Optical surface construction method based on B-splines

Abstract

This application relates to the automotive field, particularly to the field of vehicle lighting device manufacturing, and specifically to a method for creating an optical surface based on B-splines. The method includes the steps of: determining surface basis functions and initial control points according to the coordinates of the control points of the output surface after incident light is refracted or reflected by an output surface and reaches a target light distribution surface; determining the coordinates of key points on the output surface according to the values ​​of u and v in the B-spline curve definition equation and the coordinates of the control points on the output surface; generating a parameter matrix of the surface key points according to the coordinates of the key points on the output surface; and performing a matrix inversion operation on the parameter matrix of the key points to determine the coordinates of the surface control points and constructing an optical surface using the coordinates of the surface control points. The beneficial effects of the present invention are that the calculation process for the optical freeform surface is simplified, and the freeform surface control points are directly determined, and the generated freeform surface is expressed using a B-spline function, thereby reducing the amount of process data, saving computer memory, improving calculation efficiency, and significantly reducing calculation time.

Description

[Technical Field]

[0001] The present application relates to the automotive field, in particular to the field of vehicle lighting device manufacturing, and more particularly to a method for creating optical surfaces based on B-splines. [Background technology]

[0002] Vehicle lighting components are important functional components of automobiles, and many curved surfaces are provided on the vehicle lighting components to fit the vehicle type, expand the lighting range, and improve the aesthetic appeal.

[0003] The curvature of a curved surface needs to be calculated precisely during the design process. In the design method for a free-form lens for inclined surface illumination in the patent with publication number CN109116555B, the curved surface is calculated using the MA (Monge-Ampere) method, and the specific steps include step (1) of setting the initial structure of the free-form surface, step (2) of formulating a coordinate relationship equation from the light source to the target point, step (3) of formulating an energy transfer equation based on local energy conservation, step (4) of formulating a boundary condition equation, step (5) of obtaining discrete data points of the free-form surface, and step (6) of fitting the discrete points to obtain a curved surface and obtaining an entity from the curved surface.

[0004] In the above-mentioned curved surface solving method, it is necessary to obtain discrete data points on the optical curved surface and then fit the discrete points to form the curved surface. In this solving method, it is not possible to directly obtain a mathematical formula representing the curved surface. In addition, a large number of discrete data points are required to accurately fit the curved surface, which results in a very large amount of calculation and slows down the solution process. Summary of the Invention [Problem to be solved by the invention]

[0005] The technical problem that the present invention aims to solve is that the amount of surface calculation required in the conventional means is very large, the calculation process is complicated, and the calculation speed is slow. [Means for solving the problem]

[0006] In view of the above, the present invention provides a method for creating optical surfaces based on B-splines.

[0007] The technical means adopted by the present invention to solve the technical problem are: Step 1: the incident light is refracted or reflected by the light output surface and then reaches the target light distribution surface, and the surface basis function and the initial control point are determined according to the coordinates of the control points of the light output surface; Step 2: determining the coordinates of the key points on the light-emitting surface based on the u and v values ​​in the B-spline curve definition formula and the coordinates of the control points on the light-emitting surface; Step 3: generating a parameter matrix of curved surface keypoints according to the coordinates of the light-emitting surface keypoints; and step 4 of calculating the coordinates of the surface control points by performing a matrix inversion operation on the parameter matrix of the key points, and constructing the optical surface using the coordinates of the surface control points.

[0008] By adopting the above technical means, the calculation process of the optical free-form surface is simplified by representing the surface with a B-spline function, skipping the coordinates of the surface points and directly determining the control points of the free-form surface, and the generated free-form surface is represented by a B-spline function, thereby reducing the amount of process data, saving computer memory, improving calculation efficiency, and significantly reducing calculation time.

[0009] Furthermore, in step 1, the incident light is parallel light, the energy distribution of the output light forms a regular target light distribution surface, the incident surfaces formed by the incident light are parallel to the output surface and spaced apart by d, and the multiple incident surface control points arranged in a rectangular array on the incident surface and the multiple output surface control points arranged in a rectangular array on the output surface are obtained by moving parallel to each other.

[0010] Furthermore, in step 1, the incident light is diverging light, the energy distribution of the output light forms a regular target light distribution surface, a plurality of output surface control points arranged in a rectangular array are set on the output surface, the x and y coordinates of the output surface control points are known, the coordinates of the incident light source are (x7, y7, z7), the initial surface of the output surface is a conical surface, and the z coordinate of the output surface control points can be calculated using a least squares fitting method according to the conical surface formula.

[0011] Furthermore, the x and y coordinates of the light output surface key points are the same as the corresponding light output surface control points.

[0012] Furthermore, the incident light is refracted by the light output surface and then reaches the target point position, and in step 2, a mapping relationship between the light output surface and the target light distribution surface is established to determine the coordinates of the target point.

[0013] Furthermore, the light output surface control points are uniformly distributed within the light output surface.

[0014] Furthermore, the light output surface key points are uniformly distributed in the UV plane, and the number of the light output surface key points corresponds to the number of light output surface control points.

[0015] Furthermore, in step 3, a keypoint parameter matrix is ​​obtained according to the central coordinates of the incident surface and the central coordinates of the light exit surface.

[0016] Furthermore, the direction vector of the incident light, the expression of the incident surface, the refractive index of the medium between the incident surface and the exit surface, and the coordinates of the key points on the exit surface {P 42,i,j}, and by combining with Fermat's principle, the incident vector {n in,i,j}, and the coordinates of the light output surface key points {P 42,i,j} and the coordinates of the target point on the light output surface {P 62,i,j =(x 42,i,j ,y 42,i,j ,z 42,i,j )}, the exit vector {n out,i,j =P 62,i,j -P 42,i,j} is calculated, and the normal vector of the light output surface keypoint is calculated based on the incident vector of the light output surface keypoint, the exit vector of the light output surface keypoint, and the refractive index of the medium in conjunction with the law of refraction.

[0017] Furthermore, the center z coordinate of the incident surface

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[0018] The beneficial effects of the present invention are that the use of B-spline functions in the invention simplifies the calculation process for optical free-form surfaces, skipping the coordinates of the surface points and directly determining the control points of the free-form surface, and expressing the generated free-form surface using B-spline functions reduces the amount of data required in the process, saves computer memory, improves calculation efficiency, and significantly reduces calculation time. In addition, the use of normal vectors instead of surface tangent vectors and reducing the surface characteristic function from a quadratic function to a linear function simplifies the parameter matrix and reduces the amount of calculation. In addition, the format of the generated free-form surface is versatile, and the data is simplified so that it can be directly used in subsequent processes such as data merging and extraction.

[0019] The invention will now be further described with reference to the figures and examples. [Brief explanation of the drawings]

[0020] [Figure 1] 1 is a flowchart of an algorithm of the present invention. [Figure 2] FIG. 2 is a diagram showing the optical path of incident light in Example 1 of the present invention. [Figure 3] 3 is a schematic diagram of control points of the initializing light-emitting surface in Example 1 of the present invention. FIG. [Figure 4] 3 is a schematic diagram of a mapping relationship between a light output surface and a target light distribution surface in the first embodiment of the present invention. FIG. [Figure 5] 3A to 3C are schematic diagrams of the curved surface shape and control points of the light output surface before and after solving the solution in the first embodiment of the present invention. [Figure 6] 10 is a distribution comparison diagram of a light shape corresponding to the curved surface shape of the light output surface before and after the solution is obtained in Example 1 of the present invention. FIG. [Figure 7] FIG. 10 is a diagram showing the optical path of incident light in Example 2 of the present invention. [Figure 8] FIG. 10 is a schematic diagram of the distribution of control points on the initialized light-emitting surface in Example 2 of the present invention. [Figure 9] FIG. 10 is a schematic diagram of a mapping relationship between a light output surface and a target light distribution surface in Example 2 of the present invention. [Figure 10] 10A and 10B are schematic diagrams of the curved surface shape and control points of the light output surface before and after solving in Example 2 of the present invention. [Figure 11] FIG. 10 is a distribution comparison diagram of a light shape corresponding to the curved surface shape of the light output surface before and after solving in Example 2 of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0021] Next, the present invention will be described in more detail with reference to Figures 1 to 6. These figures are all simplified schematic diagrams, and only show the configurations relevant to the present invention, as they merely serve to explain the basic structure of the present invention.

[0022] In the description of the present invention, orientations and positional relationships indicated by technical terms such as "center," "thickness," "upper," "lower," "front," and "rear" are orientations and positional relationships based on the drawings and are intended merely to facilitate and simplify the description of the present invention. It should be understood that these terms do not expressly or imply that the described devices or elements necessarily have a specific orientation, are configured, or operate in a specific orientation, and should not be construed as limiting the present invention. Furthermore, features defined by "first" or "second" can expressly or imply that the feature includes one or more of the feature. In the description of the present invention, unless otherwise specified, "plurality" means two or more than two. Those skilled in the art can understand the specific meanings of the above technical terms in the present invention according to the specific circumstances.

[0023] Referring to FIG. 1, the optical surface creation method based on B-spline includes the following steps: The curved surface is initialized, and the incident light is refracted or reflected by the exit surface before reaching the target light distribution surface. In this step, the curved surface basis functions and initial control points can be obtained by a method in which the exit surface is found by the incident light passing through the refracting surface, or the curved surface basis functions and initial control points can be obtained by a method in which the entrance surface is found using the exit surface. Set the coordinates of the surface keypoints and target points. Generate a parameter matrix for the surface keypoints. Calculate the coordinates of the surface control points.

[0024] The B-spline function is a surface representation standard in the field of computer-aided design (CAD). The definition of the p-th order B-spline curve applied in this embodiment is as follows:

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[0025] In the present invention, B-splines have several properties: (1) When u and v are determined, the basis functions are real numbers, and the surface point coordinates S(u,v) are the coordinates of the control point P i,j and may be written as a matrix. S(u,v)=N(u,v) P T (1) where N is the basis function coefficient matrix, the number of rows is 1, and the number of columns is m×n, and is written as follows: N=[N 0,p (u)N 0,q (v) N n,p (u)N 0,q (v)N 0,p (u)N 1,q (v) N n,p (u)N m,q (v)] where P T is the transpose of the control point matrix P, where the number of rows of P is 1 and the number of columns is m×n, and is written as follows: P=[P 0,0 ···P n,0 P0,1 ···P n,m ] (2) When u and v are determined, the first partial derivative of the p-th order basis function with respect to u is

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[0026] As mentioned above, a B-spline surface has degree p, degree q, knot vector U, knot vector V, and control points {P i,j}, among which the control points {P i,j} can be determined at the time of surface initialization. i,j}x and y coordinates in the coordinate system i,j} and {y i,j} can also be determined at the time of initialization. Therefore, to obtain a B-spline optical surface, the z coordinate of the control point z = {z i,j As can be seen from equations 1, 2, and 3, the coordinate z of the B-spline surface point P(u,v) and the z component of the tangent vector are all P T Once the UV coordinates of P(u,v) are determined, Equation 1 is T When the normal vector n(u,v) is determined, Equation 4 and Equation 5 are T is a linear function of Example 1

[0027] Referring to the attached Figs. 2-6, in accordance with the above formulas, this embodiment obtains an optical B-spline surface by a method for obtaining a refracting surface and an exiting surface according to incident light.

[0028] In connection with FIG. 2, the incident light 1 is a given parallel light parallel to the z-axis, the energy distribution of the exit light 5 is a target light distribution surface 6 (for example, a rectangular distribution), and the refractive index of the medium 3 between the incident surface 2 and the exit surface 4 is n med and the entrance surface 2 is a given B-spline surface, the steps to obtain the exit surface 4 are as follows:

[0029] Step 1: Initialize the surface, i.e., determine the surface basis functions and initial control points.

[0030] 2 and 3, a curved surface with a smooth shape and no excessive twists can be expressed using a cubic to quintic B-spline. If the plane on which the light exit surface 4 exists is the XY plane, and the incident surface 2 is a B-spline surface with all directions being cubic, the incident surface 2 will have 4 × 4 = 16 control points. If the incident surface control points 21 of the incident surface 2 are uniformly distributed in the XY plane and the initial z-direction distance between the incident surface 2 and the light exit surface 4 is 2 mm, then the initialized light exit surface 4 will have 16 light exit surface control points 41 also uniformly distributed in the XY plane, as shown in FIG. 3. The XY coordinates of the light exit surface control points 41 are the same as those of the incident surface control points 21, and the initial z-coordinates of the light exit surface control points 41 are the z-coordinates of the incident surface control points 21 plus 2 mm, thereby obtaining the initial control points for the light exit surface 4. x 410,i,j =x 21,i,j y 410,i,j =y 21,i,j z 410,i,j =z 21,i,j +2mm

[0031] Step 2: Set the coordinates of the surface keypoints and target points.

[0032] 3 and 4, in this step, the light output surface key points 42 are points located on the surface of the light output surface 4, and are determined from the UV values ​​and the coordinates of the light output surface control points 41. The light output surface key points 42 serve two purposes: they can control the local position of the light output surface 4 by adjusting the z coordinate of the light output surface key points 42, and they can control the local light output direction of the light output surface 4 by adjusting the normal vector of the light output surface 4 at the light output surface key points 42. One method for setting the light output surface key points 42 is to distribute them uniformly within the UV plane and make the number equal to the number of control points. For example, if the u and v values ​​of the light output surface key points 42 are all set to {0, 1 / 3, 2 / 3, 1}, there will be a total of 4 × 4 = 16 key points, and the control points will be uniformly distributed within the XY plane, so the x and y coordinates of the light output surface key points 42 will be the same as the corresponding light output surface control points 41, i.e., x 42,i,j =x 21,i,j y42,i,j =y 21,i,j is.

[0033] The incident light 1 completes the first reflection at the key points 42 on the surface of the light output surface 4 and reaches the target points 62. In order to make the energy distribution of the output light 5 more consistent with the target light distribution surface 6, a mapping relationship is established between the light output surface 4 and the target light distribution surface 6, as shown in FIG. 4. This mapping relationship is not unique, and the present invention proposes one of them, that is, according to the principle of edge-to-edge, center-to-center, the light output surface key points 42 are uniformly distributed on the light output surface 4, so that the target points 62 are also uniformly distributed on the target light distribution surface 6. The rectangular target light distribution surface 6 is uniformly divided into 3×3=9 parts, and the vertices of each part are 4×4=16 in total, which are the target points 62. Therefore, the coordinates of the target points 62 {(x 6,i,j ,y 6,i,j ,z 6,i,j )} can be determined.

[0034] Step 3: Construct a parameter matrix of surface keypoints.

[0035] 3 and 4, the final coordinates of the light output surface control point 41 are {(x 411,i,j ,y 411,i,j ,z 411,i,j )}, x 411,i,j =x 410,i,j y 411,i,j =y 410,i,j and z 411 =[z 411,i,j ] can control the z-direction position and surface normal vector of the light exit surface 4. In this example, the direction vector of incident light 1 is (0,0,1), and incident light 1 completes the first refraction at incident surface 2 to reach key point 42 on the light exit surface, and then completes the second refraction at key point 42 on the light exit surface. The direction vector of incident light 1, the expression of incident surface 2, and the refractive index n of medium 3 are med and the coordinates of the light output surface key point 42 {P 42,i,j =(x 42,i,j ,y 42,i,j ,z 42,i,j)}, and by combining with Fermat's principle, the incident vector {n in,i,j The coordinates of the light output surface key point 42 {P 42,i,j} and the coordinates of target point 62 {P 62,i,j =(x 62,i,j ,y 62,i,j ,z 62,i,j )}, the exit vector {n out,i,j =P 62,i,j -P 42,i,j} can be obtained. in,i,j}, the emission vector {n out,i,j}, refractive index n of medium 3 med By combining with the law of refraction, the normal vector {n 42,i,j =(x n42,i,j ,y n42,i,j ,z n42,i,j )} can be obtained, and when substituted into formula (4),

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[0036] For the same reason, from equation (5)

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[0037] Equation (6) and equation (7) constrain the surface normal vector of the light-emitting surface 4, but do not constrain the z-direction position of the light-emitting surface 4. Since the incident surface control points 21 are uniformly distributed on the incident surface 2, the values ​​of u and v in the UV function are in the range of 0-1. Thus, the values ​​of u and v are set to 1 / 2. According to equation (1), the center z-coordinate of the incident surface 2 is a constant.

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[0038] All of the above equations (6) to (8) are

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[0039] Matrix A and matrix B are keypoint parameter matrices, where matrix A is a constant matrix with 33 rows and 16 columns, and is constructed as follows:

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[0040] Step 4: The coordinates of the surface control points are calculated by matrix inversion.

[0041] matrix A -1 is the inverse of matrix A,

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[0042] The curved surface shape and control points of output surface 4 before and after solution are shown in Figure 5. As can be seen from the figure, curved surface shape 400 of output surface 4 before solution is a parallel translation surface of incident surface 2 and has the same flat surface as incident surface 2, while curved surface shape 401 of output surface 4 after solution is a concave surface with a recessed center and protruding edges. Output surface control points 411 of output surface 4 after solution, which correspond to curved surface shape 401 of output surface 4 after solution, are significantly different from output surface control points 410 of output surface 4 before solution, which correspond to curved surface shape 400 of output surface 4 before solution. The simulation comparison results are shown in Figure 6. Example 2

[0043] This embodiment differs from the first embodiment in that the light output surface 4 is known in step 1, and the curved surface basis functions and initial control points are obtained by a method of determining the incident light 1 and incident surface 2 using the light output surface 4.

[0044] The coordinates of the light output surface control point 41 {(x 410,i,j ,y 410,i,j ,z 410,i,j )} is known, the light output surface control points 41 are uniformly distributed in the XY plane, and the light input surface control points 21 are (x 21,i,j ,y 21,i,j ,z 21,i,j )} where: x 21,i,j =x410,i,j y 21,i,j =y 410,i,j z 21,i,j =z 410,i,j -2mm. Example 3

[0045] 7-11, this embodiment differs from the first embodiment in that an optical B-spline surface is obtained by determining the reflecting surface of the light source and the light exit surface after reflection.

[0046] As shown in FIG. 7, this embodiment differs from the first embodiment in that the incident light 1 is a point light source 7 and the light emitted from the point light source 7 is divergent light. When the point light source 7 is divergent light and the energy distribution of the emitted light 5 is a given light distribution 6 (a rectangular distribution shown in FIG. 7), the steps for determining the light exit surface 4 are as follows:

[0047] Step 1: Initialize the surface, i.e., determine the surface basis functions and initial control points.

[0048] A cubic to quintic B-spline can accurately and efficiently represent a curved surface that is smooth and not excessively twisted. If the light-emitting surface 4 is a B-spline surface in which the UV direction is all cubic, the light-emitting surface 4 has 4 x 4 = 16 control points. As shown in Figure 8, the light-emitting surface 4 is represented by 16 control points 41 {(x 410,i,j ,y 410,i,j ,z 410,i,j )}, the x and y coordinates of the light output surface control point 41 are given values. The coordinates of the point light source 7 are (x7, y7, z7), and the initial surface of the light output surface 4 is a conical surface. Depending on the distance to the target to which the light source is to be projected after being reflected by the light output surface 4, the light output surface 4 may be a paraboloid, an ellipsoid, or a hyperboloid, where the distance to which the light source is to be projected after being reflected by the paraboloid is far, and the distance to which the light source is to be projected after being reflected by the ellipsoid is close. In this embodiment, the light output surface 4 is a paraboloid with a focal length of f mm, and the following paraboloid equation is satisfied: z=((x-x7) 2 +(y-y7) 2 ) / 4f+z7-f, The z coordinate of the light output surface control point 41 can be determined using a least squares fitting method.

[0049] Step 2: Set the coordinates of the surface keypoints and target points.

[0050] In this embodiment, the method of setting the light output surface key points 42 and the target points 62 is the same as in the first embodiment, so a detailed description is omitted here. There are a total of 16 key points, and their coordinates are expressed as {P 42,i,j}={(x 42,i,j ,y 42,i,j ,z 42,i,j )} and satisfy the following equation. x 42,i,j =x 410,i,j y 42,i,j =y 410,i,j z 42,i,j =((x 42,i,j -x7) 2 +(y 42,i,j -y7) 2 ) / 4f+z7-f

[0051] The mapping relationship between the light output surface 4 and the light distribution 6 is as shown in FIG. 9. The coordinates of the target point 62 are {(x 6,i,j ,y 6,i,j ,z 6,i,j )}.

[0052] Step 3: Construct a parameter matrix of surface keypoints.

[0053] The final coordinates of the light output surface control point 41 are {(x 411,i,j ,y 411,i,j ,z 411,i,j )}, x 411,i,j =x 410,i,j y 411,i,j =y 410,i,j and z 411 =[z 411,i,j] can control the z-direction position and surface normal vector of the light-emitting surface 4. In this example, the starting point of the incident light 1 is the point light source 7, and the incident light 1 completes the first reflection at the key point 42 on the light-emitting surface and reaches the target point 62. The coordinates (x7, y7, z7) of the point light source 7 and the initial value {P 42,i,j}, the incident vector {n in,i,j} can be approximately calculated, and the coordinates {P 42,i,j} and the coordinates of target point 62 {P 62,i,j}={(x 6,i,j ,y 6,i,j ,z 6,i,j )}, the exit vector {n out,i,j =P 62,i,j -P 42,i,j} can be obtained. in,i,j} and the emission vector {n out,i,j}, in conjunction with the law of reflection, the normal vector {n 42,i,j}=(x n42,i,j ,y n42,i,j ,z n42,i,j )} can be obtained. The following part is the same as in the first embodiment, and detailed explanation will be omitted here.

[0054] Step 4: The coordinates of the surface control points are calculated by matrix inversion.

[0055] matrix A -1 is the inverse of matrix A,

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[0056] The curved surface shape of the light-emitting surface 4 before and after the solution is obtained is shown in FIG. 10, and the simulation comparison results are shown in FIG.

[0057] In summary, the present invention simplifies the calculation process for optical free-form surfaces, skipping the coordinates of the surface points and directly determining the control points of the free-form surface. The generated free-form surface is then expressed using a B-spline function, thereby reducing the amount of data required, saving computer memory, improving calculation efficiency, and significantly shortening calculation time. This calculation method uses normal vectors instead of surface tangent vectors, and reduces the surface characteristic function from a quadratic function to a linear function, simplifying the parameter matrix and reducing the amount of calculation. Furthermore, the format of the free-form surface generated during the calculation process is versatile, simplifying the data so that it can be directly used in subsequent data fusion, segmentation, and other processes.

[0058] The above preferred embodiments of the present invention are given as examples, and it is understood that those skilled in the art may make various changes and modifications based on the above description without departing from the technical concept of the present invention. The technical scope of the present invention is not limited to the content of the specification, but should be determined by the claims. [Explanation of symbols]

[0059] 1 Incident light 2 Incidence plane 21 Incident plane control points 3 Refractive Media 4 Idemitsu surface 41 Light output surface control point 42 Key points of the light surface 5. Emitted light 6 Target light distribution surface 62 target point 400 Curved surface shape of the light exit surface before solving 401 Curved surface shape of the light-emitting surface after solution 410 Control points of the exit surface before solving 411 Control points of the exit surface after solution 7 point light source

Claims

1. Step 1: An incident light (1) is refracted or reflected by a light output surface (4) and reaches a target light distribution surface (6), and a surface basis function and an initial control point are determined according to the coordinates of the light output surface control points (41); Step 2: determining the coordinates of the exit surface key points (42) based on the u and v values ​​in the B-spline curve definition formula and the coordinates of the exit surface control points (41); Step 3: generating a parameter matrix of curved surface keypoints according to the coordinates of the light-emitting surface keypoints (42); and (4) determining the coordinates of the surface control points by performing a matrix inversion operation on the parameter matrix of the key points, and constructing an optical surface using the coordinates of the surface control points.

2. 2. The optical curved surface creation method based on B-splines according to claim 1, wherein in step 1, the incident light (1) is parallel light, the energy distribution of the output light (5) forms a regular target light distribution surface (6), the incident surface (2) formed by the incident light (1) is parallel to the output surface (4) at a distance d, and the plurality of incident surface control points (21) arranged in a rectangular array on the incident surface (2) and the plurality of output surface control points (41) arranged in a rectangular array on the output surface (4) are obtained by moving parallel to each other.

3. In step 1, the incident light (1) is divergent light, the energy distribution of the output light (5) forms a regular target light distribution surface (6), a plurality of output surface control points (41) arranged in a rectangular array are provided on the output surface (4), the x and y coordinates of the output surface control points (41) are known, and the coordinates of the light source of the incident light (1) are (x ７ , y ７ , z ７ ) and the initial surface of the light output surface (4) is a conical surface, and the z coordinate of the light output surface control point (41) can be calculated by a least squares fitting method using a conical surface formula.

4. 4. The optical surface creation method based on B-splines according to claim 2 or 3, wherein the x and y coordinates of the output surface key points (42) are the same as those of the corresponding output surface control points (41).

5. 4. The optical surface construction method based on B-splines as claimed in claim 3, wherein the x and y coordinates of the output surface key points (42) are the same as those of the corresponding output surface control points (41).

6. 4. The optical surface creation method based on B-splines according to claim 3, wherein the incident light (1) is refracted by the light output surface (4) before reaching the position of the target point (62), and in step 2, a mapping relationship between the light output surface (4) and the target light distribution surface (6) is established to determine the coordinate of the target point (62).

7. The optical surface creation method based on B-splines according to any one of claims 1 to 6, characterized in that the light output surface control points (41) are uniformly distributed within the light output surface (4).

8. 8. The optical surface creation method based on B-splines according to claim 7, wherein the light output surface key points (42) are uniformly distributed in the UV plane, and the number of the light output surface key points (42) corresponds to the number of light output surface control points (41).

9. 2. The optical surface creation method based on B-splines according to claim 1, wherein in step 3, a keypoint parameter matrix is ​​calculated based on the center coordinates of the incident surface (2) formed by the incident light (1) and the center coordinates of the exit surface (4).

10. The direction vector of the incident light (1), the expression of the incident surface (2) formed by the incident light (1), the refractive index of the medium between the incident surface (2) and the exit surface (4), and the coordinates of the exit surface key point (42) {P ４２，ｉ，ｊ }, and by combining with Fermat's principle, the incident vector {n ｉｎ，ｉ，ｊ }, and the coordinates of the light output surface key point (42) {P ４２，ｉ ，ｊ } and the coordinates of the target point on the light output surface {P ６２，ｉ，ｊ }={(x ４２，ｉ，ｊ , y ４２，ｉ，ｊ , z ４２，ｉ，ｊ )}, the exit vector {n ｏｕｔ，ｉ，ｊ =P ６２，ｉ，ｊ -P ４２，ｉ，ｊ }, and the light output surface key point 2. The optical surface creation method based on B-splines according to claim 1, wherein the normal vector of the exit surface key point (42) is calculated by combining the incident vector of the key point (42), the exit vector of the key point (42) on the exit surface, and the refractive index of the medium with the law of refraction.

11. The center z coordinate of the incident surface (2) [0000] and the center z coordinate of the light output surface (4) [Equation 30] By the formula [Equation 31] Combined with this, the coordinate matrix of the light output surface control point (41) [Equation 32] 3. The optical surface creation method based on B-splines according to claim 2, wherein the B-spline-based optical surface creation method calculates:

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