KR101877548B1 - Image generation system for projection on curved surface and generation method therefor - Google Patents

Abstract

A method of generating a curved projection image includes projecting an original image onto a spherical coordinate system; And projecting an image projected onto the spherical coordinate system onto a cylindrical coordinate system. According to the curved projection image generation system and method of the present invention, it is possible to project a distorted image on an internal curved surface of an incised cylindrical shape so that it can be picked up by an ultra-wide angle camera, do.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image generation system and a generation method thereof,

The present invention relates to a curved projection image generation system and a method of generating a curved projection image. More particularly, the present invention relates to a curved projection projection system for projecting a distorted image on an inner curved cylindrical surface, To an image generation system and a generation method thereof.

The various performance measurements (resolution, brightness uniformity, color characteristics, geometrical distortion, etc.) of the image module including the sensor and lens or the combined field of view (FOV, Field of View) . The camera module acquires an image of a standard image or a predetermined object at a certain distance from various illuminations and brightness, analyzes resolution, distortion quality, brightness change, and color reproducibility of the acquired image, Evaluate and define performance.

An image module having an angle of view of 100 to 140 degrees is called a wide angle module, and an image module using a lens having an angle of view of 140 degrees or more is called an ultra wide angle module.

To test a camera module with a 60-degree angle of view, you can fix the subject in a module with an angle of 60 degrees with the camera module and check the quality of the captured image. However, as the angle of view increases and the generally used planar object is used, distortion of the image of the object occurs from the center of the subject to the periphery, which makes it difficult to measure the performance of the camera module with the correct wide angle or super wide angle.

Thus, in Korean Patent No. 10-1324888 (a performance measuring mechanism of a camera module for a wide-angle lens), a measuring instrument having a cylindrical inner curved surface cut out as shown in Fig. 1 is disclosed.

FIGS. 2A and 2B are exemplary views of a test chart to be mounted on a measuring instrument disclosed in Korean Patent No. 10-1324888, respectively, and image views actually taken by an ultra-wide angle camera. FIG.

As can be seen from Figs. 2A and 2B, in the case of the measuring apparatus disclosed in the Korean Patent No. 10-1324888, it is not easy to compare the resolution of each lens, and even if an existing chart is picked up, It is difficult to directly evaluate the camera and lens characteristics such as the difference in resolution, the consistency of the lens distortion, and the difference in brightness between the center and the edge.

An object of the present invention is to solve the technical problems as described above, and it is an object of the present invention to provide an image pickup apparatus capable of projecting a distorted image on an inner curved surface of a cylindrical shape and imaging it with an ultra-wide angle camera, And an object of the present invention is to provide a method of creating a curved surface using image and a method of creating the same.

According to another aspect of the present invention, there is provided a curved projection image generation system comprising: a projection image generation unit for projecting an original image to a different coordinate system, wherein the projection image generation unit generates a projection image of a rectangular- And the fisheye lens model image, which is the result of the primary projection, is secondarily projected onto the inner curved surface of the cut cylindrical shape.

According to another aspect of the present invention, there is provided a curved projection image generation system, comprising: a projection formula calculation unit for calculating a formula for projection of a coordinate system, wherein the projection formula calculation unit comprises: A first calculator for calculating a required first expression group; And a second calculator for calculating a second group of expressions required when projecting the fisheye lens model image onto the incised cylindrical inner curved surface.

It is preferable that the image generated by the projection image generation unit is distorted by a performance measurement chart of the camera module. In addition, the image generated by the projection image generating unit is concave with respect to the outside or outside of the left side, left or right, compared with the original image, and the upper side or the lower side is higher than the upper side As shown in Fig.

로부터 어안 렌즈 모델 영상의 픽셀의 위치

로의 투영은 다음의 수학식 (1) 내지 (4)를 만족하는 것을 특징으로 한다.Specifically, the position of the pixel in the rectangular coordinate system image

The position of the pixel of the fisheye lens model image

(1) to (4): " (1) "

(One)

(2)

(3)

(4)

는 상기 어안 렌즈 모델의 반지름,

는 상기 어안 렌즈 모델의 중심을 지나는 (x, y) 평면에서 x축을 기준으로 한 회전각 및

는 상기 어안 렌즈 모델의 z축과의 천정각을 각각 의미함.) (only,

The radius of the fisheye lens model,

(X, y) plane passing through the center of the fisheye lens model, and

Represents the zenith angle with respect to the z-axis of the fisheye lens model).

로부터 절개된 원통 형상의 내부 곡면의 픽셀의 위치

로의 투영은 다음의 수학식 (5) 내지 (8)를 만족하는 것이 바람직하다.In addition, the position of the pixel of the fisheye lens model image

The position of the pixel of the inner curved surface of the cylindrical shape cut out from the

It is preferable that the projection onto the projection plane satisfies the following equations (5) to (8).

(5)

(6)

(7)

(8)

는 상기

와 동일한 값이고,

은 절개 전 원통 형상의 중심과 내부 곡면의 제 1 지점을 연결하여 연장한 축을 z축이라고 하고 절개 전 원통 형상의 중심을 지나는 높이 방향을 y축이라고 할 때 (z, x) 평면에서 z축을 기준으로 한 회전각을 의미하고,

는 y축과의 천정각을 의미함. 여기서, 상기 제 1 지점은 절개 전 원통 형상의 중심으로부터 내부 곡면까지 최단 거리를 이루도록 하는 내부 곡면의 지점임.) (only,

Quot;

Lt; / RTI >

(Z, x) plane, the axis extending from the center of the pre-incision cylindrical shape to the first point of the inner curved surface is referred to as the z-axis, and the height direction passing through the center of the incisive cylindrical shape is referred to as the y- Quot ;, and "

Means the zenith angle with the y-axis. Herein, the first point is a point of the inner curved surface that makes the shortest distance from the center of the incisive cylindrical shape to the inner curved surface.)

According to another aspect of the present invention, there is provided a method of generating a curved projection image, including: (a) projecting an original image onto a spherical coordinate system; And (b) projecting the projected image in the step (a) onto a cylindrical coordinate system.

Specifically, the projected image of step (b) is distorted by a performance measurement chart of the camera module. In addition, the projected image of the step (b) is concave with respect to the outside of the left or the right outside, compared with the original image, and the upper side or the lower side of the image is concave And is convex to the outside or the outside of the lower side.

를 구좌표계의 픽셀의 위치

로 투영하되, 직각 좌표계의 원본 영상의 픽셀의 위치

로부터 구좌표계의 픽셀의 위치

로의 투영은 다음의 수학식 (9) 내지 (12)를 만족하는 것이 바람직하다.In the step (a), the position of the pixel of the original image in the rectangular coordinate system

To the position of the pixel in the spherical coordinate system

, The position of the pixel of the original image in the rectangular coordinate system

The position of the pixel in the spherical coordinate system from

It is preferable that the projection onto the projection plane satisfies the following equations (9) to (12).

(9)

(10)

(11)

(12)

는 어안 렌즈 모델의 반지름,

는 상기 어안 렌즈 모델의 중심을 지나는 (x, y) 평면에서 x축을 기준으로 한 회전각 및

는 상기 어안 렌즈 모델의 z축과의 천정각을 각각 의미함.) (only,

The radius of the fisheye lens model,

(X, y) plane passing through the center of the fisheye lens model, and

Represents the zenith angle with respect to the z-axis of the fisheye lens model).

를 원통 좌표계의 내부 곡면의 픽셀의 위치

로 투영하되, 상기 (a) 단계에서 투영된 픽셀의 위치

로부터 원통 좌표계의 내부 곡면의 픽셀의 위치

로의 투영은 다음의 수학식 (13) 내지 (16)을 만족하는 것을 특징으로 한다.In addition, the step (b) may include the step of:

To the position of the pixel of the inner curved surface of the cylindrical coordinate system

, The position of the projected pixel in the step (a)

The position of the pixel of the inner curved surface of the cylindrical coordinate system

(13) to (16): " (13) "

(13)

(14)

(15)

(16)

는 상기

와 동일한 값이고,

은 절개 전 원통 형상의 중심과 내부 곡면의 제 1 지점을 연결하여 연장한 축을 z축이라고 하고 절개 전 원통 형상의 중심을 지나는 높이 방향을 y축이라고 할 때 (z, x) 평면에서 z축을 기준으로 한 회전각을 의미하고,

는 y축과의 천정각을 의미함. 여기서, 상기 제 1 지점은 절개 전 원통 형상의 중심으로부터 내부 곡면까지 최단 거리를 이루도록 하는 내부 곡면의 지점임.) (only,

Quot;

Lt; / RTI >

(Z, x) plane, the axis extending from the center of the pre-incision cylindrical shape to the first point of the inner curved surface is referred to as the z-axis, and the height direction passing through the center of the incisive cylindrical shape is referred to as the y- Quot ;, and "

Means the zenith angle with the y-axis. Herein, the first point is a point of the inner curved surface that makes the shortest distance from the center of the incisive cylindrical shape to the inner curved surface.)

According to the curved projection image generation system and method of the present invention, it is possible to project a distorted image on an internal curved surface of an incised cylindrical shape so that it can be picked up by an ultra-wide angle camera, do.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 shows an example of a measuring instrument with an internal curved surface in the form of an incised cylinder. Fig.
FIG. 2A and FIG. 2B are exemplary views of a test chart to be mounted on the measuring instrument of FIG. 1, respectively, and examples of images actually taken by an ultra-wide angle camera. FIG.
BACKGROUND OF THE INVENTION Field of the Invention [0001]
4 is an explanatory diagram for projecting an incised cylindrical inner surface image into a plane image of a rectangular coordinate system.
5 is an explanatory diagram of an image change according to a grid chart;
6 is an explanatory diagram of predistortion by a projection image generation unit;
Figs. 7A and 7B are EIA charts, which are actual test charts, and their predistorted results, respectively.
FIG. 8 is a flowchart illustrating a method of generating a curved surface using image according to an exemplary embodiment of the present invention. FIG.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a curved projection image generation system and a method of generating a curved projection image according to embodiments of the present invention will be described in detail with reference to the accompanying drawings.

It should be understood that the following embodiments of the present invention are only for embodying the present invention and do not limit or limit the scope of the present invention. It will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

3 is a block diagram of a curved projection image generation system 100 according to a preferred embodiment of the present invention.

3, the curved projection image generation system 100 according to the preferred embodiment of the present invention includes a projection formula calculation unit 110 and a projection image generation unit 120. As shown in FIG.

4 is an explanatory diagram for projecting an incised cylindrical inner surface image into a plane image of a rectangular coordinate system. Specifically, the incised cylindrical shape is cut in the longitudinal direction of the cylinder, and the curved surface of the incised upper surface appears as a part of the circumference of the circle.

As can be seen from FIG. 4, according to the present invention, the incised cylindrical inner surface image is primarily distorted by the fish-eye lens used in the wide-angle camera including the super-wide angle camera. In addition, the image distorted by the fisheye lens is projected as a planar image, resulting in secondary distortion.

If the projecting of the incised cylindrical inner surface image of FIG. 4 into a planar image of a rectangular coordinate system is referred to as an omnidirectional projection, a planar image of a rectangular coordinate system may be referred to as an inverted projection of an incised cylindrical inner surface image have.

FIG. 5 is an explanatory diagram of an image change according to a grid chart. FIG.

FIG. 5 shows that the grid of FIG. 2A, that is, the net structure image is projected in a two-dimensional image by the frontal image modeling, and is similar to the actual image of FIG. 2b.

It can be seen from Fig. 5 that when the grid chart is provided on the inner curved surface of the cut cylindrical shape, it is distorted in the spherical coordinate system primarily by the fish-eye lens, and again flattened and imaged.

Therefore, even if a chart which is not distorted is provided on the inner curved surface of the cylindrical shape, it is difficult for the image finally picked up by the camera to be used for measuring the performance of the camera due to two distortions.

The projection formula calculating unit 110 calculates a formula for projection of a coordinate system. In addition, the projection image generation unit 120 serves to project the original image to a different coordinate system according to the formula calculated by the projection formula calculation unit 110. [

In the present invention, it is desirable to correct the distortions as shown in Figs. 4 and 5 by the projection formula calculating section 110 and the projection image generating section 120. Fig.

The projection formula calculating unit 110 includes a first calculator 111 and a second calculator 112. The first calculator 111 calculates a first expression group required when projecting a fisheye lens model image of a rectangular coordinate system. The second calculator 112 calculates a second expression group required when projecting the fisheye lens model image onto the incised cylindrical inner curved surface.

Here, the incised cylindrical inner surface image refers to an image or a modeled image of a chart such as a performance measurement chart of a camera module mounted on a measuring instrument as shown in Fig.

Specifically, the first calculator 111 calculates the third expression group required when projecting the fisheye lens model image into the image of the rectangular coordinate system, and calculates the inverse function of the third expression group to calculate the first expression group .

Similarly, the second calculator 112 calculates the fourth formula group required when projecting the incised cylindrical inner surface image onto the fish-eye lens model, and calculates the inverse function of the fourth formula group, It is preferable to calculate the group.

The projection image generation unit 120 generates a primary projection image of the original image using the first expression group and generates a secondary projection image of the primary projection image using the second expression group . The image generated by the projection image generation unit 120 is a chart for measuring the performance of the camera module, which is a distorted image.

Specifically, the mathematical expressions of the first expression group for the primary projection of the original image will be described. The meaning of the components of each coordinate system is as shown in Fig.

First, the position of the pixel in each coordinate system and the meaning of each variable are as follows.

: 2차원 직각 좌표계 영상의 픽셀의 위치.-

The position of a pixel in a two-dimensional rectangular coordinate system image.

: 어안 렌즈 모델 영상의 픽셀의 위치로, 구 좌표계를 이용함.

는 어안 렌즈 모델의 반지름,

는 어안 렌즈 모델의 중심을 지나는 (x, y) 평면에서 x축을 기준으로 한 회전각 및

는 어안 렌즈 모델의 z축과의 천정각을 각각 의미함.-

: The position of the pixel of the fisheye lens model image, using the spherical coordinate system.

The radius of the fisheye lens model,

(X, y) plane passing through the center of the fisheye lens model, and

Represents the zenith angle with respect to the z axis of the fisheye lens model.

: 편의상 y축 상으로 놓인 원통 좌표계와 일치하기 위한 구좌표계임.

은 절개 전 원통 형상의 중심과 내부 곡면의 제 1 지점을 연결하여 연장한 축을 z축이라고 하고 절개 전 원통 형상의 중심을 지나는 높이 방향을 y축이라고 할 때 (z, x) 평면에서 z축을 기준으로 한 회전각을 의미하고,

는 y축과의 천정각을 의미함. 여기서, 제 1 지점은 절개 전 원통 형상의 중심으로부터 내부 곡면까지 최단 거리를 이루도록 하는 내부 곡면의 지점임.-

: For convenience, a spherical coordinate system to match the cylindrical coordinate system placed on the y-axis.

(Z, x) plane, the axis extending from the center of the pre-incision cylindrical shape to the first point of the inner curved surface is referred to as the z-axis, and the height direction passing through the center of the incisive cylindrical shape is referred to as the y- Quot ;, and "

Means the zenith angle with the y-axis. Here, the first point is the point of the inner curved surface which makes the shortest distance from the center of the cylindrical shape to the inner curved surface.

: 원통형 좌표계의 픽셀의 위치. 다만,

는

와 동일한 값을 가짐.-

: The position of the pixel in the cylindrical coordinate system. but,

The

Lt; / RTI >

로부터 어안 렌즈 모델 영상의 픽셀의 위치

로의 투영은 다음의 [수학식 1] 내지 [수학식 4]를 만족한다. 다만,

는 어안 렌즈 모델의 반지름으로 고정된 상수값을 이용한다.In addition, the position of the pixel in the rectangular coordinate system image

The position of the pixel of the fisheye lens model image

(1) to (4). &Quot; (4) " but,

Uses a fixed constant value as the radius of the fisheye lens model.

는, 광축(원의 중심)으로부터

의 반지름과

의 회전 각도로 표기된다. 어안 렌즈 모델에 준하여 광축으로부터 크기

은 구좌표계의 광축으로부터 멀어진 각도인

에 비례하여,

로 표기된다. 즉, 광축을 따라온 광원은 원점에 결상되고,

인 위치, 다시 말해 구 표면의 가장자리를 통과한 광선일 때에는

가 90도임을 알 수 있다. 즉,

은 광선이 통과하는 구 표면

의 천정각

이 광축에서 멀어질수록 점점 커지는 특성을 보인다.That is, the position of the pixel of the wide-

(The center of the circle) from the optical axis

Of the radius

As shown in Fig. Based on the fisheye lens model,

Is an angle that is away from the optical axis of the spherical coordinate system

In proportion to this,

Respectively. That is, the light source which has been along the optical axis is imaged on the origin,

In other words, when the ray passes through the edge of the spherical surface

Is 90 degrees. In other words,

The spherical surface through which the ray passes

Zenith angle of

As the distance from the optical axis increases.

로부터 절개된 원통 형상의 내부 곡면의 픽셀의 위치

로의 투영은 [수학식 5] 내지 [수학식 8]을 만족한다. In addition, the position of the pixel of the fisheye lens model image

The position of the pixel of the inner curved surface of the cylindrical shape cut out from the

(5) to (8). &Quot; (8) "

6 is an explanatory diagram of predistortion by the projection image generation unit 120. FIG.

That is, the image generated by the projection image generating unit 120 is predistorted. That is, the original image is firstly projected in the spherical coordinate system according to the fisheye lens model using the above-described Equations (1) to (4), and then, using Equations (5) to Thereby projecting the projection image to the cylindrical coordinates.

If the predistorted image is used as a chart, the distortion occurring in the image pickup using the wide angle camera including the ultra-wide angle camera can be corrected, and the distortion in the finally captured image is minimized. .

Figs. 7A and 7B are EIA charts, which are actual test charts, and the results of predistortion thereof, respectively.

As can be seen from Figs. 7A and 7B, the image generated by the projection image generation unit 120 appears concave with respect to the outside or right outside of the left side or the right side, as compared with the original image. Further, the image generated by the projection image generating unit 120 is convexly displayed on the upper side or the lower side with respect to the outer side of the upper side or the lower side of the lower side, as compared with the original image.

8 is a flowchart illustrating a method of generating a curved projection image according to an exemplary embodiment of the present invention. Since the curved projection image generation system 100 according to the preferred embodiment of the present invention uses the above-described curved projection image generation system 100, all the features of the curved projection image generation system 100 are included Of course.

As can be seen from FIG. 8, the method of generating a curved projection image according to an exemplary embodiment of the present invention includes calculating a fourth expression group required when projecting an incised cylindrical inner curved image onto a fisheye lens model A step S120 of calculating a third expression group required when projecting the projected fisheye lens model image in step S110 and step S110 onto an image of a rectangular coordinate system.

In steps S110 and S120, a standard image attached to the cylinder is displayed on the super-wide-angle camera. In steps S130 and S140, an appropriate image is displayed on the cylindrical coordinate system .

The cut internal cylindrical curved surface image in step S110 refers to an image or a modeled image of a chart such as a performance measurement chart of a camera module mounted on a measuring instrument as shown in Fig.

Steps S110 and S120 are performed to project an incised cylindrical inner surface image into a planar image of a rectangular coordinate system.

In addition, a method of generating a curved surface using image according to an exemplary embodiment of the present invention may include a step of projecting an original image to a spherical coordinate system (S130) and a step of projecting a projected image to a cylindrical coordinate system (S140) .

The main object of steps S130 and S140 is to perform predistortion before projecting an image on a cylindrical inner curved surface in order to prevent distortion such as steps S110 and S120. The predistortion is as described in Fig.

That is, the inverse function of the third expression group in step S120 is used in step S130, and the inverse function of the fourth expression group in step S110 is used to perform the pre-distortion.

Thus, the projected image in step S140 is characterized by being distorted as a chart for inspection.

The method of generating a curved projection image according to a preferred embodiment of the present invention is based on an example in which the present invention is applied to a chart for measuring the performance of a camera. However, the method of generating a curved surface using image of the present invention can be applied variously.

As described above, according to the curved projection image generation system 100 of the present invention and the method of generating the curved projection image, the distorted image can be projected on the incised cylindrical inner curved surface to be picked up by the ultra-wide angle camera, So that performance evaluation can be facilitated. In addition, it can be seen that the curved surface projection image generation system 100 of the present invention and its generation method can be applied not only to performance evaluation of an ultra-wide angle camera but also to games such as screen golf.

100: Surface projection image generation system
110: Projection formula calculating unit
120: Projection image generating unit
111: First calculator
112: second calculator

Claims (11)

And a projection image generation unit for projecting the original image to another coordinate system,
Wherein the projection image generation unit comprises:
The image of the rectangular coordinate system is first projected onto the fisheye lens model image and the fisheye lens model image which is the result of the primary projection is projected onto the incised cylindrical interior curved surface secondarily,
The left or right side of the image generated by the projection image generation unit may include,
Is concave relative to the outside of the left side or the outside of the right side,
The upper or lower side of the image generated by the projection-
Wherein the image of the curved surface is convex with respect to the outer side of the upper side or the lower side of the lower side as compared with the original image. The method according to claim 1,
The curved projection image generation system includes:
And a projection formula calculating unit for calculating a formula for projection of the coordinate system,
Wherein the projection-
A first calculator for calculating a first expression group required when projecting a fisheye lens model image of a rectangular coordinate system; And
And a second calculator for calculating a second group of expressions required when projecting the fisheye lens model image onto the inner curved surface of the cut cylindrical shape. The method according to claim 1,
Wherein the image generated by the projection image generation unit includes:
Wherein the image is distorted by a performance measurement chart of the camera module. delete The method according to claim 1,
The position of a pixel in a Cartesian coordinate system image

The position of the pixel of the fisheye lens model image

Wherein the projections of the curved surface projection image satisfy the following equations.
(One)

(2)

(3)

(4)

(only,

The radius of the fisheye lens model,

(X, y) plane passing through the center of the fisheye lens model, and

Represents the zenith angle with respect to the z-axis of the fisheye lens model). 6. The method of claim 5,
The position of a pixel in a fisheye lens model image

The position of the pixel of the inner curved surface of the cylindrical shape cut out from the

Wherein the projections of the curved surface projection image satisfy the following equations.
(5)

(6)

(7)

(8)

(only,

Quot;

Lt; / RTI >

(Z, x) plane, the axis extending from the center of the pre-incision cylindrical shape to the first point of the inner curved surface is referred to as the z-axis, and the height direction passing through the center of the incisive cylindrical shape is referred to as the y- Quot ;, and " Means the zenith angle with the y-axis. Herein, the first point is a point of the inner curved surface that makes the shortest distance from the center of the incisive cylindrical shape to the inner curved surface.) (a) projecting an original image onto a spherical coordinate system; And
(b) projecting the projected image in the step (a) onto a cylindrical coordinate system,
The left or right side of the projected image of step (b)
Is concave relative to the outside of the left side or the outside of the right side,
The upper or lower side of the projected image of step (b)
Wherein the image of the curved surface is convex with respect to the outer side of the upper side or the lower side of the lower side as compared with the original image. 8. The method of claim 7,
The projected image of step (b)
Wherein the image is distorted by a performance measurement chart of the camera module. delete 8. The method of claim 7,
The step (a)
The position of the pixel in the original image in Cartesian coordinate system

To the position of the pixel in the spherical coordinate system

Lt; / RTI >
The position of the pixel in the original image in Cartesian coordinate system

The position of the pixel in the spherical coordinate system from

Wherein the projections of the curved surface satisfy the following equations.
(9)

(10)

(11)

(12)

(only,

The radius of the fisheye lens model,

(X, y) plane passing through the center of the fisheye lens model, and

Represents the zenith angle with respect to the z-axis of the fisheye lens model). 11. The method of claim 10,
The step (b)
The position of the projected pixel in the step (a)

To the position of the pixel of the inner curved surface of the cylindrical coordinate system

Lt; / RTI >
The position of the projected pixel in the step (a)

The position of the pixel of the inner curved surface of the cylindrical coordinate system

Wherein the projections of the curved surface satisfy the following equations.
(13)

(14)

(15)

(16)

(only,

Quot;

Lt; / RTI >

(Z, x) plane, the axis extending from the center of the pre-incision cylindrical shape to the first point of the inner curved surface is referred to as the z-axis, and the height direction passing through the center of the incisive cylindrical shape is referred to as the y- Quot ;, and "

Means the zenith angle with the y-axis. Herein, the first point is a point of the inner curved surface that makes the shortest distance from the center of the incisive cylindrical shape to the inner curved surface.)

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