A three-dimensional isosurface extraction and quantification method and system for aviation emissions

Abstract

The application discloses a three-dimensional isosurface extraction and quantification method and system for aviation emissions, comprising obtaining flight trajectory data, constructing a three-dimensional voxel grid, mapping emission data to corresponding spatial voxels, and then constructing a three-dimensional emission field; the three-dimensional emission field is divided into a plurality of voxel blocks, the local state code of the voxel block is obtained, the edge set in the voxel block crossed by the isosurface is determined according to the local state code; the intersection position of the edge and the isosurface is calculated, and a three-dimensional isosurface grid is obtained; the minimum value and the maximum value of the emission field are obtained according to the three-dimensional emission field, and the emission threshold is determined, each emission threshold corresponds to an isosurface of the emission; the geometric parameter characteristics of the isosurface are calculated. The application aims to solve the problems of insufficient geometric accuracy, single structure recognition and lack of depth quantification in the prior art.

Description

Technical Field

[0001] This invention relates to the field of aviation emission technology, and in particular to a three-dimensional isosurface extraction and quantification method and system for aviation emissions. Background Technology

[0002] With the continuous development of the air transport industry, aviation emissions from airports and their surrounding areas have received increasing attention. Aircraft emit large amounts of carbon oxides and nitrogen oxides during takeoff and landing, and the diffusion of these pollutants exhibits distinct three-dimensional spatial characteristics. In studying aviation emissions, three-dimensional isosurface extraction and feature quantification techniques are crucial, as they can visually represent the spatial distribution of emissions and enable quantitative analysis.

[0003] Currently, existing technologies in the field of aviation emissions research include methods based on trajectory inversion and low-level emissions modeling, flight segment emissions accounting methods based on fuel consumption segment correction, methods based on airport ground multi-source high-resolution emissions inventories, airport emissions modeling methods based on improved LTO cycles and meteorological parameter optimization, and the Marching Cubes algorithm. Among these, the trajectory inversion and low-level emissions modeling method combines flight activity data and aviation environmental design tool outputs to perform fine-grained segmentation of flight paths and emissions sources, achieving high spatiotemporal resolution pollutant emissions modeling for airport areas. While this method can output fine-grained emissions path data, it often fails to form a complete three-dimensional continuous field representation and lacks the ability to model the overall spatial structure. The flight segment emissions accounting method based on fuel consumption segment correction improves the fuel consumption model and introduces aircraft type subdivision to establish a multi-component pollutant emissions accounting system. Although this improves the accuracy of emissions estimation at different flight stages, the output results remain at the numerical total level and cannot represent the overall emissions data. The evolution trend of emissions in space; the method based on airport ground multi-source high-resolution emission inventory, which constructs ground multi-source emission inventory by collecting actual operational data and quantifies the spatial distribution characteristics of pollutants in airports and taxiways. This method focuses on gridded modeling in the horizontal direction, but does not fully consider the emission characteristics of aircraft in the vertical direction, resulting in insufficient three-dimensional structure reconstruction capability; the airport emission modeling method based on improved LTO cycle and meteorological parameter optimization, which integrates meteorological data on the basis of traditional LTO stage division and corrects the emission altitude setting. Although this method improves the rationality of near-ground emission estimation, its ability to express emission boundary morphology and spatial classification is still relatively limited; the Marching Cubes algorithm, as a classic three-dimensional isosurface extraction method, is widely used in medical image processing, geological modeling and fluid field visualization. However, this method usually relies on a single threshold and linear interpolation, which can easily produce boundary blurring and structural distortion in high-gradient emission areas. Moreover, it lacks geometric quantification function and is difficult to support quantitative description and comparative analysis of complex emission structures.

[0004] Studies have found that aviation emissions fields often exhibit high concentration gradients and complex three-dimensional spatial distributions in areas such as near-ground areas and flight paths at airports. Existing techniques primarily employ linear interpolation methods, which have limited accuracy in locating the intersection points of isosurfaces and volumetric boundaries. This is particularly problematic in high-gradient regions, where significant geometric deviations can easily occur, leading to isosurfaces that fail to accurately reflect the spatial boundaries of rapidly changing emissions and impacting the accuracy of subsequent analyses. Furthermore, standard methods lack robustness in handling complex or degenerate topologies generated by interpolation (such as small holes or thin sheets), potentially resulting in discontinuous or distorted isosurface structures.

[0005] In addition, aviation emissions analysis often requires examining the spatial distribution characteristics of emissions at different concentration levels simultaneously. Existing isosurface extraction techniques are typically based on a single threshold operation. If multiple emission levels need to be analyzed, the algorithm must be repeatedly executed and external, manual comparisons must be performed. This approach is inefficient and lacks built-in mechanisms to support structured correlations, comparative analysis, and linked visualization between multi-level isosurfaces, making it difficult to systematically reveal the gradient distribution patterns of emissions spreading from the core high-value area to the periphery.

[0006] Furthermore, standard isosurface extraction algorithms primarily aim to generate visualized surfaces, typically lacking or only providing basic geometric calculations. They lack a systematic geometric feature quantification module tailored to the specific needs of aviation emissions analysis. For example, they cannot directly and integratedly calculate key parameters such as the volume enclosed by the isosurface (corresponding to the emission impact range), mean curvature (reflecting the severity of concentration gradient changes), and mean height (indicating the centroid of vertical emission distribution), hindering in-depth quantitative assessment and diagnosis of the three-dimensional spatial structure of aviation emissions. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a three-dimensional isosurface extraction and quantification method and system for aviation emissions, aiming to solve problems such as insufficient geometric accuracy, limited structural identification, and lack of depth quantization in existing technologies.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] In a first aspect, the present invention provides a three-dimensional isosurface extraction and quantification method for aviation emissions, comprising:

[0010] Acquire flight trajectory data and obtain emission data for each trajectory point; construct a three-dimensional voxel mesh, map the emission data to the corresponding spatial voxels, and complete the voxel nodes to construct a three-dimensional emission field;

[0011] The three-dimensional emission field is divided into several volume elements. The vertex state of the volume elements is determined and the local state code of the volume elements is obtained. The set of edges traversed by the isosurface within the volume element is determined based on the local state code. The intersection point of the edge and the isosurface is calculated. A set of triangular facets is formed based on the intersection point. The triangular facets are then spliced ​​into a three-dimensional isosurface mesh.

[0012] The minimum and maximum values ​​of the emission field are obtained from the three-dimensional emission field, and the emission thresholds are determined. Each emission threshold corresponds to an isosurface of the emission.

[0013] Based on the isosurface of emissions, the geometric parameter characteristics of the isosurface are calculated.

[0014] As a further technical solution, the three-dimensional empirical Bayesian Skripal interpolation method is used to complete the voxel nodes. Specifically, the predicted emission value is calculated at the target location, expressed as: Where Z(x) i Let λ be the observed value of the i-th sample point. i is the corresponding weighting coefficient, and x0 is the target position.

[0015] As a further technical solution, each volume block consists of eight vertices. When the vertex value is greater than or equal to a set threshold, the vertex state is recorded as 1; when the vertex value is less than the set threshold, the vertex state is recorded as 0. Each vertex corresponds to a binary state bit. The eight binary state bits are combined into a binary number according to the vertex number order, which is the local state code of the volume block.

[0016] As a further technical solution, the calculation steps for the intersection point position are as follows: First, calculate the unit vector of the edge direction, using the formula: in, Let l be the side direction vector, and l be the side length. and The positions of the two vertices;

[0017] Then, calculate the directional derivative of the function along the edge direction at each of the two vertices, which is the projection of the function gradient in that direction, as follows: in, The gradient at two points;

[0018] Further order: Where t represents the proportional position of the intersection point on the edge, and the function value corresponding to t is: H(t) = h0(t)f i +h1(t)f j +h2(t)lg i +h3(t)lg j After solving, the intersection point parameters and spatial coordinates are obtained, specifically: Among them, t *These are the parameters for the intersection point.

[0019] As a further technical solution, the method for determining the emission threshold includes manual setting and automatic generation; the manual setting refers to manually setting the emission threshold, and satisfies the following: in, Let C be the set of emission thresholds. mim C is the minimum value of the emission field. max This represents the maximum value of the emission field.

[0020] As a further technical solution, the automatic generation is as follows: input emission threshold intervals, and generate a threshold sequence based on the emission threshold intervals, using the following formula: Where ΔS is the emission threshold interval.

[0021] As a further technical solution, the geometric parameters of the isosurface are calculated, including surface area, volume, average curvature, and average height.

[0022] The surface area is: Among them, A i Let T be the surface area of ​​the i-th isosurface. i Let Area(Τ) be a set of triangular facets. j () represents the area of ​​a single triangular facet;

[0023] The volume is: Among them, V i Let n be the volume of the i-th isosurface. j For T j The unit normal vector, c j This is the centroid position vector of the corresponding facet;

[0024] The average curvature is: in, For the mean curvature, N p Let be the total number of vertices on the i-th isosurface. Let ρ be the average curvature of point p, and ρ1 and ρ2 be the principal curvatures.

[0025] The average height is: Among them, H avg For the average height, z i Let be the height coordinates of the i-th vertex.

[0026] Secondly, the present invention provides a three-dimensional isosurface extraction and quantification system for aviation emissions, comprising the following modules:

[0027] The emission field construction module is configured to: acquire flight trajectory data and obtain emission data for each trajectory point; construct a three-dimensional voxel mesh, map the emission data to the corresponding spatial voxels, and complete the voxel nodes to construct a three-dimensional emission field.

[0028] The three-dimensional isosurface calculation module is configured to: divide the three-dimensional emission field into several volume elements, determine the vertex state of the volume elements, obtain the local state code of the volume elements, determine the set of edges traversed by the isosurface within the volume elements based on the local state code; calculate the intersection point of the edge and the isosurface, form a set of triangular facets based on the intersection points, and then stitch the triangular facets into a three-dimensional isosurface mesh.

[0029] The multi-threshold extraction module is configured to: obtain the minimum and maximum values ​​of the emission field based on the three-dimensional emission field, and determine the emission thresholds, with each emission threshold corresponding to an isosurface of the emission.

[0030] The quantization module is configured to calculate the geometric parameter characteristics of the isosurface based on the isosurface of emissions.

[0031] One or more technical solutions of the present invention have the following beneficial effects:

[0032] 1. This invention constructs a high-resolution three-dimensional emission field to accurately reconstruct the spatial distribution characteristics of aviation emission elements around airports, overcoming the problem that traditional two-dimensional statistical methods cannot reflect emission heterogeneity. In the intersection point location process, an improved cubic Hermite interpolation is introduced, combined with local gradient information for interpolation calculations. Compared with traditional linear interpolation methods, this provides higher spatial accuracy and boundary smoothness in high-gradient change regions, effectively avoiding emission interface breaks or misalignments, and ensuring the continuity and morphological accuracy of isosurfaces.

[0033] 2. This invention introduces a multi-threshold control mechanism in the isosurface extraction process, which supports flexible configuration of different emission level thresholds, realizes the synchronous extraction and hierarchical modeling of multi-level emission areas, and reveals the evolution process of emission intensity spreading from the core area to the outside.

[0034] 3. Based on the isosurface of emissions, this invention further calculates geometric parameters such as surface area, volume, average height, and average curvature, solving the problem that existing methods only provide surface-level visualization and lack in-depth quantitative analysis. This invention forms a systematic emission characteristic index system, supporting comparative analysis of emission structures, anomaly identification, and dynamic change monitoring, significantly improving the interpretability and evaluation capability of emission modeling results. Attached Figure Description

[0035] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0036] Figure 1 This is a flowchart of the method provided in Embodiment 1 of the present invention;

[0037] Figure 2 This is a system flowchart provided in Embodiment 2 of the present invention;

[0038] Figure 3 This invention provides an isosurface display of different threshold values ​​for an airport. Figure 3 (a) represents the airport's 1×10 6 g / Voxel, 2×10 6 g / Voxel, 3×10 6 Top view of three different threshold isosurfaces of g / Voxel. Figure 3 (b) represents 1×10 of the airport 6 g / Voxel, 2×10 6 g / Voxel, 3×10 6 A diagram showing the g / Voxel isosurfaces at a tilt angle of -45°. Figure 3 (c) is for the airport 2×10 6 g / Voxel, 3×10 6 A diagram illustrating the g / Voxel isosurfaces at a dip angle of -45°. Figure 3 (d) represents the airport's 3×10 6 A diagram showing the g / Voxel isosurface at a tilt angle of -45°. Detailed Implementation

[0039] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0040] Example 1

[0041] This embodiment provides a three-dimensional isosurface extraction and quantification method for aviation emissions, such as... Figure 2 As shown, a multi-level isosurface construction and structural quantification mechanism is adopted, combined with trajectory inversion emission data, to achieve three-dimensional identification and fine analysis of aviation emission areas.

[0042] The specific steps are as follows:

[0043] S1: Acquire flight trajectory data and obtain emission data for each trajectory point; construct a three-dimensional voxel mesh, map the emission data to the corresponding spatial voxels, and complete the voxel nodes to construct a three-dimensional emission field;

[0044] S2: Divide the three-dimensional emission field into several volume blocks, determine the vertex state of the volume blocks, and obtain the local state code of the volume blocks. Based on the local state code, determine the set of edges traversed by the isosurface within the volume block; calculate the intersection point of the edge and the isosurface, form a set of triangular facets based on the intersection points, and then stitch the triangular facets into a three-dimensional isosurface mesh.

[0045] S3: Based on the three-dimensional emission field, obtain the minimum and maximum values ​​of the emission field and determine the emission thresholds. Each emission threshold corresponds to an isosurface of the emission.

[0046] S4: Calculate the geometric parameter characteristics of the isosurface based on the emission isosurface.

[0047] In step S1, ADS-B flight trajectory data is first acquired, and emission data for each trajectory point is obtained by segmented calculation based on information such as aircraft type and flight segment stage. Subsequently, a three-dimensional voxel grid (resolution 50m×50m×50m) covering the airport and its surrounding area is constructed, and the emission data is mapped to the corresponding spatial voxels.

[0048] In this embodiment, the three-dimensional empirical Bayesian Skripal interpolation method is used to complete the voxel nodes and establish a complete emission field dataset. Specifically, the predicted emission value is calculated at the target location, expressed as:

[0049] Where Z(x) i Let λ be the observed value of the i-th sample point. i Here, x represents the corresponding weight coefficients, and x0 represents the target location. The weights sum to 1, and an exponential semivariogram model is used to estimate the interpolation parameters, ensuring spatial continuity and local stability.

[0050] In step S2, after the three-dimensional emission field is constructed, isosurface calculation is performed using a local voxel block traversal and high-precision interpolation strategy. First, the entire three-dimensional emission field is divided into several voxel blocks according to a regular voxel mesh. Each voxel block consists of eight vertices, where the coordinates of the vertices are the spatial coordinates of the voxel centers, and each vertex records the corresponding emission value f. i For each volume element, the vertex state is determined based on the relationship between the amount of each vertex emitted and a set threshold c.

[0051] When the vertex value satisfies f i When f ≥ c, the state at that point is recorded as 1; if f i<c, the state of this point is recorded as 0 to prevent unstable patch topology. Based on this, each vertex corresponds to a binary state bit b i , defined as:

[0052]

[0053] Combine the eight binary state bits in the order of vertex numbers into a binary number, which is the local configuration code (Local Configuration Code) of the voxel block. Further convert it into a decimal index value:

[0054]

[0055] According to the local configuration code, query the predefined edge table (Edge Table) to determine the set of edges crossed by the isosurface within the voxel block. Each crossed edge connects two adjacent vertices. Let the positions of the two end vertices be and The corresponding emissions are

[0056] In this embodiment, the cubic Hermite interpolation method is introduced in the calculation of the intersection point position, combined with the local gradient information at the vertices. It can be known that the gradient is the first-order derivative of the scalar field in space, indicating the change trend of the function in each direction. In three-dimensional space, the function gradient at any point can be represented as a vector This embodiment uses the central difference method to approximately calculate the gradient value of each vertex of the voxel block. For the coordinate point (i, j, k), its gradient components in the three directions can be expressed as:

[0057]

[0058] where Δx, Δy, and Δz are the spatial intervals of the voxels in the x, y, and z directions respectively, and usually remain consistent with the grid point settings in the interpolation process.

[0059] The steps of introducing cubic Hermite interpolation in the calculation of the intersection point position are as follows:

[0060] First, to improve the interpolation accuracy, calculate the unit vector in the edge direction, and the formula is: where, is the edge direction vector l is the edge length, and are the positions of the two end vertices;

[0061] Then, calculate the directional derivative of the function in the edge direction at both end vertices, that is, the projection of the function gradient in this direction, and the formula is: in, The gradient at two points;

[0062] In this embodiment, in order to unify the interpolation, the interval [x] is... i ,x j The linear mapping is given by the standard interval [0,1]. Let: Where t represents the proportional position of the intersection point on the edge, c represents the set threshold, and a cubic Hermite interpolation function H(t) is constructed on t∈[0,1]. Specifically, the function value corresponding to t is: H(t)=h0(t)f i +h1(t)f j +h2(t)lg i +h3(t)lg j Where h0(t) = 2t 3 -3t 2 +1、h1(t)=-2t 3 +3t 2 h2(t)=t 3 -2t 2 +t、h3(t)=t 3 -t 2 Let H(t) be a set of basis functions that uniquely satisfies the interpolation conditions on [0,1]. Solve for H(t). * After obtaining c, the intersection point parameters are obtained, and the spatial coordinates of the intersection point are obtained, specifically: Among them, t * For the intersection point parameter, t * ∈[0,1].

[0063] After calculating and locating the intersection points of all crossing edges, the corresponding triangle topology combination table is queried based on the local status code. Each group of triangular facets consists of three intersection points, which are assembled sequentially according to the connection relationships defined in the table to form a locally continuous set of triangular facets. After all volume elements are processed in the above way, the local triangular facets are stitched together to form a globally continuous three-dimensional isosurface mesh, accurately reproducing the spatial distribution interface of emissions corresponding to the set threshold. The three-dimensional isosurface mesh is not only spatially continuous and smooth, but also accurately reflects the true changes in the boundary of high-gradient regions, laying the foundation for subsequent multi-threshold extraction and geometric feature quantification analysis.

[0064] In step S3, this embodiment uses dynamic threshold configuration, allowing users to manually input or automatically generate equally spaced threshold sequences based on the minimum and maximum values ​​of the emission field. By combining manual setting and automatic generation mechanisms, the method in this embodiment can meet the needs of local high-precision analysis while also taking into account the visualization of global trends.

[0065] Specifically: First, the three-dimensional emission field is denoted as C(x), where x = (x, y, z) represents the three-dimensional spatial coordinates, and C(x) represents the emission value at the corresponding location. Then, to extract emission characteristics at different levels, a series of emission thresholds are set. Manually set to manually set emission thresholds, satisfying: in, Let C be the set of emission thresholds. min C is the minimum value of the emission field. max This represents the maximum value of the emission field.

[0066] If no specific threshold is manually set, an emission threshold interval can be entered. The system will automatically generate a threshold sequence based on the user-input emission threshold interval ΔS. This aims to achieve a holistic observation and analysis of emission characteristics. Let N be the threshold value that satisfies the condition. The largest integer, and the automatically generated threshold is uniformly distributed within the emission value range, as shown in the formula: Where ΔS is the emission threshold interval.

[0067] In step S4, the geometric parameters of the isosurface are calculated, including surface area, volume, average curvature, and average height, which are used to quantify the spatial morphology of the emission structure.

[0068] In this embodiment, surface area is used to characterize the coverage area of ​​the emission region in three-dimensional space. Let the i-th isosurface be composed of a set of triangular facets T. i The composition, and the formula are:

[0069] Among them, A i Let T be the surface area of ​​the i-th isosurface. i ={Τ1,Τ2,…,Τ n} represents the set of triangular facets, Area(Τ) j ) represents the area of ​​a single triangular facet.

[0070] Volume is used to measure the volume of three-dimensional space enclosed by a closed isosurface, reflecting the overall scale of the emission area. The formula is:

[0071] Among them, V i Let S be the volume of the i-th isosurface. i Let n be the volume region enclosed by the closed triangular facet formed by the i-th isosurface. j For T j The unit normal vector, c jThis is the centroid position vector of the corresponding facet. In this embodiment, the volume calculation is valid only if the isosurface is a closed manifold (satisfying the manifold condition); otherwise, a warning message will be triggered.

[0072] Mean curvature is used to quantify the degree of curvature of a local isosurface, thus reflecting the spatial variation characteristics of the emission gradient. Let there be N isosurfaces in total. p There are vertices, and the formula is:

[0073] in, For the mean curvature, N p Let be the total number of vertices on the i-th isosurface. Let ρ be the average curvature of point p, and ρ1 and ρ2 be the principal curvatures.

[0074] Average height describes the overall distribution center of the isosurface in the vertical direction (Z-axis), reflecting the spatial characteristics of the emission area in the height direction. The formula is:

[0075] Among them, H avg For the average height, z i Let Z be the height coordinate of the i-th vertex. By statistically analyzing the average Z coordinate of all vertices, we can reflect the degree of concentration and distribution trend of emissions in the vertical direction.

[0076] In this embodiment, to verify the universality and reliability of the technical solution, a specific airport was selected as the test area to study and analyze its aviation CO2 emission distribution structure in October 2023. To focus on the carbon emission characteristics analysis during the LTO cycle, this embodiment, based on the aircraft type characteristics and low-altitude climb performance, set a reasonable analytical domain as the test area. Specifically, the domain is 20km × 20km along the north-south axis, with the airport's geometric center as the origin, and vertically covering the ground surface to a height of 1km. This range effectively captures emission hotspots during the LTO phase while avoiding the dilution of local emission analysis results by emissions from long-distance wide-body aircraft.

[0077] Data on discrete points of aircraft carbon emissions within the test area were obtained, including latitude and longitude, flight phase, altitude, CO2 emissions, etc. Some data are shown in Table 1.

[0078] Table 1. Discrete point data on carbon emissions from some aircraft in the test area.

[0079]

[0080]

[0081] The 3D Empirical Bayesian Skripal Kinetic (3DEBK) method was used to interpolate aircraft emission data within the airport area into a 3D unit volume emission field with a regular voxel structure. The constructed area was 20km × 20km × 1km, vertically divided upwards from the ground, with a total Voxel resolution of 50m × 50m × 50m (unit volume), covering approximately 3,200,000 voxels. Before interpolation, all trajectory emission data underwent stage decomposition and spatial localization, and an exponential semi-variogram model was used for fitting. Bayesian sampling was employed to model the uncertainty of the interpolation parameters.

[0082] like Figure 3 As shown, flight emission data from October 2023 were selected, and three sets of CO2 emission intensity thresholds (1×10⁻⁶) were set. 6 g / Voxel, 2×10 6 g / Voxel, 3×10 6 (g / Voxel), corresponding to emission areas of different intensity levels. In the extraction results, three three-dimensional isosurfaces with continuous structures and clear boundaries can be clearly observed. The emission intensity level is represented by color coding from light to dark, with the red area representing the core area with the highest emission intensity.

[0083] from Figure 3 (a) It can be seen that, except for a few localized areas with small-scale cavities, within a range of approximately 20km × 20km × 1km, the CO2 emissions per unit volume generally reach or exceed 1 × 10⁻⁶. 6 g, while higher emission levels (2×10 6 g / Voxel and 3×10 6 The g / Voxel is mainly concentrated in and around the airport center. The isosurface shows a significant height increase in the airport center and along major flight routes, reflecting that due to frequent flight takeoffs and landings and low-altitude flight activities, the carbon emission load in these areas is much higher than in the surrounding areas.

[0084] Vertically, CO2 emissions show a gradual decreasing trend in overall altitude of the isosurface, indicating that high emissions are mainly concentrated in the low-altitude region. This characteristic reflects that during the initial stage of takeoff, the engine thrust is high and fuel combustion is intense. Furthermore, the reverse thrust deceleration during landing also accelerates fuel combustion, resulting in higher CO2 emissions near the ground. As the aircraft climbs to higher altitudes, flight density decreases and emission intensity weakens, leading to a gradual decrease in CO2 emissions with increasing altitude, forming a clear vertical stratification structure.

[0085] Horizontally, the distribution pattern of high CO2 emission isosurfaces is closely related to the runway orientation and major flight routes of Beijing Capital International Airport. Specifically, the high emission distribution is most extensive from the airport center towards the southeast and south, which aligns with the high-density flight routes from Beijing to southern and southeastern coastal cities such as Shanghai, Wuhan, and Guangzhou. Secondly, the distribution towards the southwest and northeast is also significant, mainly corresponding to flight traffic between Beijing and major cities such as Chengdu, Chongqing, and Harbin. The distribution towards the northwest is relatively small, due to the relatively low flight volume and route density between Beijing and northwestern cities such as Urumqi and Lanzhou. Furthermore, the lack of large cities north of Beijing results in sparse northbound flight traffic, leading to a lower distribution of high CO2 emissions in the northern area of ​​the airport.

[0086] Table 2 Geometric characteristic parameters of each threshold isosurface in the test area

[0087]

[0088] Table 2 shows the geometric feature parameters extracted by the method of this embodiment using multi-threshold isosurfaces on the three-dimensional emission field of the airport. The isosurface visualization intuitively shows the spatial distribution characteristics of CO2 around Beijing Capital International Airport, while the corresponding geometric parameters provide solid quantitative support for emission structure analysis. As can be seen from Table 2, as the emission threshold increases from 1×10⁻⁶, the geometric parameters increase with increasing emission threshold. 6 g / Voxel increased to 3×10 6 g / Voxel, the isosurface surface area extracted from Beijing Capital International Airport is approximately 3.7 × 10⁻⁶. 8 m 2 It dropped sharply to 1.8 × 10 5 m 2 The volume is 7.4 × 10 9 m 3 Reduced to 8.5×10 5 m 3 This exhibits a typical exponential decay trend. This trend reflects a significant convergence in the spatial distribution of high emission intensity areas, with the emission structure rapidly shrinking from widespread diffusion to localized aggregation.

[0089] In terms of geometry, the average curvature of the airport isosurface is close to zero (-0.00000236m) under low threshold conditions. -1 This indicates that the emission distribution during this stage is relatively gradual and the transition is natural. However, when the threshold is increased to 3×10... 6 At g, the mean curvature rises to 0.0209m. -1 This indicates that high emission intensity areas have obvious spatial protrusions and clear boundaries, exhibiting strong spatial aggregation characteristics.

[0090] The average height index further reveals the vertical distribution patterns of emissions activities. At low thresholds, the average height of the isosurface is approximately 30 m, increasing with the threshold to 3 × 10⁻⁶ m. 6 The average altitude of CO2 emissions decreased to approximately 12 m per g / Voxel. This change indicates that areas of high CO2 emission intensity are mainly concentrated near the Earth's surface and are closely related to low-altitude flight phases such as taxiing, takeoff, and approach, demonstrating significant near-ground retention characteristics.

[0091] Overall, airports exhibit clear structural hierarchical characteristics under different thresholds: low-intensity emissions are widely distributed, while high-intensity emissions are concentrated and close to the ground surface, fully demonstrating the typical carbon emission diffusion characteristics of large hub airports under high-density operation conditions.

[0092] Example 2

[0093] This embodiment provides a three-dimensional isosurface extraction and quantification system for aviation emissions, such as... Figure 1 As shown, it includes the following modules:

[0094] The emission field construction module is configured to: acquire flight trajectory data and obtain emission data for each trajectory point; construct a three-dimensional voxel mesh, map the emission data to the corresponding spatial voxels, and complete the voxel nodes to construct a three-dimensional emission field.

[0095] The three-dimensional isosurface calculation module is configured to: divide the three-dimensional emission field into several volume elements, determine the vertex state of the volume elements, obtain the local state code of the volume elements, determine the set of edges traversed by the isosurface within the volume elements based on the local state code; calculate the intersection point of the edge and the isosurface, form a set of triangular facets based on the intersection points, and then stitch the triangular facets into a three-dimensional isosurface mesh.

[0096] The multi-threshold extraction module is configured to: obtain the minimum and maximum values ​​of the emission field based on the three-dimensional emission field, and determine the emission thresholds, with each emission threshold corresponding to an isosurface of the emission.

[0097] The quantization module is configured to calculate the geometric parameter characteristics of the isosurface based on the isosurface of emissions.

[0098] Various modifications and variations of this invention will be apparent to those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A three-dimensional isosurface extraction and quantification method for aviation emissions, characterized in that, include: Acquire flight trajectory data and obtain emission data for each trajectory point; A three-dimensional voxel grid is constructed, emission data is mapped to corresponding spatial voxels, and voxel nodes are completed to construct a three-dimensional emission field. The three-dimensional emission field is divided into several volume elements. The vertex state of the volume elements is determined and the local state code of the volume elements is obtained. The set of edges traversed by the isosurface within the volume element is determined based on the local state code. The intersection point of the edge and the isosurface is calculated. A set of triangular facets is formed based on the intersection point. The triangular facets are then spliced ​​into a three-dimensional isosurface mesh. The minimum and maximum values ​​of the emission field are obtained from the three-dimensional emission field, and the emission thresholds are determined. Each emission threshold corresponds to an isosurface of the emission. Based on the isosurface of emissions, the geometric parameter characteristics of the isosurface are calculated; The calculation steps for the intersection point position are as follows: First, calculate the unit vector of the edge direction of the volume element block, using the following formula: ;in, Let the edge direction vector be... Let be the side length. and The positions of the two vertices; Then, calculate the directional derivative of the function along the edge direction at each of the two vertices, which is the projection of the function gradient in that direction, as follows: , ;in, , The gradients at the two points are respectively; Further order: ;in, This indicates the proportional position of the intersection point on the edge. c For the set isosurface threshold, The function value corresponding to one vertex of the edge. The function value corresponding to the vertex at the other end of the edge. The corresponding function value is: ;in, This indicates that the cubic Hermite interpolation function constructed along the edge has parameters... The function value at that location; The basis functions are as follows: , , , ;make After solving, the intersection point parameters are obtained, and the spatial coordinates of the intersection point are obtained, specifically: = ( - );in, Intersection parameters; The method for determining the emission threshold includes manual setting and automatic generation; the manual setting refers to manually setting the emission threshold, and it satisfies the following: ;in, For the set of emission thresholds, This represents the minimum value of the emissions field. This represents the maximum value of the emission field; The automatic generation is as follows: input emission threshold intervals, and generate a threshold sequence based on the emission threshold intervals, using the following formula: ,in, k The positive integer index represents the first... k An automatically generated emissions threshold N The total number of automatically generated emission thresholds. This represents the emission threshold interval.

2. The three-dimensional isosurface extraction and quantification method for aviation emissions as described in claim 1, characterized in that, The voxel nodes are completed using a three-dimensional empirical Bayesian skewkin interpolation method. Specifically, the predicted emission value is calculated at the target location, as follows: ;in, For the first Observations of each sample point For the corresponding weighting coefficients, For the target location; n This represents the total number of sample points involved in the interpolation calculation.

3. The three-dimensional isosurface extraction and quantification method for aviation emissions as described in claim 1, characterized in that, Each volume block consists of eight vertices. When the vertex value is greater than or equal to a set threshold, the vertex state is recorded as 1; when the vertex value is less than the set threshold, the vertex state is recorded as 0. Each vertex corresponds to a binary state bit. The eight binary state bits are combined into a binary number according to the vertex number order, which is the local state code of the volume block.

4. The three-dimensional isosurface extraction and quantification method for aviation emissions as described in claim 1, characterized in that, The calculated geometric parameters of the isosurface include surface area, volume, mean curvature, and mean height. The surface area is: ;in, For the first Surface area of ​​an isosurface For the first A set of triangular facets of isosurfaces. The area of ​​a single triangular facet; The volume is: ;in, For the first The volume of an isosurface For the first The volume region enclosed by several isosurfaces dV It is a volume infinitesimal element. for The unit normal vector, This is the centroid position vector of the corresponding facet; The average curvature is: ;in, For the first The average curvature of the isosurfaces For the first The total number of vertices on each isosurface. No. The first isosurface Average curvature of vertices and The first The first isosurface The two principal curvatures at each vertex; The average height is: ;in, For the first Average height of each isosurface For the first The first isosurface The height coordinates of each vertex.

5. A three-dimensional isosurface extraction and quantification system for aviation emissions, characterized in that, Includes the following modules: The emission field construction module is configured to: acquire flight trajectory data and obtain emission data for each trajectory point; construct a three-dimensional voxel mesh, map the emission data to the corresponding spatial voxels, and complete the voxel nodes to construct a three-dimensional emission field. The three-dimensional isosurface calculation module is configured to: divide the three-dimensional emission field into several volume elements, determine the vertex state of the volume elements, obtain the local state code of the volume elements, determine the set of edges traversed by the isosurface within the volume elements based on the local state code; calculate the intersection point of the edge and the isosurface, form a set of triangular facets based on the intersection points, and then stitch the triangular facets into a three-dimensional isosurface mesh. The multi-threshold extraction module is configured to: obtain the minimum and maximum values ​​of the emission field based on the three-dimensional emission field, and determine the emission thresholds, with each emission threshold corresponding to an isosurface of the emission. The quantization module is configured to calculate the geometric parameter characteristics of the isosurface based on the isosurface of emissions. The calculation steps for the intersection point position are as follows: First, calculate the unit vector of the edge direction of the volume element block, using the following formula: ;in, Let the edge direction vector be... Let be the side length. and The positions of the two vertices; Then, calculate the directional derivative of the function along the edge direction at each of the two vertices, which is the projection of the function gradient in that direction, as follows: , ;in, , The gradients at the two points are respectively; Further order: ;in, This indicates the proportional position of the intersection point on the edge. c For the set isosurface threshold, The function value corresponding to one vertex of the edge. The function value corresponding to the vertex at the other end of the edge. The corresponding function value is: ;in, This indicates that the cubic Hermite interpolation function constructed along the edge has parameters... The function value at that location; The basis functions are as follows: , , , ;make After solving, the intersection point parameters are obtained, and the spatial coordinates of the intersection point are obtained, specifically: = ( - );in, Intersection parameters; The method for determining the emission threshold includes manual setting and automatic generation; the manual setting refers to manually setting the emission threshold, and it satisfies the following: ;in, For the set of emission thresholds, This represents the minimum value of the emissions field. This represents the maximum value of the emission field; The automatic generation is as follows: input emission threshold intervals, and generate a threshold sequence based on the emission threshold intervals, using the following formula: ,in, k The positive integer index represents the first... k An automatically generated emissions threshold N The total number of automatically generated emission thresholds. This represents the emission threshold interval.

6. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the three-dimensional isosurface extraction and quantification method for aviation emissions as described in any one of claims 1-4.

7. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the three-dimensional isosurface extraction and quantification method for aviation emissions as described in any one of claims 1-4.

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