Ink jet position adjusting method and three-dimensional printing apparatus
阅读说明:本技术 喷墨位置调整方法以及立体打印设备 (Ink jet position adjusting method and three-dimensional printing apparatus ) 是由 施可葳 谢欣达 黄郁庭 袁国砚 于 2018-07-09 设计创作,主要内容包括:本发明提出一种喷墨位置调整方法以及立体打印设备。所述喷墨位置调整方法包括:获取立体数字模型,对立体数字模型进行切层处理而产生具有截面轮廓的切层物件;自立体数字模型获取切层物件所对应的物件表面的法线方向;当法线方向指向第一轴向的负方向时,获取切层物件所对应的物件表面的表面倾斜程度,并依据表面倾斜程度计算切层物件的喷墨位置的内缩量;依据内缩量与截面轮廓获取切层物件的喷墨范围;以及在控制打印模块打印切层物件之后,依据喷墨范围而控制喷墨模块朝切层物件。(The invention provides an ink jet position adjusting method and a three-dimensional printing device. The ink ejection position adjustment method includes: obtaining a three-dimensional digital model, and performing layer cutting processing on the three-dimensional digital model to generate a layer cutting object with a cross section outline; acquiring the normal direction of the surface of the object corresponding to the layer-cutting object by using the stereo digital model; when the normal direction points to the negative direction of the first axial direction, the surface inclination degree of the surface of the object corresponding to the layer cutting object is obtained, and the retraction amount of the ink jet position of the layer cutting object is calculated according to the surface inclination degree; acquiring the ink jet range of the layer cutting object according to the retraction amount and the section profile; and after controlling the printing module to print the layer cutting object, controlling the ink jet module to face the layer cutting object according to the ink jet range.)
1. An ink-jet position adjusting method is suitable for printing a color three-dimensional object, and is characterized by comprising the following steps:
obtaining a three-dimensional digital model, and carrying out layer cutting processing on the three-dimensional digital model to generate a layer cutting object with a cross section outline;
acquiring the normal direction of the surface of the object corresponding to the layer-cutting object from the three-dimensional digital model;
when the normal direction points to the negative direction of the first axial direction, obtaining the surface inclination degree of the surface of the object corresponding to the layer cutting object from the three-dimensional digital model, and calculating the retraction amount of the ink jet position of the layer cutting object according to the surface inclination degree corresponding to the layer cutting object;
acquiring the ink jet range of the layer cutting object according to the retraction amount and the section profile; and
and after the printing module is controlled to print the layer cutting object, controlling the ink jetting module to jet ink towards the layer cutting object and along the cross section outline according to the ink jetting range.
2. The inkjet position adjusting method according to claim 1, wherein the step of obtaining the normal direction of the surface of the object corresponding to the sliced object from the stereoscopic digital model comprises:
obtaining at least one polygonal mesh unit corresponding to the layer cutting object from the three-dimensional digital model; and
and acquiring a normal vector of the at least one polygon mesh unit, wherein the normal vector points to the outside of the stereoscopic digital model.
3. The ink ejection position adjustment method according to claim 2, further comprising:
and judging whether the normal direction points to the negative direction of the first axial direction, wherein the first axial direction is vertical to the horizontal plane.
4. The method according to claim 2, wherein when the normal direction points to a negative direction of the first axis, the step of obtaining the surface inclination degree of the object surface corresponding to the layer-cutting object from the three-dimensional digital model, and calculating the retraction amount of the ink ejection position of the layer-cutting object according to the surface inclination degree corresponding to the layer-cutting object comprises:
calculating at least one included angle between the at least one polygonal grid unit and the horizontal plane to represent the surface inclination degree; and
and calculating the retraction amount of the ink jet position of the layer cutting object according to the at least one included angle and the preset retraction amount.
5. The method according to claim 4, wherein the step of calculating the retraction amount of the ink ejection position of the layer cutting object according to the at least one included angle and the predetermined retraction amount comprises:
and calculating the product of the cosine value of the at least one included angle, the preset retraction amount and the adjustment parameter to obtain the retraction amount.
6. The method according to claim 5, wherein the predetermined setback corresponds to a reference angle, the adjustment parameter is a reciprocal of a cosine of the reference angle, and the reference angle is between 0 and 90 degrees.
7. The method according to claim 4, wherein the at least one polygon mesh unit comprises a first polygon mesh unit and a second polygon mesh unit, and the step of calculating the at least one angle between the at least one polygon mesh unit and the horizontal plane comprises:
and calculating a first included angle between the first polygonal grid unit and the horizontal plane, and calculating a second included angle between the second polygonal grid unit and the horizontal plane.
8. The method according to claim 7, wherein the step of calculating the retraction amount of the ink ejection position of the layer cutting object according to the at least one included angle and the predetermined retraction amount comprises:
calculating a first inner shrinkage amount in the inner shrinkage amount according to the first included angle and the preset inner shrinkage amount: and
and calculating a second inner shrinkage amount in the inner shrinkage amount according to the second included angle and the preset inner shrinkage amount.
9. The inkjet position adjusting method according to claim 1, wherein obtaining the inkjet range of the layer cutting object according to the retraction amount and the cross-sectional profile comprises:
generating an inkjet image according to the retraction amount, an inkjet width and the cross-sectional profile, wherein the inkjet image includes the inkjet range formed based on the retraction amount.
10. A stereoscopic printing apparatus adapted to print a stereoscopic object in color, comprising:
a printing module comprising a printhead;
an inkjet module including an inkjet head;
a storage device in which a plurality of modules are recorded; and
a processing device coupled to the storage device and configured to execute the plurality of modules to:
obtaining a three-dimensional digital model, and carrying out layer cutting processing on the three-dimensional digital model to generate a layer cutting object with a cross section outline;
acquiring the normal direction of the surface of the object corresponding to the layer-cutting object from the three-dimensional digital model;
when the normal direction points to the negative direction of the first axial direction, obtaining the surface inclination degree of the surface of the object corresponding to the layer cutting object from the three-dimensional digital model, and calculating the retraction amount of the ink jet position of the layer cutting object according to the surface inclination degree corresponding to the layer cutting object;
acquiring the ink jet range of the layer cutting object according to the retraction amount and the section profile; and
and after the printing module is controlled to print the layer cutting object, controlling the ink jetting module to jet ink towards the layer cutting object and along the cross section outline according to the ink jetting range.
11. The stereoscopic printing apparatus of claim 10, wherein the processing device is configured to: obtaining at least one polygonal mesh unit corresponding to the layer cutting object from the three-dimensional digital model; and acquiring a normal vector of the at least one polygon mesh unit, wherein the normal vector points to the outside of the stereoscopic digital model.
12. The stereoscopic printing apparatus of claim 11, wherein the processing device is configured to: and judging whether the normal direction points to the negative direction of the first axial direction, wherein the first axial direction is vertical to the horizontal plane.
13. The stereoscopic printing apparatus of claim 11, wherein the processing device is configured to: calculating at least one included angle between the at least one polygonal grid unit and the horizontal plane to represent the surface inclination degree; and calculating the inner shrinkage of the ink jet position of the layer cutting object according to the at least one included angle and a preset inner shrinkage.
14. The stereoscopic printing apparatus of claim 13, wherein the processing device is configured to: and calculating the product of the cosine value of the at least one included angle, the preset retraction amount and the adjustment parameter to obtain the retraction amount.
15. The stereoscopic printing apparatus according to claim 14, wherein the preset amount of retraction corresponds to a reference angle, the adjustment parameter is an inverse of a cosine value of the reference angle, and the reference angle is between 0 and 90 degrees.
16. The stereoscopic printing apparatus according to claim 13, wherein the at least one polygonal mesh unit comprises a first polygonal mesh unit and a second polygonal mesh unit, the processing device being configured to: and calculating a first included angle between the first polygonal grid unit and the horizontal plane, and calculating a second included angle between the second polygonal grid unit and the horizontal plane.
17. The stereoscopic printing apparatus of claim 16, wherein the processing device is configured to: calculating a first inner shrinkage amount in the inner shrinkage amount according to the first included angle and the preset inner shrinkage amount: and calculating a second inner shrinkage amount in the inner shrinkage amount according to the second included angle and the preset inner shrinkage amount.
18. The stereoscopic printing apparatus of claim 11, wherein the processing device is configured to: generating an inkjet image according to the retraction amount, an inkjet width and the cross-sectional profile, wherein the inkjet image includes the inkjet range formed based on the retraction amount.
Technical Field
The present disclosure relates to inkjet technologies for three-dimensional printing, and particularly to an inkjet position adjusting method and a three-dimensional printing apparatus.
Background
With the advancement of Computer-Aided Manufacturing (CAM), the Manufacturing industry has developed stereoscopic printing technology to quickly make the original design. The three-dimensional printing technology is a general name of a series of Rapid Prototyping (RP) technologies, and the basic principle thereof is to manufacture a plurality of layers of cut-layer objects in a stacked manner on a printing platform by a Rapid Prototyping machine, wherein the cut-layer objects are sequentially printed on the printing platform in a scanning manner in a horizontal plane, so that the cut-layer objects can be stacked to form a three-dimensional printed object. Taking Fused Deposition Modeling (FDM) technology as an example, a molding material is made into a wire, and the molding material is heated and fused and then stacked layer by layer on a molding platform according to a required shape/contour to form a three-dimensional object.
In response to the requirement of color three-dimensional printing, the current three-dimensional printing technology further includes performing an inkjet operation on the three-dimensional printed object under printing. That is, when the three-dimensional printing device prints the cut-layer objects, the three-dimensional printing device can color each layer of cut-layer object at the same time, so as to manufacture a colored three-dimensional object. In a color three-dimensional printing technique, a three-dimensional printing device colors the contour edge of each layer-cutting object according to a preset ink-jet width, so that the surface of the three-dimensional object is colored. Specifically, when the stereo printing device performs the ink-jet operation, the ink-jet head applies ink to the edge of the upper surface of the layer-cutting object.
Ideally, the ink ejected from the ink jet head will fall completely on the upper surface of the layer-cutting object. However, when the edge of a layer-cutting object is suspended, the lower unsupported edge will slightly collapse, resulting in a difference between the actual object edge and the ideal object edge. In this case, since the ink jetting range of the inkjet head is determined based on the predetermined ink jetting width and the cross-sectional profile of the layer cutting object, and the edge of the object is collapsed as an unexpected event of the processing software, the ink sprayed based on the ink jetting range without considering the collapse may not completely fall on the layer cutting object, and the ink may spill on the platform or the object below. Fig. 1 shows an example of ink-jet operation performed on an edge portion of a sliced piece. As shown in fig. 1, when the edge of the laminated object L1 is suspended, the
Disclosure of Invention
The invention provides an ink-jet position adjusting method and a three-dimensional printing device, which can adjust the ink-jet position according to the surface inclination degree corresponding to a layer cutting object so as to avoid the phenomenon of ink spilling.
The embodiment of the invention provides an ink-jet position adjusting method which is suitable for printing a color three-dimensional object. The ink ejection position adjustment method includes: obtaining a three-dimensional digital model, and performing layer cutting processing on the three-dimensional digital model to generate a layer cutting object with a cross section outline; acquiring the normal direction of the surface of the object corresponding to the layer-cutting object by using the stereo digital model; when the normal direction points to the negative direction of the first axial direction, the surface inclination degree of the surface of the object corresponding to the layer cutting object is obtained by the independent body digital model, and the retraction amount of the ink jet position of the layer cutting object is calculated according to the surface inclination degree corresponding to the layer cutting object; acquiring the ink jet range of the layer cutting object according to the retraction amount and the section profile; and after controlling the printing module to print the layer cutting object, controlling the ink jet module to jet ink towards the layer cutting object and along the cross section contour according to the ink jet range.
In an embodiment of the present invention, the step of obtaining the normal direction of the surface of the object corresponding to the sliced object by the stereo digital model includes: obtaining at least one polygonal grid unit corresponding to the layer-cutting object by a digital model of the independent body; and acquiring a normal vector of at least one polygon mesh unit, wherein the normal vector points to the outside of the stereoscopic digital model.
In an embodiment of the present invention, the method further includes: and judging whether the normal direction points to the negative direction of a first axial direction, wherein the first axial direction is vertical to the horizontal plane.
In an embodiment of the present invention, when the normal direction points to a negative direction of the first axial direction, the step of obtaining the surface inclination degree of the surface of the object corresponding to the layer-cutting object from the stereo digital model, and calculating the retraction amount of the ink-jetting position of the layer-cutting object according to the surface inclination degree corresponding to the layer-cutting object includes: calculating at least one included angle between at least one polygonal grid unit and the horizontal plane to represent the surface inclination degree; and calculating the retraction amount of the ink jet position of the layer cutting object according to the at least one included angle and the preset retraction amount.
In an embodiment of the present invention, the step of calculating the retraction amount of the ink-jetting position of the layer-cutting object according to the at least one included angle and the predetermined retraction amount includes: and calculating the product of the cosine value of at least one included angle, the preset retraction amount related to the reference angle and the adjustment parameter to obtain the retraction amount.
In an embodiment of the invention, the adjustment parameter is an inverse of a cosine value of a reference angle, and the reference angle is between 0 and 90 degrees.
In an embodiment of the present invention, the at least one polygon mesh unit includes a first polygon mesh unit and a second polygon mesh unit, and the step of calculating the at least one included angle between the at least one polygon mesh unit and the horizontal plane includes: and calculating a first included angle between the first polygonal grid unit and the horizontal plane, and calculating a second included angle between the second polygonal grid unit and the horizontal plane.
In an embodiment of the present invention, the step of calculating the retraction amount of the ink-jetting position of the layer-cutting object according to the at least one included angle and the predetermined retraction amount includes: calculating a first inner shrinkage amount in the inner shrinkage amount according to the first included angle and a preset inner shrinkage amount: and calculating a second inner shrinkage amount in the inner shrinkage amount according to the second included angle and the preset inner shrinkage amount.
In an embodiment of the present invention, the obtaining the ink jetting range of the sliced layer object according to the shrinkage and the cross-sectional profile includes: and generating an ink jet image according to the retraction amount, the ink jet width and the cross section profile, wherein the ink jet image comprises an ink jet range formed based on the retraction amount.
From another perspective, an embodiment of the present invention provides a stereoscopic printing apparatus suitable for manufacturing a color stereoscopic object, which includes a printing module, an inkjet module, a storage device, and a processing device. The print module includes a printhead and the inkjet module includes an inkjet head. The storage device records a plurality of modules, and the processing device is coupled to the storage device and configured to execute the modules to: obtaining a three-dimensional digital model, and performing layer cutting processing on the three-dimensional digital model to generate a layer cutting object with a cross section outline; acquiring the normal direction of the surface of the object corresponding to the layer-cutting object by using the stereo digital model; when the normal direction points to the negative direction of the first axial direction, the surface inclination degree of the surface of the object corresponding to the layer cutting object is obtained by the independent body digital model, and the retraction amount of the ink jet position of the layer cutting object is calculated according to the surface inclination degree corresponding to the layer cutting object; acquiring the ink jet range of the layer cutting object according to the retraction amount and the section profile; and after controlling the printing module to print the layer cutting object, controlling the ink jet module to jet ink towards the layer cutting object and along the cross section contour according to the ink jet range.
Based on the above, the inkjet position adjusting method and the three-dimensional printing apparatus according to the embodiments of the invention can determine the retraction amount of the inkjet position according to the surface inclination degree corresponding to the layer cutting object, and translate the original inkjet position according to the retraction amount to generate a new inkjet position. Therefore, after the printing head prints the layer cutting object, the three-dimensional printing equipment can control the ink jet module to jet ink towards the layer cutting object and along the cross section outline according to the adjusted ink jet range, and the condition that the ink is spilled on the three-dimensional object or the platform below the three-dimensional object due to the collapse of the edge of the layer cutting object can be avoided.
In order to make the aforementioned and other features and advantages of the invention more comprehensible, embodiments accompanied with figures are described in detail below.
Drawings
FIG. 1 illustrates an example of ink-jetting operation on an edge portion of a sliced layer article;
FIG. 2 is a block diagram of a stereoscopic printing apparatus according to an embodiment of the invention;
FIG. 3 is a schematic diagram of a stereoscopic printing apparatus according to the embodiment of FIG. 2;
FIG. 4 is a flowchart illustrating an ink ejection position adjustment method according to an embodiment of the invention;
FIGS. 5A and 5B are schematic diagrams illustrating the determination of an ideal ink ejection range according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of an angle between a polygonal mesh unit and a horizontal plane according to an embodiment of the present invention;
FIG. 7 is a flowchart illustrating an inkjet width adjustment method according to an embodiment of the invention.
The reference numbers illustrate:
l1, 80a, 80c, 52(1), 52(2), 52(n-1), 52 (n): layer cutting article
E1: edge of physical object
E2: ideal article edge
11: edge part
12: ink jet head
20: three-dimensional printing equipment
210: printing module
220: ink jet module
230: storage device
240: processing apparatus
250: forming platform
210 a: printing head
220 a: ink jet head
220 b: ink cartridge
S1: bearing surface
80: three-dimensional object
F1: molding material
I1: ink for ink jet recording
S401 to S405, S701 to S708: step (ii) of
51: stereo digital model
T1, T2: degree of surface inclination
F1, F2: original ink jet range
F3, F4: novel ink jet range
Img1, Img 2: ink jet image
M1: triangular mesh unit
V1, V2, V3: endpoint
HP: horizontal plane
Ws1, Ws 2: internal shrinkage
Ln 1: straight line
LA, LB: vertical line
θ 1: included angle
Detailed Description
In order that the present invention may be more readily understood, the following detailed description is provided as an illustration of specific embodiments of the invention. Further, wherever possible, the same reference numbers will be used throughout the drawings and the description to refer to the same or like parts.
Fig. 2 shows a schematic diagram of a stereoscopic printing apparatus according to an embodiment of the present invention. Referring to fig. 2, the
In the present embodiment, the
In the embodiment, the
In the present embodiment, the
It should be noted that, in an embodiment, the
Fig. 3 is a schematic view of a stereoscopic printing apparatus according to the embodiment of fig. 2. Referring to fig. 3, the
In detail, in the present embodiment, the
In the present embodiment, the
In the present embodiment, the
With this arrangement, after the
It should be noted that, in the embodiment of the present invention, the
Fig. 4 is a flowchart of a method for stereoscopic color printing according to an embodiment of the invention. The method of the present embodiment is applied to the three-
In step S401, the
Next, in step S402, the
Specifically, after the slicing process is performed to obtain a plurality of sliced objects, the
Therefore, in the embodiment of the present invention, the
Next, in step S403, when the normal direction points to the negative direction of the first axis, the
For example, referring to fig. 5A and 5B together, fig. 5A and 5B are schematic diagrams illustrating the determination of an ideal ink jetting range according to an embodiment of the present invention. It is assumed that the
Take the layer cutting device 52(2) as an example. Since the normal direction of the surface of the object corresponding to the sliced layer object 52(2) points to the negative direction of the first axial direction (Z axis), the
Further, the layer-cutting object 52(n-1) is taken as an example. Since the normal direction of the surface of the object corresponding to the sliced object 52(n-1) points to the negative direction of the first axial direction (Z axis), the
It should be noted that, since the surface inclination degree T1 corresponding to the object surface of the layer cutting object 52(2) and the surface inclination degree T2 corresponding to the object surface of the layer cutting object 52(n-1) are different from each other, the retraction amount Ws1 is different from the retraction amount Ws 2. Here, since the surface inclination degree T2 corresponding to the object surface of the layer-cutting object 52(n-1) is steeper than the surface inclination degree T1 corresponding to the object surface of the layer-cutting object 52(2), the retraction amount Ws2 is smaller than the retraction amount Ws 1. That is, in one embodiment, for each layer of the sliced object, whether the ink ejection position is retracted and the corresponding amount of retraction can be determined individually.
Then, in step S405, after controlling the
However, fig. 5A and 5B are only exemplary and not intended to limit the present invention. Those skilled in the art will have sufficient teaching and suggestions to deduce how to perform similar processing for other shapes of solid digital models after the description with reference to fig. 5A and 5B.
The following examples are provided to illustrate how to obtain the surface inclination of the surface of the object corresponding to the sliced object. In one embodiment, the three-dimensional digital model is composed of a plurality of polygonal Mesh units (Mesh), and each polygonal Mesh unit has a plurality of endpoints, wherein the endpoints have different coordinates respectively. For example, the polygonal mesh cells are typically triangular mesh cells, which may be considered as triangular faces formed by three endpoints. When the layer cutting processing is executed, a certain layer cutting plane for performing the layer cutting processing passes through partial polygonal mesh units of the three-dimensional digital model, so that the section outline of the layer cutting object is extracted. Thus, in one embodiment, the
Referring to fig. 6, fig. 6 is a schematic diagram illustrating an included angle between a polygonal mesh unit and a horizontal plane according to an embodiment of the present invention. Assuming that the sliced object corresponds to the triangular mesh cell M1 formed by the endpoints V1, V2, and V3, the
As described above, when the slicing process is performed using the horizontal plane HP, the horizontal plane HP intersects the triangular mesh unit M1 at the intersection point V7 and the intersection point V8, and the straight line Ln1 between the intersection point V7 and the intersection point V8 is a partial section of the cross-sectional profile. Based on this, the
In one embodiment, after obtaining at least one angle representing the degree of surface inclination, the
WsiedalWud × cos θ xR1 formula (1)
Wherein, WsidealRepresents the amount of retraction, θ represents the angle between the polygonal mesh unit and the horizontal plane, Wd represents the preset amount of retraction, and R1 represents the adjustment parameter. Referring to the formula (1), the
In addition, in one embodiment, the predetermined setback may be configured to correspond to a reference angle, and the adjustment parameter may be an inverse of a cosine value of the reference angle, and the reference angle is between 0 and 90 degrees. For example, assuming that the reference angle is 45 degrees and the predetermined retraction amount is a reference amount corresponding to 45 degrees, such as 0.5 cm, the formula (1) can be further set as the formula (2).
Wherein, WsidealRepresents the amount of retraction, θ represents the angle between the polygonal mesh unit and the horizontal plane (e.g., the angle θ 1 shown in FIG. 6), Wd represents the predetermined amount of retraction, and θ represents the amount of retractionrRepresenting a reference angle. In this case, as can be seen from the formula (2), when the angle θ between the polygon mesh unit and the horizontal plane is equal to the reference angle (45 degrees), the
The calculation method of the formula (1) and the formula (2) is only one embodiment of the present invention. In other embodiments, the
In addition, based on the foregoing, for the three-dimensional digital model with irregular shape, the same sliced object may correspond to different surface inclinations. That is, the angles between the plurality of polygonal grid cells corresponding to the layer-cutting object and the horizontal plane are different. In this case, the polygon mesh units corresponding to the layer-cutting object may include a first polygon mesh unit and a second polygon mesh unit. In one embodiment, the
Fig. 7 is a flowchart illustrating an inkjet position adjustment method according to an embodiment of the invention, and details of the implementation of the method may refer to the description of the embodiment in fig. 2 to 6. Referring to fig. 7, in step S701, a stereo digital model is obtained, and a layer-cutting process is performed on the stereo digital model to generate a layer-cut object with a cross-sectional profile. In step S702, at least one polygonal mesh unit corresponding to the layer-cut object is obtained from the stereo digital model. In step S703, a normal vector of at least one polygon mesh unit is obtained. In step S704, it is determined whether the normal direction points to the negative direction of the first axis direction according to the normal vector of the at least one polygon mesh unit. In step S705, when the normal direction points to the negative direction of the first axis, at least one included angle between at least one polygon mesh unit and the horizontal plane is calculated to represent the surface inclination degree. In step S706, the inner shrinkage of the ink jetting position of the layer cutting object is calculated according to the at least one included angle and the predetermined inner shrinkage. In step S707, an inkjet image is generated according to the retraction amount, the inkjet width and the cross-sectional profile, wherein the inkjet image includes an inkjet range formed based on the retraction amount. In step S708, after the printing module is controlled to print the layer-cutting object, the ink-jet module is controlled to jet ink toward the layer-cutting object and along the cross-sectional profile according to the ink-jet range.
In summary, the ink-jetting position adjusting method and the three-dimensional printing apparatus according to the embodiments of the invention can determine the retraction amount of the ink-jetting position according to the surface inclination degree corresponding to the layer-cutting object, and translate the original ink-jetting position according to the retraction amount to generate a new ink-jetting position. Therefore, after the printing head prints the layer cutting object, the three-dimensional printing equipment can control the ink jet module to jet ink towards the layer cutting object and along the cross section outline according to the adjusted ink jet range, and the condition that the ink is spilled on the three-dimensional object or the platform below the three-dimensional object due to the collapse of the edge of the layer cutting object can be avoided. Therefore, the three-dimensional printing equipment can obviously improve the printing quality of color three-dimensional printing.
Although the present invention has been described with reference to the above embodiments, it should be understood that various changes and modifications can be made therein by those skilled in the art without departing from the spirit and scope of the invention.