High-precision fast tracking method for optical system

Abstract

The application provides a high-precision fast tracing method of an optical system, comprising the following steps: S1, discretely sampling optical and mechanical surfaces respectively by an optical surface height equation and a mechanical element surface NURBS characteristic function to generate an initialized triangular facet grid; S2, spatially dividing the triangular facet grid, constructing a triangular facet enclosing body based on a surface area heuristic spatial tree structure, eliminating non-intersecting facets, and obtaining triangular facets with intersection points; S3, refining the triangular facets with intersection points, obtaining an iterative initial value for numerical solution by calculating the distance d between the intersection points and the corresponding points of the height equation; and S4, constructing a single-variable implicit function characteristic function of the optical surface height equation according to the iterative initial value, and obtaining an accurate solution of the geometric intersection of the light rays by combining a Newton or quasi-Newton iterative method for high-order nonlinear equations. The optical surface height equation is constructed into a single-variable implicit function characteristic function, and fast and high-precision tracing is achieved.

Description

Technical Field

[0001] This invention relates to the field of non-sequential ray tracing technology, and in particular to a high-precision and fast ray tracing method for optical systems. Background Technology

[0002] In the field of computer geometry and graphics, triangular elements are widely used in graphics rendering. With the improvement of computer hardware configuration, the problem of excessive computer physical memory occupied by a large number of triangular elements is no longer a problem. However, due to their planar characteristics, for high-precision tracing, especially high-precision tracing in the optical field, it is difficult to meet the tracing accuracy requirements of the optical field by relying solely on triangular elements.

[0003] Implicit functions, due to their simple equations and the ability to easily determine whether any point in space lies on the positive or negative side (inside or outside) of an algebraic surface, are a very robust and fast method for representing geometric surfaces without considering computer-aided geometric design, and also conform to fast ray tracing.

[0004] For optical software analysis processes that primarily rely on non-sequential ray tracing, which require large-scale ray tracing, non-sequential, high-precision, and high-efficiency solutions, combining triangular elements and implicit function techniques for interactive ray and geometry solving will be crucial for addressing the issues of interactive accuracy and efficiency. Summary of the Invention

[0005] In view of the above problems, the purpose of this invention is to propose a high-precision and fast tracking method for optical systems. To address the interaction speed issue between optomechanical surfaces and light rays in existing optical systems while ensuring high precision, this invention utilizes the elevation equations of optical elements and the NURBS characterization of mechanical elements. By combining spatial segmentation, triangular element subdivision, and intersection techniques, good initial values ​​for iteration are obtained at a suitable accuracy level. Furthermore, by constructing the elevation equations of the optical surface shape as univariate implicit functions and combining them with Newton's or quasi-Newton's methods, fast and high-precision tracking is achieved.

[0006] To achieve the above objectives, the present invention adopts the following specific technical solution:

[0007] This invention provides a high-precision and fast tracking method for an optical system, comprising the following steps:

[0008] S1. Discretely sample the optical and mechanical surfaces respectively using the optical surface elevation equation and the NURBS characterization function of the mechanical component surface to generate an initialized triangular surface element mesh;

[0009] S2. Spatial segmentation of the triangular mesh is performed. A spatial tree structure based on surface area heuristic is used to construct the bounding volume of the triangular mesh. Non-intersecting elements are removed to obtain triangular elements with intersections.

[0010] S3. Refine the triangular facets with intersection points by calculating the distance between the intersection points and the corresponding points in the sag equation. Finally, the initial values ​​for the numerical solution are obtained;

[0011] S4. Construct a single-variable implicit function characterization function for the optical surface elevation equation based on the initial iteration value. For higher-order nonlinear equations, combine Newton's or quasi-Newton's iterative method to obtain the exact solution of the intersection of light rays and geometry.

[0012] Preferably, in step S1:

[0013] For optical surfaces, based on the outline dimensions of the optomechanical model and the accuracy requirements of different surfaces, the optical elevation equation is used to perform equally spaced sampling in the x and y directions, and the sampling points are generated by substituting them into the elevation equation.

[0014] Preferably, in step S1:

[0015] For mechanical surfaces, based on NURBS characterization, equal-interval sampling is performed on the UV parameter axes, and then mapped to the NURBS surface to generate spatial three-dimensional sampling points.

[0016] Connect adjacent points between the three-dimensional sampling points in space in sequence to generate an initial triangular mesh.

[0017] Preferably, in step S2:

[0018] A spatial tree structure based on surface area is used to construct the bounding volume of triangular facets, generating a binary tree structure of the bounding volume. The maximum number of triangular facets in a child node is set. Based on the ray vector, geometry that deviates from the ray vector and is located behind the ray origin is excluded to form a non-tracing region.

[0019] By connecting the origin of the ray and the maximum outer envelope of the geometric body, the maximum tracking interval angle is formed. θ The area within the interval angle is the tracking region, and light rays located outside the interval angle are excluded.

[0020] Preferably, in step S3:

[0021] Refine the triangular facets with intersection points;

[0022] The coordinates of the three vertices of the triangular element are respectively , , ,

[0023] Select the midpoints of each side of the original triangular element, divide the triangular element into four parts, and generate the coordinates of the new vertices as follows: , , This generates four small triangular face elements;

[0024] The four small triangular facets are numbered sequentially, and intersection tests are performed on each of the four facets. The distance between the intersection point and the corresponding point in the sag equation is calculated. :

[0025] ;

[0026] in, The difference is the coordinate.

[0027] Based on the set accuracy requirements and distance By comparing the results, we can determine whether to continue recursively subdividing the triangular facets, and finally obtain the initial values ​​for numerical solution.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0029] This invention proposes a high-precision and fast tracking method for optical systems based on implicit function algebraic representation of surfaces, combining triangular facets and implicit functions. Discrete triangular facets are constructed using the optical surface elevation equation and the NURBS representation function of the mechanical component surface. A two-stage acceleration structure is combined with an efficient processing strategy and scheme for refining the triangular facets, resulting in good initial values ​​for iteration while improving interaction efficiency. Drawing on the fast solution characteristics of implicit function algebra, the multivariate implicit function is constructed as a single variable, accelerating the solution. The exact solution for the intersection of light rays and geometry is obtained by combining Newton's or quasi-Newton's iterative methods. Attached Figure Description

[0030] Figure 1 This is a flowchart illustrating a high-precision, fast tracking method for an optical system provided according to an embodiment of the present invention.

[0031] Figure 2 This is a flowchart of a high-precision and fast tracking method for an optical system provided according to an embodiment of the present invention.

[0032] Figure 3 This is a schematic diagram of a method for quickly eliminating non-intersecting triangular facets according to an embodiment of the present invention.

[0033] Figure 4 This is a schematic diagram of triangular surface subdivision provided according to an embodiment of the present invention. Detailed Implementation

[0034] In the following description, embodiments of the invention will be described with reference to the accompanying drawings. In the description below, the same modules are denoted by the same reference numerals. Where the same reference numerals are used, their names and functions are also the same. Therefore, their detailed description will not be repeated.

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0036] Figure 1 A flowchart illustrating a high-precision, fast tracking method for an optical system according to an embodiment of the present invention is shown.

[0037] Figure 2 A flowchart of a high-precision, fast tracking method for an optical system provided according to an embodiment of the present invention is shown.

[0038] like Figures 1-2 As shown, the high-precision and fast tracking method for optical systems provided in this embodiment of the invention includes the following steps:

[0039] S1. Discretely sample the optical and mechanical surfaces respectively using the optical surface elevation equation and the NURBS characterization function of the mechanical component surface to generate an initialized triangular surface element mesh.

[0040] First, the optical and mechanical surfaces are discretized separately using the optical surface elevation equation and the NURBS characterization function of the mechanical component surface:

[0041] For optical surfaces, based on the outline dimensions of the optomechanical model and the accuracy requirements of different surfaces, the optical surface is sampled at equal intervals in the x and y directions using the optical height equation. These samples are then substituted into the height equation to generate three-dimensional sampling points.

[0042] For mechanical surfaces, based on their NURBS characterization, equally spaced samples are taken on the UV parameter axes and then mapped onto the NURBS surface to generate spatial three-dimensional sampling points.

[0043] Connect adjacent points sequentially, record and generate an initialized triangular mesh.

[0044] S2. Spatial segmentation of the triangular mesh is performed. A spatial tree structure based on surface area is used to construct the bounding volume of the triangular mesh. Non-intersecting meshes are removed to obtain triangular meshes with intersections.

[0045] Figure 3 A schematic diagram of a method for quickly eliminating non-intersecting triangular elements according to an embodiment of the present invention is shown.

[0046] like Figure 3 As shown, this invention uses a surface area-heuristic spatial tree structure to construct the bounding volume of triangular facets, generating a bounding volume binary tree structure, and setting the maximum number of triangular facets within a child node, for example, setting the maximum number of triangular facets within a child node. NIf the value is 1, then based on the ray vector, quickly eliminate geometric objects that deviate from the ray vector and are located behind the ray origin, forming a non-tracking region.

[0047] Based on the ray vector, quickly eliminate geometric objects that deviate from the ray vector and are located behind the origin of the ray. By connecting the origin of the ray and the maximum outer envelope of the geometric objects, the maximum tracking interval angle is formed. θ The area within the interval angle is the tracking region. Light rays located outside the interval angle are removed. In this intersection calculation, these light rays will no longer participate in the fast elimination of non-intersecting triangular elements.

[0048] S3. Refine the triangular facets with intersection points by calculating the distance between the intersection points and the corresponding points in the sag equation. Finally, we obtain the initial values ​​for the numerical solution.

[0049] Figure 4 A schematic diagram of triangular facet subdivision provided according to an embodiment of the present invention is shown.

[0050] like Figure 4 As shown, the triangular facets with intersection points in the intersection test are refined, such as the coordinates of the three vertices of the triangle being... , , Select the midpoints of each side of the original triangular element, divide the triangular element into four parts, and generate the coordinates of the newly generated vertices as follows: , , Four small triangular facets are generated, and each triangle is sequentially numbered. Intersection tests are performed on the four triangular facets, and the distance between the intersection point and the corresponding point in the sag equation is calculated. ( , (This is the difference in coordinates), and the required precision must be set accordingly. By comparing the results, we can determine whether to recursively subdivide the triangular facets and finally obtain good initial values ​​for numerical solutions.

[0051] S4. Construct a single-variable implicit function characterization function for the optical surface elevation equation based on the initial iteration value. For higher-order nonlinear equations, combine Newton's or quasi-Newton's iterative method to obtain the exact solution of the intersection of light rays and geometry.

[0052] Based on the initial values, the ray equation is substituted into the optical surface elevation equation to generate a value related to the distance. t The algebraic expression of the univariate implicit function is obtained. For higher-order nonlinear equations, the exact solution of the intersection of light rays and geometry is obtained by combining Newton's or quasi-Newton's iterative method.

[0053] 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 changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

[0054] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A high-precision and fast tracking method for an optical system, characterized in that, Includes the following steps: S1. Discretely sample the optical and mechanical surfaces respectively using the optical surface elevation equation and the NURBS characterization function of the mechanical component surface to generate an initialized triangular surface element mesh; S2. Spatial segmentation of the triangular facet mesh, construction of the triangular facet bounding volume using a spatial tree structure based on surface area heuristic, elimination of non-intersecting facets, and obtaining triangular facets with intersections. In step S2: A spatial tree structure based on surface area is used to construct the bounding volume of triangular facets, generating a binary tree structure of the bounding volume. The maximum number of triangular facets in a child node is set. Based on the ray vector, geometry that deviates from the ray vector and is located behind the ray origin is excluded to form a non-tracing region. By connecting the origin of the ray and the maximum outer envelope of the geometric body, the maximum tracking interval angle is formed. θ The area within the interval angle is the tracking region, and light rays located outside the interval angle are excluded; S3. Refine the triangular facets with intersection points by calculating the distance between the intersection points and the corresponding points in the sag equation. Finally, the initial values ​​for the numerical solution are obtained; In step S3: The triangular facets with intersection points are refined; The coordinates of the three vertices of the triangular element are respectively , , , Select the midpoints of each side of the original triangular element, divide the triangular element into four parts, and generate the coordinates of the new vertices as follows: , , This generates four small triangular face elements; The four small triangular facets are numbered sequentially, and intersection tests are performed on each of the four facets. The distance between the intersection point and the corresponding point in the sag equation is calculated. : ； in, The difference is the coordinate. Based on the set accuracy requirements and the distance By comparing the results, we can determine whether to continue recursively subdividing the triangular facets and finally obtain the initial values ​​for numerical solution. S4. Construct a single-variable implicit function characterization function for the optical surface elevation equation based on the initial iteration value. For higher-order nonlinear equations, use Newton's or quasi-Newton's iterative method to obtain the exact solution for the intersection of light rays and geometry.

2. The high-precision and fast tracking method for an optical system according to claim 1, characterized in that, In step S1: For the optical surface shape, based on the outline size of the optomechanical model and the accuracy requirements of different surface shapes, the optical elevation equation is used to perform equal-interval sampling in the x and y directions, and the samples are substituted into the elevation equation to generate three-dimensional sampling points in space.

3. The high-precision and fast tracking method for an optical system according to claim 2, characterized in that, In step S1: For the mechanical surface, based on the NURBS characterization, equal-interval sampling is performed on the UV parameter axis, and then mapped to the NURBS surface to generate spatial three-dimensional sampling points. The initial triangular mesh is generated by sequentially connecting adjacent points between the three-dimensional sampling points in space.

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