Graph scaling method and design rule checking method of integrated circuit

Abstract

The invention discloses a graph scaling method and a design rule checking method of an integrated circuit. The graph zooming method for the electronic design comprises the steps that vertex information and zooming parameters of a polygon are obtained, and the zooming parameters comprise the vertical distance between the edge of the zoomed polygon and the corresponding edge of an original polygon; finding a parallel line corresponding to each edge of the polygon according to the vertex information and the scaling parameter; and searching corresponding intersection points of the parallel lines according to a boundary sequence of new boundaries of the polygon defined by the parallel lines to obtain new vertex information, and obtaining the zoomed polygon. According to the invention, the graph zooming method with high efficiency and high precision can be provided.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated circuit automated design, and in particular to a graphic scaling method for electronic design. Background Art

[0002] At present, in the integrated circuit design process, DRC rule checking is a key step to ensure that the chip design meets the manufacturing specifications. Tools such as Calibre have poor execution efficiency, low precision, and inconsistent results in related rules. With the increase in the complexity of integrated circuit design, the results generated by related rules will be used many times by other DRC rules, and the requirements for speed and precision are more stringent. When scaling graphics in the prior art, taking the design of integrated circuits as an example, when processing the bevel (Any Angle), the intersection coordinates of the graphics after enlarging or reducing are often floating point numbers, which need to be aligned and rounded to integers. There is no regularity for foreign mainstream tools such as Calibre to round intersections, so there is often an unexplained offset of 1 Database Unit (standard database unit, usually in nanometers).

[0003] In addition, the current mainstream tool in China is based on the open source code Clipper2 to achieve graphics scaling. In real-world tests, the speed is slow, about 2 to 5 times slower than the algorithm proposed in this article. Moreover, Clipper2 has a serious speed degradation when it comes to complex graphics (with more than 10,000 vertices and a large number of holes), and the results are incorrect (manifested by the loss of some holes in the scaled graphics).

[0004] Therefore, how to provide a more efficient and accurate graphics scaling method is a technical problem to be solved. Summary of the invention

[0005] In order to solve the technical problems of low efficiency and inaccurate scaling in the prior art when scaling polygons of an integrated circuit layout, the present invention proposes a graphic scaling method and an integrated circuit design rule checking method.

[0006] The graphics scaling method proposed by the present invention comprises:

[0007] Obtaining vertex information and scaling parameters of the polygon, wherein the scaling parameters include a vertical distance between an edge of the scaled polygon and a corresponding edge of the original polygon;

[0008] Find the parallel lines corresponding to each edge of the polygon based on vertex information and scaling parameters;

[0009] According to the boundary order of the new boundary of the polygon defined by the parallel lines, the corresponding intersection points of the parallel lines are found to obtain new vertex information and the scaled polygon.

[0010] Further, finding the enlarged or reduced parallel line corresponding to each edge of the polygon according to the vertex information and the scaling parameter specifically includes:

[0011] According to the vertex order in the vertex information, each edge is rotated 90 degrees around the corresponding starting vertex to obtain a moving reference line perpendicular to the corresponding edge;

[0012] The corresponding edge is moved along the moving reference line by the value of the scaling parameter to obtain a parallel line parallel to the corresponding edge.

[0013] Furthermore, the scaling parameter includes a positive number or a negative number, and the enlargement or reduction of the polygon is indicated by the positive or negative value of the scaling parameter, and the numerical value of the scaling parameter is indicated by the absolute value of the scaling parameter.

[0014] Furthermore, each edge is rotated 90 degrees around the corresponding starting vertex in a counterclockwise direction.

[0015] Furthermore, the corresponding edge is represented as a vector, and the moving reference line after counterclockwise rotation is obtained through matrix operation.

[0016] Further, moving the corresponding edge along the moving reference line by the value of the scaling parameter to obtain a parallel line parallel to the corresponding edge includes:

[0017] Calculate the slope of the moving baseline;

[0018] According to the slope of the moving baseline and the value of the scaling parameter, the coordinates of the starting point of the parallel line are calculated;

[0019] Calculate the coordinate difference between the starting point of the corresponding side and the starting point of its parallel line;

[0020] The coordinates of the end point of the parallel line are calculated based on the coordinates of the end point of the corresponding side and the coordinate difference.

[0021] Furthermore, when finding the parallel lines corresponding to each edge of the polygon based on the vertex information and scaling parameters, if the edge currently being processed is a right-angled edge, the starting point and the end point are calculated using INT type variables; if the edge currently being processed is a hypotenuse, the starting point and the end point are calculated using double type variables.

[0022] Furthermore, after obtaining the vertex information and scaling parameters of the polygon, the method also includes the step of determining whether the polygon is a rectangle. If the polygon is not a rectangle, the method further includes the step of finding the parallel lines corresponding to each side of the polygon according to the scaling parameters. If the polygon is a rectangle, the scaling operation is performed directly on the vertices.

[0023] The design rule checking method for integrated circuits proposed by the present invention includes the graphic scaling method for electronic design of the above technical solution.

[0024] The graphic scaling method of the present invention is applicable to multiple rule checks in DRC rule checking (Design Rule Checking) in integrated circuit design. Specifically, in the rule checking of graphic scaling (SIZING), graphic smoothing (SMOOTH), one-way magnification (EXPAND), etc., an efficient, accurate, and re-packaged underlying graphic scaling algorithm is provided to improve the execution efficiency and accuracy of DRC rule checking and reduce the error rate. According to tests, for the same graphic, the scaling of the graphic by the present invention is about 2 to 5 times faster than that of the open source code Clipper2, which greatly improves the efficiency of DRC rule checking of integrated circuits. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The present invention is described in detail below with reference to the embodiments and accompanying drawings, wherein:

[0026] Figure 1 It is a schematic diagram of a polygon of the present invention.

[0027] Figure 2 It is a schematic diagram of another polygon of the present invention.

[0028] Figure 3 It is the overall flow chart of the present invention.

[0029] Figure 4 It is a schematic diagram of an enlarged rectangle according to an embodiment of the present invention.

[0030] Figure 5 Schematic diagram of a polygon according to an embodiment of the present invention.

[0031] Figure 6 FIG. 4 is a schematic diagram of edge movement according to an embodiment of the present invention.

[0032] Figure 7 It is an enlarged schematic diagram of a non-rectangular polygon according to an embodiment of the present invention. DETAILED DESCRIPTION

[0033] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0034] Thus, a feature indicated in this specification will be used to illustrate one of the features of an embodiment of the present invention, rather than implying that each embodiment of the present invention must have the described feature. In addition, it should be noted that this specification describes many features. Although some features can be combined together to illustrate possible system designs, these features can also be used in other combinations that are not explicitly described. Thus, unless otherwise stated, the described combinations are not intended to be limiting.

[0035] When designing and verifying integrated circuit layouts, graphic scaling algorithms (SIZING) play a vital role. Graphic scaling algorithms are not only used to adjust the size of graphics to adapt to different process requirements, but also involve rule checks such as graphic smoothing (SMOOTH) and unidirectional expansion (EXPAND) to ensure that the design meets specific process standards. Design engineers can use graphic scaling algorithms to optimize layouts and improve design quality. Graphic scaling algorithms are indispensable tools in the design and verification process of integrated circuits. They improve the accuracy and efficiency of designs in an automated way.

[0036] The graphic scaling method for electronic design of the present invention aims to provide an efficient and accurate graphic scaling algorithm, so as to improve the execution efficiency and accuracy of the design layout of the integrated circuit and reduce the error rate when performing DRC rule checking.

[0037] First, vertex information and scaling parameters of a polygon of a design layout of an integrated circuit are obtained, wherein the scaling parameters include a vertical distance between an edge of the scaled polygon and a corresponding edge of the original polygon.

[0038] Find the parallel lines corresponding to each edge of the polygon according to the vertex information and the scaling parameter. For example, if the scaling parameter is that the vertical distance between the edge of the enlarged polygon and the corresponding edge of the original polygon is 2nm, then it is necessary to find the parallel edges of each edge of the polygon after it is moved outward by 2nm.

[0039] According to the boundary order of the new boundary of the polygon defined by the parallel lines, the corresponding intersection points of the parallel lines are found to obtain new vertex information and the scaled polygon.

[0040] The present invention can realize efficient and accurate graphics scaling, and can further be implemented using C++, and does not rely on other libraries except the C++ standard library. Users can embed the algorithm into their projects as a basic algorithm library through the provided header file (C++.h file) and link library (C++.a file), which can make the algorithm conform to object-oriented specifications and provide atomic interfaces and class encapsulation. Users do not need to care about the underlying implementation, and can perform secondary development and encapsulation by calling the corresponding interface through the provided manual, thereby providing a secondary encapsulated underlying graphics scaling algorithm.

[0041] The uniqueness of the present invention compared with the prior art is that the center point of the polygonal figure is not used as the reference point for scaling, but the starting point of each edge is innovatively selected as the starting point for scaling. This processing method is not limited to horizontal or vertical edges, but can also adapt to edges of any angle. In addition, the algorithm is also applicable to polygonal figures containing holes, showing its wide applicability and excellent flexibility.

[0042] In one embodiment, the vertex information of the present invention can be acquired and stored according to the situation.

[0043] For polygons without holes, the polygon is stored as a set of coordinate sequences ordered counterclockwise. Figure 1 For the polygon without holes shown in the figure, its vertex information can be obtained and stored as {(0,0),(10,0),(10,10),(0,10)}, or {(0,0),(10,10)}. For polygons with holes, the polygons are stored as multiple ordered coordinate sequences, where the first set can be agreed to store the border, stored counterclockwise, and the subsequent sets are the holes, stored clockwise. For example, Figure 2 The vertex information of the polygon with holes shown in the figure is obtained and can be stored as {(0,0),(10,0),(10,10),(0,10)}(border, counterclockwise), {(1,1),(1,2),(2,2),(2,1)}(hole, clockwise), {(5,5),(5,6),(6,6),(6,5)}(hole, clockwise). Of course, it can also be agreed that the coordinates of the holes are stored first, and then the coordinates of the borders, and whether the storage direction is clockwise or counterclockwise, etc., can be adjusted by technicians in this field as needed.

[0044] In a specific embodiment, finding the enlarged or reduced parallel line corresponding to each edge of the polygon according to the vertex information and the scaling parameter specifically includes the following steps.

[0045] According to the vertex order in the vertex information, each edge is rotated 90 degrees around the corresponding starting vertex to obtain a moving reference line perpendicular to the corresponding edge;

[0046] The corresponding edge is moved along the moving reference line by the value of the scaling parameter to obtain a parallel line parallel to the corresponding edge.

[0047] The scaling parameters of the present invention include the vertical distance between the side of the scaled polygon and the corresponding side of the original polygon, and may further include parameters representing reduction or enlargement.

[0048] In a preferred embodiment, the scaling parameter includes a positive number or a negative number, and the positive or negative number of the scaling parameter indicates whether the polygon is enlarged or reduced, and the absolute value of the scaling parameter indicates the numerical value of the scaling parameter. For example, when the scaling parameter is a positive number, it means that the polygon is enlarged, and the numerical value of the scaling parameter is the vertical distance between the edge of the enlarged polygon and the corresponding edge of the original polygon. Correspondingly, when the polygon is a negative number, it means that the polygon needs to be reduced. Of course, in other embodiments, a positive number can also represent reducing the polygon, and a negative number represents enlarging the polygon. It is only necessary to distinguish between enlarging and reducing, which also falls within the protection scope of the present invention.

[0049] This embodiment uses only one scaling parameter to know whether the user wants to enlarge or reduce the polygon, and also knows the effect the user wants after scaling, which is beneficial to the simplicity of the underlying code implementation.

[0050] In one embodiment, each side rotates 90 degrees around the corresponding starting vertex and rotates in a counterclockwise direction. The counterclockwise direction is selected in this embodiment because in mathematics, the counterclockwise direction is usually defined as the positive direction, which is consistent with the measurement direction of the positive angle (starting from the positive x-axis, the angle is measured counterclockwise). In addition, in computer graphics, the counterclockwise direction is usually the default direction for drawing polygons, which helps to maintain consistency, especially when processing object-oriented drawing. Of course, in other embodiments, clockwise rotation can also be adopted, which is also possible, and it only needs to ensure the consistency of the rotation direction in the project.

[0051] In a specific embodiment, any edge of a polygon can be represented as a vector after knowing the coordinates of its starting point and end point (both are vertex coordinates), referring to Figure 6 For example, side AB can be represented as vector AB. Vector AB can be rotated 90 degrees counterclockwise through matrix operation to obtain the moving reference line AC.

[0052] On the moving baseline AC, the slope of the moving baseline is calculated, and the coordinates of points A1 and A2 can be calculated using the slope of the moving baseline AC and the length of delta.

[0053] By adding and subtracting the coordinate difference between A and A1 and the coordinate difference between A and A2 from the coordinate of B, we can get the coordinates of B1 and B2, and connecting them can get two parallel lines of side AB.

[0054] In the above embodiment, technicians in this field can calculate only one corresponding parallel line as needed. Since the above calculation process is also relatively simple, the corresponding two parallel lines can also be calculated at the same time, so that when necessary, the user can choose one of them, which improves the user's processing efficiency. Taking the DRC rule check of a complex integrated circuit as an example, the present invention can generate two corresponding parallel lines at the same time, which greatly reduces the time in the complex DRC rule check and improves the efficiency of chip design and verification.

[0055] When finding the parallel lines corresponding to each side of the polygon according to the vertex information and the scaling parameters, if the side currently being processed is a right-angled side, the starting point and the end point are calculated using a variable of type INT, and if the side currently being processed is a hypotenuse, the starting point and the end point are calculated using a variable of type double. This can ensure the efficiency of the algorithm while improving the accuracy of the algorithm. However, this preferred embodiment is not the only option, and those skilled in the art may also use other types of variables for calculation without considering further improving efficiency and accuracy.

[0056] When dealing with edges on the border or holes of a polygon, the process of finding parallel lines follows a consistent rule: in a zoom-in operation, always choose parallel lines on the right; in a zoom-out operation, choose parallel lines on the left. This explicit approach ensures the consistency and reliability of the algorithm. In this way, the algorithm can systematically generate corresponding parallel lines for each side of the polygon, which define the new border of the scaled polygon. This parallel line-based scaling method not only guarantees the geometric consistency of border and hole scaling operations, but also ensures the accuracy and efficiency of the results.

[0057] Although all polygons on the design layout of the integrated circuit can be enlarged or reduced by the above technical solution, in a preferred embodiment, after obtaining the vertex information and scaling parameters of the polygon, the present invention first determines whether the polygon is a rectangle. If the polygon is not a rectangle, the step of finding the parallel lines corresponding to each side of the polygon according to the scaling parameters is performed. If the polygon is a rectangle, the scaling operation is directly performed on the vertices.

[0058] Through this conditional judgment, the algorithm can flexibly deal with polygons of various shapes, whether they are regular rectangles or irregular polygons, and can find the best scaling solution.

[0059] Figure 3The overall flow chart of a preferred embodiment of the present invention is shown. In this implementation, the user first inputs the polygon and the scaling parameter delta. This embodiment uses the sign of delta to determine whether to enlarge or reduce the operation, and the absolute value of delta determines the specific size of the enlargement or reduction. Specifically, if delta is a positive value, the polygon will be enlarged; if it is a negative value, it will be reduced. The value of delta directly corresponds to the magnitude of the enlargement or reduction, so that the size adjustment of the polygon is both intuitive and easy to control. This design allows the algorithm to flexibly adapt to different design requirements, whether it is expanding the structure to accommodate a larger space, or streamlining the size to accommodate a more compact layout.

[0060] Then determine whether the polygon is a rectangle.

[0061] If it is a rectangle, the polygon is scaled based on the vertices. Since this polygon consists of only four vertices, these vertices can be directly scaled to obtain the desired enlarged or reduced graphics. Take the enlarged rectangle as an example, Figure 4 As shown in the figure, the original vertices (A, B, C, D) will be transformed into new vertex positions (A1, B1, C1, D1) after the scaling operation. In this process, each vertex is adjusted according to the given scaling parameter delta. Specifically, the position of each new vertex is determined by moving the original vertex along the coordinate axis by the distance specified by delta. For example, the vertex information of the polygon is {(x1, y1), (x2, y2)}, where (x1, y1) represents the coordinates of the vertex of the lower left corner of the rectangle, and (x2, y2) represents the coordinates of the vertex of the upper right corner of the rectangle. Then the expanded polygon can be directly expressed as (x1-delta, y1-delta, x2+delta, ly2+delta). The directness and accuracy of this method ensure the efficiency of the rectangle scaling operation. By accurately controlling the moving distance of each vertex, the algorithm can ensure that the scaled rectangle maintains its geometric characteristics while meeting the designed size requirements. This direct operation on the vertices also simplifies the calculation process and improves the execution efficiency of the algorithm.

[0062] If it is not a rectangle, that is, the polygon is an irregular polygon, the internal angles of the two sides may be 270 degrees or other angles in addition to 90 degrees, such as Figure 5 The vertices include two groups. The vertices of the first group are marked A, B, C, D, E, F, G and H in sequence, and the vertices of the second group are marked I, J, K, L in sequence.

[0063] First, find the parallel lines corresponding to each edge of the polygon according to the scaling parameter delta, then find the intersection points based on the parallel lines to form a new polygon, and then output the new polygon.

[0064] This solution ensures the geometric integrity and accuracy of non-rectangular polygons during scaling. Specifically, this embodiment analyzes each edge of the non-rectangular polygon and determines the scaling direction based on the positive or negative delta value. Figure 6 As shown, the input polygon vertices are arranged in counterclockwise order. For each edge, if the delta value is positive, it means that the figure needs to be enlarged. Therefore, a parallel line will be found on the right side of the corresponding edge, and the distance between the parallel line and the original edge is equal to the delta value, so as to determine the boundary of the enlarged polygon. If the delta value is negative, it means that the figure needs to be reduced. Accordingly, a parallel line will be found on the left side of the edge, and the distance between the parallel line and the original edge is equal to the absolute value of delta, so as to determine the boundary of the reduced polygon. In this way, the algorithm can systematically generate corresponding parallel lines for each side of the polygon, and these parallel lines define the new boundary of the scaled polygon. This parallel line-based scaling method not only ensures the geometric consistency of the scaling operation, but also ensures the accuracy and efficiency of the results.

[0065] like Figure 6 As shown, taking the side AB of the non-rectangular polygon as an example, first determine the perpendicular line AC of the side AB. By rotating AB 90° counterclockwise, the line segment AC is obtained.

[0066] Next, we need to determine the new position of point A in the direction of AC. If delta is positive, it means that AB needs to expand outward, so move the absolute value of delta in the direction of AC to find the new position of point A, A1. Conversely, if delta is negative, it will move in the opposite direction of AC to determine the new position of point A, A2. Once the new position of point A is determined, we can calculate the difference between the original coordinates of point A and the new coordinates. Adding this difference to the coordinates of point B, we get the new position of point B. In this way, we get line segments parallel to the hypotenuse AB, namely A1B1 and A2B2. This process ensures that the new line segments are parallel to the original hypotenuse AB, and their positions are adjusted according to the positive and negative signs of delta.

[0067] This embodiment will use the results of the parallel line algorithm to construct the scaled polygon, which is the key to achieving geometric transformation. Figure 7As shown, it is assumed that corresponding parallel lines have been found for each side of the polygon. These parallel lines are the direct product of the scaling operation, and they define the new boundaries of the original polygon boundary. In the specific implementation process, the algorithm starts from the parallel lines of the starting side AB and searches for the intersection of each parallel line along the boundary order of the polygon (the boundary order can be obtained based on the stored vertex information when processing the parallel edges). These intersections are the exact positions of the vertices of the new polygon, and they together constitute the scaled polygon. The boundary order is the same as the direction and order of the corresponding original edge. For the polygon's boder, the new boundary order is counterclockwise, and for the polygon's hole, the new boundary order is clockwise.

[0068] For example, the vertices A, B, C, D, E, F, G, H on the boundary of the original polygon will be transformed into new vertices A1, B1, C1, D1, E1, F1, G1, H1 after scaling, and the vertices of the hole in the polygon will be transformed from I, J, K, L to new vertices I1, J1, K1, L1. In this way, the algorithm not only preserves the overall structure and proportions of the original polygon, but also ensures that the scaled polygon corresponds geometrically to the original polygon. The elegance of this method lies in that it transforms the scaling operation into a series of precise geometric construction steps, so that the scaled polygon is visually and functionally consistent with the original design.

[0069] The present invention also protects a design rule checking method for an integrated circuit, which includes the graphic scaling method for electronic design of the above technical solution.

[0070] Integrated circuit (IC) design rule check (DRC) is an important step to ensure that the design meets the manufacturing process requirements, and is usually part of the back-end design stage in the chip design process.

[0071] Extract graphics from the designed layout to form physical graphic data that can be checked. This process usually extracts the design of each layer in the circuit into geometric graphics and prepares them for subsequent inspection. The DRC check mainly verifies whether the physical layout of the chip meets the limitations of the manufacturing process through a series of rules, such as minimum line width, spacing, inter-layer alignment, etc. During the verification process, it is usually necessary to scale the graphics so that the predefined process rules (provided by the manufacturer) can be used to check the design to ensure that each circuit element meets the process requirements.

[0072] Taking the graphic smoothing process in DRC inspection as an example, SMOOTH eliminates Spikes by first shrinking the graphic, shrinking the Spikes until they are eliminated, and then enlarging and restoring the shrunken graphic. At this time, the graphic scaling method of the present invention can be used. SMOOTH eliminates Gap (seam) by first enlarging the graphic, enlarging and filling the Gap until it is eliminated, and then enlarging and restoring the enlarged graphic. At this time, the scaling method of the present invention can also be used. Through this efficient graphic scaling method of the present invention, engineers can be helped to quickly iterate within the design cycle and shorten the time from design to production. The application of the graphic scaling algorithm of the present invention is not limited to integrated circuit design, but can also be extended to other fields that require precise graphic processing, such as image processing, computer graphics, and data visualization.

[0073] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A graphics scaling method, characterized in that: include: Acquire vertex information and scaling parameters of a polygon in a graphic, wherein the scaling parameters include a vertical distance between an edge of the scaled polygon and a corresponding edge of the original polygon; Find the parallel lines corresponding to each edge of the polygon based on vertex information and scaling parameters; According to the boundary order of the new boundary of the polygon defined by the parallel lines, the corresponding intersection points of the parallel lines are found to obtain new vertex information and the scaled polygon.

2. The graphics scaling method according to claim 1, wherein: Finding the enlarged or reduced parallel lines corresponding to each edge of the polygon based on vertex information and scaling parameters specifically includes: According to the vertex order in the vertex information, each edge is rotated 90 degrees around the corresponding starting vertex to obtain a moving reference line perpendicular to the corresponding edge; The corresponding edge is moved along the moving reference line by the value of the scaling parameter to obtain a parallel line parallel to the corresponding edge.

3. The graphics scaling method according to claim 2, wherein: The scaling parameter includes a positive number or a negative number. The positive or negative value of the scaling parameter indicates whether the polygon is enlarged or reduced. The absolute value of the scaling parameter indicates the numerical value of the scaling parameter.

4. The graphics scaling method according to claim 2, wherein: When each edge is rotated 90 degrees around the corresponding starting vertex, it rotates in a counterclockwise direction.

5. The graphics scaling method according to claim 4, characterized in that: The corresponding edge is represented as a vector, and the moving reference line after counterclockwise rotation is obtained through matrix operation.

6. The graphics scaling method according to claim 5, characterized in that: The corresponding edge is moved along the moving reference line by the value of the scaling parameter to obtain a parallel line parallel to the corresponding edge, including: Calculate the slope of the moving baseline; According to the slope of the moving baseline and the value of the scaling parameter, the coordinates of the starting point of the parallel line are calculated; Calculate the coordinate difference between the starting point of the corresponding side and the starting point of its parallel line; The coordinates of the end point of the parallel line are calculated based on the coordinates of the end point of the corresponding side and the coordinate difference.

7. The graphics scaling method according to claim 6, wherein: When finding the parallel lines corresponding to each edge of the polygon based on vertex information and scaling parameters, if the edge currently being processed is a right-angled edge, use INT type variables to calculate the starting point and the end point. If the edge currently being processed is a hypotenuse, use double type variables to calculate the starting point and the end point.

8. The graphics scaling method according to any one of claims 1 to 6, characterized in that: After obtaining the vertex information and scaling parameters of the polygon, the method also includes the step of determining whether the polygon is a rectangle. If the polygon is not a rectangle, the method further includes the step of finding the parallel lines corresponding to each side of the polygon according to the scaling parameters. If the polygon is a rectangle, the scaling operation is performed directly on the vertices.

9. A design rule checking method for an integrated circuit, characterized in that: The method comprises a graphics scaling method as described in any one of claims 1 to 7.

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