An analytic geometry-based building parameterization modeling plug-in system and method

Abstract

This invention belongs to the field of architectural design technology and relates to a parametric architectural model-finding plug-in system and method based on analytical geometry. The plug-in system includes: a reference point matrix generation module, which generates a regularly distributed initial point matrix framework based on input geometric parameters using analytical geometric formulas; a graphic point set generation module, which transforms the input geometric parameters into a graphic point set with a specific mathematical form according to preset analytical geometric rules and generates corresponding geometric formulas; a 3D point matrix projection module, which projects the graphic point set onto a 3D position defined by 3D analytical geometry to obtain the corresponding 3D projection point set and its parametric equation expression; a model generation module, which generates the final 3D architectural model surface morphology based on the input point matrix framework; and a data structure tool module, used for processing data sequences. Its beneficial effects include reducing modeling steps, lowering parameter redundancy, alleviating data blindness problems, and improving model readability.

Description

Technical Field

[0001] This invention relates to the field of architectural design technology, and in particular to a parametric architectural model-finding plug-in system and method based on analytical geometry. Background Technology

[0002] Currently, such as Figure 1 As shown, existing GH parametric modeling technology tends towards procedural geometric stitching. Its core logic is to perform step-by-step operations on discrete geometric elements (points, lines, surfaces, and volumes) through the combination of visual components to ultimately generate the target shape. Specifically, this includes the following four points: 1. Morphological Construction Method: A fixed process is adopted, which involves generating point sets → generating curves → generating loft / sweep surfaces → performing Boolean operations on entities. This process relies on splicing together a large number of discrete points, piecewise curves, or local surfaces to form the overall shape. Taking the roof shape as an example, its undulations require manually arranging multiple control points, then connecting them with interpolated curves to form ridges / valleys, and finally generating them through surface commands. The entire process lacks a unified underlying logic support.

[0003] 2. Parameter control logic: The control parameters are mostly intermediate variables in the geometric operation process (such as the coordinates of curve control points, curve segment values, etc.), and there is no unified mathematical relationship between the parameters; for the adjustment of different local shapes (such as the ridges and valleys of the wavy surface), it is necessary to implement them separately through multiple sets of independent components, and the parameter system presents a decentralized and isolated characteristic.

[0004] 3. Model Data Storage: The core storage object is the specific information of discrete geometric elements, including the 3D coordinates of each point, control point data of each curve, and mesh subdivision values ​​of each surface, etc., without defining the essential form through mathematical formulas. Therefore, the model needs to store a large amount of figurative geometric data, resulting in high data redundancy.

[0005] 4. Form Deduction Mode: This mode adopts a trial-and-error or intuitive adjustment logic. Form optimization relies heavily on directly dragging control points (such as Graph Mapper curves, interfering objects, or the control points of the curve itself) and observing the real-time results in order to pursue visual aesthetics or rationality. However, the underlying mathematical relationships remain implicit and difficult to describe.

[0006] However, the existing GH parametric modeling technology has the following key drawbacks when applied to the design of complex buildings such as airport terminals: 1. Loose geometric relationships and insufficient morphological rationality: Due to the lack of underlying mathematical logic (such as the equation constraints of analytic geometry), the form generation relies on the splicing of discrete elements, which easily leads to the problem of "local rationality but overall abruptness": for example, the relative position of the roof ridge line and valley line may cause abrupt turns due to manual adjustment, or the curved surface may not be aligned, and the shape lacks unified geometric rules.

[0007] Lacking underlying mathematical logic such as analytic geometric equation constraints, the form generation relies on the splicing of discrete elements, which easily leads to the problem of "local rationality but overall abruptness". For example, the relative positions of the roof ridge line and valley line may produce abrupt turns due to manual adjustment, or the curved surface joints may not be aligned, resulting in the form lacking a unified geometric rule.

[0008] 2. The model is large in size and has low running efficiency: Because a large amount of discrete geometric data needs to be stored (such as a large amount of auxiliary geometric object data generated during the derivation process), and because redundant conversion operations of "point to line → line to point" are often repeatedly performed to control the shape, the model file size increases dramatically and memory usage becomes high. This ultimately manifests as slow loading of GH files, lag in the calculation process, and in severe cases, even exceeding the software's operating limits, leading to memory overflow or program crashes.

[0009] 3. The parameter system is complex and difficult to adjust: The control parameters suffer from numerous and scattered issues—each local shape corresponds to an independent set of parameters, easily leading to data blindness; moreover, there is a lack of clear correlation between parameters, usually only through the superposition of numerical sequences to form data change patterns, making the modeling process overly abstract, and the original compilation logic easily forgotten after long-term use. If overall adjustments are required (such as raising the overall roof height), it is necessary to modify the coordinates of multiple sets of control points such as ridge lines, valley lines, and baselines one by one, which is not only cumbersome but also prone to parameter conflicts. When facing multi-objective optimization needs that balance aesthetics and structural economy, the adjustment process becomes even more complex, resulting in extremely low optimization efficiency and poor model readability.

[0010] 4. The model has low fault tolerance and reusability: Excessive parameters can lead to data blindness and are prone to "hidden defects" due to operational errors or parameter conflicts (e.g., if a curve at the same position is controlled by multiple logics, it is easy to miss changes; and as the number of model parameters increases, the overall control capability of the model gradually decreases); and due to the lack of a unified mathematical analytical formula, if a local component of the model (such as a ridge line or a curved surface) is lost, it is impossible to deduce its precise position and shape through formulas, and it can only be reconstructed, resulting in low fault tolerance and reusability of the model. Summary of the Invention

[0011] Technical problems to be solved In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a parametric building form-finding plug-in system and method based on analytical geometry, which solves the technical problems of insufficient morphological rationality, large model size, complex parameter system and low model fault tolerance caused by the lack of underlying mathematical logic in the existing GH parametric modeling technology.

[0012] Technical solution To achieve the above objectives, the main technical solutions adopted by the present invention include: In a first aspect, the present invention provides a parametric building type-finding plugin system based on analytical geometry, comprising: The reference lattice generation module is used to generate an initial lattice framework with a regular distribution based on the input geometric parameters and analytical geometric formulas. The graphic point set generation module is used to transform the input geometric parameters into a graphic point set with a specific mathematical form according to the preset analytical geometric rules, and generate the corresponding geometric formula. The three-dimensional dot matrix projection module is used to project the graphic point set onto a three-dimensional position defined by three-dimensional analytical geometry, and obtain the corresponding three-dimensional projection point set and its parametric equation expression; The model generation module is used to generate the final 3D architectural surface model's surface morphology and structural lines based on the input raster frame. The data structure tool module is used to process data sequences and output the processed data sequences. The processing includes number sequence conversion, empty branch filtering, first and last filtering, and interval segmentation.

[0013] As a further improvement to the system of the present invention, the reference dot matrix generation module further includes: The straight line dot matrix generation unit is used to generate intervals and dot spacing based on the input dot matrix, and generate the corresponding straight line dot matrix through the linear parametric equation; The planar dot matrix generation unit is used to generate the corresponding planar dot matrix based on the input number of rows, row spacing, number of columns, and column spacing, and through the planar parametric equation. The sector matrix generation unit is used to generate the corresponding sector matrix based on the input reference plane, first circle radius, sector angle, radial spacing, number of branches and number of concentric layers through polar coordinate parametric equations. The column grid generation unit is used to generate the corresponding column grid based on the input numerical sequences in the X-axis and Y-axis directions.

[0014] As a further improvement to the system of the present invention, the graphic point set generation module further includes: The curve graph dot matrix generation unit is used to generate the corresponding curve dot matrix and its curve formula based on the input calculation reference plane, original coordinate points, curve center position, curve steepness coefficient and Y-axis scaling coefficient. The normal distribution graphic dot matrix generation unit is used to generate the corresponding normal distribution dot matrix and its normal distribution formula based on the input calculation reference plane, original coordinate points, highest X-axis position, distribution curve height and distribution curve width. The Lissajous figure dot matrix generation unit is used to generate the corresponding Lissajous curve and its parametric equation expression formula based on the input reference plane, X-direction amplitude, Y-direction amplitude, X-direction frequency, Y-direction frequency, phase difference and sampling steps. The rose curve graphic dot matrix generation unit is used to generate the corresponding rose curve dot matrix and its parametric equation expression based on the input reference plane, rose curve amplitude, frequency numerator, frequency denominator, phase offset and number of sampling points. The spiral pattern dot matrix generation unit is used to generate the corresponding spiral dot matrix and its parametric equation expression based on the input reference plane, initial radius, number of rotations and angular step size. The Lamé graphic dot matrix generation unit is used to generate the corresponding Lamé curve dot matrix and its parametric equation expression based on the input reference plane, X-axis radius, Y-axis radius, curve exponent and curve segment number; The spring dot matrix generation unit is used to generate the corresponding spring dot matrix and its parametric equation expression based on the input reference plane, spring radius, number of spring coils, total spring height, and number of segments per coil.

[0015] As a further improvement to the system of the present invention, the three-dimensional dot matrix projection module further includes: The ellipsoid projection element is used to obtain the positive and negative projection points and their parametric equations based on the input centroid, lattice, X-axis length, Y-axis length, Z-axis length, and ellipsoid index. The cone projection unit is used to obtain the positive and negative projection points and their parametric equations based on the input centroid, lattice, cone base radius, and cone height.

[0016] As a further improvement to the system of the present invention, the data structure tool module further includes: The number sequence conversion module is used to convert a list of numbers to be converted into Num-marked format, generating a list of strings with both the start and end numbers marked. The empty branch filtering unit filters out empty branches in the list of numbers, reconstructs the data in a new order, and outputs a renumbered data sequence. The beginning and end filtering unit is used to remove the beginning and end of the number list and output the processed data sequence. The interval segmentation unit is used to segment the list of numbers into intervals according to the input segmentation parameters and output the start / end data sequence of the interval segmentation. The object position marking unit is used to randomly select geometric objects and output the object position markings of the set.

[0017] As a further improvement to the system of the present invention, it also includes: a fitting calculation module and an analysis module; The fitting operation module includes at least four fitting methods: curve, normal distribution, control point optimization, and circular arc segment, which are used to sample the target curve, generate formulas, evaluate fitness, and analyze errors based on input parameters. The analysis module is used to generate corresponding analytical geometric formulas based on the properties of the geometric object and mark the position of the object; it is also used to perform rainwater runoff analysis based on the shape of the input geometric object, and generate water flow path curves, path endpoint sets, and sets of all path points.

[0018] As a further improvement to the system of the present invention, the fitting calculation module further includes: The curve fitting unit is used to generate sampling points, evaluate the fit fitness, and generate curve formula text from the input target curve, number of sampling points, curve steepness factor, and curve midpoint position parameters. The normal distribution graph fitting unit is used to generate sampling points, evaluate the fit fitness, and generate the normal distribution formula text based on the input target curve, number of sampling points, normal distribution mean, normal distribution standard deviation, and Y-axis scaling factor. The curve control point optimization unit is used to generate the actual curve and evaluate the fit fitness based on the input target curve and the number of curve control points. The circular arc fitting unit is used to generate the fitted circular arc segment and its fitting degree and local difference based on the input target curve, segmentation factor and number of sampling points.

[0019] Secondly, this invention provides a parametric model finding method for buildings based on analytical geometry, comprising the following steps: Step 1: Based on the basic geometric parameters of the building form, generate a regularly distributed basic point matrix using analytical geometric formulas; Step 2: Perform coordinate transformation on the basic point matrix according to the preset analytical geometric rules to generate a set of intermediate points with a clear mathematical form; Step 3: Project the points in the intermediate point set onto the preset target surface to generate a three-dimensional point set; Step 4: Use complex shape point sets to reconstruct the surface and generate the surface morphology and structural lines of the three-dimensional curved surface model of the building.

[0020] As a further improvement to the method of the present invention, in step 2, the analytical geometric pattern includes the normal distribution curve pattern, the Lissajous curve pattern, the rose curve pattern, the spiral pattern, or the Lamé curve pattern.

[0021] As a further improvement to the method of the present invention, in step 3, the projection is a projection onto the surface of an ellipsoid or onto the surface of a cone.

[0022] Beneficial effects The beneficial effects of this invention are: By transforming the entropy increase law of architectural form into quantifiable mathematical logic, and anchoring the essence of complex shapes through analytical geometric formulas, the high-entropy visual morphological elements are transformed into minimalist mathematical language, achieving precise compression of morphological information. This provides a new formulaic entropy reduction path for the morphological order design of ultra-large-scale buildings, fundamentally avoiding the problem of a lack of logical relationships in form.

[0023] With model simplification, countering disorder, and information entropy reduction as its three core objectives, mathematical formulas are integrated into the form generation and optimization process, resulting in a form design based on established rules: values ​​generated by analytical geometric formulas eliminate discretized redundant data, eliminating the need to store a large number of procedural geometric objects and retaining only the point set, thereby significantly reducing model file size and memory usage, effectively solving the problems of large model size and low running efficiency; random form adjustments are constrained by analytical geometric rules, avoiding abrupt form changes caused by manual adjustments and ensuring the overall form logic; relying on the global correlation of formulas, the global form can be deduced from local form parameters, and the global form can be deduced from the local, allowing the geometric model to be restored and giving the form geometric robustness.

[0024] Compared to the trial-and-error approach of traditional Ghost modeling, which relies on numerous parameter adjustments, the plug-in system locks in the essential form through formulaic logic. It eliminates the need to adjust individual parameters; the overall form can be adjusted simply by modifying the core formula parameters. For example, when adjusting the basic roof form, replacing different 3D point projection modules completes the modification of the basic surface's shape; similarly, when adjusting local structural lines, replacing the corresponding graphic point set module completes the modification, improving the design efficiency of complex shapes. Unified control of the basic form logic achieves overall surface formation, reducing hidden defects such as gaps and discontinuous normals caused by complex surface tiling. This provides crucial technical support for the accurate form of ultra-large-scale complex buildings such as airports and stadiums. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the traditional GH type-finding method in this embodiment of the invention. Figure 2 A module structure diagram of a parametric building form-finding plug-in system based on analytical geometry is provided in an embodiment of the present invention. Figure 3 This is a flowchart illustrating the analytical geometry finding method of the plug-in system in this embodiment of the invention. Figure 4 A flowchart of a parametric building form-finding method based on analytical geometry is provided in an embodiment of the present invention; Figure 5 This is the T2 terminal roof model generated using the analytical geometry-based parametric model finding method in this embodiment of the invention. Figure 6This is a comparison chart of the GH file sizes obtained by the traditional GH type finding method and the plug-in system in an embodiment of the present invention. Detailed Implementation

[0026] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0027] Firstly, such as Figure 2 As shown, this embodiment of the invention provides a parametric form-finding plugin system for buildings based on analytical geometry. The plugin system is developed using C#, based on the Visual Studio 2022 integrated development environment, and runs on Rhino 7 and above, and GH 1.0.0007 and above. The plugin system contains 30 computational unit components, divided into the following functional modules: The reference dot matrix generation module is used to generate an initial dot matrix framework with a regular distribution based on the input geometric parameters and analytical geometric formulas. The dot matrix framework includes linear dot matrix, planar dot matrix, sector dot matrix, and column grid dot matrix.

[0028] The reference dot matrix generation module further includes: The straight line dot matrix generation unit is used to generate intervals and dot spacing based on the input dot matrix, and generate the corresponding straight line dot matrix through the linear parametric equation; The planar dot matrix generation unit is used to generate the corresponding planar dot matrix based on the input number of rows, row spacing, number of columns, and column spacing, and through the planar parametric equation. The sector matrix generation unit is used to generate the corresponding sector matrix based on the input reference plane, first circle radius, sector angle, radial spacing, number of branches and number of concentric layers through polar coordinate parametric equations. The column grid generation unit is used to generate the corresponding column grid based on the input numerical sequences in the X-axis and Y-axis directions.

[0029] The graphic point set generation module is used to transform the input geometric parameters into a graphic point set with a specific mathematical form according to preset analytical geometric rules, and generate the corresponding geometric formula.

[0030] The graphic point set generation module further includes: The curve graph dot matrix generation unit is used to generate the corresponding curve dot matrix and its curve formula based on the input calculation reference plane, original coordinate points, curve center position, curve steepness coefficient and Y-axis scaling coefficient. The normal distribution graphic dot matrix generation unit is used to generate the corresponding normal distribution dot matrix and its normal distribution formula based on the input calculation reference plane, original coordinate points, highest X-axis position, distribution curve height and distribution curve width. The Lissajous figure dot matrix generation unit is used to generate the corresponding Lissajous curve and its parametric equation expression formula based on the input reference plane, X-direction amplitude, Y-direction amplitude, X-direction frequency, Y-direction frequency, phase difference and sampling steps. The rose curve graphic dot matrix generation unit is used to generate the corresponding rose curve dot matrix and its parametric equation expression based on the input reference plane, rose curve amplitude, frequency numerator, frequency denominator, phase offset and number of sampling points. The spiral pattern dot matrix generation unit is used to generate the corresponding spiral dot matrix and its parametric equation expression based on the input reference plane, initial radius, number of rotations and angular step size. The Lamé graphic dot matrix generation unit is used to generate the corresponding Lamé curve dot matrix and its parametric equation expression based on the input reference plane, X-axis radius, Y-axis radius, curve exponent and curve segment number; The spring dot matrix generation unit is used to generate the corresponding spring dot matrix and its parametric equation expression based on the input reference plane, spring radius, number of spring coils, total spring height, and number of segments per coil.

[0031] The three-dimensional point projection module is used to project the graphic point set onto a three-dimensional position defined by three-dimensional analytical geometry, and obtain the corresponding three-dimensional projection point set and its parametric equation expression.

[0032] The three-dimensional dot matrix projection module further includes: The ellipsoid projection element is used to obtain the positive and negative projection points and their parametric equations based on the input centroid, lattice, X-axis length, Y-axis length, Z-axis length, and ellipsoid index. The cone projection unit is used to obtain the positive and negative projection points and their parametric equations based on the input centroid, lattice, cone base radius, and cone height.

[0033] The model generation module is used to generate the final 3D architectural surface model and its structural lines based on the input raster framework.

[0034] The data structure tools module is used to process data sequences and output the processed data sequences. During the modeling process, the structure of the data tree can become chaotic as the model becomes more complex. This data structure tool module is used to organize and restate the data structure to ensure the validity of the input, that is, to ensure that the data format can be correctly read and written by the plug-in system. The processing includes number sequence conversion, empty branch filtering, first and last filtering, and interval segmentation.

[0035] The data structure tool module further includes: The number sequence conversion module is used to convert a list of numbers to be converted into Num-marked format, generating a list of strings with both the start and end numbers marked. The empty branch filtering unit filters out empty branches in the list of numbers, reconstructs the data in a new order, and outputs a renumbered data sequence. The beginning and end filtering unit is used to remove the beginning and end of the number list and output the processed data sequence. The interval segmentation unit is used to segment the list of numbers into intervals according to the input segmentation parameters and output the start / end data sequence of the interval segmentation. An object position marking unit is used to randomly select geometric objects and output the object position markings of the set. Specifically, based on the input set of geometry to be processed, the number to be retained, and a seed generated by random numbers, the geometry to be retained, the geometry to be removed, the index of the geometry to be retained, and the index of the geometry to be removed are generated.

[0036] The fitting calculation module includes at least four fitting methods: curve, normal distribution, control point optimization, and circular arc segment. It is used to sample the target curve based on the input parameters, generate formulas, evaluate fitness, and perform error analysis.

[0037] In practical applications, the fitting calculation module can fit the preliminarily modeled building model and convert it into a data format compatible with the plug-in system for subsequent output.

[0038] The fitting operation module further includes: The curve fitting unit is used to generate sampling points, evaluate the fit fitness, and generate curve formula text from the input target curve, number of sampling points, curve steepness factor, and curve midpoint position parameters. The normal distribution graph fitting unit is used to generate sampling points, evaluate the fit fitness, and generate the normal distribution formula text based on the input target curve, number of sampling points, normal distribution mean, normal distribution standard deviation, and Y-axis scaling factor. The curve control point optimization unit is used to generate the actual curve and evaluate the fit fitness based on the input target curve and the number of curve control points. The circular arc fitting unit is used to generate the fitted circular arc segment and its fitting degree and local difference based on the input target curve, segmentation factor and number of sampling points.

[0039] The analysis module is used to generate corresponding analytical geometric formulas based on the properties of geometric objects and mark the positions of the objects; it is also used to perform rainwater runoff analysis based on the shape of the input geometric objects, generating water flow path curves, a set of path endpoints, and a set of all path points.

[0040] Secondly, such as Figure 3 and Figure 4 As shown, this embodiment of the invention provides a parametric building model finding method based on analytical geometry, including the following steps: Step 1: Based on the basic geometric parameters of the building shape, generate a regularly distributed basic point matrix using analytical geometric formulas.

[0041] Specifically, based on the basic geometric parameters of the building form (such as the range of length, width, and height), a regularly distributed base point matrix is ​​generated using analytical geometric formulas. The (x, y, z) values ​​generated by these formulas are then used to eliminate discretized redundant data from the point matrix set. This eliminates the need to store a large number of procedural geometric objects, retaining only the point set, thus significantly reducing model file size and memory usage, effectively solving the problems of large model size and low running efficiency.

[0042] This step involves establishing a morphological entropy reduction design system driven by analytical geometric formulas. This transforms the entropy increase law of architectural form into quantifiable mathematical logic and anchors the essence of complex shapes through analytical geometric formulas, converting high-entropy visual morphological elements into extremely simple mathematical language. The originally disordered and scattered visual elements in architectural form (such as discrete points, piecewise curves, and local curved surfaces) are mathematically abstracted through analytical geometric formulas, transforming them into forms with clear mathematical expressions, including but not limited to ellipsoid equations, normal distribution graphs, and S-curve equations. Through this step, precise compression of morphological information is achieved.

[0043] Step 2: Perform coordinate transformation on the basic point matrix according to the preset analytical geometric rules to generate a set of intermediate points with a clear mathematical form.

[0044] This step supports various analytical geometry types, including but not limited to: ellipsoid equation point sets, normal distribution graph point sets, and S-curve equation point sets.

[0045] The analytical geometric patterns mentioned include normal distribution curve patterns, Lissajous curve patterns, rose curve patterns, spiral patterns, or Lamé curve patterns.

[0046] In practice, the corresponding mathematical graph type is selected according to the design requirements, and relevant equation parameters (such as the semi-axis length of the ellipsoid, the mean and standard deviation of the normal distribution, etc.) are input. The module automatically transforms the spatial coordinates of the reference point matrix according to the selected mathematical rules to generate a set of intermediate points with a clear mathematical form.

[0047] This step analyzes the spatial differences between point sets with different parameters to resolve geometric constraints on shape adjustment, thus avoiding abrupt shape changes caused by manual adjustments.

[0048] Step 3: Project the points in the intermediate point set onto the preset target surface to generate a three-dimensional point set.

[0049] Specifically, each point in the initial point matrix is ​​projected along a specified direction (such as the Z-axis direction or the normal direction) onto a preset target surface to generate a three-dimensional point set of complex shapes, realizing the mapping transformation from planar mathematics to three-dimensional architectural form.

[0050] The projection is either a projection onto the surface of an ellipsoid or a projection onto the surface of a cone.

[0051] Step 4: Use complex shape point sets to reconstruct the surface and generate the surface morphology and structural lines of the three-dimensional curved surface model of the building.

[0052] After the surface is generated, the structural lines (such as ridge lines, valley lines, contour lines, etc.) of the surface can be extracted according to the design requirements through the built-in tool modules of the plugin.

[0053] In this embodiment, as Figure 5 and Figure 6 As shown, using the generation of a T2 terminal roof model of the same depth as the test standard, the following methods were compared with the Crinoid plugin system used in this invention: Bézier curve modeling method, catenary curve modeling method, dynamic modeling workflow based on Kangroo, modeling method based on the standard equation of a circle, lightweight C# modeling method based on the standard equation of a circle, three different versions of modeling methods based on ellipsoid + standard equation of a circle, and the method for generating full formulas for longitudinal structural lines. The comparison results are as follows. Figure 6 As shown, the plug-in system of this invention exhibits significant performance advantages during model generation: the output GH file is only 514KB in size, compared to the largest file of 3260KB in the same depth model, reducing the size by approximately 84.2%, and only 15.8% of the original largest file. Simultaneously, the plug-in optimizes the core performance of the model, improving robustness by describing the shape structure curves using mathematical formulas; it also alleviates the problem of data blindness and improves model readability by reducing modeling steps and parameter redundancy.

[0054] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0055] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

[0056] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make modifications, alterations, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A parametric form-finding plugin system for buildings based on analytical geometry, characterized in that, include: The reference lattice generation module is used to generate an initial lattice framework with a regular distribution based on the input geometric parameters and analytical geometric formulas. The graphic point set generation module is used to transform the input geometric parameters into a graphic point set with a specific mathematical form according to the preset analytical geometric rules, and generate the corresponding geometric formula. The three-dimensional dot matrix projection module is used to project the graphic point set onto a three-dimensional position defined by three-dimensional analytical geometry, and obtain the corresponding three-dimensional projection point set and its parametric equation expression; The model generation module is used to generate the final 3D architectural surface model's surface morphology and structural lines based on the input raster frame. The data structure tool module is used to process data sequences and output the processed data sequences. The processing includes number sequence conversion, empty branch filtering, first and last filtering, and interval segmentation.

2. The parametric building form-finding plugin system based on analytical geometry according to claim 1, characterized in that, The reference dot matrix generation module further includes: The straight line dot matrix generation unit is used to generate intervals and dot spacing based on the input dot matrix, and generate the corresponding straight line dot matrix through the linear parametric equation; The planar dot matrix generation unit is used to generate the corresponding planar dot matrix based on the input number of rows, row spacing, number of columns, and column spacing, and through the planar parametric equation. The sector matrix generation unit is used to generate the corresponding sector matrix based on the input reference plane, first circle radius, sector angle, radial spacing, number of branches and number of concentric layers through polar coordinate parametric equations. The column grid generation unit is used to generate the corresponding column grid based on the input numerical sequences in the X-axis and Y-axis directions.

3. The parametric building form-finding plugin system based on analytical geometry according to claim 2, characterized in that, The graphic point set generation module further includes: The curve graph dot matrix generation unit is used to generate the corresponding curve dot matrix and its curve formula based on the input calculation reference plane, original coordinate points, curve center position, curve steepness coefficient and Y-axis scaling coefficient. The normal distribution graphic dot matrix generation unit is used to generate the corresponding normal distribution dot matrix and its normal distribution formula based on the input calculation reference plane, original coordinate point, highest X-axis position, distribution curve height and distribution curve width. The Lissajous figure dot matrix generation unit is used to generate the corresponding Lissajous curve and its parametric equation expression formula based on the input reference plane, X-direction amplitude, Y-direction amplitude, X-direction frequency, Y-direction frequency, phase difference and sampling steps. The rose curve graphic dot matrix generation unit is used to generate the corresponding rose curve dot matrix and its parametric equation expression based on the input reference plane, rose curve amplitude, frequency numerator, frequency denominator, phase offset and number of sampling points. The spiral pattern dot matrix generation unit is used to generate the corresponding spiral dot matrix and its parametric equation expression based on the input reference plane, initial radius, number of rotations and angular step size. The Lamé graphic dot matrix generation unit is used to generate the corresponding Lamé curve dot matrix and its parametric equation expression based on the input reference plane, X-axis radius, Y-axis radius, curve exponent and curve segment number; The spring dot matrix generation unit is used to generate the corresponding spring dot matrix and its parametric equation expression based on the input reference plane, spring radius, number of spring coils, total spring height, and number of segments per coil.

4. The parametric building form-finding plugin system based on analytical geometry according to claim 3, characterized in that, The three-dimensional dot matrix projection module further includes: The ellipsoid projection element is used to obtain the positive and negative projection points and their parametric equations based on the input centroid, lattice, X-axis length, Y-axis length, Z-axis length, and ellipsoid index. The cone projection unit is used to obtain the positive and negative projection points and their parametric equations based on the input centroid, lattice, cone base radius, and cone height.

5. The parametric building form-finding plugin system based on analytical geometry according to claim 4, characterized in that, The data structure tool module further includes: The number sequence conversion module is used to convert a list of numbers to be converted into Num-marked format, generating a list of strings with both the start and end numbers marked. The empty branch filtering unit filters out empty branches in the list of numbers, reconstructs the data in a new order, and outputs a renumbered data sequence. The beginning and end filtering unit is used to remove the beginning and end of the number list and output the processed data sequence. The interval segmentation unit is used to segment the list of numbers into intervals according to the input segmentation parameters and output the start / end data sequence of the interval segmentation. The object position marking unit is used to randomly select geometric objects and output the object position markings of the set.

6. The parametric building form-finding plugin system based on analytical geometry according to claim 1, characterized in that, Also includes: Fitting calculation module and analysis module; The fitting operation module includes at least four fitting methods: curve, normal distribution, control point optimization, and circular arc segment, which are used to sample the target curve, generate formulas, evaluate fitness, and analyze errors based on input parameters. The analysis module is used to generate corresponding analytical geometric formulas based on the properties of the geometric object and mark the position of the object; it is also used to perform rainwater runoff analysis based on the shape of the input geometric object, and generate water flow path curves, path endpoint sets, and sets of all path points.

7. The parametric building form-finding plugin system based on analytical geometry according to claim 4, characterized in that, The fitting operation module further includes: The curve fitting unit is used to generate sampling points, evaluate the fit fitness, and generate curve formula text from the input target curve, number of sampling points, curve steepness factor, and curve midpoint position parameters. The normal distribution graph fitting unit is used to generate sampling points, evaluate the fit fitness, and generate the normal distribution formula text based on the input target curve, number of sampling points, normal distribution mean, normal distribution standard deviation, and Y-axis scaling factor. The curve control point optimization unit is used to generate the actual curve and evaluate the fit fitness based on the input target curve and the number of curve control points. The circular arc fitting unit is used to generate the fitted circular arc segment and its fitting degree and local difference based on the input target curve, segmentation factor and number of sampling points.

8. A parametric model finding method for buildings based on analytical geometry, characterized in that, Includes the following steps: Step 1: Based on the basic geometric parameters of the building form, generate a regularly distributed basic point matrix using analytical geometric formulas; Step 2: Perform coordinate transformation on the basic point matrix according to the preset analytical geometric rules to generate a set of intermediate points with a clear mathematical form; Step 3: Project the points in the intermediate point set onto the preset target surface to generate a three-dimensional point set; Step 4: Use complex shape point sets to reconstruct the surface and generate the surface morphology and structural lines of the three-dimensional curved surface model of the building.

9. The parametric building model finding method based on analytical geometry according to claim 8, characterized in that, In step 2, the analytical geometric pattern includes the normal distribution curve pattern, the Lissajous curve pattern, the rose curve pattern, the spiral pattern, or the Lamé curve pattern.

10. The parametric building form-finding method based on analytical geometry according to claim 9, characterized in that, In step 3, the projection is either a projection onto the surface of an ellipsoid or a projection onto the surface of a cone.

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