A building photovoltaic roof shadow generation method and system based on a grasshopper platform

The method for generating photovoltaic roof shadows using the Grasshopper platform solves the problem of shadow analysis under complex building forms, and realizes efficient and intelligent shadow analysis and layout diagram generation, supporting the application of BIPV in diverse scenarios.

CN120832717BActive Publication Date: 2025-12-12CENT INT GROUP
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Patent Information

Application Number
CN202511310041.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-09-15
Publication Date
2025-12-12
Estimated Expiration
2045-09-15

AI Technical Summary

Technical Problem

Existing photovoltaic shadow analysis tools struggle to handle shadow analysis of complex building forms. 3D modeling is cumbersome and lacks intelligence, resulting in large shadow boundary errors, which fails to meet the application needs of BIPV in diverse scenarios.

Method used

A method for generating shadows on photovoltaic roofs based on the Grasshopper platform is adopted. By constructing a shadow bar diagram, generating a solar ray direction vector, an outer contour line, and a shadow volume, and combining shadow line judgment and boundary line extraction, the method can intelligently generate time shadow lines and shadow layout diagrams, and support dynamic shadow simulation of complex shading objects.

Benefits of technology

It achieves efficient shadow analysis of complex building forms, simplifies the 3D modeling process, improves the level of intelligence, generates highly accurate shadow boundary lines, and supports photovoltaic applications in diverse scenarios.

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Abstract

The application discloses a building photovoltaic roof shadow generation method and system based on a Grasshopper platform, constructs a daily shadow stick chart generation model according to the latitude and longitude, shadow time and shadow line relationship of a building photovoltaic roof location, obtains the corresponding sunlight direction vector of each time interval point according to the daily shadow stick chart, respectively generates the outer contour line of the photovoltaic roof and the shelter on the photovoltaic roof at each time interval point by using the sunlight direction vector, generates a shadow body along the sunlight direction vector at the respective time interval point, and obtains the shadow line of the shelter on the photovoltaic roof and the shadow line of the photovoltaic roof itself by respectively intersecting the obtained shadow body with the photovoltaic roof, that is, the shadow line for shadow analysis. The application supports dynamic shadow simulation of complex shelters on any plane or curved surface, and can intelligently generate the shadow line at each time period and a shadow layout chart for CAD drawing.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of building photovoltaic roof, and particularly relates to a building photovoltaic roof shadow generation method based on a Grasshopper platform and a system thereof. BACKGROUND

[0002] Building photovoltaic integration (BIPV) has become the core direction of the integration development of building and energy field, and the integration demand of complex building forms such as special-shaped metal roof and hyperbolic surface modeling and photovoltaic system has increased rapidly. The traditional plane photovoltaic component arrangement technology has been difficult to meet the parametric design requirements, and the large-scale application still faces the technical challenges of complex scene adaptation, such as in the field of shadow analysis.

[0003] At present, the photovoltaic shadow analysis tools on the market are mostly based on traditional plane model design, and can only deal with the analysis of simple scenes in industrial plants. Such tools have the following significant limitations:

[0004] (1) The analysis dimension is limited to the plane and regular shelter, and it is difficult to analyze the influence of the slope change of the curved roof on the shadow projection, and it is difficult to handle the shadow analysis of complex forms such as hyperbolic surface, special-shaped surface and discontinuous geometry in industrial and public buildings;

[0005] (2) The three-dimensional modeling is difficult and the operation process is complicated, and it is difficult to effectively and reasonably model the complex buildings and shelters, and the data processing process needs to be converted to multiple software platforms;

[0006] (3) The analysis and calculation time is slow, the intelligent degree is poor, the error of the shadow boundary analyzed is large, and manual processing is needed to delete and draw the shadow boundary line. SUMMARY

[0007] In view of the above problems and deficiencies, the present application provides a building photovoltaic roof shadow generation method based on a Grasshopper platform and a system thereof, which can intelligently generate time shadow lines and shadow layout diagrams for CAD drawing at each time period, and provides technical support for efficient application of BIPV in diversified scenarios.

[0008] The present application adopts the following technical solutions:

[0009] On the one hand, the present application provides a building photovoltaic roof shadow generation method based on a Grasshopper platform, which includes a time shadow line shadow analysis method, including the following steps:

[0010] Step 1, according to the latitude and longitude of the location of the building photovoltaic roof, the shadow time and the time shadow line relationship, a day shadow stick chart generation model is constructed;

[0011] Step 2, according to the sun shadow stick figure, obtain the sun ray direction vector of each time interval point;

[0012] Step 3, generate the outer contour line of the shelter and the photovoltaic roof itself at each time interval point respectively by using the sun ray direction vector;

[0013] Step 4, generate the shadow volume along the sun ray direction vector of each time interval point;

[0014] Step 5, intersect the obtained shadow volume at each time interval point with the photovoltaic roof respectively to obtain the shadow line of the shelter on the photovoltaic roof and the shadow line of the photovoltaic roof itself, that is, the time shadow line for shadow analysis.

[0015] Or further, make a judgment on whether the obtained shadow line of the photovoltaic roof itself at each time interval belongs to the shadow line of the shelter part, and delete the shadow line not belonging to the shadow line of the shelter part.

[0016] Further, the method further comprises a boundary line shadow generation method, comprising the following steps:

[0017] The step 2, generate the sun ray direction sun shadow trajectory surface according to the sun shadow stick figure;

[0018] The step 3, generate all the outer contour lines of the shelter and the photovoltaic roof itself respectively;

[0019] The step 4, scan the sun shadow trajectory surface according to the outer contour lines of the shelter and the photovoltaic roof itself as the path to obtain the shadow volume corresponding to the shelter and the photovoltaic roof;

[0020] The step 5, intersect the obtained shadow volume with the photovoltaic roof respectively to obtain the shadow line of the shelter on the photovoltaic roof and the shadow line of the photovoltaic roof itself.

[0021] Further, the boundary line shadow generation method further comprises step 6 of extracting the outer contour closed curve of the obtained shadow line and projecting the equidistant filling line to obtain the boundary line for shadow analysis.

[0022] Further preferably, the sun shadow trajectory surface scans the shadow volume of the photovoltaic roof according to the outer contour line of the photovoltaic roof itself as the path, intersects the shadow volume with the photovoltaic roof to obtain the shadow line, and makes a judgment on whether the shadow line belongs to the shadow line of the shelter part, and deletes the shadow line not belonging to the shadow line of the shelter part.

[0023] Preferably, in the step 6, the specific method of extracting the outer contour closed curve of the obtained shadow line is:

[0024] Step 6.1, project all curves onto XY coordinate plane, break all curves at intersection position, and delete repeated curves;

[0025] Step 6.2, obtain the total envelope rectangular box of all curves;

[0026] Step 6.3, take a point on the right side of the envelope rectangular box, and extend horizontally to the inside of the envelope rectangular box, and take the first curve encountered as the first boundary line of the outer contour closed curve;

[0027] Step 6.4, take the first boundary line as the starting line, take the end point of the starting line on the upper part of the Y axis as the starting point, and rotate the starting line counterclockwise around the starting point, and take the curve encountered with the same end point as the second boundary line of the outer contour closed curve;

[0028] Step 6.5, rotate the second boundary line counterclockwise around the other end point, and take the curve encountered with the same end point as the third boundary line of the outer contour closed curve;

[0029] Step 6.6, determine the next boundary line according to the last boundary line and its end point, until the next boundary line is the first boundary line, and obtain all boundary lines of the outer contour closed curve.

[0030] In another aspect, the present application also provides a building photovoltaic roof shadow generation system based on the Grasshopper platform, which is embedded in a CAD drawing module and is a time shadow line shadow generation subsystem, specifically comprising:

[0031] An input module for inputting latitude and longitude, shadow formation time and interval time;

[0032] A sun shadow stick chart generation model for automatically generating a sun shadow stick chart corresponding to the input time interval point according to the input data in the input module;

[0033] An outer contour generation module for generating an outer contour line of each obstruction and the photovoltaic roof itself under the sun light direction vector of each time interval point respectively by using the sun shadow stick chart generated by the sun shadow stick chart generation model;

[0034] A shadow body generation module for generating a shadow body along the sun light direction vector of each time interval point according to the obtained outer contour line;

[0035] A time shadow line generation module for obtaining a shadow line of each time interval point on the photovoltaic roof by intersecting the obtained shadow body of each time interval point with the photovoltaic roof respectively, and obtaining a shadow line of the photovoltaic roof itself.

[0036] Further, the system further comprises a boundary line shadow generation subsystem, comprising:

[0037] A shadow body generation module generates a shadow body corresponding to the shelter and the photovoltaic roof by scanning the shadow trajectory surface of the sun ray direction generated by the sun shadow stick figure generation model along all the outer contour lines of the shelter and the photovoltaic roof as a path.

[0038] A shadow line generation module obtains the shadow line of the shelter on the photovoltaic roof and the shadow line of the photovoltaic roof by intersecting the obtained shadow body with the photovoltaic roof, respectively.

[0039] A boundary line extraction module is used for extracting the outer contour closed curve of the shadow line and projecting the outer contour closed curve to generate equidistant filling lines.

[0040] The outer contour closed curve is directly presented on the CAD drawing module as a shadow arrangement drawing.

[0041] Further, the system further comprises a shadow line judgment module which judges whether the shadow line of the photovoltaic roof itself is the shadow line formed by the shelter of the photovoltaic roof itself and deletes the shadow line not formed by the shelter.

[0042] Compared with the prior art, the present application has the following advantages:

[0043] A. The photovoltaic shadow analysis method and system based on the Grasshopper platform provided by the present application breaks through the limitation of traditional tools through a parameterized algorithm, supports dynamic shadow simulation of complex shelters on any plane or curved surface, is convenient, easy to model and simple to operate with a CAD interface, and can intelligently generate time shadow lines of each period and a shadow arrangement drawing for CAD drawing, thereby providing technical support for efficient application of BIPV in diversified scenarios.

[0044] B. The photovoltaic roof adopted by the present application can be a complex shape such as a plane or a curved surface, and the shelter can be a complex form such as a regular or irregular shape, and the slope, size, modeling and form can be ignored, so that the shadow of each shelter on each photovoltaic roof can be quickly analyzed, the time shadow line intelligently generated can be used to view the corresponding shadow at each time, and the shadow boundary line intelligently generated can be directly used to draw a shadow arrangement drawing, which is helpful for designers to quickly complete photovoltaic shadow analysis.

[0045] C. The present application not only can realize photovoltaic shadow analysis on a building roof, but also can realize shadow analysis of centralized or distributed photovoltaic in various natural environments such as ground, hillside and desert. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the specific embodiments of the present application, the drawings needed to be used in the specific embodiments will be briefly introduced as follows. Obviously, the drawings described in the following specific embodiments are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0047] Figure 1 is a method block diagram for generating shadow lines of the building photovoltaic roof provided by the present application;

[0048] Figure 2 is a method block diagram for generating boundary lines of the building photovoltaic roof provided by the present application;

[0049] Figure 3 is a schematic diagram of the shelter on the photovoltaic roof provided by the present application;

[0050] Figure 4 is a 1000mm sun shadow stick diagram provided by the present application;

[0051] Figure 5 is a schematic diagram of the shelter outer contour line at a certain time interval point;

[0052] Figure 6 is a shadow volume diagram of the shelter at a certain time interval point;

[0053] Figure 7 is a time shadow line diagram of the shelter at each time interval point;

[0054] Figure 8 is a schematic diagram of the photovoltaic roof itself outer contour line at a certain time interval point;

[0055] Figure 9 is a schematic diagram of the photovoltaic roof itself shadow volume at a certain time interval point;

[0056] Figure 10 is a non-final shadow line diagram of the photovoltaic roof itself at each time interval point;

[0057] Figure 11 is a schematic diagram of the edge line of the non-shelter part which needs to be deleted;

[0058] Figure 12 is a shadow line diagram of the shelter part which needs to be reserved;

[0059] Figure 13 is a time shadow line diagram of the photovoltaic roof itself at each time interval point;

[0060] Figure 14a and Figure 14b is a time shadow line diagram of the shelter and the photovoltaic roof itself at each time interval point;

[0061] Figure 15is the shadow volume formed by the photovoltaic roof itself;

[0062] Figure 16 is the all-outer-contour-line illustration of each shelter generated;

[0063] Figure 17 is the shadow volume illustration scanned along the outer contour line of the shelter;

[0064] Figure 18 is Figure 17 the shelter shadow line (non-final boundary line) formed by the shadow volume shown intersecting the photovoltaic roof;

[0065] Figure 19 is the extraction Figure 18 the outermost closed curve illustration;

[0066] Figure 20 is the boundary line of the shelter;

[0067] Figure 21 is the outer contour line of the photovoltaic roof itself;

[0068] Figure 22 is the shadow volume formed by the photovoltaic roof itself;

[0069] Figure 23 is the shadow line (non-final boundary line) of the photovoltaic roof itself;

[0070] Figure 24 is the shadow line illustration of the shelter part that needs to be retained;

[0071] Figure 25 is the outermost closed curve of the shadow volume formed by the photovoltaic roof itself;

[0072] Figure 26 is the boundary line formed by the photovoltaic roof itself;

[0073] Figure 27 is the boundary line illustration of the shelter and the photovoltaic roof itself;

[0074] Figures 28 to 33 is the principle illustration of the extraction of the outermost closed curve of the shadow line provided by the present application.

[0075] The signs shown in the figure are as follows: 1- photovoltaic roof; 2- shelter; 3- time shadow line; 4- shadow volume. DETAILED DESCRIPTION

[0076] The technical solutions of the present application will be described clearly and completely in the following description of the drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0077] In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" and the like indicate the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second", "third" are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0078] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0079] As shown in Figure 1 The present application provides a building photovoltaic roof shadow generation method based on the Grasshopper platform, wherein the photovoltaic roof 1 can be a plane, a curved surface or other complex hyperboloid, etc., and there are also cuboids, cylinders, spheres and other complex irregular shapes, etc. Figure 3 As shown in

[0080]

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[0085] As shown in Figures 10 to 13 , a judgment is made on whether the obtained shadow line of the photovoltaic roof itself at each time interval belongs to the shadow line of the shelter part ( Figure 10 ), and the shadow line not belonging to the shelter part is deleted ( Figure 11 ), and the shadow line of the photovoltaic roof itself sheltering at each time interval point is reserved ( Figure 12 ), and finally the time shadow line of the photovoltaic roof itself at each time interval point is obtained, as shown in Figure 13 .

[0086] Figure 14a and Figure 14b The time shadow line at each time interval point can be viewed for shadow analysis from the time shadow line diagram formed by the shelter on the photovoltaic roof and the photovoltaic roof itself.

[0087] As shown in Figure 2 , the method of the application further includes a boundary line shadow generation method, which specifically includes the following steps:

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[0093] The sun shadow trajectory surface is scanned along the outer contour line of the photovoltaic roof itself to obtain the shadow body of the photovoltaic roof, and the shadow body is intersected with the photovoltaic roof to obtain the shadow line, as shown in Figure 23 The shadow line of the photovoltaic roof itself is formed, and it is judged whether the shadow line belongs to the shadow line of the shelter part or not. If it does not belong to the shadow line of the shelter part, it is deleted, and if it does, it is retained. Wherein Figure 24 is the shadow line of the photovoltaic roof itself formed by the shelter part retained.

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[0095] As shown in Figures 28 to 33 , wherein the specific method for extracting the outer contour closed curve of the obtained shadow line is:

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[0102] According to the above-mentioned principle of obtaining the outer contour closed curve, the corresponding mathematical model is established, and the specific method is as follows:

[0103] (1) Number all the curves in sequence L{0, 1, 2, ……}, and number all the end points in sequence P{0, 1, 2, ……};

[0104] (2) Put the two end points of each curve into list A {(Pi, Pj), ……};

[0105] (3) Find the corresponding curves shared by each end point, take one of the corresponding curves as the starting point, sort the corresponding curves counterclockwise around the end point, and put the sorted curve sequence number into list B {(Lx, Ly, ……), ……};

[0106] (4) The starting line obtained by the above-mentioned envelope box geometric method and the starting point, the corresponding curve and the end point sequence number are L1 and P1, and L1 is stored in list C, L1 is assigned to L0, and P1 is assigned to P0;

[0107] (5) through the end point number P0, obtain the P0th element (Lx, ……, L0, Ly, ……) in the B list, obtain the next element Ly of L0 in the element list, Ly is the second boundary line, and Ly is stored in the list C;

[0108] (6) through the straight line number Ly, obtain the Lyth element (P0, Pj) in the A list, obtain another element Pj in the element list, and Pj is another end point of the second boundary line;

[0109] (7) Pj is assigned to P0, Ly is assigned to L0, and the above e and f are cycled;

[0110] (8) until Ly=L1, the loop ends, that is, the curve is closed, and the list C is the serial number of the boundary curve.

[0111] Through the above method, the outermost closed curve can be extracted from a plurality of curves connected at the head and tail and in disorder, and the generated boundary line makes it easier for a technician to perform photovoltaic shadow analysis and obtain corresponding data.

[0112] In addition, the application also provides a building photovoltaic roof shadow generation system based on a Grasshopper platform, which is embedded in a CAD drawing module and includes a time shadow line shadow generation subsystem, which specifically includes: an input module, a day shadow stick chart generation model, an outer contour generation module, a shadow body generation module and a time shadow line generation module, wherein the input module is used for inputting longitude and latitude, shadow forming time and interval time; the day shadow stick chart generation model automatically generates a day shadow stick chart corresponding to the input time interval point according to the input data in the input module; the outer contour generation module generates the outer contour line of each shelter and the solar ray direction vector of the photovoltaic roof itself at each time interval point by using the day shadow stick chart generated by the day shadow stick chart generation model; the shadow body generation module generates a shadow body along the solar ray direction vector at each time interval point; and the time shadow line generation module intersects the obtained shadow body at each time interval point with the photovoltaic roof to obtain the shadow line of each shelter on the photovoltaic roof and the shadow line of the photovoltaic roof itself corresponding to each time interval point.

[0113] The application further sets a boundary line shadow generation subsystem in the system, which comprises a shadow body generation module, a shadow line generation module and a boundary line extraction module, wherein the shadow body generation module uses the sun shadow trajectory surface of the sun light direction generated by the sun shadow stick figure generation model, and obtains the shadow body corresponding to the shelter and the photovoltaic roof by scanning the sun shadow trajectory surface along all the outer contour lines of the shelter and the photovoltaic roof as a path; the shadow line generation module obtains the shadow line of the shelter on the photovoltaic roof and the shadow line of the photovoltaic roof itself by intersecting the obtained shadow body with the photovoltaic roof respectively; the boundary line extraction module is used for extracting the outer contour closed curve of the shadow line and projecting the equal division to generate the equally spaced filling lines; the outer contour closed curve is directly presented on the CAD drawing module as a shadow layout diagram.

[0114] In order to more accurately obtain the shadow line of the photovoltaic roof itself, the system further sets a shadow line judgment module, which judges whether the shadow line of the photovoltaic roof itself is the shadow line formed by the shelter, and deletes the shadow line not formed by the shelter, so that the obtained shadow line on the photovoltaic roof is more accurate. The application can also be used on other irregularly shaped reference datum surfaces such as planes and curved surfaces, which will not be described here.

[0115] The unmentioned part of the application is applicable to the prior art.

[0116] Obviously, the above embodiments are only examples for clearly illustrating, and are not limitation to the embodiments. For those skilled in the art, other different forms of changes or variations can be made on the basis of the above description. All the embodiments do not need to be exhausted, and the obvious changes or variations derived therefrom are still within the protection scope of the application.

Claims

1. A method for generating shadows on building photovoltaic roofs based on the Grasshopper platform, characterized in that, The method is a boundary line shadow generation method, comprising the following steps: Step 1, constructing a daily shadow stick chart generation model according to the latitude and longitude of the building photovoltaic roof, shadow time and shadow line relationship; Step 2, generating a daily shadow trajectory surface of the direction of sunlight according to the daily shadow stick chart; Step 3, generating all the outer contour lines of the shelter and the photovoltaic roof respectively; Step 4, scanning the daily shadow trajectory surface along the outer contour lines of the shelter and the photovoltaic roof itself as a path to obtain the shadow body corresponding to the shelter and the photovoltaic roof; Step 5, intersecting the obtained shadow body with the photovoltaic roof respectively to obtain the shadow line of the shelter on the photovoltaic roof and the shadow line of the photovoltaic roof itself; Step 6, extracting the outer contour closed curve of the obtained shadow line and projecting it to generate equally spaced filling lines, i.e. the boundary line for shadow analysis; the daily shadow trajectory surface along the outer contour line of the photovoltaic roof itself as a path is scanned to obtain the shadow body of the photovoltaic roof, the shadow body is intersected with the photovoltaic roof to obtain the shadow line, and it is judged whether the shadow line belongs to the shadow line of the shelter part or not, and the shadow line not belonging to the shadow line of the shelter part is deleted; in the step 6, the specific method of extracting the outer contour closed curve of the obtained shadow line is: Step 6.1, projecting all curves onto the XY coordinate plane, breaking all curves at the intersection position, and deleting the repeated curves; Step 6.2, obtaining the total envelope rectangular box of all curves; Step 6.3, taking a point on the right side of the envelope rectangular box, and extending it horizontally into the envelope rectangular box, and taking the first curve encountered during the extension as the first boundary line in the outer contour closed curve; Step 6.4, taking the first boundary line as the starting line, taking the end point of the starting line on the upper part of the Y axis as the starting point, rotating the starting line counterclockwise around the starting point, and taking the curve encountered as the second boundary line in the outer contour closed curve which has the same end point as the first boundary line; Step 6.5, rotating the second boundary line counterclockwise around the other end point, and taking the curve encountered as the third boundary line in the outer contour closed curve which has the same end point as the second boundary line; Step 6.6, determining the next boundary line according to the last boundary line and its end point in turn until the next boundary line is the first boundary line, and obtaining all the boundary lines of the outer contour closed curve.

2. A Grasshopper platform based architectural photovoltaic roof shading generation system characterized in that, It is embedded in a CAD drawing module, which is a boundary line shadow generation subsystem, and adopts the boundary line shadow generation method of claim 1, and specifically comprises: an input module for inputting latitude and longitude, shadow forming time and interval time; a daily shadow stick chart generation model for automatically generating a daily shadow stick chart corresponding to the input time interval point according to the input data in the input module; a shadow body generation module for scanning the daily shadow trajectory surface of the direction of sunlight generated by the daily shadow stick chart generation model along all the outer contour lines of the shelter and the photovoltaic roof itself as a path to obtain the shadow body corresponding to the shelter and the photovoltaic roof; a shadow line generation module for intersecting the obtained shadow body with the photovoltaic roof respectively to obtain the shadow line of the shelter on the photovoltaic roof and the shadow line of the photovoltaic roof itself; a shadow line generation module for intersecting the obtained shadow body with the photovoltaic roof respectively to obtain the shadow line of the shelter on the photovoltaic roof and the shadow line of the photovoltaic roof itself; The boundary line extraction module is used for extracting an outer contour closed curve of the shadow line and projecting the outer contour closed curve to generate equidistant filling lines. The outer contour closed curve is directly presented on the CAD drawing module as a shadow layout.

3. The Grasshopper platform based architectural photovoltaic roof shading generation system according to claim 2, wherein, The system further comprises a shadow line judgment module which judges whether the shadow line of the photovoltaic roof itself is the shadow line formed by the self-shading, and deletes the shadow line not formed by the shading part.

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