A method for automatically positioning blanks in a strip and for calculating the associated scrap ratio.

Abstract

A method for a computerized layout of two blanks to be cut out in a strip extending in the longitudinal direction, including the step of determining the inner dimensions of each blank in the longitudinal direction, the step of determining the distance between the left side of blank A and the right side of blank B in the longitudinal direction and, if the blanks overlap, the reverse distance, and the step of estimating the pitch between two adjacent blanks A and B and between two adjacent blanks B and A. A method for computerized scrap ratio calculation using the blank layout method, and a method for computerized calculation of the material cost of a blanking operation using the scrap ratio calculation.

Description

[Technical Field]

[0001] The present invention relates to the manufacture of blanks, and more particularly to the manufacture of blanks cut from rectangular planar strips of material that generally extend in the longitudinal direction. [Background technology]

[0002] In many material manufacturing processes for materials that are generally planar, the continuous nature of the manufacturing process suggests that the final manufactured product generally takes the form of long strips extending longitudinally. This is true, for example, in the production of flat sheet metals such as flat steel products or flat aluminum products. This is also true in the pulp and paper industry, or when manufacturing fabrics and textiles. The strips mentioned above are often prepared by winding them into coils to efficiently store or transport them.

[0003] One common method for using material in subsequent deformation processes is to cut out shapes with a predetermined contour from the strip. For example, in the case of metal strips, metal blanks can be cut out, or in the fashion industry, fabric or textiles can be cut out. In the case of metal strips, this operation is called blanking, and the resulting product is called a metal blank, that is, a generally flat piece of metal with a predetermined contour suitable for use in subsequent deformation processes. This operation can be performed, for example, by punching, water jet cutting, oxygen cutting, or laser cutting.

[0004] For simplicity's sake, the term "blank" will be used below, but as will be easily understood, the field of application of this invention is not limited to metallic materials.

[0005] The material remaining in the strip after the blanks have been cut is designated as scrap. Scrap is waste material from the blanking process and should be kept to a minimum in order to optimize productivity, minimize environmental impact, and minimize the cost of blanking operations. In the case of environmental impact, the production process for manufacturing the raw material strips themselves has an environmental footprint, such as CO2 emissions. By minimizing scrap and thus maximizing the overall output of the industrial process, environmental impact can be kept as low as possible.

[0006] In this invention, the term "cost" generally refers to, for example, environmental costs, productivity costs, or economic costs.

[0007] The present invention has the following configuration: a strip from which two blanks are cut, each blank having a predetermined contour, each having a fixed orientation in the longitudinal direction, and having a given offset from each other in the transverse direction. The arrangement of the two blanks relative to each other in the longitudinal direction determines the pattern, and this pattern is repeated insofar as the strip extends in the longitudinal direction. The fact that the orientation of the blanks is fixed can be an industrial constraint, for example, due to the anisotropic properties inherited from the rolling process in the case of metallic materials, such as steel or aluminum; this can further be linked to other considerations, such as patterns in the fabric industry. [Overview of the project] [Problems that the invention aims to solve]

[0008] The object of the present invention is to provide an automated method for arranging a given blank in a strip with an optimal material usage configuration, and for calculating the subsequent scrap ratio. The scrap ratio is defined as the ratio between the scrap generated by the blanking process and the total amount of strip material used.

[0009] Another object of the present invention is to provide an automated method for calculating blank costs associated with the use of material in a blanking operation. [Means for Solving the Problems]

[0010] By providing an optimized computer-implemented method for arranging blanks, calculating scrap ratio, and calculating material cost, the present invention enables efficient design and evaluation of costs of a blanking process. Furthermore, automation of said operations allows their use in subsequent optimization routines. For example, said operations can be used in a subsequent routine for finding the best combination of blank orientation and lateral offset amount to minimize overall scrap.

[0011] The object of the present invention is achieved by providing a computerized method for arranging two blanks in a strip according to claim 1, optionally comprising the features of claims 2 to 4, by providing a computerized scrap ratio calculation method according to claim 5, and by providing a computerized blank cost calculation method according to claim 6, optionally comprising the features of claim 7. The object of the present invention is further achieved by providing a computer program according to claim 8 and a computer-readable storage medium according to claim 9.

[0012] Next, the present invention will be described and illustrated in detail by way of example without introducing constraints, with reference to the accompanying drawings. [Brief Description of the Drawings]

[0013] [Figure 1] It is a schematic diagram showing the configuration of an arrangement of two blanks in a strip, wherein the longitudinal direction is indicated by an arrow labeled "L", while the transverse direction is indicated by an arrow labeled "T". [Figure 2A]This diagram shows how dAA is calculated. [Figure 2B] This diagram shows how to calculate dBB. [Figure 3A] This diagram shows how to calculate dAB. [Figure 3B] This diagram shows how to calculate dBA. [Figure 4] This figure shows another example of determining the type value of dAiA in more complex shapes. [Figure 5A] This figure shows examples of determining dAA, dBB, dAB, and dBA for more complex shapes. [Figure 5B] This figure shows the arrangement of blanks A and B in the strip, as shown in Figure 5A. [Figure 6A] This figure shows a blank with the same shape but a different orientation, following the same principle as Figures 5A and 5B. [Figure 6B] This figure shows a blank with the same shape but a different orientation, following the same principle as Figures 5A and 5B. [Figure 7A] This figure shows a blank with the same shape but a different orientation, following the same principle as Figures 5A and 5B. [Figure 7B] This figure shows a blank with the same shape but a different orientation, following the same principle as Figures 5A and 5B. [Figure 8] This figure shows a specific embodiment of the present invention in which blanking tolerances and strip width tolerances are taken into account to calculate the scrap ratio and blank cost. [Figure 9] This figure shows a specific embodiment of the present invention in which blanking tolerances and strip width tolerances are taken into account to calculate the scrap ratio and blank cost. [Modes for carrying out the invention]

[0014] Referring to Figure 1, in the present invention, the longitudinal direction refers to the main direction in which the strip 1 extends, and the transverse direction refers to the direction perpendicular to the longitudinal direction in a plane. Furthermore, the strip 1 extends over a limited width between two parallel edges 2 and 3 in the transverse direction Y, and over a width W in the same direction.

[0015] Strip 1 has an upper and a lower side, also referred to as the top and bottom surfaces. All attached figures are two-dimensional top views, with only the upper side visible. The distance between the top and bottom surfaces is specified as the thickness of the strip. The thickness may be measured, for example, using a micrometer, with the micrometer's spindle and anvil placed on the top and bottom surfaces.

[0016] In the following description and claims, the terms longitudinal and horizontal have the same meaning, and the terms transverse and vertical have the same meaning. The terms “left” and “right” are used in the following description and claims to refer to relative positions further back and further along the longitudinal direction, i.e., along the direction marked by the “L” arrow in Figure 1, respectively. The terms “upwards” (and “above,” “above,” etc.) and “downwards” (and “below,” “above,” etc.) are used in the following description and claims to refer to relative positions further back and further along the transverse direction, i.e., along the direction marked by the “T” arrow in Figure 1, respectively.

[0017] Referring to Figure 1, a first blank A having a first contour and a second blank B having a second contour are cut from strip 1.

[0018] Blank B is offset laterally from Blank A by a lateral offset amount dy, and the lateral offset amount dy is defined as the difference in the amount of lateral rise between the lowest points of Blank contour B and Blank contour A in the lateral direction.

[0019] The first objective of the present invention is to determine, by an automated method, how to arrange blanks A and B in strip 1 in order to use the smallest possible amount of material. This is true when a first set of blanks A and B touches the next set of blanks A and B at at least one point without overlap, and the resulting pattern is repeated along the longitudinal direction. There are potentially several other methods for arranging blanks A and B to optimize material usage. Each of these configurations is equivalent in terms of material usage. The present invention aims to reveal only one such possible configuration.

[0020] The missing elements for positioning blanks A and B are the pitch Δ1 between the left end of blank A and the left end of blank B adjacent to it in the longitudinal direction, and the pitch Δ2 between the left end of blank B and the left end of blank A adjacent to it. Once the pitches are determined, it becomes possible to position the blanks in the strip, and then, as will be further described, to calculate the scrap ratio and the material cost of blanking.

[0021] The pitches Δ1 and Δ2 take into account the shapes and internal dimensions of A and B along the longitudinal direction, as well as the interrelationship between blanks A and B in the longitudinal direction.

[0022] To optimize computation time, the inventors developed a method that deals only with the internal distance between the vertices and edges of each individual blank A and blank B in the longitudinal direction, and only with the longitudinal relationship between blank A and blank B at a width point where a vertex of either blank A or blank B is located.

[0023] Since the number of vertices in each blank is discrete and generally very limited, the method of the present invention allows for the calculation of the scrap ratio very quickly.

[0024] Referring to Figures 2A and 2B, an X-Y coordinate system is used to determine the positions of the vertices and contours of blanks A and B. The X-axis is parallel to the longitudinal direction of the strip, while the Y-axis is parallel to the transverse direction of the strip. Conventionally, blank A is positioned in the coordinate system such that its leftmost point is at X=0 and its lowest point is at Y=0. Blank B is positioned such that its leftmost point is at X=0 and its lowest point is at Y=dy.

[0025] The blank contours of A and B are represented, respectively, by vertices A1, A2, A3, A4 and B1, B2, B3, which are joined by straight edges. i Its coordinates (XA i ,YA i Identified by ) and each vertex B i Its coordinates (XB i ,YB i Identified by ).

[0026] For clarity, blanks A and B in the figure have simple shapes with long straight edges. However, this method can be applied to any two-dimensional contour. In the case of contours with curved edges, the curved edges are approximated by successive smaller straight segments, thereby defining a set of vertices and connecting the edges.

[0027] Therefore, in a typical case, blank A is the set of its p vertices {A1,...,A P Represented by}, the blank B is the set of its q vertices {B1,...,B q It is expressed as}, where p and q are integers greater than or equal to 3.

[0028] In order to determine Δ1 and Δ2, it is necessary to first calculate the maximum dimensions dAA and dBB in the longitudinal direction of blanks A and B respectively, and, when said blanks overlap (see FIGS. 3A and 3B), the respective maximum longitudinal offset amounts dAB and dBA of blank B from blank A and of blank A from blank B.

[0029] This is done by carrying out the following steps: - For each vertex A i , for the Y-value of vertex A i , calculating distance dA i A defined as the difference between the maximum X-value taken by the contour of blank A and the minimum X-value taken by the contour of blank A, and calculating the maximum internal transverse distance dAA defined as the maximum value among all A i A, - For each vertex B i , for the Y-value of vertex B i , calculating distance dB i B defined as the difference between the maximum X-value taken by the contour of blank B and the minimum X-value taken by the contour of blank B, and calculating the maximum internal transverse distance dBB defined as the maximum value among all B i B.

[0030] For example, in the simple case of FIG. 2A, dA2A and dA4A are equal to 0, while dA3A and dA1A have equal values, and thus dAA = dA3A = dA1A.

[0031] Blanks A and B in Figures 2A and 2B are simple shapes for clarity, but in the case of more complex shapes, such as blank U depicted in Figure 4, there may be examples where a straight line parallel to the X-axis intersects the contour several times, as in the cases of U1 and U2. In this case, the segments corresponding to dU1U and dU2U, as depicted in Figure 4, may intersect the blank contour in order to extend from the leftmost point to the rightmost point of the contour. To illustrate another possible configuration, in the case of dU5U, the segment does not have vertex U5 as one of its endpoints because U5 lies between the leftmost and rightmost points of the contour in its Y value.

[0032] Next, the longitudinal offset amounts dAB and dBA are calculated by applying the following method: - Each vertex A located at a Y value where at least one point on the contour of blank B exists i Regarding vertex A, i In the Y value, the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank A, and vertex A i In terms of Y values, the oriented distance dA is defined as the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank B. i B and dBA i Calculate. - Each vertex B located at a Y value where at least one point on the contour of blank A exists i Regarding vertex B, i In the Y value, the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank A, and vertex B i In terms of Y values, the oriented distance dAB is defined as the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank B. i and dB i Calculate A. - All dA i B and dAB I The directed distance dB is calculated as the maximum value of all dB iA and dBA I calculate a directed distance dBA defined as the maximum value of the values.

[0033] value dA i B and dAB i In the example of Figure 3A, which represents a directed vector corresponding to, dAB will be equal to dAB2.

[0034] value dB i A and dBA i In the case of Figure 3B, which represents a directed vector corresponding to, dBA will be equal to dBA3.

[0035] After calculating dAA, dBB, dAB, and dBA, it becomes possible to calculate Δ1 and Δ2 by the following method: - Δ1 = dBA, - if dAB + dBA ≧ dAA + dAB and dAB + dBA ≧ dBB, then Δ2 = dBA - if dAB + dBA < dAA and dAA ≧ dBB, then Δ2 = dAA - dBA - if dAB + dBA < dBB and dBB > dAA, then Δ2 = dBB - dBA.

[0036] Knowing Δ1 and Δ2, blanks A and blanks B can be arranged on strip 1 by: arranging the first blank A on the strip, arranging the first blank B using a vertical offset amount dy and a longitudinal offset amount Δ1 relative to said first blank A, arranging the next blank A so as to be aligned laterally with said first blank A and using a longitudinal offset amount Δ2 directed towards said first blank B, and repeating the pattern along strip 1 as long as strip 1 extends in the longitudinal direction.

[0037] The inventors have found that this method makes it possible to efficiently and automatically optimize the arrangement of blanks A and B.

[0038] Figures 5A, 6A, and 7A show examples of determining dAA, dBB, dAB, and dBA for more complex shapes. In each figure, the upper left shows how dBB is determined (maximum dB for clarity). i (Only B is drawn), the bottom left shows how dAA is determined, the top right shows how dAB and dBA are determined, and the table in the bottom right shows the values ​​of dAA, dBB, dAB, and dBA, and their corresponding individual dA i A, dB i B / dAB i dB i A / dBA i This summarizes the situation. For example, in the configuration of Figure 6A, dAB is negative, and the reason is that all individual dA i This is because B / dABi is negative (within the range of Y values ​​of the relationship between overlapping blanks A and B, there are no points of contour A to the left of blank B). In this case, dAB is actually all of the individual dA i B / dAB i dA has the smallest absolute value i B / dAB i And this is dA i B / dAB i This corresponds to the maximum value. The table in the lower right summarizes all dAA, dBB, dAB, and dBA values ​​and details the calculation steps for determining the pitch Δ1 and Δ2.

[0039] Figures 6C, 7C, and 8C illustrate implementations of the computerized placement method using previously calculated pitches Δ1 and Δ2.

[0040] Knowing Δ1 and Δ2, the following equation is given:

number

[0041] To calculate the cost_blank of blanks A and B, defined as the material cost of blanks A and B, taking into account the cost of materials, the scrap ratio, and the cost of scrap if a scrap buyback market is available, the following additional information is required: • The strip thickness t, defined above as the distance between the top and bottom of the strip, is expressed, for example, in mm. • For example, the cost of a single unit of mass of material, expressed in currency / ton, Cost_material For example, in cases where scrap material can be bought back, such as in the steel industry where scrap is remelted, the scrap cost per unit mass, expressed, for example, in currency / ton, Cost_Scrap, Material density ρ, defined as the ratio between the mass and volume of a material, is usually kg / m³. 3 It is represented as follows.

[0042] Cost_blank is expressed as follows: M_Section=ρ*t*W*(Δ1+Δ2) Cost_blank=Cost_material*M_Section-Cost_Scrap*%Scrap*M_Section It can be calculated automatically using [this method].

[0043] In a particular embodiment, the material cost Cost_material depends on the width W of the strip, and in fact, there are n elements (Width_range i Cost_material i Provided in the form of a database Cost_database containing a set of values, where n is an integer greater than or equal to 2, and i is between 1 and n, where Width_range i This is a width range having a minimum strip width value and a maximum strip width value, and Cost_material i The width W of the strip is Width_range i This is the material cost per unit of mass when contained within.

[0044] Variable costs that depend on strip width can arise when the industrial cost of producing the strip actually depends on the width. For example, if an increase in width is associated with a decrease in productivity, the industrial cost may increase with the width. For example, if wider material can only be produced in a specific industrial facility, and this results in higher logistics costs, the material cost may increase with the width.

[0045] In certain embodiments, the coil width W takes into account a width tolerance W_tol, typically expressed in mm. This further affects the width value W used to calculate scrap and blanking costs. The width tolerance corresponds, for example, to the precision that the strip production line can achieve with respect to width. To ensure that blanks A and B will fit into the strip even when the width of the manufactured strip is at the lower end of the width tolerance spectrum, it is necessary to add a width tolerance W_tol to target a strip width W that corresponds to at least the minimum width required to fit blanks A and B into the strip. This configuration is shown in Figure 8, where a margin of W_tol / 2 is left on either side of strip 1.

[0046] In certain embodiments, a blanking tolerance, typically expressed in mm, Blank_tol, is taken into consideration when positioning blanks A and B in the strip, and therefore also when calculating the scrap ratio and blank cost. The blanking tolerance corresponds to the precision of the tool used to cut the blanks in the strip. To ensure that there is no overlap between blanks when cutting them from the strip, the distance between two adjacent blanks should not be less than 2*Blank_tol (in practice, each blank is cut to an accuracy of Blank_tol, and the risk of overlap can be completely avoided simply by providing the distance between two adjacent blanks taking into account the blanking tolerance of each individual blank). This is also shown in Figure 8.

[0047] In a particular embodiment as shown in Figure 9, blanking tolerances are taken into account in the calculation methods for Δ1 and Δ2 described above, as well as in the related methods for determining blank placement, scrap ratio, and blank cost. This is done by first geometrically enlarging blanks A and B by Blank_tol before applying the blank placement method. The enlarged blank contours of A and B are taken into account in the calculation of Δ1 and Δ2, but it should be noted that when calculating the scrap ratio %Scrap, Area_A and Area_B in the formulas are the areas of the unenlarged blank contours. In practice, the amount of material used in the strip remains a direct function of areas Area_A and Area_B, and not a direct function of the area of ​​the enlarged blank contours.

[0048] In certain embodiments, such as those depicted in Figures 5A-B, 6A-B, and 7A-B, the method described above is applied to a configuration in which blank B has exactly the same contour as blank A after being rotated about an axis perpendicular to the top surface of the strip. This is a very common case in which, in fact, there is only one blank shape to be cut from strip 1.

[0049] In certain embodiments, the method described above is applied to a configuration in which blank B is rotated about an axis perpendicular to the top surface of the strip, after which blank B has a mirror image contour of blank A. This is a common example, for example, in the automotive industry, where many parts exist on both sides of the vehicle as right-side and left-side parts, and these are generally mirror images of each other.

Claims

1. A computer-implemented method for ultimately positioning blanks A and B in a rectangular planar strip (1) having a rectangular shape and generally extending in the longitudinal direction L and over a limited width in the transverse direction T, such that one of blanks A and B contacts the other at at least one point without overlap, wherein the lowest point of blank B is laterally offset by an offset amount dy compared to the lowest point of blank A, and the method is A step of establishing an X,Y coordinate system parallel to L and T, wherein a blank A is placed in the X,Y coordinate system such that the leftmost point of blank A is at X=0 and the lowest point of blank A is at Y=0, and a blank B is placed such that the leftmost point of blank B is at X=0 and the lowest point of blank B is at Y=dy, Within the aforementioned X,Y coordinate system, a discrete set of vertices {A １ , . . , A Ｐ } and {B １ , . . , B ｑ A step of providing a numerical representation of the contours of blank A and blank B consisting of}, wherein p and q are integers of 3 or more, and the vertices are joined by the edges of a straight line, Each vertex A ｉ Regarding vertex A, ｉ In terms of Y values, the distance dA is defined as the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank A. ｉ Calculate A and all dA ｉ A step of calculating the maximum internal lateral distance dAA, which is defined as the maximum value of A. Each vertex B ｉ For the above, for vertex B ｉ with respect to the Y value of, a distance dB defined as the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank B ｉ B is calculated, and all dB ｉ a step of calculating a maximum internal lateral distance DBB defined as the maximum value of B, Each vertex A located at a Y value where at least one point on the outline of blank B exists ｉ Regarding vertex A, ｉ In the Y value, the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank A, and vertex A ｉ In terms of Y values, the oriented distance dA is defined as the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank B. ｉ B and dBA ｉ Steps to calculate Each vertex B located at a Y value where at least one point on the outline of blank A exists ｉ Regarding vertex B, ｉ In the Y value, the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank A, and vertex B ｉ In terms of Y values, the oriented distance dAB is defined as the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank B. ｉ and dB ｉ Steps to calculate A, All da ｉ B and dAB ｉ Calculate the oriented distance dAB, which is defined as the maximum value of all dB ｉ A and dBA ｉ A step of calculating the directed distance dBA, which is defined as the maximum value of the value of Δ １ However, it is defined as the longitudinal pitch between the left edge of blank A and the left edge of blank B, which is to its right. Δ １ Steps to set the value to dBA, Δ ２ However, it is defined as the pitch between the left edge of the B blank and the left edge of the A blank to its right. - When dAB + dBA ≥ dAA and dAB + dBA ≥ dBB, Δ ２ Set this to dBA, - When dAB + dBA < dAA and dAA ≥ dBB, Δ ２ Set it to dAA-dBA, - When dAB + dBA < dBB and dBB > dAA, Δ ２ Steps to set it to dBB-dBA, A first blank A is placed in the strip, and the lateral offset amount of dy and Δ are compared with the first blank A. １ The first blank B is positioned using the longitudinal offset amount of the first blank A, so as to be aligned laterally with the first blank A, and with a Δ towards the first blank B. ２ Using the longitudinal offset amount, the next blank A is positioned, and the pattern is repeated along strip 1 as long as strip 1 extends in the longitudinal direction. A method consisting of the following.

2. The method according to claim 1, further comprising an initial step of providing a blanking tolerance Blank_tol, wherein the method further comprises as a first step the step of geometrically enlarging blanks A and B by the amount of Blank_tol, and then applying the method of claim 1 to the enlarged blank contours resulting from blanks A and B.

3. The method according to claim 1, wherein after rotating the blank B about an axis perpendicular to the upper surface of the strip 1, the blank B has exactly the same contour as the blank A.

4. The method according to claim 1, wherein after rotating the blank B about an axis perpendicular to the upper surface of the strip, the blank B has a mirror image contour of the blank A.

5. A computerized method for calculating the scrap ratio %Scrap, defined as the ratio between the scrap generated by the blanking process for cutting blanks A and B from strip 1 and the total amount of strip material used, wherein blanks A and B have surface areas Area_A and Area_B, respectively, and strip 1 extends transversely over a width W, Δ １ and Δ ２ The pitch is calculated according to any one of claims 1 to 4, and %Scrap is given by the following formula [Math 1] A computerized method for calculating the scrap ratio %Scrap, which is calculated according to the method described below.

6. A computerized method for calculating the blank cost Cost_blank, defined as the material cost of blanks A and B, taking into account the cost of the material used to make the strips, the scrap ratio, and the cost of the scrap, wherein t is the strip thickness, defined as the distance between the top and bottom sides of strip 1; Cost_material is the material cost per unit mass; Cost_Scrap is the scrap cost per unit mass; ρ is the material density, defined as the ratio of mass to volume of the material; Δ1 and Δ2 are pitches calculated according to any one of claims 1 to 4; and Cost_blank is given by the following formula M_Section=ρ*t*W*(D １ +D ２ ) Cost_blank=Cost_material*M_Section-Cost_scrap*%Scrap*M_Section A method for the computerized calculation of the blank cost Cost_blank, which is calculated using [a specific method].

7. Taking into account the variable material cost per unit mass, Cost_material, which depends on the width of the strip, if Cost_material has n elements (Width_range) ｉ ,Cost_material ｉ Provided in the form of a database Cost_database containing a set of ) where n is an integer greater than or equal to 2, i is between 1 and n, and Width_range ｉ However, it is a width range having a minimum strip width value and a maximum strip width value, Cost_material ｉ However, Width_range ｉ A method for computerized calculation of the blank cost Cost_blank according to claim 6, which is the material cost per unit of mass when the width W of the strip is included within it.

8. A computer program that, when executed by a computer, includes instructions causing the computer to perform the methods described in claims 1 to 4.

9. A computer-readable storage medium that, when executed by a computer, includes instructions causing the computer to perform the methods according to claims 1 to 4.

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