Automatic closed loop search method based on line-to-angle

Abstract

The present invention discloses a closed loop automatic search method based on straight line to angle, which reads node and unit information; determines the units and nodes connected to each node; starts a cyclic search according to the starting unit and the corresponding starting point and end point, calculates the angle between all units connected to the end point and the unit, and selects the unit with the largest angle within a range of less than 180° as the component edge line of the closed loop; if all nodes connected to the end point contain the starting point corresponding to the starting unit, the loop is closed and the search of the loop is completed; the closed loop component units just searched are eliminated from the starting search unit set; until all units are searched. The closed loop automatic search method based on straight line to angle provided by the present invention can establish surface units through the nodes around the closed loop by searching the closed loop of the single-layer rod of the grid structure, thereby forming a loading surface, without judging whether all nodes around the closed loop are coplanar, and only triangular surface units can be established.

Description

Technical Field

[0001] The present invention relates to the technical field of large-span space structures, and more specifically to an automatic closed loop search method based on straight lines to angles. Background Art

[0002] For large-span space structures, the structural layout is usually selected according to the building type, such as grid or lattice shell structure; then the loading analysis is performed. The correct application of various loads that need to be considered is a key link in engineering design. Most loading methods are through surface loads, such as additional dead loads, dead loads, wind loads, snow loads, etc. In particular, according to the results of wind tunnel tests, the equivalent loads of different wind angles must be accurately applied to the structural model. Loading surface units must be established. There are many large-span space structures, and the workload of establishing loading surfaces is huge. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide an automatic search method for closed loops based on straight line angles. By calculating the angles between adjacent rods, the rods with the largest angles within a range less than 180° are selected, and the closed loops are calculated step by step, thereby realizing the construction of the loading surface.

[0004] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows.

[0005] The closed loop automatic search method based on straight line to angle includes the following steps:

[0006] A. Read node and unit information;

[0007] B. Determine the units and nodes connected to each node;

[0008] C. Start a circular search based on the starting unit and the corresponding starting and ending points, calculate the angles between all units connected to the end point and the unit, and select the unit with the largest angle within a range of less than 180° as the component edge of the closed loop;

[0009] D. If all nodes connected to the end point contain the starting point corresponding to the starting unit, the loop is closed and the search is completed;

[0010] E. Remove the closed loop component unit just found from the initial search unit set;

[0011] F. Until all units are searched.

[0012] To further optimize the technical solution, in step C, the units required to form a closed plane are boundary units, and the angle between two units is positive in the counterclockwise direction and negative in the clockwise direction, and the angle range is 0° to 360°.

[0013] To further optimize the technical solution, in step C, the angle between two vectors is calculated by performing dot product and cross product of three-dimensional vectors to determine the direction of rotation.

[0014] To further optimize the technical solution, the vector cross product obtains a vector perpendicular to the plane where the two vectors are located, and the direction is determined by the right-hand rule.

[0015] To further optimize the technical solution, the rotation direction is determined by whether the value of the normal vector obtained during the vector cross multiplication is positive or negative. When the value of the normal vector is positive, no rotation is required. When the value of the normal vector is negative, rotation is required.

[0016] Due to the adoption of the above technical scheme, the technical progress achieved by the present invention is as follows.

[0017] The automatic closed loop search method based on straight line to angle provided by the present invention can establish surface units through nodes around the closed loop by searching the closed loop of the single-layer rod of the grid structure, thereby forming a loading surface. There is no need to judge whether all nodes around the closed loop are coplanar, and triangular surface units can be established. Designers can be freed from the tedious work of manually establishing surface units and concentrate on safe and reasonable design. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flow chart of the present invention;

[0019] Figure 2 A schematic diagram of a boundary unit search of the present invention;

[0020] Figure 3 It is a schematic diagram of two straight lines to an angle of the present invention;

[0021] Figure 4 It is a schematic diagram of the boundary unit corresponding to the closed area of ​​the present invention. DETAILED DESCRIPTION

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] Based on the automatic closed loop search method from straight line to angle, combined with Figure 1 As shown, the following steps are included:

[0024] A. Read node and unit information.

[0025] B. Determine the units and nodes connected to each node.

[0026] C. Start a circular search based on the starting unit and the corresponding starting and ending points, calculate the angles between all units connected to the end point and the unit, and select the unit with the largest angle within a range of less than 180° as the component edge of the closed loop.

[0027] First, assume that the units required to form a closed plane are boundary units. The boundary unit search diagram is as follows: Figure 2 As shown, the angle between two boundary units, unit i and unit j, for any unit i, is positive if it is counterclockwise and negative if it is clockwise, and the angle range is 0° to 360°.

[0028] The schematic diagram of two straight lines to an angle is as follows Figure 3 As shown, there are two straight lines in the plane,

[0029] l1:A1x+B1y+C1=0 l2:A2x+B2y+C2=0 (1)

[0030] The angle formed by rotating counterclockwise from straight line L1 to straight line L2 is called the L1 to L2 angle, straight line L1 is called the initial side, and straight line L2 is called the terminal side.

[0031] It can be seen that:

[0032] θ=θ2-θ1

[0033] According to trigonometric function deduction:

[0034]

[0035] Therefore, the angle and the slopes of the two lines satisfy:

[0036]

[0037] Assumptions Figure 1 The coordinates of the three points A, B, and C are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3), respectively. Unit i corresponds to vector AB (x2-x1, y2-y1, z2-z1), and unit j corresponds to vector BC (x3-x2, y3-y2, z3-z2). To calculate the angle between two vectors, we must introduce the dot product and cross product of three-dimensional vectors.

[0038] The vector cross product is a vector perpendicular to the plane where the two vectors are located, and the direction is determined by the right-hand rule. The modulus of the cross product vector is:

[0039]

[0040] The vector point multiplication yields a number whose magnitude is:

[0041]

[0042] The angle between the vector dot product and itself is zero, so the answer is 1, that is:

[0043]

[0044] From the above formula, we can get:

[0045]

[0046] Where n is the unit vector of C.

[0047] Combining equation (3) and equation (6), we can get:

[0048]

[0049] Combining equation (8) and equation (5):

[0050]

[0051] The value returned by the above formula is a value between 0 and π, not the desired value of 0 to 2π, that is, there is a problem with the direction of rotation. To this end, we need to determine the direction of rotation, that is, whether the z value of the normal vector obtained in the process of vector cross multiplication is positive or negative. If the z value of the normal vector is negative, then we need to use 2π-θ to get the actual rotation angle.

[0052] D. If all the nodes connected to the end point contain the starting point corresponding to the starting unit, the loop is closed and the search is completed.

[0053] E. Eliminate the closed loop unit just found from the initial search unit set.

[0054] F. Until all units are searched.

[0055] The present invention calculates the angles between adjacent rods, selects the rod with the largest angle within a range less than 180 degrees, and gradually calculates closed loops, thereby realizing a method for realizing a component loading surface.

Claims

1. The closed loop automatic search method based on straight line to angle is applied to search the closed loop of single-layer rods of grid structure, which is characterized by: The following steps are involved: A. Read node and unit information; B. Determine the units and nodes connected to each node; C. Start a circular search based on the starting unit and the corresponding starting and ending points, calculate the angles between all units connected to the end point and the unit, and select the unit with the largest angle within a range of less than 180° as the component edge of the closed loop; calculate the angle between the two vectors through the dot product and cross product of the three-dimensional vector to determine the direction of rotation; Assume that the units required to form a closed plane are boundary units, two boundary units are unit i and unit j, and the angle between the two units, for any unit i, is positive in counterclockwise direction and negative in clockwise direction, and the angle range is 0°~360°; There are two straight lines in the plane, （1） The angle formed by rotating counterclockwise from line L1 to line L2 is called the angle from L1 to L2, line L1 is called the initial side, and line L2 is called the terminal side; It can be seen that: According to trigonometric function derivation: （2） Therefore, the angle and the slopes of the two lines satisfy: （3） Assume that the coordinates of three points A, B, and C are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3), respectively. Unit i corresponds to vector AB (x2-x1, y2-y1, z2-z1), and unit j corresponds to vector BC (x3-x2, y3-y2, z3-z2). To calculate the angle between two vectors, the dot product and cross product of three-dimensional vectors must be introduced. The vector cross product is a vector perpendicular to the plane where the two vectors are located. The direction is determined by the right-hand rule. The modulus of the cross product vector is: （4） The vector point multiplication yields a number whose magnitude is: （5） The angle between the vector dot product and itself is zero, so the answer is 1, that is: （6） From the above formula, we can get: （7） Where n is the unit vector of C; Combining equation (3) and equation (6), we can get: （8） Combining equation (8) and equation (5): （9） The value returned by the above formula is a value between 0 and π, not the desired value of 0 to 2π, that is, there is a problem with the direction of rotation; the direction of rotation is determined by whether the z value of the normal vector obtained in the process of vector cross multiplication is positive or negative. If the value of the normal vector is positive, no rotation is required. If the z value of the vector is negative, then 2π-θ is needed to get the actual rotation angle; D. If all nodes connected to the end point contain the starting point corresponding to the starting unit, the loop is closed and the search is completed; E. Remove the closed loop component unit just found from the initial search unit set; F. Until all units are searched.

2. The closed loop automatic search method based on straight line to angle according to claim 1, characterized in that: In the step C, the units required to form a closed plane are boundary units, and the angle between two units is positive in the counterclockwise direction and negative in the clockwise direction, and the angle range is 0° to 360°.

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