Patent Publication Number: US-2017361533-A1

Title: Method and system for continuous extrusion additive manufacturing

Description:
FIELD AND BACKGROUND OF THE INVENTION 
     The present invention, in some embodiments thereof, relates to extrusion additive manufacturing and, more particularly, but not exclusively, to a method and system for additive manufacturing by continuous extrusion. 
     An extrusion-based additive manufacturing system builds a three-dimensional object from a digital representation of the 3D object in a layer-by-layer manner by extruding a flowable modeling material. The modeling material is extruded through an extrusion tip carried by an extrusion head on a support platform in an x-y plane. 
     The extruded modeling material fuses to previously deposited layer of modeling material, and solidifies when cooled off. After completion of a layer, the extrusion of the material is temporarily ceased, and a vertical relative movement occurs between the support platform and the extrusion tip of a distance equal to the thickness of the layer in a direction away from the support platform, so as to prepare the extrusion tip to initiate making a subsequent layer, until a 3D object resembling the digital representation is formed. 
     Movement of the extrusion head with respect to the support platform is performed under computer control, in accordance with build data that represents the 3D object. The build data is obtained by initially slicing the digital representation of the 3D object into multiple horizontally sliced layers. Then, for each sliced layer, the host computer generates a build path for depositing modeling material to form the 3D object. 
     In conventional fabrication of 3D objects by depositing layers of a modeling material, supporting layers or structures are typically built underneath overhanging portions or in cavities of objects under construction, which are not supported by the modeling material itself. A support structure is built utilizing the same deposition techniques by which the modeling material is deposited. The host computer generates additional geometry acting as a support structure for the overhanging or free-space segments of the 3D object being formed. The support material is then deposited from a second nozzle pursuant to the generated geometry during the build process. The support material adheres to the modeling material during fabrication, and is removable from the completed 3D object when the build process is complete. 
     SUMMARY OF THE INVENTION 
     According to an aspect of some embodiments of the present invention there is provided a method of additive manufacturing of a three-dimensional object. The method comprises: extruding contours of a modeling material to form a plurality of layers corresponding to slice data of the object; wherein at least one of the contours is extruded generally horizontally above a three-dimensional region which is devoid of any solid support. 
     According to an aspect of some embodiments of the present invention there is provided a method of additive manufacturing of a three-dimensional object. The method comprises: extruding from a tip of an extruder contours of a modeling material to form on a supporting platform a plurality of layers corresponding to slice data of the object; and establishing a vertical relative movement between the tip and the supporting platform while the material is extruded. According to some embodiments of the invention at least one of the contours is extruded generally horizontally above a three-dimensional region which is devoid of any solid support. 
     According to some embodiments of the invention a vertical distance between the tip and the supporting platform increases gradually during the entire extrusion of a contour onto which another contour is to be directly extruded. 
     According to some embodiments of the invention the vertical relative movement is during extrusion of a contour onto which another contour is to be directly extruded, but only at a vicinity of a starting point and an ending point of the contour. 
     According to some embodiments of the invention the establishing the vertical movement is executed to form a contour segment having a vertical slope which is less than 45 degrees. 
     According to some embodiments of the invention the method comprises, for at least one contour, varying a thickness of the contour synchronously with the variation of the vertical movement. 
     According to some embodiments of the invention a largest horizontal dimension of the three-dimensional region is larger than a characteristic diameter of the contours by a factor of at least 5. 
     According to some embodiments of the invention a largest horizontal dimension of the three-dimensional region is larger than a characteristic diameter of the contours by a factor of at least 10. 
     According to some embodiments of the invention the three-dimensional region is internal to the object. 
     According to some embodiments of the invention the three-dimensional region is external to the object. 
     According to some embodiments of the invention the at least one contour is supported by at least two vertical walls bordering the three-dimensional region. 
     According to some embodiments of the invention the at least one contour is supported by only one wall bordering the three-dimensional region. 
     According to some embodiments of the invention the at least one contour forms a continuous layer which completely covers the three-dimensional region. 
     According to some embodiments of the invention at least a segment of the at least contour is extruded outwardly from a vertical wall of the object, and above the three-dimensional region, in a manner that the segment is not tangential to any other previously extruded segment. 
     According to some embodiments of the invention the at least one contour forms a layer which only partially covers the three-dimensional region. 
     According to some embodiments of the invention the layer has an opening above the three-dimensional region. 
     According to some embodiments of the invention at least a segment of the at least one contour is extruded horizontally along a spiral path. 
     According to some embodiments of the invention the object has a curvature along a vertical direction, and wherein for at least a portion of the layers, a number of contours or contour segments forming each layer is varied as a function of a slope of the curvature along the vertical direction. 
     According to some embodiments of the invention the method comprises, for at least one layer, determining a containment relation between an outermost contour of the layer and an outermost contour of a preceding or a subsequent layer, and selecting an extrusion path for the at least one layer based on the containment relation. 
     According to some embodiments of the invention the at least one layer has an opening above the three-dimensional region, and the method comprises: determining a locus of intersection between a periphery of the opening and the extrusion path; and updating the extrusion path based on the locus of intersection. 
     According to some embodiments of the invention the method comprises receiving as a user input a starting point for at least one contour relative to a respective at least one layer, wherein the extrusion of the at least one contour at the respective at least one layer is initiated at the starting point. 
     According to some embodiments of the invention the method comprises automatically selecting starting points for all contours other than the at least one contour, based on an outline of the three-dimensional object. 
     According to an aspect of some embodiments of the present invention there is provided a system for additive manufacturing of a three-dimensional object. The system comprises: a supporting platform; a modeling material extruder; and a controller operatively associated with a computer and being configured to receive slide data of the object from the computer and to control the extruder to extrude contours of a modeling material thereby to form on the supporting platform a plurality of layers corresponding to the slice data, wherein at least one of the contours is extruded generally horizontally above a three-dimensional region which is devoid of any solid support. 
     According to an aspect of some embodiments of the present invention there is provided a system for additive manufacturing of a three-dimensional object. The system comprises: a supporting platform; a modeling material extruder; a drive for establishing relative motion between the modeling material extruder and the supporting platform; and a controller operatively associated with a computer and being configured to receive slide data of the object from the computer and to control the drive and the extruder to extrude contours of a modeling material thereby to form on the supporting platform a plurality of layers corresponding to the slice data, wherein a vertical relative movement between the tip and the supporting platform is established while the material is extruded. 
     According to some embodiments of the invention the controller is configured to ensure that wherein a vertical distance between the tip and the supporting platform increases gradually during the entire extrusion of a contour onto which another contour is to be directly extruded. 
     According to some embodiments of the invention the controller is configured to establish the vertical relative movement during extrusion of a contour onto which another contour is to be directly extruded, but only at a vicinity of a starting point and an ending point of the contour. 
     According to some embodiments of the invention the controller is configured to establish the vertical relative movement so as to form a contour segment having a vertical slope which is less than 45 degrees. 
     According to some embodiments of the invention the controller is configured to vary a thickness of at least one contour synchronously with the variation of the vertical distance. 
     According to some embodiments of the invention the three-dimensional region is internal to the object. 
     According to some embodiments of the invention the three-dimensional region is external to the object. 
     According to some embodiments of the invention the at least one contour is supported by at least two vertical walls bordering the three-dimensional region. 
     According to some embodiments of the invention the at least one contour is supported by only one wall bordering the three-dimensional region. 
     According to some embodiments of the invention the at least one contour forms a continuous layer which completely covers the three-dimensional region. 
     According to some embodiments of the invention at least a segment of the at least contour is extruded outwardly from a vertical wall of the object, and above the three-dimensional region, in a manner that the segment is not tangential to any other previously extruded segment. 
     According to some embodiments of the invention the at least one contour forms a layer which only partially covers the three-dimensional region. 
     According to some embodiments of the invention the layer is continuous. 
     According to some embodiments of the invention the layer is discontinuous. 
     According to some embodiments of the invention the layer has an opening above the three-dimensional region. 
     According to some embodiments of the invention at least a segment of the at least one contour is extruded horizontally along a spiral path. 
     According to some embodiments of the invention the system comprises the computer. 
     According to some embodiments of the invention the computer is configured to determine a containment relation between an outermost contour of the layer and an outermost contour of a preceding or a subsequent layer, and to select an extrusion path for the at least one layer based on the containment relation. 
     According to some embodiments of the invention the at least one layer has an opening above the three-dimensional region, and wherein the computer is configured to determine a locus of intersection between a periphery of the opening and the extrusion path, and to update the extrusion path based on the locus of intersection. 
     According to some embodiments of the invention the system comprises a user interface configured for receiving as a user input a starting point for at least one contour relative to a respective at least one layer, wherein the extrusion of the at least one contour at the respective at least one layer is initiated at the starting point. 
     According to an aspect of some embodiments of the present invention there is provided a method of additive manufacturing of a three-dimensional object. The method comprises: receiving as a user input a starting point for at least one contour relative to a respective at least one layer; and extruding contours of a modeling material to form a plurality of layers corresponding to slice data of the object, wherein the extrusion of the at least one contour at the respective at least one layer is initiated at the starting point. 
     According to some embodiments of the invention the method comprises automatically selecting starting points for all contours other than the at least one contour, based on an outline of the three-dimensional object and based on the input starting point. 
     According to an aspect of some embodiments of the present invention there is provided a system for additive manufacturing of a three-dimensional object. The system comprises: a supporting platform; a modeling material extruder; a controller operatively associated with a computer; and a user interface configured for receiving as a user input a starting point for at least one contour relative to a respective at least one layer; wherein the controller is configured to receive slide data of the object from the computer and to control the extruder to extrude contours of a modeling material thereby to form on the supporting platform a plurality of layers corresponding to the slice data, wherein the extrusion of the at least one contour at the respective at least one layer is initiated at the starting point. 
     According to some embodiments of the invention the computer is configured to automatically select starting points for all contours other than the at least one contour, based on an outline of the three-dimensional object. 
     According to an aspect of some embodiments of the present invention there is provided a method of processing a data file for extrusion additive manufacturing. The data file having slice data including three-dimensional contour coordinates defining a plurality of planes corresponding to planar slices of an object. The method comprises, for each of at least some slices: identifying coordinates of outermost contours and coordinates of inner contours with respect to the outermost contours; determining a containment relation between an outermost contour of the slice and an outermost contour of a preceding slice or a subsequent slice; ordering the contours in the slice based on the identification and based on the containment relation, thereby processing the data file; and storing the processed data file in a medium readable by a controller of an extrusion additive manufacturing system. 
     According to some embodiments of the invention, when: the slice is an intermediate slice and the outermost contour of the slice contains the outermost contour of a subsequent slice; then: the contours are ordered from the outermost contour of the slice to a contour below the outermost contour of the subsequent slice. 
     According to some embodiments of the invention, when: the slice is an intermediate slice, the coordinates of inner contours are identified and the outermost contour of the slice contains the outermost contour of the subsequent slice; then: the contours are ordered from a contour below the outermost contour of the subsequent slice to an innermost contour of the slice. 
     According to some embodiments of the invention when: the slice is a non-bottommost slice and the outermost contour of the slice contains the outermost contour of the preceding slice; then: the contours are ordered from a contour above the outermost contour of the preceding slice to the outermost contour of the slice. 
     According to some embodiments of the invention when: the slice is non-bottommost slice, the coordinates of inner contours are identified and the outermost contour of the slice contains the outermost contour of the preceding slice; then: the contours are ordered from a contour above the outermost contour of the preceding slice to an innermost contour of the slice. 
     According to an aspect of some embodiments of the present invention there is provided a method of processing a data file for extrusion additive manufacturing, the data file having slice data including three-dimensional contour coordinates. The method comprises: identifying closed planar contours in the data; for each of at least some of the closed contours, updating vertical coordinates of at least a segment of the contour, such that, following the update, the segment is tilted at an angle relative to a plane engaged by the contour prior to the update, thereby processing the data file; and storing the processed data file in a medium readable by a controller of an extrusion additive manufacturing system. 
     According to some embodiments of the invention the method comprises, for each segment, selecting a point over the contour, and defining the segment as comprising the point and having a predetermined length. 
     According to some embodiments of the invention the tilt is selected such that the contour connects to a contour engaging another plane being above the plane, thereby defining a contour having a helical shape. 
     According to some embodiments of the invention the method comprises identifying coordinates of outermost contours and coordinates of inner contours with respect to the outermost contours, wherein the updating the vertical coordinates is based on the identification. 
     According to some embodiments of the invention the at least a segment of the contour is a plurality of segments and the vertical coordinates are updated to gradually increase along the plurality of segments. 
     According to some embodiments of the invention the method comprises updating horizontal coordinates of at least one contour engaging a plane, so as to connect an ending point of the contour with a starting point of another contour engaging the plane, thereby providing a combined contour. 
     According to some embodiments of the invention the combined contour forms a spiral shape in the plane. 
     According to an aspect of some embodiments of the present invention there is provided a computer software product, comprising a computer-readable medium in which program instructions are stored, which instructions, when read by a data processor, cause the data processor to execute the method as described herein and optionally as further detailed below. 
     Unless otherwise defined, all technical and/or scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of embodiments of the invention, exemplary methods and/or materials are described below. In case of conflict, the patent specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and are not intended to be necessarily limiting. 
     Implementation of the method and/or system of embodiments of the invention can involve performing or completing selected tasks manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of embodiments of the method and/or system of the invention, several selected tasks could be implemented by hardware, by software or by firmware or by a combination thereof using an operating system. 
     For example, hardware for performing selected tasks according to embodiments of the invention could be implemented as a chip or a circuit. As software, selected tasks according to embodiments of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In an exemplary embodiment of the invention, one or more tasks according to exemplary embodiments of method and/or system as described herein are performed by a data processor, such as a computing platform for executing a plurality of instructions. Optionally, the data processor includes a volatile memory for storing instructions and/or data and/or a non-volatile storage, for example, a magnetic hard-disk and/or removable media, for storing instructions and/or data. Optionally, a network connection is provided as well. A display and/or a user input device such as a keyboard or mouse are optionally provided as well. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       Some embodiments of the invention are herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of embodiments of the invention. In this regard, the description taken with the drawings makes apparent to those skilled in the art how embodiments of the invention may be practiced. 
       In the drawings: 
         FIG. 1  is a schematic illustration of extrusion additive manufacturing system, according to some embodiments of the present invention; 
         FIG. 2  is a flowchart diagram of a method suitable for additive manufacturing of a three-dimensional object, according to some embodiments of the present invention; 
         FIGS. 3A-B  are schematic illustrations of an object having an internal cavity at least partially covered by overhanging structures, according to some embodiments of the present invention; 
         FIGS. 4A-B  are schematic illustrations of an object having external overhanging structures, according to some embodiments of the present invention; 
         FIGS. 5A-C  are schematic illustrations of a hollow object in which one or more of its internal cavities is completely closed from all sides, according to some embodiments of the present invention; 
         FIG. 6  is a schematic illustration of a hollow object in which one or more of its internal cavities is covered by a layer having an opening above the cavity, according to some embodiments of the present invention; 
         FIG. 7  is a schematic illustration of an object having a curvature along the vertical direction, according to some embodiments of the present invention; 
         FIG. 8  is a schematic illustration of a layer in which one or more of the contours is extruded horizontally along a spiral path, according to some embodiments of the present invention; 
         FIGS. 9A-D  are schematic illustrations describing a procedure in which a vertical wall is fabricated by extruding a modeling material, while maintaining a continuous or stepwise relative vertical movement, according to some embodiments of the present invention; 
         FIG. 10  is a schematic illustration describing a procedure in which the vertical distance between the tip of the extruder and the supporting platform is varied only at a vicinity of a starting point and an ending point of the contour, according to some embodiments of the present invention; 
         FIG. 11  is a schematic illustration of an embodiment in which the thickness of one or more contours is increased synchronously with the vertical relative motion during extrusion; 
         FIG. 12  is a flowchart diagram of a method suitable for processing a data file for extrusion additive manufacturing, according to some embodiments of the present invention; 
         FIGS. 13A-I  are flowchart diagrams describing a procedure based on a set of criteria for ordering contours according to some embodiments of the present invention; 
         FIG. 14  is a flowchart diagram of another method suitable for processing a data file for extrusion additive manufacturing, according to some embodiments of the present invention; 
         FIG. 15  is a flowchart diagram of a method that combines the methods shown in  FIGS. 12 and 14 , according to some embodiments of the present invention; and 
         FIG. 16  is a flowchart diagram of an additional method suitable for additive manufacturing of a three-dimensional object, according to some embodiments of the present invention. 
     
    
    
     DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION 
     The present invention, in some embodiments thereof, relates to extrusion additive manufacturing and, more particularly, but not exclusively, to a method and system for fabricating hollow objects by extrusion additive manufacturing. 
     Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not necessarily limited in its application to the details of construction and the arrangement of the components and/or methods set forth in the following description and/or illustrated in the drawings and/or the Examples. The invention is capable of other embodiments or of being practiced or carried out in various ways. 
       FIG. 1  is a schematic illustration of extrusion additive manufacturing system  10 , according to some embodiments of the present invention. System  10  comprises an extruder  12  for extruding contours of modeling material onto a supporting platform  24  or onto previously extruded modeling material contours supported by supporting platform  24 . 
     Extruder  12  can comprise an extrusion barrel  14  for holding the modeling material, a motor-driven rotating screw  16  for forcing the modeling material through extrusion barrel  14 , and a hollow tip  22  serving as a nozzle through which the modeling material is extruded onto supporting platform  24  or onto a previously formed extruded layer. System  10  can further comprise a feed hopper  18  for providing modeling material to extruder  12 , and a heater  20  for heating the modeling material in extrusion barrel  14 . 
     Extruder  12  is optionally and preferably designed in accordance with the modeling material being extruded. 
     As used herein, “modeling material” refers to any material that constitutes the final object to be fabricated once all the building and post building operations are completed. 
     Representative examples of modeling materials that can be extruded by system  10 , including, without limitation, a polymeric material, a wax material, a ceramic material, a metal, a metal alloy, composite material, material enforced by a fiber, such as, but not limited to, glass, carbon, wood, metal, and the like. The modeling material can be supplemented with an aqueous or non-aqueous binder and/or an additive such as, but not limited to, a viscosity modifier, a dispersant, and a lubricant. In some embodiments of the present invention extruder  12  extrudes only modeling material, and does not extrude any support material, throughout the fabrication of the object. In some embodiments, system  10  is devoid of any extruder that extrudes support material. 
     As used herein, “support material” refers to material that is dispensed to support the object being built and that is ultimately separated from the object in a post-build operation. 
     In various exemplary embodiments of the invention tip  22  of extruder  12  has a diameter of from about 0.3 mm to about 50 mm, or about 0.3 mm to about 5 mm, or from about 20 mm to about 50 mm. 
     For extruding the modeling material, the material is fed into extrusion barrel  14  where it is melted by heater  20  and pressurized to flow through tip  22  by means of rotating screw  16 . 
     System  10  also comprises a controller  26  operatively associated with a computer  28 . In some embodiments of the present invention system  10  further comprises computer  28 . Controller  26  receives slide data of an object to be fabricated from computer  28  and controls extruder  12  to extrude contours of the modeling material thereby to form on supporting platform  24  a plurality of layers corresponding to the slice data. Controller  26  can communicate with any of the components of extruder  12  and platform  24  via communication lines (not shown) or wirelessly. 
     System  10  can also comprise a user interface  29  for allowing the operator to provide various parameters as an input to system  10 . For example, the operator can provide a starting point for one or more contours that form the object to be manufactured as further detailed hereinbelow. 
     Any of extruder  12  and supporting platform  24  can be movable horizontally and/or vertically, so as to establish relative motion between extruder  12  and platform  24 , wherein the horizontal motion facilitates the patterning of the individual layers, and the vertical motion facilitates the buildup of the layers on top of each other as known in the art. Thus, for example, in some embodiments extruder  12  is static and supporting platform  24  is movable both horizontally and vertically, in some embodiments extruder  12  is movable both horizontally and vertically and supporting platform  24  is static, in some embodiments both extruder  12  and supporting platform  24  are movable both horizontally and vertically (for example, in opposite directions), in some embodiments extruder  12  is movable horizontally and supporting platform  24  is movable vertically, in some embodiments extruder  12  is movable both horizontally and vertically, and supporting platform  24  is movable only vertically, in some embodiments extruder  12  is movable vertically and supporting platform  24  is movable horizontally, and in some embodiments extruder  12  is movable only vertically and supporting platform  24  is movable both horizontally and vertically. The relative motion between extruder  12  and platform  24  is controlled by controller  26  based on slice data received by controller  26  from computer  28 . 
     The operation of system  10  is based on slice data that is typically received as a data file containing three-dimensional contour coordinates which define a plurality of planes corresponding to planar slices of the object, such that the overall shape of the object is described by the slices. Typically, the data file is in a format that is readable by the controller of the system. Representative examples of computer readable formats suitable for the present embodiments include, without limitation, STL, DWG/DXF, IDEAS, IGES, and VRML. The data file can be processed, preferably by computer  28 , wherein the processing may include various operations, including, without limitation, updating of vertical coordinates, updating of horizontal coordinates, ordering and reordering of contours, updating extrusion paths, and the like. 
     Representative examples of processing techniques are described hereinunder. 
     Once the data file is processed, the slice data are transferred from computer  28  to controller  26 , which controls the operation of extruder  12 , and optionally also platform  24 . Controller  26  signals extruder  12  to extrude the modeling material onto platform  24  and also signals at least one of extruder  12  and platform  24  to move along the vertical and horizontal direction, according to the slice data. 
       FIG. 1  also shows a three-dimensional Cartesian coordinate system, defining an x direction a y direction and a z direction. Herein, “vertical direction” refers to a direction which is parallel or anti-parallel to the z direction, and a “horizontal direction” refers to any direction parallel to or in the x-y plane. 
     In some embodiments of the present invention controller  26  and optionally also computer  28  can perform various operations, according to embodiments of the invention. Representative examples of some operations are described below with reference to flowchart diagrams. 
     While the methods that are described hereinbelow may be used in conjunction with system  10 , these methods can be used in conjunction with other extrusion additive manufacturing systems, provided such extrusion additive manufacturing system are configured to execute one or more of the operations of the methods that are described hereinbelow. 
     It is to be understood that, unless otherwise defined, the operations described hereinbelow can be executed either contemporaneously or sequentially in many combinations or orders of execution. Specifically, the ordering of the flowchart diagrams is not to be considered as limiting. For example, two or more operations, appearing in the following description or in the flowchart diagrams in a particular order, can be executed in a different order (e.g., a reverse order) or substantially contemporaneously. Additionally, several operations described below are optional and may not be executed. 
     Selected operations of the methods described below can be embodied in many forms. For example, they can be embodied in on a tangible medium such as a computer (e.g., computer  28 ) for performing the method steps. They can be embodied on a computer readable medium, optionally and preferably non-transitory computer readable medium, comprising computer readable instructions for carrying out the operations. They can also be embodied in electronic device having digital computer capabilities arranged to run the computer program on the tangible medium or execute the instruction on a computer readable medium. 
     Computer programs implementing some of the operations described below can commonly be distributed to users on a distribution medium such as, but not limited to, a CD-ROM or a flash drive, or they can be provided via a communication network, such as, but not limited to, the internet. From the distribution medium, the computer programs can be copied to a hard disk or a similar intermediate storage medium. The computer programs can be run by loading the computer instructions either from their distribution medium or their intermediate storage medium into the execution memory of the computer, configuring the computer to act in accordance with one or more operations of the method of the present embodiments. All these operations are well-known to those skilled in the art of computer systems. 
     Following is a description of methods suitable for additive manufacturing of a three-dimensional object, according to some embodiments of the present invention. 
     One or more of the operations described below can be executed by system  10 . 
       FIG. 2  is a flowchart diagram of a method suitable for additive manufacturing of a three-dimensional object, according to some embodiments of the present invention. 
     The method begins at  30  and continues to  31  at which slice data are received. 
     The slice data can be received from a local computer (e.g., computer  28 ) connected to an extrusion additive manufacturing system, such as, but not limited to, system  10  that is configured for receiving the slice data and executing the method. 
     Alternatively, the slice data can be received from a remote computer that communicates with the system over a communication network, such as, but not limited to, a local network or the internet. 
     The method optionally and preferably continues to  33  at which for at least one layer defined by the slice data, a containment relation is determined, within the layer, between an outermost contour of the layer and an outermost contour of a preceding and/or a subsequent layer. 
     A containment relation is a well known operation in the art of computer aid design. Generally, a contour C 1  is said to contain a contour C 2  if all the points of contour C 2  are in the area enclosed by contour C 1 . 
     In the context of the present embodiments, containment relation is determined between contours of different layers, namely contours engaging different planes. Such a relation can be determined by considering only the horizontal coordinates of the contours without considering their vertical coordinates. This is mathematically equivalent to an operation in which one or both of the contours are projected onto a plane parallel to the contours, such that both contours engage the same plane, wherein the containment relation is determined after the projection. 
     The present inventors found that such a determination of containment relation is advantageous because it allows manufacturing hollows three-dimensional objects, without using support material. 
     The method optionally and preferably continues to  34  at which an extrusion path is selected for the respective layer. The selection of the path is based on one or more predetermined criteria. In some embodiments the selection of the path is based on the containment relation determined at  33 , and in some embodiments the selection of the path is based one or more other criteria. Representative examples of procedures suitable for selecting the extrusion path are provided hereinunder. Operations  33  and  34  are optionally and preferably executed by a data processor. Alternatively, operations  33  and  34  can be executed by the controller of the system. 
     The method continues to  35  at which contours of a modeling material are extruded to form a plurality of layers corresponding to the slice data of the object. At least part of the extrusion is executed while there is a horizontal relative motion between the extruder and the supporting platform so as to form the contours. 
     Preferably, the horizontal relative motion is along a path selected at  34 , so that the formed contours are also along that path. In some embodiments of the present invention, only modeling material is extruded, without extruding any support material, throughout the fabrication of the object. 
     In some optional embodiments of the present invention, which optional embodiments can be employed in combination with any other embodiment described herein, one or more of the contours is extruded generally horizontally above a three-dimensional region which is devoid of any solid support. The size, for example, the largest horizontal dimension, of the three-dimensional region is preferably larger than a characteristic diameter of the contours by a factor of at least 1 or at least 2 or at least 3 or at least 4 or at least 5. 
     The three-dimensional region can be internal or external to object. When the region is internal, the manufactured object has one or more internal cavities  302  that are generally empty, except from air or other gases that may occupy the cavity, wherein the cavities are at least partially covered by overhanging structures  304 . 
     These embodiments are illustrated in  FIGS. 3A-B . When the region is external, the manufactured object has one or more overhanging structures, such as shelves or balconies  402  or the like, extending outwardly from one or more of the external walls of the object. These embodiments are illustrated in  FIGS. 4A-B . Manufacturing of objects having both types of overhanging structures is also contemplated according to some embodiments of the present invention. 
     One or more of the contours that are above the three-dimensional region and therefore form the overhanging structures can be supported by at least two vertical walls bordering the three-dimensional region. These embodiments are particularly useful when the three-dimensional region is internal to the object, as illustrated, for example, on  FIGS. 3A-B , wherein overhanging contours  304  are supported by walls  306  at opposite sides or surrounding of the internal cavity, but are not supported at any other location within the cavity. The overhanging contours can form a continuous layer which completely covers the three-dimensional region. A representative example of these embodiments is the manufacturing of a hollow object in which one or more of its internal cavities is completely closed from all sides, as schematically illustrated in  FIGS. 5A  (perspective view) and  5 B (cross sectional view) and  5 C (side view). It is recognized that it is not possible to manufacture such a hollow objects by conventional techniques which require the use of support material, because it is not possible to remove support material from internal cavities that are closed from all sides. 
     The overhanging contours can also form a continuous or discontinuous layer which only partially covers the three-dimensional region. A representative example of these embodiments is the manufacturing of a hollow object in which one or more of its internal cavities is covered by a layer  502  having an opening  504  above the cavity, as illustrated, for example, in  FIG. 6 . In some embodiments of the present invention the method determines a locus of intersection between a periphery of the opening and the extrusion path, and updates the extrusion path selected at  34  based on the locus. 
     Typically, wherever a contour (typically an overhanging contour) intersects the periphery of the opening, its extrusion is terminated. Once all the contours that intersect the periphery are defined, the extrusion path is updated, so as to extrude an additional contour along the locus of intersection. A representative example of a contour along the locus of intersection is illustrated at  506 . It is to be understood that it is not necessary to determine the locus of intersection and to update the extrusion path while or after the respective contours are extruded (although such operation is also contemplated). In various exemplary embodiments of the invention both the determination of the locus of intersection and the updating of the extrusion path is executed by a data processor before the extrusion is initiated. For example, a data processor can process the data file, and define and update the extrusion path before uploading the file to the controller of the system. 
     One or more of the contours that are above the three-dimensional region can alternatively or additionally supported by only one wall bordering the three-dimensional region. These embodiments are particularly useful when the three-dimensional region is external to the object, as illustrated, for example, in  FIGS. 4A-B , wherein overhanging contours are supported only by the wall  404  from which the overhanging contours outwardly extend, but are not supported at any other location within the cavity. Such overhanging structures can be manufactured by extruding at least a segment of at least contour outwardly from the vertical wall, and above the three-dimensional region, in a manner that the segment is not tangential to any other previously extruded segment. 
     For objects having a curvature along the vertical direction, the extrusion is optionally and preferably such that, for at least a portion of the layers, the number of contours or contour segments forming each layer is varied as a function of a slope of the curvature along the vertical direction. A representative example of these embodiments is illustrated in  FIG. 7 , showing a cross sectional view of a dome  702  that encloses a three-dimensional region  704  from above, wherein the three-dimensional region is devoid of any solid support. As shown, dome  702  has a curvature along the vertical direction, and the number of contours that form each layer vary as a function of the vertical slope. Specifically, the number of contours that form a layer at which the absolute value of the slope is smaller is larger than the number of contours that form a layer at which the absolute value of the slope is greater. 
     In some optional embodiments of the present invention, which optional embodiments can be employed in combination with any other embodiment described herein, at least a segment of one or more of the contours is extruded horizontally along a spiral path, as illustrated, for example, in  FIGS. 4A, 5A, 6 and 8 . The advantage of these embodiments is that it allows forming horizontal two-dimensional regions in a continuous manner. When the slice data do not originally include spiral paths, the data file containing the slice data is preferably updated by a data processor before it is being uploaded to the controller of the extrusion additive manufacturing system. This can be done, for example, by selecting a plane corresponding to a slice of the object, identifying coordinates of open contours engaging the plane, and updating the horizontal coordinates of one or more of these open contours so as to connect an ending point of the contour with a starting point of another contour engaging the same plane. 
     The method optionally and preferably continues to  36  at which a vertical relative movement between the tip of the extruder and the supporting platform is established, while the modeling material is extruded. These embodiments are unlike conventional extrusion-based additive manufacturing systems, in which the extrusion of the material is temporarily ceased before the vertical relative movement between the tip and supporting platform is established. Typically, the vertical relative movement during extrusion is executed on the outermost contours of the respective layer. For example, such vertical relative movement during extrusion can be employed for contours on which other contours are to be directly extruded in a subsequent layer. 
     The relative movement can occur according to more than one protocol. For example, in some embodiments, the vertical distance between the tip of the extruder and the supporting platform is increased gradually during the entire extrusion of a contour onto a previously extruded contour. These embodiments are particularly useful when manufacturing a vertical wall that surrounds a three-dimensional region which is devoid of any solid material (e.g., when manufacturing an object without extruding a support material). Such a vertical wall can be fabricated by extruding a modeling material contour shaped in accordance with the shape of the respective slice, while maintaining a continuous or stepwise relative vertical movement between the tip and the supporting platform. 
     A representative example of such a procedure is schematically illustrated in  FIGS. 9A-D . The total number n of segments of the contour for a given slice is determined ( FIG. 9A ). In the schematic illustration of  FIG. 9A , which is not to be considered as limiting, n=12. The thickness h of the layer ( FIG. 9B ) is then divided by n, to provide a vertical step Δz=hln. For example, when h=1.5 mm and n=12, Δz=0.125 mm. The vertical distance between the tip and the platform is then varied continuously or step wise at a rate of Δz per contour segment ( FIG. 9C ). The end point of the last segment of the contour is optionally and preferably connected to the start point of the contour on the subsequent layer. In various exemplary embodiments of the invention there is no change in the vertical distance during the extrusion of the contour(s) that form the topmost layer of the surrounding wall of the cavity. The resulting manufactured object is illustrated in  FIG. 9D . 
     In some embodiments, the vertical distance between the tip of the extruder and the supporting platform is varied only at a vicinity of a starting point and an ending point of the contour. 
     A representative example of such a procedure is schematically illustrated in  FIG. 10 . For a respective layer, closed contour(s) onto which other contours are to be extruded in a subsequent layer are identified. An example of such a contour is the outermost contour of a layer which is part of a vertical wall. On each identified contour c in the respective layer, a point is selected. There after, a gap is defined in the contour at the selected point. For example, the selected point can be defined as a starting point of the closed contour, and the gap can be defined from that point over a predetermined distance along the contour. The vertical relative movement between the tip and the supporting platform is established at the beginning of the gap (namely when the tip is above the beginning of the gap) and is maintained until the tip is above the end of the gap. Typically, during the vertical relative movement, the vertical distance between the tip and the platform increases by an amount that equals to the height of a layer. In various exemplary embodiments of the invention the contour above contour c is extruded from the point at which the vertical relative movement was ceased, and without ceasing the extrusion. Such extrusion protocol ensures that the end point of contour c merges with the start point of the contour that is extruded directly above contour c. 
     The length of the gap is preferably predetermined. Typically, the length of the gap is more than the typical height of the layer. In these embodiments, a contour segment having a vertical slope which is less than 45 degrees is formed along the gap. 
     Representative examples of objects manufactured according to the embodiments described with respect to  FIG. 10  are illustrated in  FIGS. 5C and 6 . 
     In some embodiments of the present invention the thickness of one or more contours is varied, preferably increased, synchronously with the vertical relative motion during extrusion. These embodiments are particularly useful for the bottommost layer, in cases in which it is desired to manufacture an object having a substantially planar base. In such cases, the lower part of the contour engages the same plane, while the upper part passes through at least two layers of the manufactured object. 
     A representative example of an object manufactured according to these embodiments is illustrated in  FIG. 11 . 
     In some embodiments of the present invention, prior to operation  34  (for example, immediately after  31 ), the method receives, at  38 , a starting point for one more contours relative to its respective layer. In these embodiments, the extrusion path  34  of this contour at the respective layer is initiated at the input starting point. 
     The advantage of letting the operator to decide regarding the starting point is that it allows placing the starting point in a non-random manner. For example, the operator of the extrusion additive manufacturing system can select the starting point at a hidden location over the layer, thereby improving the aesthetic appearance of the manufactured object. 
     In some embodiments of the present invention the starting points of all contours, other than the contours for which input starting points have been received, are selected automatically, optionally and preferably by a data processor or a computer. The calculation is preferably based on the input starting point as received at  38  and also based the outline of the three-dimensional object. Generally, the starting points are optionally and preferably selected to follow a line that that is parallel to the outline of the object, but is not-parallel to the layers. The followed line preferably intersects the starting point received as input at  38 . For example, when the object or a part thereof has a shape of a cuboid (e.g., a rectangular cuboid) the line that can be followed is a straight line that is perpendicular to the layers and that intersects the starting point received as input. In this example, all the starting points for the contours of the layers that form the cuboid can be set to be equal (relative to the respective layer) to the starting point received at  38 . When the object has a shape that does not belong to the cuboid family, the line that is followed is not a straight line and/or is not at a right angle to the layers. 
     The method ends at  37 . 
       FIG. 12  is a flowchart diagram of a method suitable for processing a data file for extrusion additive manufacturing, according to some embodiments of the present invention. The method can be executed by a data processor (e.g., computer  28 , or one or more components thereof) being in communication with a controller (e.g., controller  26 ) of an extrusion additive manufacturing system (e.g., system  10 ). The method begins at  50  and continues to  51  at which the data file is received. The data file comprises slice data in the form of three-dimensional contour coordinates which define a plurality of planes corresponding to planar slices of the object, as further detailed hereinabove. 
     The method optionally and preferably continues to  52  at which coordinates of outermost contours and coordinates of inner contours with respect to outermost contours are identified. Operation  52  is executed separately for each of at least some of the slices in the data file. Preferably, operation  52  is executed separately for each slice in a block of several (e.g., 3 or more) adjacent slices in the data file. More preferably, operation  52  is executed for each slice in the data file. The method optionally and preferably continues to  53  at which the containment relation between an outermost contour of the respective slice and an outermost contour of a preceding slice or a subsequent slice in the data file, is determined. 
     The method optionally and preferably continues to  54  at which the contours in the respective slice are ordered based on the identification  52  and based on the containment relation determined at  53 . 
     The term “ordering”, when applied to contours in a data file, refers to a sequence of contour extrusion instructions for the controller of the extrusion additive manufacturing system. Specifically, for any given pair of contours C 1  and C 2 , the coordinates of contour C 1  in the data file are said to be “before” the coordinates of contour C 2  in the data file, when the controller is instructed to extrude contour C 1  before contour C 2 ; and the coordinates of contour C 1  in the data file are said to be “after” the coordinates of contour C 2  in the data file, when the controller is instructed to extrude contour C 1  after contour C 2 . 
     Following are several criteria that can be used according to some embodiments of the present invention for ordering the contours in a given slice, referred to as slice s n , where n=1, 2, . . . , n max  is a positive integer denoting the position of the given slice within the object, with n=1 denoting the bottommost slice, and n=n max  denoting the topmost slice. 
     Several criteria are optionally and preferably considered when s n  is an intermediate slice (namely it is above at least one slice and below at least one slice). 
     According to one criterion, when, according to  52  and  53 , the outermost contour of the respective slice contains an outermost contour of the subsequent slice s n+1 , then the contours in s n  are ordered from the outermost contour of s n  to a contour in s n  which is below the outermost contour of the subsequent slice s n+1 . According to another criterion, when, according to  52  and  53 , coordinates of an inner contour are identified in s n  and the outermost contour in s n  contains the outermost contour of the subsequent slice s n+1 , then the contours are ordered from a contour below the outermost contour of s n+1  to the innermost contour of s n . 
     Several criteria are optionally and preferably considered when s n  is a non-bottommost slice of the object (namely it is above at least one slice). According to one criterion, when the outermost contour of s n  contains the outermost contour of the preceding slice s n−1 , then the contours are ordered from a contour above the outermost contour of s n−1  to the outermost contour of s n . According to another criterion, when coordinates of inner contours are identified in s n  and the outermost contour in s n  contains the outermost contour of s n−1 , then the contours are ordered from a contour above the outermost contour of s n−1  to the innermost contour of slice s n . 
     A flowchart diagram, describing in more detail a procedure based on a set of criteria for the ordering of the contours according to some embodiments of the present invention is shown in  FIGS. 13A-I . 
     As shown, in decisions  601  and  603  the procedure determines whether the slice is the bottommost slice (n=1), a non bottommost slice (1&lt;n≦n max ) or an intermediate slice (1&lt;n&lt;n max ). For the bottommost slice, the procedure preferably does not manipulate the data file, and continues directly to  620  at which n is increased by 1. Otherwise, the procedure continues to fork  602  from which the procedure continues both to decision  612  and decision  603 , which can be executed at any order or contemporaneously. 
     At decision  603 , the procedure determines whether or not the slice is an intermediate slice (1&lt;n&lt;n max ). If the slice is an intermediate slice, the procedure proceeds to decision  604  at which the procedure determine the containment relation between the outermost contour of slice s n , hereinafter contour o n , and the outermost contour of slice, hereinafter contour o n+1 . 
     If the contour o n  contains contour o n+1 , the procedure optionally continues to  626  at which the procedure quantifies the containment. This is optionally and preferably done by calculating the minimal lateral distance M MIN  and the maximal lateral distance D MAX  between contours o n  and o n+1 . From  626  or  604  the procedure moves to fork  622  from which the procedure continues both to decision  608  and process  605 , which can be executed at any order or contemporaneously. 
     The quantification of the containment can be used as a criterion for defining intersecting contours as will now be explained with reference to  FIGS. 13E-I . 
       FIGS. 13E and 13F  illustrate two outermost contours  630  and  632  of two sequential slices, where  FIG. 13E  is a top view and  FIG. 13F  is a cross-sectional view along the line A-A of  FIG. 13E . The outermost contour  632  is laterally contained in the outermost contour  630 . In the representative illustration, the slice to which the containing contour  630  belongs precedes the slice to which the contained contour  632  belongs (for example, contour  630  can be the outermost contour o n  of slice s n  and contour  632  can be the outermost contour o n+1  of slice s n+1 ), but this need not necessarily be the case. 
     Also shown, are the minimal D MIN  and maximal D MAX  lateral distances between contours  632  and  630  ( FIG. 13E ). The lateral distances D MIN  and D MAX  are preferably expressed in units of contour thickness. Suppose, for example, that for contours  630  and  632  the difference D MAX −D MIN  is larger than a predetermined threshold X. According to some embodiments of the present invention, an intersecting contour  634  is defined within the slice that include the containing contour (the slice s n , in the present example), wherein the shape and size of the intersecting contour  634  are the same as those of the contained contour  632 . This embodiment is illustrated in  FIG. 13G . A typical value for the threshold X, in units of contour thickness, is from about 2 to about 6, or from about 2 to about 5, or from about 2 to about 4, or from about 2 to about 3. 
     Another situation is illustrated in  FIGS. 13H and 13I , which illustrate two outermost contours  636  and  638  of two sequential slices, where  FIG. 13H  is a top view and  FIG. 13I  is a cross-sectional view along the line A-A of  FIG. 13H . The outermost contour  638  is laterally contained in the outermost contour  636 . In the representative illustration, the slice to which the containing contour  636  belongs precedes the slice to which the contained contour  638  belongs (for example, contour  636  can be the outermost contour o n  of slice s n  and contour  638  can be the outermost contour o n+1  of slice s n+1 ), but this need not necessarily be the case. 
     As shown in  FIGS. 13E and 13F , the difference between D MAX  and D MIN  is larger for contours  630  and  632  than for contours  636  and  638 . Suppose, for example, that for contours  636  and  638  the difference D MAX −D MIN  is not larger than the predetermined threshold X. In this case, no additional intersecting contour is defined in the slice that includes the containing contour  636 . 
     Referring again to  FIG. 13C , at  605  the contours are ordered from contour o n  to the contour below contour o n+1 Once all the points of the contour in s n  which is below contour o n+1  have been reached (decision  606 ), the procedure optionally and preferably proceeds to decision  627  at which the procedure compares the difference D MAX −D MIN  to the threshold X. If the difference is not larger than X, the procedure continues to  620  at which n is increased by 1. Otherwise, the procedure optionally and preferably moves to  607  at which an intersecting contour is defined, and then continues to  620  at which n is increased by 1. 
     At  608  the procedure determines if there are inner contours in the slice. If there are inner contours in the slice, the procedure proceeds to  609  at which the contours are ordered from the contour in s n  below contour o n+1  to contour o n . Once all the points of the innermost contour of s n  have been reached (decision  610 ), the procedure optionally and preferably proceeds to decision  628  at which the procedure compares the difference D MAX −D MIN  to the threshold X. If the difference is not larger than X, the procedure continues to  620  at which n is increased by 1. Otherwise, the procedure optionally and preferably moves to  611  at which an intersecting contour is defined, and then continues to  620  at which n is increased by 1. 
     At decision  612 , the procedure determine the containment relation, within slice s n , between contour o n  and the outermost contour of slice s n−1 , hereinafter o n−1 . If contour o n  contains contour o n−1  within slice s n , the procedure optionally continues to  623  at which the procedure quantifies the containment. This is optionally and preferably done by calculating the minimal distance D MIN  and the maximal distance D MAX  between contours o n  and o n−1 . From  623  or  612  the procedure moves to fork  621  from which the procedure continues both to decision  613  and process  614 , which can be executed at any order or contemporaneously. 
     At  614 , the contours are ordered from the contour above contour o n−1  to contour o n . Once all the points of contour o n  have been reached (decision  615 ), the procedure optionally and preferably proceeds to decision  624  at which the procedure compares the difference D MAX −D MIN  to the threshold X. If the difference is not larger than X, the procedure continues to  620  at which n is increased by 1. Otherwise, the procedure optionally and preferably moves to  616  at which an intersecting contour is defined, and then continues to  620  at which n is increased by 1. 
     At  613 , the procedure determine whether or not there are inner contours in the slice s n . If there are inner contours in the slice, the procedure proceeds to  617  at which the contours are ordered from the contour above the contour o n−1  to the innermost contour of s n . Once all the points of the innermost contour of s n  have been reached (decision  618 ), the procedure optionally and preferably proceeds to decision  625  at which the procedure compares the difference D MAX −D MIN  to the threshold X. If the difference is not larger than X, the procedure continues to  620  at which n is increased by 1. Otherwise, the procedure optionally and preferably moves to  619  at which an intersecting contour is defined, and then continues to  620  at which n is increased by 1. 
     The procedure continues until all the slices have been visited. 
     The data file is then updated with the ordered contours and the method ( FIG. 12 ) continues to  55  at which the processed data file with the ordered contours is stored in a medium readable by the controller of the extrusion additive manufacturing system. 
     The method ends at  56 . 
       FIG. 14  is a flowchart diagram of another method suitable for processing a data file for extrusion additive manufacturing, according to some embodiments of the present invention. The method can be executed by a data processor (e.g., computer  28 , or one or more components thereof) being in communication with a controller (e.g., controller  26 ) of an extrusion additive manufacturing system (e.g., system  10 ). 
     The method begins at  60  and continues to  61  at which the data file is received. 
     The data file comprises slice data in the form of three-dimensional contour coordinates which define a plurality of planes corresponding to planar slices of the object, as further detailed hereinabove. The method proceeds to  62  at which closed planar contours are identified in the data. The method proceeds to  63  at which, for each of at least some of the closed contours, the vertical coordinates of at least a segment of the respective contour is updated, such that, following the update, the segment is tilted at an angle relative to a plane engaged by the contour prior to the update. Representative examples of such a procedure are described hereinabove with reference to  FIGS. 9 and 10 . 
     In some embodiments of the invention, the method proceeds to  64  at which the horizontal coordinates of one or more contours engaging a plane are updated, so as to connect an ending point of contour with a starting point of another contour engaging plane, thereby providing a combined contour. These embodiments are particularly useful when it is desired to extrude one or more segments of a contour along a spiral path. 
     Once the coordinates of the contours are updated the method continues to  65  at which the processed data file with the updated coordinates is stored in a medium readable by the controller of the extrusion additive manufacturing system. 
     The method ends at  66 . 
     Method  60  can be executed independently, or it can be combined with method  50  above. For example, before, during or after the processing of the contours of a particular layer according to method  50 , the contours of the layer can additionally be processed according to method  60 . Such two-fold processing can optionally and preferably be executed for each layer of the data file. A representative flowchart diagram of a method that combines methods  50  and method  60  is illustrated in  FIG. 15 . This method can be executed by a data processor (e.g., computer  28 , or one or more components thereof) being in communication with a controller (e.g., controller  26 ) of an extrusion additive manufacturing system (e.g., system  10 ). This method begins at  70  and continues to  71  at which the data file is received, as further detailed hereinabove. 
     The method optionally and preferably continues to  52  at which coordinates of outermost contours and coordinates of inner contours with respect to outermost contours are identified, as further detailed hereinabove. The method optionally and preferably continues to  53  at which the containment relation between an outermost contour of the respective slice and an outermost contour of a preceding slice or a subsequent slice in the data file is determined, as further detailed hereinabove. The method optionally and preferably continues to  54  at which the contours in the respective slice are ordered based on the identification and containment relation, as further detailed hereinabove. The method proceeds to  62  at which closed planar contours are identified in the data, and to  63  at which, for each of at least some of the closed contours, the vertical coordinates of at least a segment of the respective contour is updated, as further detailed hereinabove. In some embodiments of the invention, the method proceeds to  64  at which the horizontal coordinates of one or more contours engaging a plane are updated, as further detailed hereinabove. 
     Once the contours are ordered, and the coordinates of the contours are updated the method continues to  72  at which the processed data file with the ordered contours and updated coordinates is stored in a medium readable by the controller of the extrusion additive manufacturing system. 
     The method ends at  73 . 
       FIG. 16  is a flowchart diagram of an additional method suitable for additive manufacturing of a three-dimensional object, according to some embodiments of the present invention. The method can be executed by system  10 . 
     The method begins at  80  and continues to  31  at which slice data are received, as further detailed hereinabove. Optionally, the method continues to  38  at which the method receives a starting point for one more contours relative to its respective layer, as further detailed hereinabove. The method continues to  35  at which contours of a modeling material are extruded to form a plurality of layers corresponding to the slice data of the object, as further detailed hereinabove. Optionally, the method continues to  36  at which at which a vertical relative movement between the tip of the extruder and the supporting platform is established, while the modeling material is extruded, as further detailed hereinabove. 
     Any of optional operations  38  and  36  of method  80  can be executed independently. Thus, in some embodiments of the present invention operations  35  and  36  are executed and operation  38  is not executed, in some embodiments of the present invention operations  35  and  38  are executed and operation  36  is not executed, and in some embodiments of the present invention operations  35 ,  38  and  36  are executed. 
     The method ends at  81 . 
     It is expected that during the life of a patent maturing from this application many relevant extrusion additive manufacturing will be developed and the scope of the term extrusion additive manufacturing system is intended to include all such new technologies a priori. 
     As used herein the term “about” refers to ±10%. 
     The word “exemplary” is used herein to mean “serving as an example, instance or illustration”. Any embodiment described as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments and/or to exclude the incorporation of features from other embodiments. 
     The word “optionally” is used herein to mean “is provided in some embodiments and not provided in other embodiments”. Any particular embodiment of the invention may include a plurality of “optional” features unless such features conflict. 
     The terms “comprises”, “comprising”, “includes”, “including”, “having” and their conjugates mean “including but not limited to”. 
     The term “consisting of” means “including and limited to”. 
     The term “consisting essentially of” means that the composition, method or structure may include additional ingredients, steps and/or parts, but only if the additional ingredients, steps and/or parts do not materially alter the basic and novel characteristics of the claimed composition, method or structure. 
     As used herein, the singular form “a”, “an” and “the” include plural references unless the context clearly dictates otherwise. For example, the term “a compound” or “at least one compound” may include a plurality of compounds, including mixtures thereof. 
     Throughout this application, various embodiments of this invention may be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range. 
     Whenever a numerical range is indicated herein, it is meant to include any cited numeral (fractional or integral) within the indicated range. The phrases “ranging/ranges between” a first indicate number and a second indicate number and “ranging/ranges from” a first indicate number “to” a second indicate number are used herein interchangeably and are meant to include the first and second indicated numbers and all the fractional and integral numerals therebetween. 
     It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination or as suitable in any other described embodiment of the invention. Certain features described in the context of various embodiments are not to be considered essential features of those embodiments, unless the embodiment is inoperative without those elements. 
     Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims. 
     All publications, patents and patent applications mentioned in this specification are herein incorporated in their entirety by reference into the specification, to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention. To the extent that section headings are used, they should not be construed as necessarily limiting.