A method for constructing optical surfaces based on B-splines

Abstract

The present application relates to the automotive field, especially the field of vehicle lighting equipment manufacturing, and specifically to a method for constructing an optical surface based on B-spline, comprising the following steps: incident light reaches a target light distribution surface after refraction or reflection from a light-emitting surface, and surface basis functions and initial control points are determined by the coordinates of the control points of the light-emitting surface; the coordinates of key points of the light-emitting surface are calculated according to the u and v values ​​in the B-spline curve definition formula and the coordinates of the control points of the light-emitting surface; a parameter matrix of the key points of the surface is generated according to the coordinates of the key points of the light-emitting surface; the coordinates of the surface control points are solved by performing a matrix inversion operation on the parameter matrix of the key points, and an optical surface is composed of the coordinates of the surface control points. The beneficial effect of the present invention is that the calculation process of the optical free-form surface is simplified, the free-form surface control points are directly solved, and the generated free-form surface is described by 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 equipment manufacturing, and specifically to a method for constructing an optical surface based on B-splines. Background Art

[0002] Vehicle lighting is an important functional component of a car. In order to adapt to the car model, expand the lighting range and improve the viewing experience, many curved surfaces are set in the car lighting components.

[0003] During the design process, the curvature of the surface needs to be precisely calculated. Patent No. CN109116555B discloses a design method for a free-form surface lens for inclined surface lighting. The MA (Monge-Ampère) method is used to calculate the surface. The specific steps are as follows: (1) setting the initial structure of the free-form surface, (2) establishing the coordinate relationship equation between the light source and the target point, (3) establishing the energy transfer equation based on the local energy conservation, (4) establishing the boundary condition equation, (5) solving the discrete data points of the free-form surface, and (6) fitting the discrete points to obtain the surface, and obtaining the entity from the surface.

[0004] In the above surface solving method, it is necessary to first solve the discrete data points on the optical surface, and then fit the discrete points to form a surface. This solution method cannot directly obtain the surface expression, and requires a large number of discrete data points to accurately fit the surface, resulting in a huge amount of calculation and a slow solution process. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the existing method has a huge amount of surface calculation, a complicated calculation process and a slow calculation speed.

[0006] To this end, the present invention provides a method for constructing an optical surface based on B-splines.

[0007] The technical solution adopted by the present invention to solve its technical problem is:

[0008] A method for constructing an optical surface based on B-splines, comprising the following steps:

[0009] Step 1: The incident light reaches the target light distribution surface after being refracted or reflected by the light-emitting surface. The surface basis function and initial control points are determined by the coordinates of the control points on the light-emitting surface.

[0010] Step 2: Calculate 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;

[0011] Step 3: Generate the parameter matrix of the key points of the surface according to the coordinates of the key points of the light-emitting surface;

[0012] Step 4: Calculate the coordinates of the surface control points by performing a matrix inversion operation on the parameter matrix of the key points, and form an optical surface based on the coordinates of the surface control points.

[0013] By adopting the above technical solution and using B-spline functions to describe the surface, the calculation process of the optical free-form surface is simplified, the surface point coordinates are skipped, and the free-form surface control points are directly solved. The generated free-form surface is described by the B-spline function, thereby reducing the amount of process data, saving computer memory, improving calculation efficiency, and significantly reducing calculation time.

[0014] Furthermore, in step one, the incident light is parallel light, and the energy distribution of the outgoing light forms a regular target light distribution surface. The incident surface and the light-emitting surface formed by the incident light are parallel to each other and the spacing is d. The multiple incident surface control points arranged in a rectangular array in the incident surface and the multiple light-emitting surface control points arranged in a rectangular array in the light-emitting surface can be obtained by mutual translation.

[0015] Furthermore, in step one, the incident light is scattered light, and the energy distribution of the outgoing light forms a regular target light distribution surface. A plurality of light-emitting surface control points arranged in a rectangular array are provided in the light-emitting surface. The x and y coordinates of the light-emitting surface control points are known. Assuming that the coordinates of the incident light source are (x7, y7, z7), the initial surface of the light-emitting surface is a conic surface. According to the conic surface formula and the least squares fitting method, the z coordinate of the light surface control point can be obtained.

[0016] Furthermore, the x-coordinate and the y-coordinate of the key point of the light-emitting surface are the same as the corresponding control point of the light-emitting surface.

[0017] Furthermore, the incident light reaches the target point after being refracted by the light emitting surface, and in step 2, a mapping relationship between the light emitting surface and the target light distribution surface is established to determine the coordinates of the target point.

[0018] Furthermore, the light emitting surface control points are evenly distributed within the light emitting surface.

[0019] Furthermore, the key points of the light-emitting surface are evenly distributed in the UV plane, and the number of the key points of the light-emitting surface is adapted to the number of the control points of the light-emitting surface.

[0020] Furthermore, in the step three, a key point parameter matrix is ​​obtained according to the central coordinates of the incident surface and the central coordinates of the light emitting surface.

[0021] Furthermore, according to 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 light-emitting surface, and the coordinates of the key points of the light-emitting surface {P 42，i，j}, combined with Fermat's principle, the incident vector of the light at the key point of the light-emitting surface is obtained {n in，i，j}; According to the coordinates of the key points of the light-emitting surface {P 42，t，j} and the coordinates of the target point on the light-emitting surface {P 62，t，j =(x 42，i，j ,y 42，i，j , z 42，i，j )}, and find the light's exit vector {n out，i，j =P 62，i，j -P 42，i，j}; According to the incident vector of the key point of the light-emitting surface, the exit vector of the key point of the light-emitting surface, the refractive index of the medium, and the law of refraction, the normal vector of the key point of the light-emitting surface is obtained.

[0022] Furthermore, according to the center z coordinate of the incident surface And the center z coordinate of the light emitting surface Combined formula Calculate the coordinate matrix of the light-emitting surface control points

[0023] The beneficial effects of the present invention are that the invention simplifies the calculation process of the optical free-form surface by adopting the B-spline function, skips the coordinates of the surface points, and directly solves the control points of the free-form surface. The generated free-form surface is described by the B-spline function, thereby reducing the amount of process data, saving computer memory, improving calculation efficiency, and significantly reducing calculation time; using the normal vector instead of the surface tangent vector, the surface characteristic function is reduced from a quadratic function to a linear function, thereby simplifying the parameter matrix and reducing the amount of calculation; the generated free-form surface format is universal and the data is streamlined, and can be directly used for subsequent data stitching, cutting and other processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The present invention will be further described below with reference to the accompanying drawings and examples.

[0025] Figure 1 It is the algorithm flow chart of the present invention.

[0026] Figure 2 This is the optical path diagram of the incident light in Example 1 of the present invention.

[0027] Figure 3 Schematic diagram of initializing control points of the light emitting surface in embodiment 1 of the present invention.

[0028] Figure 4 It is a schematic diagram of the mapping relationship between the light emitting surface and the target light distribution surface in Example 1 of the present invention.

[0029] Figure 5 Schematic diagram of the surface shape and control points of the light-emitting surface before and after solving in Example 1 of the present invention.

[0030] Figure 6This is a comparison diagram of the light pattern distribution corresponding to the surface shape of the front light-emitting surface and the light pattern distribution corresponding to the surface shape of the rear light-emitting surface in Example 1 of the present invention.

[0031] Figure 7 This is the incident light path diagram of Example 2 of the present invention.

[0032] Figure 8 Schematic diagram of the control point distribution of the initialized light emitting surface in embodiment 2 of the present invention.

[0033] Figure 9 It is a schematic diagram of the mapping relationship between the light emitting surface and the target light distribution surface in embodiment 2 of the present invention.

[0034] Figure 10 Schematic diagram of the surface shape and control points of the light-emitting surface before and after solving in Example 2 of the present invention.

[0035] Figure 11 This is a comparison diagram of the light pattern distribution corresponding to the surface shape of the front light-emitting surface and the light pattern distribution corresponding to the surface shape of the rear light-emitting surface in Example 2 of the present invention.

[0036] In the figure: 1. Incident light; 2. Incident surface; 21. Incident surface control point; 3. Refractive medium; 4. Light-emitting surface; 41. Light-emitting surface control point; 42. Light-emitting surface key point; 5. Outgoing light; 6. Target light distribution surface; 62. Target point; 400. Solving the surface shape of the front light-emitting surface; 401. Solving the surface shape of the rear light-emitting surface; 410. Solving the control point of the front light-emitting surface; 411. Solving the control point of the rear light-emitting surface; 7. Point light source. DETAILED DESCRIPTION

[0037] Now combine with Figure 1-6 The present invention will be described in further detail. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0038] In the description of the present invention, it should be understood that the terms "center", "thickness", "up", "down", "front", "back", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they cannot be understood as limitations on the present invention. In addition, features defined as "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, "multiple" means two or more. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0039] Reference Figure 1, a method for constructing an optical surface based on B-splines, comprising the following steps:

[0040] Step 1: Initialize the surface. The incident light reaches the target light distribution surface after refraction or reflection from the light-emitting surface. In this step, the surface basis function and initial control points can be obtained by solving the light-emitting surface through the refraction surface of the incident light, or by solving the incident surface through the light-emitting surface.

[0041] Set the coordinates of surface key points and target points;

[0042] Generate parameter matrix of surface key points;

[0043] Solve the coordinates of the surface control points.

[0044] The B-spline function is a surface description standard in the field of computer-aided design (CAD). The definition of the p-order B-spline curve used in this embodiment is as follows:

[0045]

[0046] Among them, {P i =[x i ,y i , z i ]} is the control point, {N i，p (u)} is the p-order B-spline basis function, which is obtained through the node vector U and the recursive formula. The recursive formula is as follows:

[0047]

[0048] The independent variable u is an implicit expression parameter with a value range of [0, 1]. The coordinates C(u) of any point on the curve are a mapping of u. The algorithm can be extended to two dimensions. The B-spline surfaces of degree p and degree q in two directions are defined by the control point grid as follows:

[0049]

[0050] Among them, {P i，j =[x i，j ,y i，j , z i，j ]} is the control point, {N i，p (u)} is the p-order B-spline basis function, {N j，q (v)} is a q-order B-spline basis function, the independent variables u and v are implicit expression parameters, and the coordinates S(u, v) of any point on the surface are a mapping with respect to u and v.

[0051] In the present invention, B-spline has the following characteristics:

[0052] (1) When u and v are determined, the basis function is a real number, and the surface point coordinates S(u, v) are the control point P i，j The linear superposition of can also be written in matrix form:

[0053] S(u,v)=N(u,v)·P T (1)

[0054] Where N is the basis function coefficient matrix, with 1 row and m×n columns, written as:

[0055] 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)]

[0056] Among them, P T is the transpose of the control point matrix P, where P has 1 row and m×n columns, written as:

[0057] P=[P 0，0 …P n，0 P 0，1 …P n，m ]

[0058] (2) When u and v are determined, the first-order partial differential of the p-order basis function with respect to u is It can be obtained by the ρ-1 order basis function, and the first-order partial differential of the q order basis function with respect to v is It can be obtained by the q-1 order basis function:

[0059]

[0060]

[0061] The tangent vectors of the surface in the u and v directions are also control points P i，j The linear superposition of , written in matrix form:

[0062]

[0063]

[0064] (3) Let the normal vector of the B-spline surface at (u, v) be n(u, v) = [x n ,y n , z n ], since the normal vector and the tangent vector are perpendicular, we can know that:

[0065] n(u, v)·S′u =0

[0066] n(u, v)·S′ v =0

[0067] Substituting formula 2 and formula 3 into the equation, we can get:

[0068] x n x′ u +y n y′ u +z n N′ u (u, v)·Z T =0 (4)

[0069] x n x′ v +y n y′ v +z n N′ v (u, v)·Z T =0 (5)

[0070] As mentioned above, the B-spline surface is composed of degree p, degree q, knot vector U, knot vector V, control points {P i，j} jointly decide, where the control point {P i，j The coefficients other than} can be determined when initializing the surface. In general, the control point {P i，j} coordinates in the x- and y-coordinates {x i，j} and {y i，j} can also be determined during initialization. Therefore, solving the B-spline optical surface is to solve the control point z coordinate Z = {z i，j From formulas 1, 2, and 3, we can see that the coordinate z of the B-spline surface point P(u, v) and the z component of the tangent vector are both about P T A linear function of P(u, v); when the UV coordinates of P(u, v) are determined, Formula 1 is about Z T A linear function of Z; when the normal vector n(u, v) is determined, Formula 4 and Formula 5 are about Z T A linear function of .

[0071] Example 1,

[0072] Refer to the attached Figure 2-6 According to the above formula, this embodiment solves the optical B-spline surface by solving the refractive surface and the light-emitting surface through the incident light.

[0073] Combine Figure 2 , when the incident light 1 is a given parallel light parallel to the z-axis, the energy distribution of the outgoing light 5 is the target light distribution surface 6 (for example, a square distribution), and the refractive index of the medium 3 between the incident surface 2 and the light-emitting surface 4 is nmed When the incident surface 2 is a given B-spline surface, the steps for solving the light-emitting surface 4 are as follows:

[0074] Step 1: Initialize the surface: determine the surface basis functions and initial control points.

[0075] Combine Figure 2 and Figure 3 For smooth and non-distorted surfaces, 3-5 degree B-splines are used to describe the surface. Assuming the plane where the light-emitting surface 4 is located is the XY plane, and assuming that the incident surface 2 is a cubic B-spline surface with all directions, then the incident surface 2 has 4×4=16 control points; assuming that the incident surface control points 21 of the incident surface 2 are evenly distributed in the XY plane, and the initial z-direction distance between the incident surface 2 and the light-emitting surface 4 is 2mm, then Figure 3 As shown, the initialized light-emitting surface 4 also has 16 light-emitting surface control points 41 evenly distributed in the XY plane:, and the XY coordinates of the light-emitting surface control point 41 are the same as those of the incident surface control point 21. The initial z coordinate of the light-emitting surface control point 41 is the z coordinate of the incident surface control point 21 plus 2 mm, that is, the initial control point of the light-emitting surface 4 is obtained:

[0076] x 410，i，j =x 21，i，j

[0077] y 410，i，j =y 21，i，j

[0078] z 410，i，j =z 21，i，j +2mm

[0079] Step 2: Set the coordinates of the surface key points and target points.

[0080] Combine Figure 3 and Figure 4 In this step, the key point 42 of the light-emitting surface is a point located on the surface of the light-emitting surface 4, which is obtained by the UV value and the coordinates of the light-emitting surface control point 41. The key point 42 of the light-emitting surface plays two roles: by adjusting the z coordinate of the key point 42 of the light-emitting surface, the local position of the light-emitting surface 4 can be controlled; by adjusting the normal vector of the light-emitting surface 4 at the key point 42 of the light-emitting surface, the local light-emitting direction of the light-emitting surface 4 can be controlled. One way to set the key points 42 of the light-emitting surface is to make them evenly distributed in the UV plane and the number is equal to that of the control points. For example, if the u and v values ​​of the key points 42 of the light-emitting surface are all {0, 1 / 3, 2 / 3, 1}, there are 4×4=16 key points in total. Since the control points are evenly distributed in the XY plane, the x coordinates and y coordinates of the key points 42 of the light-emitting surface are the same as those of the corresponding light-emitting surface control points 41, that is:

[0081] x 42，i，j =x 21，i，j

[0082] y 42，i，j =y 21，i，j

[0083] The incident light 1 completes a reflection at the key point 42 on the surface of the light-emitting surface 4 and reaches the target point 62. In order to make the energy distribution of the outgoing light 5 conform to the target light distribution surface 6, as shown in FIG. Figure 4 As shown, a mapping relationship is established between the light-emitting surface 4 and the target light distribution surface 6. This mapping relationship is not unique, and the present invention provides one of them: following the principle of edge to edge and center to center, since the key points 42 of the light-emitting surface are evenly distributed on the light-emitting surface 4, the target points 62 are also evenly distributed on the target light distribution surface 6; the rectangular target light distribution surface 6 is evenly divided into 3×3=9 blocks, and the vertices of each block are 4×4=16 in total, which are used as the target points 62. From this, the coordinates of the target point 62 {(x 6，i，j ,y 6，i，j , z 6，i，j )}.

[0084] Step 3: Construct the parameter matrix of the key points of the surface.

[0085] Combine Figure 3 and Figure 4 , the final coordinates of the light-emitting surface control point 41 are marked as {(x 411，i，j ,y 411，i，j , z 411，i，j )},but:

[0086] x 411，i，j =x 410，i，j

[0087] y 411，i，j =y 410，i，j

[0088] By 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 direction vector of the incident light 1 is (0, 0, 1). The incident light 1 completes the first refraction at the incident surface 2, reaches the key point 42 of the light-emitting surface, and completes the second refraction at the key point 42 of the light-emitting surface. According to the direction vector of the incident light 1, the expression of the incident surface 2, the refractive index n of the medium 3 med and the coordinates of the key point 42 on the light-emitting surface {P 42，i，j =(x 42，i，j ,y 42，i，j , z 42，i，j )}, combined with Fermat's principle, we can obtain the incident vector {n in，i，j}; According to the coordinates of the key point 42 on the light-emitting surface {P 42，i，j} and the coordinates of the target point 62 {P 62，i，j=(x 6，i，j ,y 6，i，j , z 6，i，j )}, we can get the light's exit vector {n out，i，j =P 62，i，j -P 42，i，j}. According to the incident vector {n in，i，j}, outgoing vector {n out，i，j}、Refractive index n of medium 3 med , combined with the law of refraction, we can calculate the normal vector {n 42，i，j =(x n42，i，j ,y n42，i，j , z n42，i，j )}, substituting into formula (4), we have:

[0089]

[0090] Among them, x n42，i，j , x′ u，i，j 、y n42，i，j , y′ u，i，j and z n42，i，j are all given values, N′ u，i，j is a given matrix, is the z coordinate matrix of the control points of the light-emitting surface 4 to be determined. Transforming the above formula, it becomes The 16 linear equations:

[0091]

[0092] Similarly, we can obtain from formula (5) The 16 linear equations:

[0093]

[0094] Equations (6) and (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 evenly distributed on the incident surface 2, in the UV function, the value range of u and v is between 0 and 1, and the value of u and v is 1 / 2. According to formula (1), the center z coordinate of the incident surface 2 is a constant Similarly, the center z coordinate of the light emitting surface 4 is This gives the following equation, constraining the center thickness of the light-emitting surface 4 to 2 mm:

[0095]

[0096] The above equations (6) to (8) are all The linear equation of , where all the right sides of the equation are constants, can be constructed as follows:

[0097]

[0098] Matrix A and Matrix B are key point parameter matrices, where Matrix A is a constant matrix with 33 rows and 16 columns, constructed as follows:

[0099]

[0100] Matrix B is a constant matrix with 33 rows and 1 column, constructed as follows:

[0101]

[0102] Step 4: Solve the coordinates of the surface control points through matrix inversion operation.

[0103] Let matrix A -1 is the inverse matrix of matrix A, satisfying Then the z coordinate of the control point of light surface 4 can be solved from equation (9):

[0104]

[0105] The surface shape and control points of the light-emitting surface 4 before and after solution are as follows: Figure 5 As shown, it can be seen that the surface shape 400 of the front light-emitting surface 4 is a translation surface of the incident surface 2, and has the same flat surface as the incident surface 2; the surface shape 401 of the rear light-emitting surface 4 is a concave surface with a concave center and convex edges. The surface shape 401 of the rear light-emitting surface 4 corresponding to the solution of the light-emitting surface control point 411 of the rear light-emitting surface 4 is also significantly different from the surface shape 400 of the front light-emitting surface 4 corresponding to the solution of the light-emitting surface control point 410 of the front light-emitting surface 4. The simulation comparison results are shown in Figure 1. Figure 6 shown.

[0106] Example 2

[0107] The difference between this embodiment and embodiment 1 is that the light emitting surface 4 is known in step 1, and the surface basis function and the initial control points are obtained by solving the incident light 1 and the incident surface 2 through the light emitting surface 4.

[0108] The coordinates of the light-emitting surface control point 41 {(x 410，i，j ,y 410，i，j , z 410，i，j )}, the light exit surface control points 41 are evenly distributed in the XY plane, and the light incident surface control points 21 are {(x 21，i，j ,y 21，i，j , z 21，i，j )},in:

[0109] x 21，i，j =x 410，i，j

[0110] y 21，i，j=y 410，i，j

[0111] z 21，i，j =z 410，i，j -2mm

[0112] Example 3

[0113] Refer to the attached Figure 7-11 The difference from Example 1 is that this embodiment solves the optical B-spline surface by solving the reflection surface of the light source and the light-emitting surface after reflection.

[0114] like Figure 7 As shown, the difference from Example 1 is that the incident light 1 is a point light source 7, and the light emitted by the point light source 7 is astigmatism. When the point light source 7 is astigmatism, the energy distribution of the outgoing light 5 is a given light distribution 6 (such as Figure 7 When the light-emitting surface 4 is obtained as shown in the square distribution, the steps for solving the light-emitting surface 4 are as follows:

[0115] Step 1: Initialize the surface: determine the surface basis functions and initial control points.

[0116] For smooth and non-distorted surfaces, 3-5 degree B-splines can be used to accurately and efficiently describe them. Assume that the light-emitting surface 4 is a B-spline surface with a cubic shape in the UV direction and has 4×4=16 control points. Figure 8 As shown, it is assumed that the light emitting surface 4 has 16 control points 41 evenly distributed in the XY plane: {(x 410，i，j ,y 410，i，j , z 410，i，j )}, then the x-coordinate and y-coordinate of the light-emitting surface control point 41 are given values. Assume that the coordinates of the point light source 7 are (x7, y7, z7), and the initial surface of the light-emitting surface 4 is a conical surface. Depending on the required distance of the light source projected by the light-emitting surface 4 after reflection, the light-emitting surface 4 can be a parabola, an ellipsoid, or a hyperboloid. The light source projected by the parabola has a longer distance after reflection, while the light source projected by the ellipsoid has a shorter distance after reflection. In this embodiment, the light-emitting surface 4 is a parabola with a focal length of fmm. According to the parabola formula:

[0117] z=((x-x7) 2 +(y-y7) 2 ) / 4f+z7-f

[0118] The z coordinate of the light surface control point 41 can be obtained by using the least square fitting method.

[0119] Step 2: Set the coordinates of the surface key points and target points.

[0120] The method of setting the key points 42 and target points 62 of the light-emitting surface in this embodiment is the same as that in embodiment 1, and will not be repeated here. There are 16 key points in total, and their coordinates are marked as {P42，i，j}={(x 42，i，j ,y 42，i，j , z 42，i，j )},satisfy:

[0121] x 42，i，j =x 410，i，j

[0122] y 42，i，j =y 410，i，j

[0123] z 42，i，j =((x 42，i，j -x7) 2 +(y 42，i，j -y7) 2 ) / 4f+z7-f

[0124] The mapping relationship between the light emitting surface 4 and the light distribution 6 is as follows: Figure 9 As shown, the coordinates of the target point 62 are marked as {(x 6，i，j ,y 6，i，j , z 6，i，j )}.

[0125] Step 3: Construct the parameter matrix of the key points of the surface.

[0126] The final coordinates of the light-emitting surface control point 41 are marked as {(x 411，i，j ,y 411，i，j , z 411，i，j )},but:

[0127] x 411，i，j =x 410，i，j

[0128] y 411，i，j =y 410，i，j

[0129] By 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. The incident light 1 completes a reflection at the key point 42 of the light-emitting surface and reaches the target point 62. According to the coordinates (x7, y7, z7) of the point light source 7 and the initial value {P 42，i，j}, we can approximately obtain the incident vector {n in，i，j}; According to the coordinates of the key point 42 on the light-emitting surface {P 42，i，j} and the coordinates of the target point 62 {P 62，i，j =(x 6，i，j ,y 6，i，j , z 6，i，j )}, we can get the light's exit vector {nout，i，j =P 62，i，j -P 42，i，j}. According to the incident vector {n in，i，j} and the outgoing vector {n out，i，j}, combined with the law of reflection, we can get the normal vector {n 42，i，j =(x n42，i，j ,y n42，i，j , z n42，i，j The subsequent parts are the same as those in Example 1 and will not be described again here.

[0130] Step 4: Solve the coordinates of the surface control points through matrix inversion operation.

[0131] Let matrix A -1 is the inverse matrix of matrix A, satisfying Then the z coordinate of the light surface control point 41 can be solved from equation (9):

[0132]

[0133] The surface shape of the light-emitting surface 4 before and after the solution is as follows Figure 10 The simulation comparison results are shown in Figure 11 shown.

[0134] In summary, this invention streamlines the calculation process for optical freeform surfaces, bypassing the surface point coordinates and directly solving for the freeform surface control points. The resulting freeform surface is described using a B-spline function, thereby reducing the amount of process data, conserving computer memory, improving computational efficiency, and significantly reducing computation time. This calculation method replaces the surface tangent vector with a normal vector, reducing the surface characteristic function from a quadratic function to a linear function, thereby simplifying the parameter matrix and reducing the amount of computation. The freeform surface generated during the calculation process is in a universal format and streamlined, making it directly usable for subsequent data stitching, shearing, and other processing.

[0135] With the above-described preferred embodiments of the present invention as a guide, and with reference to the above description, relevant personnel are fully capable of making various changes and modifications without departing from the technical spirit of this invention. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for constructing an optical surface based on B-splines, characterized in that: The following steps are included: Step 1: The incident light (1) reaches the target light distribution surface (6) after being refracted or reflected by the light-emitting surface (4), and the surface basis function and the initial control point are determined by the coordinates of the light-emitting surface control point (41); Step 2: Calculate the coordinates of the key point (42) on the light-emitting surface according to the u and v values ​​in the B-spline curve definition formula and the coordinates of the light-emitting surface control point (41); Step 3: Generate a parameter matrix of the key points of the surface according to the coordinates of the key points (42) of the light-emitting surface; Step 4: performing matrix inversion operation on the parameter matrix of the key points to solve the coordinates of the surface control points, and forming an optical surface from the coordinates of the surface control points; Specifically, according to the direction vector of the incident light (1), the expression of the incident surface (2), the refractive index of the medium between the incident surface (2) and the light-emitting surface (4), and the coordinates of the key point (42) of the light-emitting surface , combined with Fermat's principle, the incident vector of the light at the key point (42) on the light-emitting surface is obtained According to the coordinates of the key point (42) of the light-emitting surface and the coordinates of the target point on the light-emitting surface , find the exit vector of the light at the key point (42) of the light exit surface According to the incident vector of the key point (42) of the light-emitting surface, the exit vector of the key point (42) of the light-emitting surface, the refractive index of the medium, and the law of refraction, the normal vector of the key point (42) of the light-emitting surface is obtained.

2. The method for constructing an optical surface based on B-splines according to claim 1, wherein: In the step 1, the incident light (1) is parallel light, the energy distribution of the outgoing light (5) forms a regular target light distribution surface (6), the incident surface (2) formed by the incident light (1) and the light-emitting surface (4) are parallel to each other and the distance d is d, and a plurality of incident surface control points (21) arranged in a rectangular array in the incident surface (2) and a plurality of light-emitting surface control points (41) arranged in a rectangular array in the light-emitting surface (4) can be obtained by mutual translation.

3. The method for constructing an optical surface based on B-splines according to claim 1, wherein: In the step 1, the incident light (1) is divergent light, the energy distribution of the outgoing light (5) forms a regular target light distribution surface (6), a plurality of light-emitting surface control points (41) arranged in a rectangular array are provided in the light-emitting surface (4), the x and y coordinates of the light-emitting surface control points (41) are known, and the coordinates of the light source of the incident light (1) are assumed to be The initial surface of the light-emitting surface (4) is a conical surface. According to the conical surface formula, the z coordinate of the light surface control point (41) can be obtained by using the least square fitting method.

4. The method for constructing an optical surface based on B-splines according to claim 2 or 3, wherein: The x-coordinate and y-coordinate of the key point (42) on the light-emitting surface are the same as those of the corresponding control point (41) on the light-emitting surface.

5. The method for constructing an optical surface based on B-splines according to claim 3, wherein: The incident light (1) reaches the target point (62) after being refracted by the light-emitting surface (4). In step 2, a mapping relationship between the light-emitting surface (4) and the target light distribution surface (6) is established to determine the coordinates of the target point (62).

6. The method for constructing an optical surface based on B-splines according to any one of claim 1, wherein: The control points of the light-emitting surface (4) are evenly distributed within the light-emitting surface (4).

7. The method for constructing an optical surface based on B-splines according to claim 6, wherein: The key points of the light-emitting surface (4) are evenly distributed in the UV plane, and the number of the key points of the light-emitting surface (4) is adapted to the number of control points of the light-emitting surface (4).

8. The method for constructing an optical surface based on B-splines according to claim 2, wherein: In the step three, a key point parameter matrix is ​​obtained based on the central coordinates of the incident surface (2) and the central coordinates of the light-emitting surface (4).

9. The method for constructing an optical surface based on B-splines according to claim 2, wherein: The coordinates of the surface points are the linear superposition of the control points, written in matrix form: ,in is the basis function coefficient matrix, is the control point matrix The transpose of the incident surface (2) is expressed as the center z coordinate The center z of the light-emitting surface (4) is expressed as ,in, is the basis function coefficient matrix, is the transpose of the matrix of the incident surface control points (21), combined with the formula Calculate the coordinate matrix of the light-emitting surface control point (411) after solution .

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