CN114357549A - Arc surface glass cutting method based on coordinate transformation - Google Patents

Abstract

The invention discloses a method for cutting arc glass based on coordinate transformation, which comprises the following steps: based on the central point of a two-dimensional contour map of a drawn workpiece, projecting the central point to a projection point on a spherical surface, recording the workpiece taking the projection point as the central point as an arc-surface workpiece, collecting a contour coordinate point set of the arc-surface workpiece, recording a plane included angle between the central point and an X axis, translating the drawn workpiece to obtain a translated workpiece, projecting the translated workpiece onto the spherical surface, recording a contour coordinate point set of the projected workpiece, and obtaining a polar coordinate point set of the contour of the projected workpiece through coordinate transformation; rotating the polar coordinate point set of the projected workpiece outline to the cambered surface workpiece to obtain a polar coordinate point set of the cambered surface workpiece outline; obtaining a three-dimensional coordinate point set by coordinate transformation of the polar coordinate point set of the cambered surface workpiece; and collecting the three-dimensional space coordinate points to generate a code identification file of the operation track processed by the numerical control tool bit.

Description

A method of cutting arc surface glass based on coordinate transformation

technical field

The invention relates to the fields of spherical coordinate transformation, arc glass cutting and the like, in particular to a method for cutting arc glass based on coordinate transformation.

technical background

Glass is widely used in our lives, from craft accessories to special buildings, and its market potential is very large. The processing of glass requires batching, melting, forming, annealing and other processes. The processed glass also needs to be further cut and peeled to produce the glass with the required shape. Glass is a fragile material,

When cutting, it is necessary to control the pressure of the cutter head and the force of the knife. The cutting of glass presents many problems. Ordinary flat glass can be cut by the three-dimensional coordinate system of the four-axis CNC system. Three-dimensional curved glass cutting will bring about many problems such as deformation of processing shape, excessive space complexity, uneven glass processing chamfer, and fragile glass (a polar coordinate circular saw blade wire cutting method and wire cutting equipment based thereon) .

However, because of its special shape characteristics and optical characteristics, curved glass has extremely important reuse in the fields of car rearview mirrors and glass reflectors. At present, there is very little reference to the cutting method of curved spherical glass in the field of glass cutting.

SUMMARY OF THE INVENTION

In view of the above-mentioned deficiencies, the present invention proposes a method for cutting circular arc surface glass based on coordinate transformation, which utilizes the two-dimensional plane-to-spherical coordinate transformation of the workpiece to locate the spatial coordinates (plane workpiece mapping, center point angle transformation, spherical coordinate zenith) Angle rotation, etc.), and then realize arc glass cutting, this method has important applications in the processing of car rearview mirrors, arc mirrors and other fields to solve the realization problem of arc glass cutting; map the drawn two-dimensional CAD graphics Combined with the arc radius of the workpiece mold to the spherical surface to describe the entire processed arc workpiece.

The present invention is realized by at least one of the following technical solutions.

A method for cutting arc surface glass based on coordinate transformation, the steps include:

S1, draw n workpieces to be processed on the arc surface, the drawn workpiece graphics are the two-dimensional contour map of each arc workpiece projected on the plane, and take the center point of the two-dimensional contour map of each workpiece;

；S2. Based on the center point of the drawn two-dimensional contour map of the workpiece, the center point is projected to the projection point on the spherical surface through the projection algorithm, the workpiece with the projection point as the center point is recorded as the arc surface workpiece, and the contour coordinates of the arc surface workpiece are collected. Set of points, and record the angle between the center point and the X-axis plane on the drawing sheet as

;

S3, translate the drawn workpiece to make the center point of the workpiece coincide with the origin of the plane coordinates, obtain the translated workpiece, project the translated workpiece onto the spherical surface, obtain the projected workpiece, and record the outline coordinate point set of the projected workpiece ( x _n , y _n , z _n ), n is the n points describing the contour edge taken from the projected workpiece contour, and the polar coordinate point set of the projected workpiece contour is obtained through the transformation from the three-dimensional coordinate system to the polar coordinate system

旋转到弧面工件处，得到弧面工件轮廓的极坐标点集合

S4. Calculate the coordinate center point of the cambered workpiece, the included angle θ of the zenith angle between the cambered workpiece and the Z-axis, and set the polar coordinate points of the projected workpiece contour through the rotation of the space coordinates

Rotate to the cambered workpiece to obtain the polar coordinate point set of the cambered workpiece contour

S5, obtain the three-dimensional coordinate point set (x′ _n , y′ _n , z′ _n ) by transforming the polar coordinate point set of the camber workpiece into the three-dimensional coordinate system;

S6 , generating an nc code file for identifying the running trajectory of the CNC tool head machining from the set of three-dimensional space coordinate points of the cambered workpiece.

Further, the n small workpieces processed on the arc surface are the maximum number of workpieces to be processed that are allowed to be densely arranged by the base material of the arc surface; The two-dimensional coordinate point set map of the workpiece contour mapped by the vertical projection on the map;

The center point P _n of the two-dimensional contour of each small workpiece is the coordinate position of the center point on the geometry of the small workpiece, and n=1, 2, , , N, where N is the maximum number of workpieces allowed to be densely arranged.

Further, the transformation formula from the three-dimensional coordinate system to the polar coordinate system is:

为方向角，θ_n为天顶角，(x_n,y_n,z_n)为投影工件轮廓在三维坐标系里面的坐标，

为投影工件轮廓在极坐标系里面的坐标。Among them, rn _is the arc radius of the arc workpiece,

is the direction angle, θ _n is the zenith angle, (x _n , y _n , z _n ) is the coordinates of the projected workpiece contour in the three-dimensional coordinate system,

It is the coordinates of the projected workpiece contour in the polar coordinate system.

为绕着每一个小工件的轮廓线条取遍一周得到的坐标点集合。Further, the polar coordinate point set

A set of coordinate points obtained by traversing the outline of each small workpiece.

Further, the included angle of the zenith angle is the included angle θ between a certain point in the three-dimensional space and the Z axis.

后得到的点集合。Further, the described space coordinate point set is the zenith angle included angle θ and the azimuth angle that are changed according to the polar coordinate rotation transformation of the center point of the projection workpiece to the center point P' of the camber workpiece.

The set of points obtained after.

和天顶角θ，进而得到弧面工件工件的变换，得到的弧面工件极坐标轮廓点集合为：Further, the described polar coordinate rotation transformation is to project the polar coordinate contour point set of the workpiece by rotating the phase angle.

and the zenith angle θ, and then obtain the transformation of the cambered workpiece, and the obtained polar coordinate contour point set of the cambered workpiece is:

r _n ′=r _n

θ _n '=θ _n +θ

为弧面工件轮廓的极坐标点集合，

为投影工件轮廓的极坐标点集合，天顶角夹角θ，方向角为

。in

is the polar coordinate point collection of the contour of the cambered workpiece,

is the set of polar coordinate points for projecting the contour of the workpiece, the included angle of the zenith angle is θ, and the direction angle is

.

Further, the transformation formula from polar coordinates to three-dimensional coordinate system is:

z′ _n =r′ _n cosθ′ _n

为投影工件轮廓在极坐标系里面的坐标。Among them, (x′ _n , y′ _n , z′ _n ) are the coordinates of the projected workpiece contour in the three-dimensional coordinate system,

It is the coordinates of the projected workpiece contour in the polar coordinate system.

Further, the running track of the CNC tool head is a point set of three-dimensional coordinates of the contour of the cambered workpiece, and the point set of the three-dimensional coordinates of the contour of the cambered workpiece is converted into a coordinate code file that can be read by the CNC turning and milling machine equipment.

Further, the workpiece to be processed on the arc surface drawn on the CAD and CAM software.

Further, the generated code file that can be read by the CNC turning and milling machine equipment is an nc code file.

Compared with the prior art, the beneficial effects of the present invention are:

The algorithm of this method is simple and practical, and the problem of curved glass cutting can be effectively solved by several coordinate transformations. The method effectively solves many problems caused by three-dimensional curved glass cutting, such as deformation of the processing shape, excessive space complexity, uneven glass processing chamfers, and fragile glass. The method is highly original, does not require the help of other auxiliary equipment or auxiliary software, and the algorithm is simple to implement. The estimation of the transformation of this method does not require the use of other interpolation algorithms.

The invention utilizes the characteristics of spherical space coordinate transformation to realize arc glass cutting, and effectively realizes the cutting and processing method of arc glass by multi-axis CNC lathes. The spherical radius information of the arc glass workpiece can process and cut the desired arc small workpiece.

The invention provides an arc cutting scheme for a multi-axis numerical control glass cutting machine, while ensuring the accuracy of the workpiece and preventing the deformation of the workpiece. The method of the invention involves the mapping of a two-dimensional plane coordinate system to a three-dimensional spherical surface, which greatly reduces the glass cutting process. Deformation of the processed glass workpiece. At the same time, it also reduces the increase in the scrap rate and the glass being cut during the glass cutting process.

Description of drawings

FIG. 1 is a coordinate transformation diagram of an arc-shaped workpiece, and is also a workpiece transformation information diagram of the method disclosed in the present invention.

Fig. 2 is a method flow chart of a method for cutting a circular arc surface glass based on coordinate transformation of this example;

Fig. 3 is the flow chart of embodiment 1 small and medium-sized car rearview mirror cutting machine cutting algorithm;

Fig. 4 is the flow chart of the cutting algorithm of arc mirror cutting machine in embodiment 2;

FIG. 5 is a flowchart of the cutting algorithm of the spectacle lens cutting machine in Embodiment 3. FIG.

Detailed ways

Next, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings of the present invention, and the described embodiments are only a part of the embodiments of the present invention, rather than all examples. Based on the examples in the present invention, other embodiments obtained by those of ordinary skill in the art without creative work shall fall within the protection scope of the present invention.

Example 1

A method for cutting arc surface glass based on coordinate transformation in this embodiment, the embodiment can be used in a car rearview mirror arc glass cutting machine, as shown in Fig. 1 is a coordinate transformation diagram of an arc-shaped workpiece, as shown in Fig. 2 shows a flowchart of the specific steps and method of this embodiment, and this embodiment includes the following specific implementation contents.

Specifically, create a new project on CAD and CAM software, create a new drawing drawing in the project, and use CAD and CAM software to draw multiple small car rearview mirror workpieces n (n=1, 2, , , n), the drawn graph is the two-dimensional contour map of each small workpiece of the rearview mirror arc projected on the plane, and the center point P _n (n=1, 2, ) of the two-dimensional contour map of each small workpiece is taken. , n).

Specifically, the origin coordinate O of the drawing is set as the center position of the whole drawing. In order to save workpiece materials, the graphics of each workpiece are drawn on the drawing board closely around point O, and the distance between the center point of each workpiece and the coordinate center point is calculated. The calculated spatial distance is convenient for subsequent calculation of the projected coordinates P' and P' of each workpiece on the arc surface and the zenith angle θ of the Z axis.

得到各个工件中心P离着坐标原点O的距离，该距离表示工件离弧形玻璃的最上顶方的垂线距离，同时记录P’点到球心的连线和弧形玻璃中心轴线的夹角为θ和相位角

，记录下该夹角θ和相位角

。Specifically, the center position coordinates of each workpiece are obtained on the drawing plane, and the Pythagorean theorem is used.

Obtain the distance between the center P of each workpiece and the coordinate origin O, which represents the vertical distance between the workpiece and the top of the curved glass, and record the connection between the point P' and the center of the sphere and the angle between the center axis of the curved glass for θ and the phase angle

, record the included angle θ and the phase angle

.

，并且记录下该夹角。Specifically, select a small workpiece T1 as a representative, record the center point of its two-dimensional contour map as P, project the center point P to the point P' on the spherical surface through the projection algorithm, and record the workpiece with the projected point P' as the center point. As T4, T4 is the cambered workpiece to be processed, and the set of contour coordinate points of T4 is the set of coordinate points to be obtained. The purpose of the following steps is to obtain the contour diagram of the T4 workpiece, and calculate and record the P point on the drawing sheet. The angle between the plane and the X1 axis is

, and record the included angle.

(n为绕工件轮廓取的n个描述轮廓边的点)。Specifically, translate the small workpiece T1 to be processed so that the center point P of the small workpiece coincides with the point O of the plane coordinates to obtain the translated workpiece T2, project the workpiece T2 onto the spherical surface to obtain the projected workpiece T3, and record the workpiece T3 The set of contour coordinate points (x _n , y _n , z _n ) (n is the n points describing the contour edge taken around the contour of the workpiece), and the set of contour polar coordinate points of the T3 workpiece is obtained through polar coordinate transformation

(n is the n points describing the contour edge taken around the workpiece contour).

，和天顶角θ的极坐标位置信息。工件T4中心点P’和球的圆心的连线和中轴线Z轴的夹角θ和相位角

，将工件轮廓的极坐标通过夹角θ和相位角

变换到P’点对应的位置处即可。并且用数组保存起来。Specifically, in the plane, the workpiece center point P is translated to the position of the coordinate origin O, and after the center point P of the workpiece T1 is aligned with the coordinate origin, the translated workpiece is T2, and the contour of T2 is obtained after the contour of T1 is translated, obtain The actual two-dimensional plane coordinates (X, Y) of the workpiece T2, after obtaining the coordinates of the workpiece on the XOY plane, through the projection principle, according to the calculation formula of spherical coordinates R ² =X ² +Y ² +Z ² to obtain the projected contour of the workpiece T3. Z coordinate, record the coordinates (x _n , y _n , z _n ) of each point of the contour of the workpiece T3 in the spherical coordinate system, and obtain the (x _n , _yn , z _n ) of the three-dimensional coordinate system of each point of the contour of the workpiece T3, Obtain the coordinate position information of the workpiece T3 contour in the XYZ coordinate axis of the spherical coordinate system, and use the python language to define an array to store the coordinate information (x _n , y _n , z _n ) of the workpiece mapped to the spherical coordinate system, and the obtained workpiece coordinates The specific coordinate point set (x _n , y _n , z _n ) on the three-dimensional coordinate system XYZ, through the transformation relationship from the three-dimensional coordinate system to the polar coordinate system, first transform the coordinate information of (X, Y, Z) stored in the array into a camber radius R, direction angle

, and the polar coordinate position information of the zenith angle θ. The line connecting the center point P' of the workpiece T4 and the center of the ball and the included angle θ and phase angle of the central axis Z axis

, pass the polar coordinates of the workpiece contour through the included angle θ and the phase angle

It can be transformed to the position corresponding to the point P'. And save it in an array.

Specifically, the obtained polar coordinate point set of the contour of the workpiece T4 is transformed to obtain a three-dimensional coordinate point set on the three-dimensional coordinate system XYZ, and the three-dimensional coordinate point set is the real coordinate system of the workpiece contour mapping on the XYZ plane of the world coordinate system, which is also a glass The position information of the knife that should be passed during the cutting process of the cutting machine. The contour information of the workpiece drawn in the drawing contains all the information of the pass.

Specifically, the last generated contour cutting information of each workpiece is stored in the array, each workpiece has a cutting contour, and each contour contains a set of coordinates of coordinate points, the coordinate point set (x′ _n , y′ _n , z′ _n ) is the actual cutting point. Use the python code to set the coordinate points to generate the specific nc code of the cutting tool, the CNC system reads the nc code, and the curved glass can be processed on the actual multi-axis CNC lathe through the servo system.

Example 2

A method for cutting circular arc glass based on coordinate transformation in this embodiment, the embodiment can be used in a user arc mirror arc glass cutting machine, and the embodiment includes the following specific implementation contents.

Specifically, open the CAM software, create a new drawing project, and create a new drawing board in the project as a drawing for cutting the glass mirror. The origin coordinate of the drawing is defined as O, and the O point is the center position of the whole drawing. The midpoint corresponds to the rotation axis of the workpiece grinding tool, that is, the Z axis of the spherical coordinate system. In order to save the workpiece material, draw the outline of each workpiece on the drawing board around the O point and calculate the center point coordinates of each workpiece, take the center point coordinate of a mirror workpiece T1 as P, and calculate the workpiece outline center point coordinate The distance between P and point O of the artboard coordinate system.

Specifically, the center point of the mirror workpiece T1 is mapped to the P' point on the spherical surface, and the workpiece coordinate with the P' point as the center point is called T4. The Z axis is mapped to T3, and then T3 is rotated to form T4. The three-dimensional coordinate point set of the contour of the workpiece T4 needs to obtain the trajectory of the cutter head cutting and processing (the workpiece T2 and the workpiece T3 will be introduced later).

。Specifically, the angle between the point P' and the Z axis is calculated, which is called the zenith angle, which is calculated as θ, and the mapping of the point P' on the XOY plane and the angle between the X axis are calculated, and the angle is called is the direction angle, calculated as

.

Specifically, the mirror workpiece T1 is translated so that its center point coincides with the coordinate origin O, so that the translation workpiece T2 with the point O as the center point is obtained, and the translated contour of T1 is the contour of the workpiece T2. Since T1 is a figure drawn by CAD and CAM, its workpiece contour coordinate information is unique. Then, the set of contour coordinate information points of the workpiece T2 can be obtained.

便可以得到工件的Z轴坐标信息，此时可以得到工件T3轮廓的三维坐标点集合为(x_n,y_n,z_n)。Specifically, the contour of T2 is mapped to the spherical surface again through the Z axis to obtain the workpiece T3. The X and Y coordinates of T3 are the X and Y coordinates of the T2 workpiece. According to the formula

The Z-axis coordinate information of the workpiece can be obtained. At this time, the three-dimensional coordinate point set of the contour of the workpiece T3 can be obtained as (x _n , y _n , z _n ).

变换公式为：Specifically, the set of three-dimensional coordinate points (x _n , y _n , z _n ) of the T3 contour is obtained by transforming the three-dimensional coordinate system to the polar coordinate system to obtain the set of polar coordinate points of the T3 contour

The conversion formula is:

已知，于是T4工件的轮廓的极坐标点集合便可以得到。旋转公式为：Specifically, rotate the workpiece T3 so that the center point of the T3 workpiece rotates to P', and the contour after the rotation of the T3 workpiece is the contour of the workpiece T4, because the polar coordinate point collection of the T3 contour

It is known that the polar coordinate point set of the contour of the T4 workpiece can be obtained. The rotation formula is:

r _n '=r _n

θ _n '=θ _n +θ

为T4轮廓的极坐标点集合，

为T3轮廓的极坐标点集合，天顶角夹角θ，方向角为

。in

is the polar coordinate point set of the T4 contour,

is the polar coordinate point set of the T3 contour, the included angle of the zenith angle θ, and the direction angle is

.

Specifically, the set of three-dimensional coordinate points of the contour of the T4 workpiece is obtained by transforming the polar coordinate point set of the contour of the T4 workpiece through the transformation from polar coordinates to a three-dimensional coordinate system.

Specifically, using the python code programming method, the 3D coordinate point set of the outline of the T4 workpiece is used to calculate the nc code that the machine tool can recognize, and the curved glass can be processed on the actual multi-axis CNC lathe through the servo system.

Example 3

The present embodiment of a method for cutting arc-shaped glass based on coordinate transformation can be used in an ophthalmic lens arc-shaped glass cutting machine, because the arc-shaped cutting of spectacle lenses only needs to cut a lens directly above the arc surface. , but the user can draw on the drawing at will, and this embodiment includes the following specific implementation content.

Specifically, open CAD and CAM software, create a new drawing project, and create a new drawing drawing board in the project as a drawing for spectacle lens cutting. The origin coordinate of the drawing is defined as O, and the O point is the center position of the whole drawing. The midpoint corresponds to the rotation axis of the workpiece grinding tool, that is, the Z axis of the spherical coordinate system. The coordinate of the center point of drawing the spectacle lens workpiece T1 around O is P, and the distance between the coordinate P of the center point of the workpiece outline and the point O of the drawing board coordinate system is calculated.

Specifically, the spectacle lens workpiece T1 is translated so that the center point of the workpiece coincides with the coordinate origin O, so that the translation workpiece T2 with the point O as the center point is obtained. The set information of contour coordinate points of T2 can be obtained.

计算出T3的轮廓的坐标点集(x_n,y_n,z_n)，T3的轮廓信息即为要求得的三维坐标系点集信息，也是眼镜片的轮廓信息。Specifically, the workpiece T3 is obtained by mapping T2 to the spherical coordinate system along the Z axis. The abscissa and ordinate of T3 are the same as the abscissa and ordinate of T2. Through the formula

The coordinate point set (x _n , y _n , z _n ) of the contour of T3 is calculated, and the contour information of T3 is the required three-dimensional coordinate system point set information, and is also the contour information of the spectacle lens.

The above-disclosed preferred embodiments of the present invention are provided only to help illustrate the present invention. The preferred embodiments do not exhaust all the details, nor do they limit the invention to only the described embodiments. Obviously, many modifications and variations are possible in light of the content of this specification. The present specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can well understand and utilize the present invention. The present invention is to be limited only by the claims and their full scope and equivalents.

Claims (10)

1. A circular arc surface glass cutting method based on coordinate transformation is characterized by comprising the following steps:

s1, drawing n workpieces to be machined on the arc surface, wherein the drawn workpiece graphs are two-dimensional contour graphs of each arc workpiece projected on a plane, and the central point of each workpiece two-dimensional contour graph is taken;

s2, based on the central point of the drawn two-dimensional contour map of the workpiece, projecting the central point to a projection point on the spherical surface through a projection algorithm, recording the workpiece taking the projection point as the central point as an arc workpiece, collecting a contour coordinate point set of the arc workpiece, and recording the plane included angle of the central point and the X axis on a drawing as

S3, translating the drawn workpiece to make the central point of the workpiece coincide with the origin of the plane coordinate to obtain a translated workpiece, projecting and mapping the translated workpiece onto a spherical surface to obtain a projected workpiece, and recording a contour coordinate point set (x) of the projected workpiece_n，y_n，z_n) N is n points of describing contour sides taken by the projection workpiece contour, and a polar coordinate point set of the projection workpiece contour is obtained through the transformation from a three-dimensional coordinate system to a polar coordinate system

S4, calculating the coordinate center point of the arc workpiece, the zenith angle included angle theta between the arc workpiece and the Z axis, and collecting the polar coordinate points of the projected workpiece outline through space coordinate rotation

Rotating to the cambered surface workpiece to obtain a polar coordinate point set of the cambered surface workpiece outline

S5, converting the polar coordinate point set of the cambered surface workpiece into a three-dimensional coordinate system through polar coordinates to obtain a three-dimensional coordinate point set (x)_n'，y_n'，z_n')；

And S6, collecting the three-dimensional space coordinate points of the cambered surface workpiece to generate an identification nc code file of the running track processed by the numerical control tool bit.

2. The method for cutting the arc glass based on the coordinate transformation as claimed in claim 1, wherein:

the n small workpieces machined on the arc surface are the maximum number of the workpieces which are machined on the arc surface and are allowed to be densely arranged by the arc surface base material; the two-dimensional contour map of the plane projection is a two-dimensional coordinate point set map of the workpiece contour mapped by the vertical projection of the arc workpiece to be processed on the plane;

two-dimensional profile central point P of each small workpiece_nThe coordinate position of the central point on the geometry of the small workpiece is N, which is 1, 2, N is the maximum number of workpieces which are allowed to be densely arranged.

3. The method for cutting the arc glass based on the coordinate transformation as claimed in claim 1, wherein: the transformation formula from the three-dimensional coordinate system to the polar coordinate system is as follows:

wherein r is_nIs the arc radius of the arc workpiece,

is the angle of orientation, θ_nIs the zenith angle (x)_n,y_n,z_n) To project the coordinates of the workpiece contour within the three-dimensional coordinate system,

coordinates of the projected workpiece contour in the polar coordinate system.

4. The method for cutting the arc glass based on the coordinate transformation as claimed in claim 1, wherein: set of polar points

A set of coordinate points taken one revolution around the outline of each small workpiece.

5. The method for cutting the arc glass based on the coordinate transformation as claimed in claim 1, wherein: the included angle of the zenith angle is an included angle theta between a certain point of the three-dimensional space and the Z axis.

6. The method for cutting the arc glass based on the coordinate transformation as claimed in claim 1, wherein: the space coordinate point set is transformed to the central point of the cambered surface workpiece according to the rotation of the central point of the projection workpiece and the polar coordinatesAngle of zenith angle theta and azimuth angle changed by P

The resulting set of points.

7. The method for cutting the arc glass based on the coordinate transformation as set forth in claim 6, wherein: the polar coordinate rotation transformation is to set the polar coordinate contour points of the projection workpiece through a rotation phase angle

And a zenith angle theta is calculated, so that the transformation of the cambered surface workpiece is obtained, and the obtained cambered surface workpiece polar coordinate contour point set is as follows:

r_n'＝r_n

θ_n’＝θ_n+θ

wherein

Is a polar coordinate point set of the contour of the cambered surface workpiece,

is a set of polar coordinate points projecting the contour of the workpiece, the zenith angle is an included angle theta, and the direction angle is

8. The method for cutting the arc glass based on the coordinate transformation as claimed in claim 1, wherein: the transformation formula from polar coordinates to a three-dimensional coordinate system is as follows:

z_n'＝r_n'cosθ′_n

wherein (x)_n',y_n',z_n') is the coordinate of the cambered surface workpiece outline in a three-dimensional coordinate system,

the coordinates of the contour of the cambered surface workpiece in a polar coordinate system are shown.

9. The method for cutting the arc glass based on the coordinate transformation as claimed in claim 1, wherein: the running track of the numerical control tool bit is a point set of the three-dimensional coordinate of the outline of the cambered workpiece, and the point set of the three-dimensional coordinate of the outline of the cambered workpiece is converted into a coordinate code file which can be read by numerical control turning and milling machine equipment.

10. The method for cutting the arc glass based on the coordinate transformation as claimed in claim 1, wherein: drawing a workpiece to be machined on the cambered surface on CAD and CAM software.

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