A high-precision oriented distance field model reconstruction method

Abstract

This invention discloses a high-precision method for reconstructing a directed distance field model in the field of solid rocket motor burnout calculation technology. The method includes: obtaining the directed distance field function based on a fixed mesh; reconstructing initial isosurfaces / lines using linear interpolation based on the type and spatial dimension of the fixed mesh, and marking isosurfaces / lines that make the directed distance field function zero; and obtaining and classifying the mesh nodes of the mesh cells intersecting the isosurfaces / lines obtained by searching using linear interpolation, resulting in directly adjacent nodes, a set of directly adjacent nodes, and a set of non-adjacent nodes. This invention constructs a reference base circle and uses a local optimization method to find isosurfaces / lines that are tangent to as many base circles as possible, ensuring that the directed distance field calculated based on the reconstructed isosurfaces / lines is consistent with the input directed distance field, avoiding non-physical offsets of the isosurfaces / lines, thereby eliminating systematic errors and improving calculation accuracy.

Description

Technical Field

[0001] This invention relates to the field of solid rocket motor combustion surface thrust calculation technology, specifically a high-precision method for reconstructing a directional distance field model. Background Technology

[0002] A directed distance field (SDF) is defined as the absolute value at any point equal to the shortest distance from a given starting point to the boundary of a given geometric shape. The sign of the SDF depends on whether the point is inside or outside the shape. SDFs have wide applications in scientific research and production practices. Typically, SDF functions are defined in a two-dimensional plane or three-dimensional space, but theoretically they can be extended to higher dimensions. SDFs can be used to describe the evolution of the combustion surface over time. In solid rocket motors, the propellant is a solid geometric body pre-filled within the combustion chamber. During operation, the combustion surface moves into the propellant at a certain rate, and the SDF can be used to describe the geometric relationship from any point to the combustion surface.

[0003] In practical applications, it is often necessary to reconstruct the actual geometry based on a discrete directed distance field defined at grid points. This process is essentially equivalent to reconstructing the zero contour lines (in two-dimensional cases) or isosurfaces (in three-dimensional cases) from the discrete distance field function. This task is generally accomplished using Marching Squares or Marching Triangles algorithms in two-dimensional cases, and Marching Cubes or Marching Tetrahedra algorithms in three-dimensional cases. The core idea of ​​these algorithms is the same: using linear interpolation, find points on the grid boundary where the directed distance field function is exactly zero; furthermore, connect all the found points in an appropriate way to form several complete polygons (in two-dimensional cases) or polyhedra (in three-dimensional cases), which serve as approximations of the actual shape expressed by the directed distance field. These methods are all mature and publicly available, and their details will not be elaborated here.

[0004] Although the aforementioned methods have been widely used for a long time, existing algorithms still have the following theoretical shortcomings: Due to the potentially complex nature of the geometry, the gradient of the directed distance field function is non-uniformly distributed along a grid boundary, and this non-uniformity does not decrease infinitely with grid refinement. Therefore, linear interpolation inevitably introduces errors under the premise of non-uniform function gradients. Generally, this error tends to reduce the curvature of the calculated isosurfaces or contour lines, shifting towards the side that reduces the surface area and shortens the curve length. Since this error is not significant in a single calculation, and the error in calculating the isosurfaces or contour lines will not exceed one grid cell, its impact is not significant. However, in cases requiring iterative calculations and where sub-grid accuracy is critical, this error becomes a stable systematic error, posing difficulties for the entire calculation. Summary of the Invention

[0005] The purpose of this invention is to provide a high-precision method for reconstructing a directed distance field model. By constructing a reference base circle, a local optimization method is used to find isosurfaces / lines that are as tangent as possible to all base circles, so that the directed distance field calculated based on the reconstructed isosurfaces / lines is consistent with the input directed distance field, avoiding non-physical offsets of the isosurfaces / lines, thereby eliminating systematic errors and improving calculation accuracy.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A high-precision method for reconstructing a directional range field model includes: S1: The directed distance field function is obtained based on the fixed grid. S2: Based on the fixed grid type and spatial dimension, the initial isosurfaces / lines are reconstructed using linear interpolation, and the isosurfaces / lines that make the directed distance field function zero are marked; S3: Based on the linear interpolation method, the mesh elements that intersect with the isosurface / line are searched, the mesh nodes of the mesh elements are obtained and classified, and the directly adjacent nodes, the set of directly adjacent nodes and the set of non-adjacent nodes are obtained. S4: Based on the isosurface / line graphic primitives, obtain the vertices and vertex coordinates that make up the primitives, and construct the correspondence between primitives and vertices; S5: Calculate the nearest point from the grid node in the set of directly adjacent nodes and the set of non-adjacent nodes to the isosurface / line, obtain the set of primitives where the nearest point is located or adjacent to it, and obtain the set of nearest points; S6: Traverse all primitives, search for all nearest point sets containing the primitives, and obtain the grid nodes corresponding to the nearest point sets; S7: For each element in the set of all nearest points containing the primitive, generate a corresponding base circle information, and construct a base circle set based on the base circle information; S8: Based on the set of base circles, traverse and calculate the precise position of each primitive, and use the parameter optimization method to calculate the set of intersection coordinates; S9: Calculate the weighted average of the coordinates of all points in the pair to obtain the weighted spatial coordinates of the vertex; S10: Reconstructing the zero isosurface / line of the directed distance field function based on weighted spatial coordinates.

[0007] As a further aspect of the present invention: the grid nodes of the grid cell are obtained and categorized to obtain directly adjacent nodes, a set of directly adjacent nodes, and a set of non-adjacent nodes, including: Determine whether the grid node is directly adjacent to the isosurface / line, wherein the adjacent relationship includes at least one adjacent node whose directed distance field function value is opposite to that of the grid node; When an adjacency relationship is determined, the grid node is treated as an element of the set of directly adjacent nodes, and the spatial coordinates of the grid node are marked. All grid nodes that do not belong to the set of directly adjacent nodes but whose grid cells intersect with isosurfaces / lines are included as elements to form the set of non-adjacent nodes, thus constructing the set of non-adjacent nodes.

[0008] As a further aspect of the present invention: the graphic primitive comprises one or more elements.

[0009] As a further aspect of the present invention: traverse all primitives, search for all nearest point sets containing the primitives, and obtain the grid nodes corresponding to the nearest point sets, including: Using sets: Record grid nodes, where e i n is an element of the set of directly adjacent nodes. i f is an element of the set of non-adjacent nodes. k As the basic unit, C F (e) i Let C be the set of nearest points to directly adjacent nodes. F (n) i ) is the set of nearest points to non-adjacent nodes.

[0010] As a further aspect of the present invention: the base circle information includes the base circle center coordinates, the base circle radius, and the base circle weight, wherein the base circle includes a circle and a sphere.

[0011] As a further aspect of the present invention: the step of traversing and calculating the precise position of each primitive based on the set of base circles includes: Obtain the coefficients of the equation of the line or plane containing the primitive element; The objective function for constructing the precise location is as follows: ,in, Parameters to be optimized The line or plane represented The function is the base circle From the center of the circle to Euclidean distance, In order to consider weights Evaluation under the premise and The function of the difference.

[0012] As a further aspect of the present invention: the step of traversing and calculating the precise position of each primitive based on the set of base circles further includes: A parameter optimization algorithm is used to optimize the center of a base circle with a non-zero radius, and the center of the circle is optimized to be located on the same side of the line or plane represented by the Euclidean distance; Obtain the vertices of the isosurfaces / lines corresponding to the primitives, obtain at least two grid lines containing the vertices, calculate the intersection points and intersection coordinates of the isosurfaces / lines and the grid lines, and obtain the set of intersection coordinates.

[0013] As a further aspect of the present invention: when the spatial dimension is two-dimensional, the primitives lie on the linear equation.

[0014] As a further aspect of the present invention: when the spatial dimension is three-dimensional, the primitives lie on the plane equation.

[0015] As a further aspect of the present invention, the parameter optimization algorithm includes the Sequential Quadratic Programming (SQP) algorithm.

[0016] Compared with the prior art, the beneficial effects of the present invention are: This invention obtains the basic topological structure of isosurfaces / lines using a reconstruction method based on linear interpolation. Then, a series of reference base circles are constructed based on the original directed distance field. Furthermore, a local optimization method is used to find isosurfaces / lines that are as tangent as possible to all base circles, so that the directed distance field calculated based on the reconstructed isosurfaces / lines is consistent with the input directed distance field, avoiding non-physical offsets of isosurfaces / lines, eliminating systematic errors in this process, and improving the overall calculation accuracy. Attached Figure Description

[0017] Figure 1 This is an example diagram illustrating the positional relationship of the grid, contour lines, primitive vertices, grid nodes, and corresponding nearest points in a two-dimensional context according to the present invention. Figure 2 For the present invention, in the two-dimensional case, it corresponds to Figure 1 Schematic diagram of the base circle of the region; Figure 3 This is a diagram illustrating the method steps of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Example: Please see Figures 1-3 This embodiment provides a high-precision method for reconstructing a directional range field model, including: S1: The directed distance field function is obtained based on the fixed grid. S2: Based on the fixed grid type and spatial dimension, the initial isosurfaces / lines are reconstructed using linear interpolation, and the isosurfaces / lines that make the directed distance field function zero are marked; S3: Based on the linear interpolation method, the mesh elements that intersect with the isosurface / line are searched, the mesh nodes of the mesh elements are obtained and classified, and the directly adjacent nodes, the set of directly adjacent nodes and the set of non-adjacent nodes are obtained. S4: Based on the isosurface / line graphic primitives, obtain the vertices that make up the primitives and their coordinates, and construct the correspondence between primitives and vertices; S5: Calculate the nearest point from the grid node in the set of directly adjacent nodes and the set of non-adjacent nodes to the isosurface / line, obtain the set of primitives containing or adjacent to the nearest point, and obtain the set of nearest points.

[0020] S6: Traverse all primitives, search for all nearest point sets containing the primitives, and obtain the grid nodes corresponding to the nearest point sets.

[0021] S7: For each element in the set of all nearest points containing the primitive, generate a corresponding base circle information, and construct a base circle set based on the base circle information.

[0022] S8: Based on the set of base circles, traverse and calculate the precise position of each primitive, and use a parameter optimization method to calculate the set of intersection coordinates.

[0023] S9: Calculate the weighted average of the coordinates of all points in the pair to obtain the weighted spatial coordinates of the vertex.

[0024] S10: Reconstructing the zero isosurface / line of the directed distance field function based on weighted spatial coordinates.

[0025] In this embodiment, if it is necessary to reconstruct isosurfaces corresponding to other values, then the directed distance field functions of all nodes can be first applied. Subtract this value from the value, and then use the above method to reconstruct the isosurface.

[0026] For step S1, specifically, let any grid node on the fixed grid... Spatial position coordinates are Let the directed distance field function to be reconstructed be . ,but Indicates from departing from point The shortest directed distance of the geometric object being represented; such as Figure 1 As shown, the thin solid-line grid dots represent a portion of an example two-dimensional rectangular grid.

[0027] For step S2, specifically, based on the grid type and spatial dimension, a general linear interpolation-based method is used (depending on the dimension and grid type of the actual problem, the Marching Squares, Marching Triangles, Marching Cubes, or Marching Tetrahedra algorithm, or other similar publicly available algorithms, are selected) to calculate... isosurfaces (lines) and denoted as Depending on the spatial dimension, The content is different: a) When performing two-dimensional calculations, the resulting contour lines are composed of line segments. It is a collection of line segment primitives; b) When performing three-dimensional calculations, the resulting surface is composed of triangular facets. It is a set of triangular primitives; such as Figure 1 As shown, the thick solid lines represent the contour lines in the case of a two-dimensional rectangular grid. Part of it.

[0028] Preferably, the process involves acquiring and classifying the grid nodes of the grid cell to obtain directly adjacent nodes, a set of directly adjacent nodes, and a set of non-adjacent nodes. This includes: determining whether a grid node is directly adjacent to an isosurface / line; if an adjacency is determined, the grid node is included as an element of the set of directly adjacent nodes, and the spatial coordinates of the grid node are marked; all grid nodes that do not belong to the set of directly adjacent nodes but whose grid cell intersects with the isosurface / line are included as elements of the set of non-adjacent nodes, thus constructing the set of non-adjacent nodes. Specifically, in step S2 above, several linear interpolation-based algorithms will search for all nodes that intersect with the isosurface / line. Intersecting grid cells serve as intermediate data, recording all grid nodes contained within these cells, and categorizing them as follows: a) For a node directly adjacent to an isosurface (line), i.e., at least one adjacent node is adjacent to this node. Nodes with opposite signs are denoted as "directly adjacent nodes", and the set of all such nodes is denoted as . Each node in it is denoted as Similar to S1, its spatial coordinates are denoted as ,Right now ={ | For grid nodes, There exists at least one node among its adjacent nodes. Make and Different signs}; b) For those not belonging to the set However, its grid cell is different from... The set of intersecting grid nodes is denoted as . Each node in the series is denoted as . Its spatial coordinates are as follows ,Right now ={ | For grid nodes, containing At least one of the grid cells is related to intersect, }; Appendix Figure 1 The middle mark is , The points represent the set in that part of the grid. The vertices included.

[0029] Specifically, for step S4, Each graphic primitive (triangular facet or line segment) in the diagram is denoted as Each vertex that makes up the primitive is denoted as As attached Figure 1 , Spatial coordinates are Organize and record as follows: and Correspondence between them: each graphic primitive The two included (when) (for line segments) or three (when) The set of vertices of a triangular facet is denoted as . ;like Figure 1 As shown, Figure 1 Each thick solid line segment represents a graphical primitive in a two-dimensional context. This marks the vertices of that section of contour lines.

[0030] Preferably, the graphic primitive contains one or more elements, specifically, using the geometry constructed in S2. Calculate from S3 Grid nodes in the set and Grid nodes in the set Starting point, to the geometric shape The nearest point on the surface, denoted as or (Hereinafter referred to as, unless there is any confusion) The set of nearest or adjacent graphical primitives is denoted as or (Hereinafter referred to as, unless there is any confusion) );gather There may be one or more elements, depending on: a) when Falling When the set is inside a line segment primitive or a triangular facet, There is only one element, namely b) When the line segment primitive or triangular facet is located; Falling When the set is at the endpoint of a line segment primitive, the boundary of a triangular facet, or a vertex, the set... The general contains multiple elements, including All adjacent primitives of a point should be recorded in In this step, we directly find the nearest point. Exhaustive attempts are required. All primitives Until the distance is found or The nearest point involves a large amount of computation. In actual calculations, publicly available methods such as AABB trees and Voronoi diagrams can be used to significantly reduce the computational load and quickly obtain the results. Details of these fast algorithms are not the subject of this invention and are all mature, publicly available algorithms; therefore, they will not be elaborated upon here. Figure 1 As shown in the figure The set corresponding to the point Including the process Two line segments of a point; Appendix Figure 1 The closest point in the middle, in order to make the attached Figure 1 concise, or Labeled as and ,For example upper distance The nearest point to the node is on the line segment Above, marked as .

[0031] Traverse each The search includes All The set corresponds to the grid node, which corresponds to each The set of search results is denoted as ; Right now: ,like Figure 1 As shown, line segment (For the sake of brevity, attached) Figure 1 China did not use " (The format is used for annotation) The set is .

[0032] Traverse each For the generated in S6 corresponding Each element in the set or Generate a "base circle" information and store it in the corresponding set The steps for generating the "base circle" and the information it contains are as follows: a) Each deposit The "base circle" of a set is denoted as It contains the following information: coordinates of the base circle center. Base circle radius Base circle weight ; b) For those by Grid nodes in the set The generated "base circle" has a weight For those by Grid nodes in the set The generated "base circle" has a weight ; and There are two scalars, generally there are This practice reflects the following facts: The grid nodes in the set are generally far from each other. More recently, it includes information about Information The grid nodes in the set are more reliable; c) If grid nodes or corresponding The nearest point on or lie in If a line segment or triangular facet is located inside the circle, then the center of the circle is considered to be located within it. or Location, radius is or The "base circle" is tangent to the exact solution of the isosurface (line); in this case, it is stored... The center coordinates of the base circle of the set equal or Base circle radius equal or .

[0033] d) If grid nodes or corresponding The nearest point on or lie in If the endpoint of a line segment primitive, the boundary of a triangular facet, or a vertex is on the vertex, then it is considered that... There is a vertex located at the center of the circle. or Location, radius is or On the "base circle"; in this case, store coordinates of the base circle center of the set equal or The radius is zero; a radius of zero essentially means that the isosurface (line) should pass through the center of the base circle. Note that the above description of the "base circle" is for the two-dimensional case. In the three-dimensional case, the corresponding concept of the "base circle" should be a sphere. The vector calculation formulas related to the base circle in this specification can be applied to the sphere in the three-dimensional case without modification. For the sake of simplicity, this specification does not distinguish between the two-dimensional "base circle" and the conceptually equivalent sphere in the three-dimensional case, but uniformly uses "base circle" to describe it. Figure 2 As shown, the corresponding appendix is ​​displayed. Figure 1 The base circles generated by the directed distance location; due to the errors introduced by the linear interpolation method in S2, the vast majority of the base circles do not correspond to those generated in S2. The primitives in the image are tangent; attached Figure 2 The arrow in the lower right corner points to a location based on the attached... Figure 1 of The primitives generated by the node with a radius of zero are labeled with a solid origin.

[0034] Traverse each Based on the base circle set constructed in S7 above Its precise location can be calculated using the following local optimization method: a) The parameters to be optimized are The equation of the line in which it lies (in two dimensions) coefficient Or, the plane equation (in the three-dimensional case). coefficient For the sake of simplicity, the two sets of coefficients mentioned above will be referred to together as follows. ; b) The objective function for optimization is: ,in, Indicates the parameters to be optimized The line or plane represented Function representing the base circle From the center of the circle to Euclidean distance, This indicates that weights are being considered. Evaluation under the premise and The function of difference, The specific form of the function can be the difference of absolute values, the square of the difference, or other objective function evaluation forms available in optimization problems. This invention is applicable to various forms. Function; in the base circle set When the radii of all base circles are not zero, The function is a multi-extremum function, when When its maximum or minimum value is obtained, The distance to all base circles is matched to the radius of each base circle to the greatest extent possible; c) Parameters to be optimized The initial value is calculated in S2. The coefficients of the equation of the line or plane in which it lies; during the optimization process, we should... Apply constraints or other equivalent means to ensure that the centers of all base circles with non-zero radii are always located within the zero radius. The same side of the line or plane represented, not because Changes during the optimization process make The line or plane represented is moved to the other side of a base circle with a non-zero radius; d) Under the above definition of the optimization problem, this invention is applicable to a variety of optimization algorithms, such as the Sequential Quadratic Programming (SQP) algorithm; since there are many types of optimization algorithms available, they will not be described in detail here; e) After solving the optimization problem, we obtain the solution that makes the optimization convergent. Find the primitive Calculate the two (or three) grid lines containing the endpoints (or vertices) of this line segment (or triangle). The coordinates of the intersections with these grid lines are based on the base circle set. right Each vertex The position calculation result; since the same vertex may belong to several graphic primitives, the result obtained in this step may differ slightly from the calculation result based on other graphic primitives; in order to obtain a unique calculation result, the corresponding... Each calculation result of the vertex Store in collection At the same time, record the Length or area , used for weighted averages.

[0035] In all After performing the S8 calculation, for each vertex The corresponding set of calculation results The vertex is obtained by taking a weighted average of the coordinates of all points. The required spatial coordinates: The weighted average reflects the view that the goal is to minimize the error of the reconstruction result. The larger the length or area, the more information it provides about the vertices. The more important the spatial coordinate information, the better.

[0036] Based on the above calculations, the values ​​obtained in S2 are... The coordinates of each vertex are modified to the coordinates calculated in S9, but the coordinates calculated in S2 are still retained. The same connection relationship, at this time, after modification The curve or surface represented is the one corresponding to the directed distance field function given in this invention. The zero isosurface (line) reconstruction result; if it is necessary to reconstruct isosurfaces corresponding to other values, then the directed distance field functions of all nodes can be used first. Subtract this value from the value, and then use the above method to reconstruct the isosurface.

[0037] It should be noted that: In this invention, the purpose of step S8 is to find a straight line or plane such that its distance to all base circles matches the radius of each base circle to the greatest extent; the calculation and optimization operation performed in this step has many similar or equivalent forms, such as transforming the optimization problem into other forms through equivalent mathematical transformations of the equations of the straight line or plane; these equivalent or similar ideas should all fall within the protection scope of this invention patent. In the aforementioned S5, other methods besides the listed fast algorithms (AABB tree and Voronoi diagram method) can be used for calculation, as long as the method used can give the location of the nearest point, it will not affect the innovativeness of the present invention.

[0038] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A high-precision method for reconstructing a directional range field model, characterized in that... ,include: S1: The directed distance field function is obtained based on the fixed grid. S2: Based on the fixed grid type and spatial dimension, the initial isosurfaces / lines are reconstructed using linear interpolation, and the isosurfaces / lines that make the directed distance field function zero are marked; S3: Based on the linear interpolation method, the mesh elements that intersect with the isosurface / line are searched, the mesh nodes of the mesh elements are obtained and classified, and the directly adjacent nodes, the set of directly adjacent nodes and the set of non-adjacent nodes are obtained. S4: Based on the isosurface / line graphic primitives, obtain the vertices and vertex coordinates that make up the primitives, and construct the correspondence between primitives and vertices; S5: Calculate the nearest point from the grid nodes in the set of directly adjacent nodes and the set of non-adjacent nodes to the isosurface / line, obtain the set of primitives containing or adjacent to the nearest point, and obtain the set of nearest points; S6: Traverse all primitives, search for all nearest point sets containing the primitives, and obtain the grid nodes corresponding to the nearest point sets; S7: For each element in the set of all nearest points containing the primitive, generate a corresponding base circle information, and construct a base circle set based on the base circle information; S8: Based on the set of base circles, traverse and calculate the precise position of each primitive, and use the parameter optimization method to calculate the set of intersection coordinates; S9: Calculate the weighted average of the coordinates of all points in the pair to obtain the weighted spatial coordinates of the vertex; S10: Reconstructing the zero isosurface / line of the directed distance field function based on weighted spatial coordinates.

2. The high-precision directional distance field model reconstruction method according to claim 1, characterized in that: The grid nodes of the grid cell are obtained and categorized to obtain directly adjacent nodes, a set of directly adjacent nodes, and a set of non-adjacent nodes, including: Determine whether the grid node is directly adjacent to the isosurface / line, wherein the adjacent relationship includes at least one adjacent node whose directed distance field function value is opposite to that of the grid node; When an adjacency relationship is determined, the grid node is treated as an element of the set of directly adjacent nodes, and the spatial coordinates of the grid node are marked. All grid nodes that do not belong to the set of directly adjacent nodes but whose grid cells intersect with isosurfaces / lines are included as elements to form the set of non-adjacent nodes, thus constructing the set of non-adjacent nodes.

3. The high-precision directional distance field model reconstruction method according to claim 2, characterized in that: The graphic primitive contains one or more elements.

4. The high-precision directional distance field model reconstruction method according to claim 3, characterized in that: Iterate through all primitives, search for the set of all nearest points containing the primitive, and obtain the grid nodes corresponding to the set of nearest points, including: Using sets: Record grid nodes, where e i n is an element of the set of directly adjacent nodes. i f is an element of the set of non-adjacent nodes. k As the basic unit, C F (e) i Let C be the set of nearest points to directly adjacent nodes. F (n) i ) is the set of nearest points to non-adjacent nodes.

5. The high-precision directional distance field model reconstruction method according to claim 3, characterized in that: The base circle information includes the coordinates of the base circle center, the base circle radius, and the base circle weight. The base circle can be a circle or a sphere.

6. The high-precision directional distance field model reconstruction method according to claim 4, characterized in that: The process of traversing and calculating the precise position of each primitive based on the set of base circles includes: Obtain the coefficients of the equation of the line or plane containing the primitive element; The objective function for constructing the precise location is as follows: ,in, Parameters to be optimized The line or plane represented The function is the base circle From the center of the circle to Euclidean distance, In order to consider weights Evaluation under the premise and The function of the difference.

7. The high-precision directional distance field model reconstruction method according to claim 6, characterized in that, The method of traversing and calculating the precise position of each primitive based on the set of base circles also includes: A parameter optimization algorithm is used to optimize the center of a base circle with a non-zero radius, and the center of the circle is optimized to be located on the same side of the line or plane represented by the Euclidean distance; Obtain the vertices of the isosurfaces / lines corresponding to the primitives, obtain at least two grid lines containing the vertices, calculate the intersection points and intersection coordinates of the isosurfaces / lines and the grid lines, and obtain the set of intersection coordinates.

8. The high-precision directional distance field model reconstruction method according to claim 7, characterized in that: When the spatial dimension is two-dimensional, the primitives lie on the equation of a straight line.

9. The high-precision directional distance field model reconstruction method according to claim 8, characterized in that: When the spatial dimension is three-dimensional, the primitives lie on the plane equation.

10. The high-precision directional range field model reconstruction method according to claim 9, characterized in that, The parameter optimization algorithm includes a sequential quadratic programming algorithm.

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