, a cylinder sector, a U, a V, a parabola, a wave. For example, the surface-based component is an isotropic deformation a planar sheet having undergone further anisotropic deformation that comprises one or more of stretching, compressing, and double-curvature bending in an additional range of, for example, up to 20% of the isotropic deformation of the planar sheet. 
     For example, one or more of the one or more elongate fiber tow models  100 ,  100 R,  100 F,  100 F 2  is formed of one or more longitudinally-folded fiber tape models  100 F,  100 F 2 . For example, one or more of the one or more elongate fiber tow models  100 ,  100 R,  100 F,  100 F 2  comprises a rectangular cross-section. For example, one or more of the one or more elongate fiber tow models  100 ,  100 R,  100 F,  100 F 2  comprises a width  100 W comprised in a range from 0.2 mm to 4 mm, for example from 0.4 mm to 2 mm. For example, one or more of the one or more elongate fiber tow models  100 ,  100 R,  100 F,  100 F 2  further comprises a height  100 H comprised in a range from 0.03 mm to 0.5 mm, for example from 0.12 mm to 0.25 mm. 
     For example, forming one or more paths comprises forming one or more concentric paths  100 PC,  10201 ,  10202 ,  10203 ,  10204 ,  10205  that are concentrically adjacent to each other. For example, forming one or more paths  100 P,  100 PC comprises forming one or more contour paths  100 P,  100 PC,  10101 ,  10102 ,  10103 ,  10104 ,  10201 ,  10202 ,  10203 ,  10204 ,  10205  that follow at least a portion of a contour  10100 C,  10200 C of one or more of the one or more surface-based component models  10100 ,  10200 ; and forming a first layer  16010 L comprising a first plurality of parallel paths  16010 P and forming a second layer  16020 L comprising a second plurality of parallel paths  16020 P, wherein the second layer  16020 L overlaps the first layer  16010 L and the paths  16020 P in the second layer  16020 L are orthogonal to the paths  16010 P in the first layer  16010 L; and wherein the area covered by the first layer  16010 L and the second layer  16020 L is at least partially bounded by the one or more contour paths  100 PC. 
     For example, forming one or more paths  100 P,  100 PC comprises acquiring  15042  a value for a number of layers  16102  of paths  100 P,  100 PC to form. For example, forming one or more paths comprises acquiring  15044  a value for a number of coplanar adjacent paths  16104  to form. For example, forming one or more paths comprises adjusting  15046  a spread  16106  of two or more coplanar adjacent paths to form. For example, forming one or more paths comprises acquiring a value for adjusting a spread of two or more coplanar adjacent paths to form over a selected region  16108  comprising one or more dimensions. For example, forming one or more paths comprises acquiring  15050  a value for a minimum longitudinal tow extremity offset  16110  from a surface-based component&#39;s contour  16100 C 1 . 
     For example, forming one or more paths comprises actuating  15052  a tow cutter  2300  as a function of one or more of a minimum tow extremity longitudinal offset  16110  from a surface-based component&#39;s contour, a path extremity longitudinal distance from a surface-based component&#39;s contour  16100 C, and a lower limit on the tow length  2341 . 
       FIG.  7    is a top view of an object  7000  comprising a layer of tows  7100  comprising a plurality of fiber tow segments  101 ,  102 ,  103 . For example, a method for manufacturing object  7000  comprises one or more of translating and rotating the pressure foot device  1100  along a path  7001 ,  7002 ,  7003  from a path start  7001 -S,  7002 -S,  7003 -S to a path end  7001 -E,  7002 -E, wherein the straight foot segment  1110  is collinear with a tangent  7001 T to the path of the pressure foot device  1100  and the point of tangency  7001 PT to the path  7001  is comprised within the groove midplane  1130 MP. For example, the method comprises simultaneous translation and rotation. A method to form a spiral path  7300  comprises forming one or more path, for example successively arranged paths  7001 ,  7002 ,  7003 , that form a spiral arrangement. For example, the method comprises forming an internal region  7500 , also called an infill  7500 , that fills the area or volume, for example in a plurality of stacked rows or layers  7100 , comprised within one or more of the external contour formed by the path  7001 ,  7002 ,  7003  of the object  7000 . For example, the instructions  15000  comprise instructions to store  6400  one or more numerical toolpath instructions  7001 -S,  7001 - 1 ,  7001 - 2 ,  7001 - 3 ,  7001 -E,  7002 -S,  7002 - 1 ,  7002 - 2 ,  7002 -E,  7003 -S,  7003 - 1  comprising one or more of position and orientation of the pressure foot device  1100 . 
     For example, forming one or more paths comprises forming  15054  one or more adjacently concentric spiral paths  7001 ,  7002 ,  7003 . For example, an adjacently concentric spiral comprises a spiral path comprising one or more tows that are adjacent along their longitudinal side. For example, a tow in a spiral path is longitudinally adjacent to itself upon completing one or more loops. In some embodiments, a filler, for example comprising a thermoplastic material, is formed between the tows forming the loops of the spiral path  7001 ,  7002 ,  7003 . 
     For example, forming one or more paths comprises forming  15056  one or more concentric contour paths  100 PC,  10201 ,  10202 ,  10203 ,  10204 ,  10205  that follow at least a portion of a contour  10200 C of one or more of the one or more surface-based component models. For example, forming one or more paths comprises forming  15058  one or more contour paths at one or more offsets  7300 - 0  from a contour  7100 C of one or more of the one or more surface-based component models. 
     For example, the method comprises acquiring  15060  path instructions comprised in a path pattern library  4121 . For example, the path pattern library  4121  comprises forming one or more of: a rectangular path pattern; a rounded rectangular path pattern  10504 ; a circular path pattern  10502 ; and a figure of eight path pattern. For example, forming one or more paths comprises forming  15062  one or more path patterns  10502 ,  10504  selected from a path pattern library  4121 . 
     For example, forming one or more paths comprises defining  15064  one or more regions of interest  16108  comprising one or more dimensions X, Y, Z and wherein the one or more regions of interest are highlighted on a computer display  4132  comprising, for example, a user interface  4130 , presenting one or more views  16001  of the surface-based components. For example, forming one or more paths comprises forming  15066  one or more path patterns selected from a path pattern library at one or more offsets  16110  from the one or more regions of interest  16108 . 
     For example, the method comprises acquiring a digital model of the object to be manufactured comprises storing in computer memory forbidden regions wherein the forming of paths comprising one or more elongate fiber tow models is excluded. For example, the method comprises highlighting, on a computer display presenting one or more views of the surface-based components, one or more of the forbidden regions. For example, the acquired digital model of the object to be manufactured comprises designated forbidden regions wherein the forming of paths comprising one or more elongate fiber tow models is excluded. 
     For example, forming of one or more paths comprising one or more elongate fiber tow models comprises a lower limit on the tow length. For example, forming one or more paths comprising one or more elongate fiber tow models comprises instructions to read from memory a lower limit on the tow length. For example, the method comprises highlighting, on a computer display presenting one or more views of: one or more of the surface-based components; one or more of the paths; and one or more of the elongate fiber tow models; wherein one or more of the elongate fiber tows the length of which is less than the lower limit on the tow length. 
     For example, forming one or more paths comprising one or more elongate fiber tow models comprises reading from a computer memory a lower limit on the radius of curvature of the paths wherein a fiber tow follows the path continuously. For example, the method comprises highlighting, on a computer display presenting one or more views of the surface-based components, one or more of the tow paths wherein the radius of curvature is lower than the radius of curvature lower limit stored in memory. 
     For example, forming one or more paths comprising one or more elongate fiber tow models comprises instructions to store in memory the tow twist at one or more locations along the path. For example, the method comprises highlighting, on a computer display presenting one or more views of the surface-based components, one or more of the tow paths wherein the tow twist is greater than a tow twist threshold stored in memory. 
     For example, forming of one or more paths comprising one or more elongate fiber tow models comprises a lower limit on the radius of curvature of the paths wherein a fiber tow follows the path continuously. For example, forming of one or more paths comprising one or more elongate fiber tow models comprises recording the tow twist at one or more locations along the path. For example, forming of one or more paths comprising one or more elongate fiber tow models comprises forming a discontinuity in the fiber tow at one or more locations in the path comprising a radius of curvature that is less than a lower limit. For example, forming of one or more paths comprises actuating a tow cutter  2300 . 
     For example, forming of one or more paths comprising one or more elongate fiber tow models comprises forming one or more dimensional values of tow-free space enclosed by one or more paths. For example, the one or more dimensional values of tow-free space are estimated, for example using a computation on a processor, in 2 or 3 dimensions. For example, an alarm is raised, for example visually on a display, for example as a highlight projected onto the model, if one or more tow-free space values are greater than a predefined threshold, for example stored in memory. For example, if a value of tow-free space is greater than a tow-free space threshold value, one or more reinforcing paths are formed within the tow-free space. 
     For example, forming of one or more paths comprising one or more elongate fiber tow models comprises forming along the path one or more values of tow-free distance to one or more paths around one or more of the path&#39;s centerline and the path&#39;s edge. For example, if a value of tow-free distance is greater than a tow-free distance threshold value, one or more waypoints defining the one or more paths are adjusted to decrease the tow-free distance of the one or more paths. For example, if a value of tow-free distance is greater than a tow-free distance threshold value, adjusting one or more waypoints defining the one or more paths to decrease the tow-free distance of the one or more paths. For example, the method comprises highlighting, on a computer display presenting one or more views of the surface-based components, one or more of the tow paths wherein the tow-free distance is greater than a tow-free distance threshold stored in a computer memory. 
     For example, forming of one or more paths comprising one or more elongate fiber tow models comprises forming a plurality of parallel paths that are spaced apart by a distribution profile specified by one or more distribution components. For example, the distribution profile comprises one or more of a ramp, an ellipse, a parabola, a hyperbola, and a curve specified using a user-edited function, for example rendered visually as one or more of a two- and three-dimensional graph. 
     For example, segmenting the digital model comprises forming a first surface-based component  17100  comprising a first half-joint  17100 HJ comprising one or more of a tenon  17100 T and a mortise  17200 M and forming a second surface-based component  17200  comprising a second half-joint  17200 HJ matching the first half-joint  17100  and comprising one or more of a mortise  17200  and a tenon  17100 . For example, segmenting the digital model comprises: 
     forming a first surface-based component  17100  and forming a second surface-based component  17200  that forms a joining  17000 J between the first surface-based component  17100 , wherein one or more of the first surface-based component  17100  and the second surface-based component  17200  comprises one or more fillets  17300  at the joining  17000 J between the first surface-based component  17100  and the second surface-based component  17200 . For example, segmenting the digital model comprises forming a first surface-based component and forming a second surface-based component that forms a joining  17000 J between the first surface-based component at a joining region  17000 J, and wherein the forming one or more path model comprises forming on the second surface-based component, at the joining region  17000 J, one or more path that forms an angle of at most 80°, for example at most 60°, with a normal to the first surface-based component at the joining region  17000 J. 
     For example, the method comprises acquiring one or more axis of symmetry in one or more of the surface-based component and dividing the one or more of the surface-based component at the one or more axis of symmetry into a plurality of component regions; and wherein the forming one or more path model comprises forming one or more first path model into a first component region of the plurality of component region and mirroring the first path model into one or more of the other component region of the plurality of component regions. 
     For example, the method comprises highlighting, on a computer display presenting one or more view of the surface-based component, one or more of the component region. For example, the method comprises highlighting, on a computer display presenting one or more view of the surface-based component, one or more axis of symmetry in one or more of the surface-based component. 
     For example, forming a three-dimensional model decomposition comprises enlarging one or more of the one or more surface-based component in one or more direction. For example, the method comprises a step of simulating a step comprising one or more of heating and compressing an assembly comprising one or more surface-based component model comprising one or more elongate fiber tow. For example, the simulating step comprises simulating a compression molding step. For example, the simulating step comprises forming one or more of a heating simulation and a compression simulation and rendering its results on a computer display. For example, the simulating step comprises estimating a decrease in size in one or more direction of one or more of the one or more surface-based component. For example, the simulating step comprises deforming one or more of the one or more surface-based component in one or more three-dimensional direction at one or more surface location. For example, the simulating step comprises forming instructions to adjust a computer-controlled compression molding process. For example, the simulating step comprises simulating a flow of infill material. For example, the simulating step comprises estimating a decrease in size in one or more dimension of one or more region comprising infill material. For example, the simulating step comprises estimating the displacement in one or more dimension of one or more path. For example, the simulating step comprises estimating the displacement in one or more dimension of one or more elongate tow. For example, the simulating step comprises highlighting, on a computer display presenting one or more view of the surface-based component, one or more region wherein a displacement of infill material is greater than an an infill displacement threshold stored in memory. 
     For example, rendering results on a computer display  16000  comprises rendering a three-dimensional model  16100  overlaid with one or more of a color coding, for example a color gradient, a vector field, and an animation, for example an animation of a three-dimensional model undergoing a compression molding process, representing one or more of: distribution of temperature during or after compression molding; displacement of one or more elongate tow during or after compression molding; flow of infill material during or after compression molding; and decrease in size in one or more dimension during or after compression molding. For example, the rendering provides guidance to an operator, for example by displaying one or more of a vector, a highlighting feature (a color modification, a contour), and an animation, to indicate locations on the displayed model where the operator, for example, introduces or requests from the computer-implemented method one or more elongate tow path adjustment to reduce an offset from a desired geometry or from a desired mechanical property. 
     For example, forming one or more path comprises forming one or more command to rotate a pressure foot device. For example, forming one or more path comprises forming one or more command to rotate a pressure foot device to an orientation angle with respect to a local tangent to the path being formed. For example, forming one or more path comprises actuating one or more pinch roller. 
     The disclosure also presents a system  4000  comprising: one or more computer processor  4110 ; and memory  4160 ,  4120  with executable instructions that, when executed by the one or more processor, cause the system to: receive  15010  a digital model  10100 ,  10200  comprising two or more spatial dimensions of an object  10000  to be manufactured; form  15020  a three-dimensional model decomposition of the object to be manufactured, wherein forming the three-dimensional model decomposition comprises segmenting  15030  at least a portion of the digital model comprising two or more spatial dimensions into one or more surface-based component  10100 ,  10200 ; and form  15040 , on a surface of the one or more surface-based component model, one or more path  100 P,  100 PC,  10101 ,  10102 ,  10103 ,  10104 ,  10201 ,  10202 ,  10203 ,  10204 ,  10205  comprising one or more elongate fiber tow model  100 ,  100 R,  100 F,  100 F 2 . For example, one or more of the one or more elongate fiber tow model is formed of one or more longitudinally-folded fiber tape model  100 F,  100 F 2 . 
     For example, the system  4000  comprises an apparatus comprising a pressure foot device  1100  comprising a channel  2400  for guiding an elongate fiber tow  100  onto an object surface  200 ,  10000 . For example, the channel comprises a groove  1130 . For example, the pressure foot device  1100  is coupled to a pressure foot device rotation driving assembly or actuator  1350 ,  4180 . For example, the pressure foot device  1100  is comprised in a foot shaft housing  2100 , characterized by a pressure foot device&#39;s axis of rotation Z, defining a Z-axis, wherein the pressure foot device&#39;s axis of rotation Z is collinear with the channel  2400  for guiding an elongate fiber tow  100  onto an object surface  10000 ,  10100 ,  10200 . 
     For example, the system comprises a computer display  4132 ,  16000 . For example, the system comprises a communication network  4150  connected to a system  2000  for applying an elongate fiber tow  100 . For example, the system  2000  comprises one or more rangefinding detector assemblies  2600  each comprising a rangefinder  2650 , one or more of the rangefinder&#39;s measurement axes ZR being oriented along a direction parallel that of the foot shaft&#39;s axis of rotation Z. The rangefinder detector  2600  is a sensor  4170  that provides, for example, data to the processor  4110  to adjust the distance of the pressure foot device  1100  with respect to the surface onto which the fiber tow  100  is applied. Data from the rangefinder  2650  therefore enables, for example. the processor to adjust the pressure that the foot applies onto the tow  100  and, for example, the width as a result of compression of the tow  100  onto the surface. 
     For example, the system comprises a communication network interface  4140  connected to a computer server  4200  comprising, for example, a non-volatile storage medium comprising instructions describing one or more of: one or more digital model  10100 ,  10200  comprising two or more spatial dimensions of one or more object  10000  to be manufactured; one or more plane-based component  10100 ,  10200 ; and one or more path  100 P,  100 PC,  10101 ,  10102 ,  10103 ,  10104 ,  10201 ,  10202 ,  10203 ,  10204 ,  10205 . For example, one or more of the system  4000  and the computer server  4200  one or more of receive and transmit data indicating the status of the system  4000  and the state of an object being manufactured. For example, the data transmitted enables a remote operator or system to remotely monitor the progress of a manufacturing task. For example, the data transmitted is presented as an overlay on a displayed rendering of a digital model  10100 ,  10200 . For example, the data transmitted comprises one or more of: position and orientation of the pressure foot device  1100 , for example with respect to the digital model  10100 ,  10200 ; pressure foot device temperature, for example measured by one or more temperature sensor  4170 ; length of path deposited versus total path length; time spent depositing tow  100 ; estimated time remaining to deposit tow, for example computed as a function of one or more of remaining tow length to deposit, number of curved paths, and average radius of curvature of the curved paths. 
     The disclosure also presents a non-transitory computer-readable storage medium  4120  comprising executable instructions that, when executed by one or more processor  4110  of a computer system, cause the computer system to at least: acquire  15010  a digital model  10100 ,  10200  comprising two or more spatial dimensions of an object  10000  to be manufactured; form  15020  a three-dimensional model decomposition of the object to be manufactured, wherein forming the three-dimensional model decomposition comprises segmenting  15030  at least a portion of the digital model comprising two or more spatial dimensions into one or more surface-based component  10100 ,  10200 ; and form  15040 , on a surface of the one or more surface-based component model, one or more path  100 P,  100 PC,  10101 ,  10102 ,  10103 ,  10104 ,  10201 ,  10202 ,  10203 ,  10204 ,  10205  comprising one or more elongate fiber tow model  100 . 
     For example, the instructions to form one or more path further comprise instructions to execute one or more of forming, loading, and storing into memory one or more elongate fiber tow model  100  formed of one or more longitudinally-folded fiber tape model  100 F,  100 F 2 . For example, the elongate fiber tow model  100  is a digital model, for example comprised in a digital library, for example stored on a non-transitory computer-readable storage medium  4120 . For example, one or more of the one or more elongate fiber tow model comprises a rectangular cross-section. For example, one or more of the one or more elongate fiber tow model comprises a width comprised in a range from 0.2 mm to 4 mm, for example from 0.4 mm to 2 mm. For example, one or more of the one or more elongate fiber tow model further comprises a height comprised in a range from 0.03 mm to 0.5 mm, for example from 0.12 mm to 0.25 mm. 
     For example, the instructions to form one or more paths comprises instructions to form one or more concentric paths  100 PC,  10201 ,  10202 ,  10203 ,  10204 ,  10205  that are concentrically adjacent to each other. For example, the instructions to form one or more paths comprise instructions to: form one or more contour paths  100 P,  100 PC,  10101 ,  10102 ,  10103 ,  10104 ,  10201 ,  10202 ,  10203 ,  10204 ,  10205  that follow at least a portion of a contour  10100 C,  10200 C of one or more of the one or more surface-based component model  10100 ,  10200 ; and form a first layer  16010 L comprising a first plurality of parallel paths  16010 P and form a second layer  16020 L comprising a second plurality of parallel paths  16020 P, wherein the second layer  16020 L overlaps the first layer  16010 L and the paths  16020 P in the second layer  16020 L are orthogonal to the paths  16010 P in the first layer  16010 L; and wherein the area covered by the first layer and the second layer is at least partially bounded by the one or more contour path. For example, the instructions to form one or more path comprise instructions to acquire a value for a number of layers of paths to form. For example, the instructions to form one or more path comprise instructions to acquire a value for a number of coplanar adjacent paths to form. For example, the instructions to form one or more path comprise instructions for adjusting a spread  16112  of two or more coplanar adjacent paths to form. 
     For example, the instructions to form one or more paths comprise instructions to acquire a value for adjusting a spread  16112  of two or more coplanar adjacent paths to form over a selected region comprising one or more dimension. For example, the instructions to form one or more path comprise instructions to acquire a value for a minimum longitudinal tow extremity offset  7300 -O from a surface-based component&#39;s contour  7100 C. 
     For example, the instructions to form one or more paths comprise instructions to actuate a tow cutter (not visible in  FIG.  2 A ), for example via actuating a tow cutter motor  2350 , as a function of one or more of a minimum tow extremity longitudinal offset  7500 -OL from a surface-based component&#39;s contour  7100 C, a path extremity longitudinal distance  7001 -PL from a surface-based component&#39;s contour, and a lower limit on the tow length. 
     For example, the instructions to form one or more path comprise instructions to form one or more adjacently concentric spiral path  7001 ,  7002 ,  7003 . For example, an adjacently concentric spiral path is a spiral path wherein the separation of the path forming incremental revolutions of the spiral remains constant. For example, the instructions to form one or more path comprise instructions to form one or more concentric contour path  10101 ,  10102 ,  10103 ,  10104 ,  10201 ,  10202 ,  10203 ,  10204 ,  10205 ,  7001 ,  7002 ,  7003  that follow at least a portion of a contour of one or more of the one or more surface-based component model  10100 ,  10200 ,  7000 . For example, the instructions to form one or more path comprise instructions to form one or more contour path  7001 ,  7002 ,  7003  at one or more offset  7300 -O specified in one or more direction from a contour  7100 C of one or more of the one or more surface-based component model  10100 ,  10200 ,  7000 . 
     For example, the instructions further comprise instructions to acquire path instructions comprised in a path pattern library. For example the path pattern library is stored on a non-volatile storage medium  4120 . For example, the instructions comprised in the path pattern library comprise instructions to form one or more of: a rectangular path; a rounded rectangular path; a triangular path; a rounded triangular path; a circular path; and a figure of eight path  7801 . For example, the instructions to form one or more paths comprise instructions to form one or more path pattern selected from a path pattern library  4121 . For example, the instructions to form one or more paths comprise instructions to form one or more portion of a path pattern selected from the path pattern library. 
     For example, the instructions to form one or more paths comprise instructions to define one or more region of interest comprising one or more dimension and wherein the one or more region of interest  16108  is highlighted on a computer display presenting one or more view of the surface-based component. For example, the instructions to form one or more path comprise instructions to form one or more path pattern selected from a path pattern library  4121  at one or more offset  7300 -O from the one or more region of interest  16108 . 
     For example, the instructions to acquire a digital model of the object to be manufactured comprise instructions to store in memory  4160  one or more forbidden region  16030  wherein the forming of paths comprising one or more elongate fiber tow model is excluded. For example, the instructions to acquire a digital model of the object to be manufactured comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more of the forbidden region  16030 . 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to read from memory  4160  a lower limit on the tow length. For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of: one or more of the surface-based components; one or more of the paths; and one or more of the elongate fiber tow models; wherein one or more of the elongate fiber tows the length of which is less than the lower limit on the tow length. 
     For example, highlighting comprises displaying using one or more different line color, different line thickness, different transparency, different background, and different animation. Based on the visual highlighting cue, an operator decides, for example, to adjust a design. For example, a design is adjusted manually. For example, a design is adjusted by selecting an algorithmic operator comprised in the instructions to form one or more path pattern. For example, the algorithmic operator comprises instructions to form a pattern conferring one or more of mechanical and appearance properties. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to read from memory a lower limit on the radius of curvature of the paths wherein a fiber tow follows the path continuously. For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more of the tow path wherein the radius of curvature is lower than the radius of curvature lower limit stored in memory  4160 ,  4120 . 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to store in memory the tow twist at one or more location along the path. For example the instructions comprise instructions to highlight, on a computer display presenting one or more views of the surface-based components, one or more of the tow paths wherein the tow twist is greater than a tow twist threshold stored in memory  4160 ,  4120 . 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to form a discontinuity in the fiber tow at one or more location in the path comprising a radius of curvature that is less than a lower limit. For example, the instructions to form one or more path comprise instructions to actuate a tow cutter  2300 , for example via a tow cutter motor  2350 . For example, the cut is commanded upon reaching a cut position  7001 -C,  7002 -C,  7003 -C to form a complete cut across the entirety of the tow&#39;s cross-section. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow models comprise instructions to form one or more dimensional value of tow-free space enclosed by one or more path. For example, the instructions comprise instructions wherein if a value of tow-free space is greater than a tow-free space threshold value, for example by raising an alarm, for example one or more of a visual and a haptic alarm, instructions are provided to form one or more reinforcing path within the tow-free space. For example, tow-free space is a convex area (two-dimensional space) or volume (three-dimensional space) where no tow is comprised. For example, if a value of tow-free space is greater than a threshold, structural integrity of a structure, for example deformation beyond a threshold, is compromised under load, for example a simulated load. For example, the computer-based monitoring of tow-free space with respect to a threshold provides a method to guide an operator to add one or more reinforcing tow structure one or more of within and around the tow-free space. 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow models comprise instructions to form along the path and store in memory one or more value of tow-free distance to one or more path around one or more of the path&#39;s centerline and the path&#39;s edge. For example, a path&#39;s centerline is the set of points along the centerline of a tow, for example after the tow has been pressed by a pressure foot device  1100 . For example the elongate fiber tow model comprises instructions to model the pressing of the tow by the pressure foot device. For example, around the centerline or edge means one or more direction orthogonal to the centerline or edge, respectively. For example, the instructions comprise instructions wherein if a value of tow-free distance is greater than a tow-free distance threshold value, instructions are provided to adjust one or more waypoint defining the one or more path to decrease the tow-free distance of the one or more path. For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more of the tow paths wherein the tow-free distance is greater than a tow-free distance threshold stored in memory  4160 ,  4120 . 
     For example, the instructions to form one or more path comprising one or more elongate fiber tow model comprise instructions to form a plurality of parallel paths that are spaced apart by a distribution profile specified by reading from memory  4160 ,  4120  one or more distribution component. For example, a distribution profile specifies the distance separating the centerline of a first path from the centerline of a second adjacent path, for example parallel to the first path. For example, a distribution profile specifies a progression of separation distances between a plurality of paths. For example, a distribution profile is presented as a two dimensional plot with number of first to n-th path in abscissa and distance from first path in ordinates. For example, a ramp represents constant separation between a plurality of sequentially adjacent paths. For example a parabola represents increasing separation with the number of the path within the plurality of sequentially adjacent paths. 
     For example, the instructions to segment  15030  the digital model  1700  comprise instructions to form a first surface-based component  17100  comprising a first half-joint  17100 HJ comprising one or more of a tenon  17100 T and a mortise  17200 M and to form a second surface-based component  17200  comprising a second half-joint  17200 HJ matching the first half-joint  17100  and comprising one or more of a mortise  17200  and a tenon  17100 . For example, instructions to segment  15030  the digital model  17000  comprise instructions to form a first surface-based component and to form a second surface-based component that forms a joining  17000 J between the first surface-based component and the second surface-based component, wherein one or more of the first surface-based component and the second surface-based component comprises one or more fillet at the joining  17000 J between the first surface-based component and the second surface-based component. For example, the instructions to segment  15030  the digital model  17000  comprise instructions to form a first surface-based component and form a second surface-based component that forms a joining  17000 J between the first surface-based component and the second surface-based component at a joining region  17000 J, and wherein the instructions to form one or more path model comprise instructions to form on the second surface-based component, at the joining region  17000 J, one or more path that forms an angle of at most 80°, for example at most 60°, with a normal to the first surface-based component at the joining region  17000 J. 
     For example, the instructions comprise instructions to acquire one or more axis of symmetry in one or more of the surface-based components and to divide the one or more of the surface-based components at the one or more axis of symmetry into a plurality of component regions; and wherein the instructions to form one or more path model comprises instructions to form one or more first path model into a first component region of the plurality of component regions and instructions to mirror the first path model into one or more of the other component regions of the plurality of component regions. For example the instructions comprise instructions to highlight, on a computer display presenting one or more views of the surface-based components, one or more of the component regions. 
     For example, the instructions comprise instructions to highlight, on a computer display presenting one or more views of the surface-based component, one or more axis of symmetry in one or more of the surface-based component. 
     For example, the instructions to form a three-dimensional model decomposition comprise instructions to enlarge one or more of the one or more surface-based component in one or more direction. 
     For example, the instructions comprise instructions to simulate a step comprising one or more of heating and compressing an assembly comprising one or more surface-based component model comprising one or more elongate fiber tow. For example, the instructions for the simulation step comprise instructions to estimate a decrease in size in one or more direction of one or more of the one or more surface-based components. For example, the instructions for the simulation step comprise instructions to deform one or more of the one or more surface-based components in one or more three-dimensional direction at one or more surface location. For example, the instructions for the simulation step comprise forming instructions to adjust a computer-controlled compression molding process. For example, the instructions to adjust a computer-controlled compression molding process comprise instructions to adjust one or more of compression rate and compression temperature. For example, the instructions for the simulation step comprise instructions to simulate a flow of infill material. For example, the instructions for the simulation step comprise instructions to estimate a decrease in size in one or more dimensions of one or more regions comprising infill material. For example, the instructions for the simulation step comprise instructions to estimate the displacement in one or more dimension of one or more path. For example, the instructions for the simulation step comprise instructions to estimate the displacement in one or more dimension of one or more elongate tow. For example, the instructions comprise instructions to highlight, on a computer display presenting one or more view of the surface-based components, one or more region wherein a displacement of infill material is greater than an an infill displacement threshold stored in memory  4160 ,  4120 . 
     For example, the instructions to form one or more paths comprise instructions to form one or more command to rotate a pressure foot device  1100 , for example via a foot rotation motor  1350  coupled to the pressure foot device  1100 . For example, the instructions to form one or more path comprise instructions to form one or more command to rotate the pressure foot device  1100  to an orientation angle with respect to a local tangent  7001 T to the path  7001 PT being formed. For example, the instructions to form one or more path comprise instructions to actuate one or more pinch roller or pinch roller motor  2550 , for example comprised in a one or more pinch roller assembly  2500 , for example a pinch roller driving the output speed of the tow  100  from the system  2000  for applying an elongate fiber tow  100 .