Perspective ruler display method

Abstract

When users draw on a virtual canvas using drawing software, they can more easily depict illustrations similar to those taken with a fisheye lens. The disclosed technology provides a perspective ruler display method comprising the following steps: setting the angle ∠OPW formed by a point O on the canvas, a point P on a straight line V passing through point O and orthogonal to the plane of the canvas, and a point W existing in the three-dimensional space as θ; setting the distance between point O and point P as 1; transforming the straight line on the canvas or the graphic existing in the three-dimensional space using a function f(θ, k) that converts the coordinates of point W to the coordinates of point B on the canvas at a distance f(θ, k) from point O; obtaining a curve with the same shape as the curve obtained by transforming the straight line using the function f(θ, k); and displaying a perspective ruler having the obtained curve.

Description

Technical Field

[0001] This invention relates to a method for displaying a perspective ruler. Background Technology

[0002] In the past, when using drawing software to depict three-dimensional objects such as illustrations, perspective rulers based on the method of distance, or perspective (shortened to "perspective"), were sometimes used.

[0003] When drawing illustrations, perspective rulers are used to create accurate perspective views based on the principle of perspective. An example of how to use a perspective ruler is as follows.

[0004] When a user is drawing an object, the perspective ruler is positioned aligned with the object to be drawn. For example, if the object is shaped like a box, the perspective ruler is positioned along the shape of the box. Lines for the perspective view can then be drawn along the perspective ruler. When drawing lines, the user can use the perspective ruler to draw along its guide lines, thus enabling the accurate drawing of straight lines according to perspective even when hand-drawing. By repeating the same steps, illustrations based on perspective can be drawn on a two-dimensional canvas.

[0005] In the composition of typical illustrations, perspective is used in the linear projection method known as perspective projection, but when creating a more impactful effect, a special perspective known as fisheye perspective is sometimes employed.

[0006] Fisheye perspective differs from regular perspective projection because it requires drawing curves, making it difficult to draw accurate lines manually. Therefore, a ruler tool is needed to assist in drawing such complex fisheye lenses.

[0007] As a common fisheye perspective ruler that has existed for a long time, it is known to use a perspective ruler with curved grid lines.

[0008] There is drawing software that provides a curved perspective ruler, which can be used to depict distorted illustrations, such as those taken with a fisheye lens. By using the curved perspective ruler, users can depict objects that represent the same perspective as images taken with a fisheye lens. Using this software makes it easier to draw perspective views taken with a fisheye lens.

[0009] In addition, there are non-patent documents that disclose methods for depicting fisheye perspective (for example, see Non-patent Document 1). This document discloses a general methodology for depicting distorted illustrations, such as photographs taken using a camera with a fisheye lens.

[0010] However, existing fisheye perspective rulers have the following characteristics.

[0011] It can depict curves obtained by taking pictures of lines parallel to the coordinate axes of a virtual camera using a fisheye lens, but it does not provide a perspective ruler that can depict lines with various directions.

[0012] Furthermore, fisheye lenses come in various types, each with different degrees of distortion. However, existing fisheye perspective rulers do not provide users with the capability to perform drawing tasks with such diverse distortions.

[0013] The fisheye perspective ruler is also displayed in a grid pattern in redundant areas that are not related to drawing, which may hinder the user's drawing process.

[0014] Prior art literature

[0015] Non-patent literature

[0016] Non-patent literature 1: https: / / oekaki-zukan.com / articles / 11818 Summary of the Invention

[0017] The technical problem that the invention aims to solve

[0018] The purpose of the disclosed technology is to make it easier for users to draw illustrations, like those taken with a fisheye lens, when using drawing software to depict pictures on a virtual canvas.

[0019] Technical means for solving technical problems

[0020] The disclosed technology provides a method for displaying a perspective ruler, wherein the perspective ruler is placed on a planar canvas existing in a virtual three-dimensional space, and the computer displays the perspective ruler according to instructions from the user to depict a fisheye lens effect, so as to draw lines along the perspective ruler on the canvas.

[0021] The perspective ruler display method includes the following steps:

[0022] A function f(θ, k) is defined, wherein f(θ, k) is used to set the angle ∠OPW formed by point O on the canvas, point P on a straight line V passing through point O and orthogonal to the plane of the canvas, and point W existing in the three-dimensional space as θ, the distance between point O and point P is set to 1, and the coordinates of point W are converted to the coordinates of point B on the canvas that is separated from point O by a distance f(θ, k).

[0023] Furthermore, the function f(θ, k) satisfies the following conditions:

[0024] Within the range of θ used for transformation, 0 ≤ θ < π / 2.

[0025] Satisfy 0≦f(θ,k)≦R*tan(θ),

[0026]

[0027] and satisfy

[0028] When the range of θ includes the region greater than π / 2, and within the range of θ where π / 2 ≤ θ ≤ π,

[0029] Satisfying f(θ, k) > 0,

[0030] as well as

[0031] The function f(θ, k) is used to transform the straight lines on the canvas or the graphics existing in the three-dimensional space to obtain a curve with the same shape as the curve obtained by transforming the straight lines using the function f(θ, k). A perspective ruler with the obtained curve is then displayed.

[0032] Here, k is a parameter representing the intensity of the deformation exhibited by the fisheye lens in the perspective ruler.

[0033] R is a parameter representing the overall scaling of the perspective ruler centered at point O.

[0034] Alternatively, in the disclosed technology, point B may exist on a straight line that is perpendicularly projected onto the plane of the canvas by the line connecting point O and point W.

[0035] Alternatively, in the disclosed technology, the point W may be a point existing on the canvas, and the perspective ruler refers to a perspective ruler that displays a curve obtained by transforming a straight line on the canvas using the function f(θ, k).

[0036] Alternatively, in the disclosed technology, point B may exist on the straight line connecting point O and point W.

[0037] Alternatively, in the disclosed technology, a curved surface G with an axisymmetric shape about the straight line V can also be formed.

[0038] Let point Q be the point where the line connecting point P and point W intersects the surface G. Let point D be the point where the line connecting point S and point Q intersects the canvas. Point S is a point S existing on the line V and located on the opposite side of point O relative to point P.

[0039] The value of k is proportional to the distance between point P and point S.

[0040] The value of the function f(θ, k) is proportional to the distance between point O and point D.

[0041] Alternatively, in the disclosed technology, a curved surface G with an axisymmetric shape about the straight line V can also be formed.

[0042] Let point Q be the point where the line connecting point P and point W intersects the surface G; let point C be the point on the line connecting point P and point W; let α be the angle between the plane of the canvas and vector OQ; and let β be the angle between the plane of the canvas and vector OC.

[0043] The value of k is proportional to the value of β / α.

[0044] The value of the function f(θ, k) is proportional to the distance between point O and point C.

[0045] Alternatively, in the disclosed technology, the function f(θ, k) may be consistent with or approximately equal to R*tan(θ) when the intensity k of the deformation is a specified value.

[0046] Alternatively, in the disclosed technology, it is also possible that the function f(θ, k) is in the case that the intensity k of the deformation is a predetermined value.

[0047] With 2*R*tan(θ / 2) as a stereo projective,

[0048] R*θ as an equidistant projective

[0049] As the equiangular projection of 2*R*sin(θ / 2) and

[0050] At least one of the consistent or approximate R*sin(θ) as the orthographic projection.

[0051] Alternatively, in the publicly available technology, determining the function f(θ, k) may include the following steps:

[0052] When determining the coordinates of point B, different functions f(θ, k) are applied to the X-coordinate and Y-coordinate of point B on the coordinate axes that are orthogonal to each other with point O as the origin on the plane of the canvas, to obtain the coordinates of point B on the canvas.

[0053] Alternatively, in the publicly available technology, displaying the perspective ruler may also include the following steps:

[0054] The deformation intensity k and scaling factor R are set in such a way that the magnitude of the function f(π / 2, k) is kept constant.

[0055] Alternatively, in the disclosed technology, the function f(θ, k) can also be defined by the following formula: f(θ, k) = R*(k+1)*sin(θ) / (k+cos(θ)).

[0056] Here, 0≦k≦∞.

[0057] Alternatively, in the publicly available technology, the function f(θ, k) can also be defined by the following formula: f(θ, k) = R*sin(θ) / cos(θ-θ*k / 2).

[0058] Here, 0 ≦ k ≦ 2.

[0059] Alternatively, the disclosed technology can also provide a perspective ruler display method, wherein the perspective ruler is placed on a flat canvas, and a computer displays the perspective ruler according to instructions from a user to depict the appearance of a fisheye lens, so as to draw lines along the perspective ruler on the canvas.

[0060] The perspective ruler display method includes the following steps:

[0061] Define a function g(r, k). This function g(r, k) is used to convert the coordinates of point W to the coordinates of point B on the canvas, where the distance between point O and point W on the canvas is r, and the distance between point W and point O is g(r, k).

[0062] The g(r, k) satisfies:

[0063] 0≦g(r,k)≦R*r,

[0064]

[0065] as well as

[0066] The function g(r, k) is used to transform the straight lines on the canvas to obtain curves, and a perspective ruler displaying the obtained curves is then generated.

[0067] Here, k is a parameter representing the intensity of the deformation exhibited by the fisheye lens in the perspective ruler.

[0068] R is a parameter representing the overall scaling of the perspective ruler centered at point O. Alternatively, in the disclosed art, the function g(r, k) can also be defined by the following formula:

[0069] g(r, k) = R*(k+1)*sin(tan) -1 (r)) / (k+cos(tan -1 (r)),

[0070] Here, 0≦k≦∞.

[0071] Alternatively, in the publicly available technology, the function g(r, k) can also be defined by the following formula:

[0072] g(r, k) = R*sin(tan -1 (r)) / cos(tan -1 (r)-tan -1 (r)*k / 2),

[0073] Here, 0 ≦ k ≦ 2.

[0074] Additionally, the disclosed technology provides a perspective ruler display method. The perspective ruler is a planar canvas placed in a virtual three-dimensional space. The computer displays the perspective ruler based on instructions from the user to depict a fisheye lens effect, so that lines can be drawn along the perspective ruler on the canvas.

[0075] The perspective ruler display method includes the following steps:

[0076] Based on user instructions, rules are determined to convert straight lines on the canvas or virtual straight lines in the three-dimensional space into curves on the canvas that are suitable for the fisheye lens display.

[0077] Generate the perspective ruler, which is determined by a curve based on the rules and by a curve at a specified position on the canvas specified by the user;

[0078] The locations of the vanishing points, or points where the curves of the perspective rulers converge, are determined on the plane including the canvas, so that the user can identify them; and

[0079] The perspective ruler is displayed on the canvas.

[0080] Alternatively, in publicly available technologies, determining the rule may include the following steps:

[0081] If the user instructs a change in the intensity of the distortion exhibited by the fisheye lens, the rule is modified in response to the change in the intensity of the distortion.

[0082] Generating the perspective ruler includes the following steps:

[0083] The perspective ruler generated before the rule change will be changed to a perspective ruler determined by a curve based on the changed rule and at the specified position specified by the user before the rule change.

[0084] Alternatively, in publicly available technologies, determining the rules can also be done in the following ways:

[0085] The rule is determined based on at least one of the following: the intensity of the distortion represented by the fisheye lens, the scale factor, and the position of the intersection of the central axis of the virtual lens represented by the fisheye lens and the canvas, as specified by the user.

[0086] Alternatively, in publicly available technologies, determining the rules may also include the following steps:

[0087] The curves of the two perspective rulers are determined by drawing two curves on the canvas based on the user's instructions;

[0088] The intersection of the two curves is taken as the vanishing point; and

[0089] The intensity of the deformation exhibited by the fisheye lens is determined based on at least the degree of curvature of at least one of the two curves.

[0090] Alternatively, in the publicly available technology, generating the perspective ruler may also include the following steps:

[0091] If the user instructs that the tilt of the perspective ruler be changed, the rule is applied to change the position of the specified vanishing point of the perspective ruler in response to the change in tilt.

[0092] Alternatively, in the publicly available technology, generating the perspective ruler may also include the following steps:

[0093] If the user's instruction is to change the specified position, in response to the change of the specified position, the rule is applied, and the position of the vanishing point of the specified perspective ruler is not changed, but the curve of the specified perspective ruler passing through the changed specified position is changed.

[0094] Alternatively, in the publicly available technology, generating the perspective ruler may also include the following steps:

[0095] The perspective ruler cannot be changed if the user has instructed that the position of the specified vanishing point be fixed, and the specified position of the perspective ruler that converges to the specified vanishing point is not changed.

[0096] Alternatively, in the publicly available technology, the perspective ruler can also be generated in a way that prevents the specified position from shifting even if the intensity of the deformation is changed by the user.

[0097] Alternatively, in the publicly available technology, generating the perspective ruler may also include the following steps:

[0098] If the position of the vanishing point is changed according to the user's instructions, the curve of the perspective ruler is changed.

[0099] Alternatively, in the disclosed technology, displaying the perspective ruler may also include the following steps:

[0100] In the case of changing the display of the perspective ruler,

[0101] The image is drawn according to the user's instructions, adapting to changes in each of the multiple perspective rulers.

[0102] Alternatively, in the disclosed technology, displaying the perspective ruler may also include the following steps:

[0103] In the case of changing the display of the perspective ruler,

[0104] The image on the canvas is altered to adapt to changes in each of the multiple perspective rulers.

[0105] Alternatively, the disclosed technology could also be a program that enables a computer to execute a perspective ruler display method.

[0106] Invention Effects

[0107] The publicly available technology can provide an environment where users can more easily depict illustrations, similar to those taken with a fisheye lens, when drawing on a virtual canvas using drawing software. Attached Figure Description

[0108] Figure 1 is a diagram illustrating the disclosed technical overview. Figure 1A It refers to an illustration created by a user using publicly available technology. Figure 1B This refers to the reference image used by the user when drawing the illustration.

[0109] Figure 2 is a diagram illustrating a user's use of publicly available technology to create an illustration.

[0110] Figure 3 This diagram shows the setup of a fisheye perspective ruler in conjunction with a reference image.

[0111] Figure 4 This is a diagram showing the state of drawing curve 410 along a fisheye perspective ruler.

[0112] Figure 5 This is a diagram indicating that the display of the reference image is turned off.

[0113] Figure 6 This is a graph representing an example of the function f(θ, k) used to generate a fisheye perspective ruler.

[0114] Figure 7 It means in relation to Figure 6 A diagram of an example of the same method and function f(θ, k) where θ exceeds 90°.

[0115] Figure 8This is a graph representing other examples of the function f(θ, k) used when generating a fisheye perspective ruler.

[0116] Figure 9 It means in relation to Figure 8 A diagram of an example of the same method and function f(θ, k) where θ exceeds 90°.

[0117] Figure 10 This is a diagram representing an example of a surface G that is a surface other than a sphere.

[0118] Figure 11 is a diagram illustrating an example of setting the deformation intensity and determining the vanishing point based on user instructions. Figures 11A to 11D This is an example of a user interface that allows users to intuitively manipulate the intensity of deformation, the determination of the vanishing point, and the determination of the two fisheye perspective rulers.

[0119] Figure 12 is an example of the fisheye perspective ruler display when the user changes the intensity of the deformation. Figure 12A The fisheye perspective ruler is displayed before the change in the strength of the deformation. Figure 12B The display shows the fisheye perspective ruler after the intensity of the deformation has been changed.

[0120] Figure 13 illustrates the movement of the vanishing point as the inclination of the fisheye perspective ruler changes. Figure 13A This indicates the state before the tilt of the fisheye perspective ruler was changed. Figure 13B This indicates the state after changing the tilt of the fisheye perspective ruler.

[0121] Figure 14 shows an example of adding a fisheye perspective ruler. Figures 14A to 14C The image shows an example of adding a fisheye perspective ruler.

[0122] Figure 15 is a diagram showing the state when the fisheye perspective ruler is moved to a specified position based on the user's instructions. Figure 15A It indicates the state before the specified position is moved. Figure 15B This indicates the state after the specified position has been moved.

[0123] Figure 16 shows an example of the handle display when the user provides an indication of the location of a fixed vanishing point. Figure 16A This indicates the state before the user provides an indication of the location of the fixed vanishing point. Figure 16B This indicates the status after the user provides an indication of the location of the fixed vanishing point.

[0124] Figure 17 is a diagram showing the state transition when the point O (the center point O of the lens) where the straight line V of the central axis of the virtual lens intersects the canvas is moved. Figure 17A This is the diagram before the center point O of the lens was moved. Figure 17B This is the diagram after the center point O of the lens has been moved.

[0125] Figure 18 is a diagram illustrating the state transition when the vanishing point is moved. Figure 18A This is the graph before the vanishing point is moved. Figure 18B This is the graph after the vanishing point has been moved.

[0126] Figure 19 is a diagram showing the state transition when the strength of the deformation is changed. Figure 19A It is a diagram showing the state before the deformation strength is changed. Figure 19B It is a diagram showing the state after the strength of the deformation has been changed.

[0127] Figure 20 is a diagram showing the state transition when the scaling factor R is changed. Figure 20A This is a diagram showing the state before the scaling factor R was changed. Figure 20B This is a diagram showing the state after changing the scaling factor R.

[0128] Figure 21 is a diagram showing the changes in the display of the fisheye perspective ruler. Figure 21A It is a diagram showing the state before the deformation strength is changed. Figure 21B It is a diagram showing the state after the strength of the deformation has been changed.

[0129] Figure 22 is a diagram showing the changes made to the curve already drawn along the fisheye perspective ruler as the display changes. Figure 22A It is a diagram showing the state before the deformation strength is changed. Figure 22B It is a diagram showing the state after the strength of the deformation has been changed.

[0130] Figure 23 shows a situation where the image on the canvas changes along with the change in the display of the fisheye perspective ruler. Figure 23A It is a diagram showing the state before the deformation strength is changed. Figure 23B It is a diagram showing the state after the strength of the deformation has been changed.

[0131] Figure 24 shows how the image on the canvas changes as the fisheye perspective ruler is changed. Figure 24A It is a diagram representing the state before the change. Figure 24B It is a diagram representing the changed state.

[0132] Figure 25 This is a flowchart for generating the curves of a fisheye perspective ruler used to depict the fisheye lens representation.

[0133] Figure 26 It means to use in Figure 6 and Figure 7 The flowchart illustrates the processing of the functions described in the document.

[0134] Figure 27 It means to use in Figure 8 and Figure 9 The flowchart illustrates the processing of the functions described in the document.

[0135] Figure 28 This is a flowchart showing how to display a fisheye perspective ruler on a canvas.

[0136] Figure 29A and Figure 29B This is a flowchart illustrating an example of a subroutine for steps S2802 and S2804 described above.

[0137] Figure 30 This describes the process related to the determination of rules.

[0138] Figure 31 This refers to other processes related to the determination of rules.

[0139] Figure 32 This is a flowchart illustrating an example of the process for generating a fisheye perspective ruler.

[0140] Figure 33 This is a flowchart illustrating other examples of the processing flow for generating a fisheye perspective ruler.

[0141] Figure 34 This is a flowchart showing an example of a fisheye perspective ruler.

[0142] Figure 35 This is a flowchart showing other examples of fisheye perspective rulers.

[0143] Figure 36 This is a hardware configuration diagram of the implementation method.

[0144] Figure 37 This is a graph that shows how the position of point B is obtained based on the position of point W on the canvas without using θ.

[0145] Figure 38 This is a diagram showing the user interface for easily setting up multiple orthogonal fisheye perspective rulers. Detailed Implementation

[0146] The disclosed technology will now be described with reference to the accompanying drawings.

[0147] A perspective ruler is provided along with various functions when a user draws on a virtual canvas on a flat surface using an input interface (e.g., pen, mouse, touch panel, tablet, pointing device, etc.). It should be noted that in this specification, descriptions of generally known functions among the existing features related to the perspective ruler are sometimes omitted.

[0148] Furthermore, virtual three-dimensional space is sometimes mentioned in this specification. However, it should be noted that this virtual three-dimensional space is used for the purpose of easily understanding and explaining this technology (such as the method for generating a perspective ruler), and its existence is not necessary when the user uses this technology (such as a perspective ruler) to draw.

[0149] Furthermore, this specification uses the example of drawing a line drawn with a straight line under normal perspective projection using a curve based on fisheye perspective. However, the disclosed technique is not limited to drawing lines, and can certainly be used for other drawing methods such as points, circles, rectangles, and areas to be colored.

[0150] <Implementation Method 1>

[0151] Figure 1 is a diagram illustrating the outline of the disclosed technology. Figure 1A It refers to an illustration created by a user using publicly available technology. Figure 1B This refers to the reference image used by the user when drawing the illustration.

[0152] Figure 1A This is an illustration 102A depicted on canvas 100. Illustration 102A, like a photograph taken with a fisheye lens, presents an image where objects that would normally be straight lines are distorted into curves. For example, window 104A, in a typical perspective projection, would have a window frame composed of straight lines. However, as in a photograph taken with a fisheye lens, the frame of window 104A is distorted and curved. Such an illustration, unlike typical perspective projection, becomes a more impactful illustration.

[0153] Figure 1B The window 104B present in the reference image 102B is also a curved window, and the reference image 102B itself is also an image intended to represent a fisheye lens.

[0154] In the disclosed technology, the illustration 102A, which mimics the appearance of a fisheye lens, is provided and can be easily drawn by a user. Furthermore, when a user draws illustration 102A, it is preferable to also overlay a reference image 102B as a draft on the canvas. It should also be noted that referring to image 102B is not necessary when a user draws the illustration.

[0155] Alternatively, consider the case where reference image 102B exists only in the user's mind as the intended image to be drawn. Typically, the user has in their mind an image they will subsequently draw (an illustration of their intention). To materialize such a virtual image, the user uses a fisheye perspective ruler in conjunction with the virtual image to draw a curve along the configured fisheye perspective ruler.

[0156] Figure 2 is a diagram illustrating a user's use of publicly available technology to create an illustration. Figure 2AIt is a diagram that displays a fisheye perspective ruler, etc., superimposed on the canvas. Figure 2B It is a line drawing of the shape of a building, created by a computer using publicly available technology and based on user instructions. Figure 2C It is a picture depicting buildings and the scenery around them. Figure 2D This is a diagram representing a completed illustration.

[0157] Figure 2A This refers to a drawing aid 200 that includes a fisheye perspective ruler displayed overlapping the canvas. Preferably, the drawing aid 200 exists on a different layer than the drawing layer used to draw the illustration.

[0158] exist Figure 2A In this context, the line at eye level 260, also known as the horizon, is used when aligning the vanishing point of the perspective ruler with the horizon. For example, it is known that in projection methods such as perspective projection, a plane parallel to the ground converges to the horizon at infinity. Similarly, it is known that a set of parallel lines in three-dimensional space, such as the wall of a road extending to infinity, converges to a vanishing point at eye level 260 at infinity. This eye level 260 is used as a reference when setting the vanishing point of the fisheye perspective ruler. An interface can also be provided where, if the vanishing point is brought close to the eye level, the vanishing point is attached to the eye level.

[0159] exist Figure 2A In the image, vanishing points 210, 220, and 230 exist. Vanishing points 220 and 230 exist on a line at the viewing level 260. Furthermore, fisheye perspective rulers 222, 224, and 226 converge to vanishing point 220 on the line at the viewing level 260. Similarly, fisheye perspective rulers 232, 234, and 236 converge to vanishing point 230 on the line at the viewing level 260. Fisheye perspective rulers 212, 214, and 216 converge to vanishing point 210 on a line that does not exist at the viewing level 260. By using fisheye perspective rulers with vanishing points on the line at the viewing level 260, curves that distort straight lines parallel to the ground based on the fisheye lens can be easily drawn. Furthermore, fisheye perspective rulers with vanishing points that do not exist on the line at the viewing level 260 can be used when drawing curves that distort straight lines that are not parallel to the ground based on the fisheye lens.

[0160] exist Figure 2A The image depicts a 180-degree circle 202. In virtual 3D space, the 180-degree circle corresponds to a 90-degree angle from the front of the camera. That is, the inside of the 180-degree circle corresponds to the area in virtual 3D space that is in front of the camera, and the outside of the 180-degree circle corresponds to the area in virtual 3D space that is behind the camera.

[0161] The lens circle refers to the circle formed by the edges of the image projected onto the photographing surface by a fisheye lens. The lens circle of a fisheye lens with a 180-degree field of view is the same as the 180-degree circle.

[0162] The fisheye perspective ruler with a vanishing point on the 180-degree circle 202 has another vanishing point (not shown) at the point where the line passing through one vanishing point and the center point O of the lens intersects the 180-degree circle.

[0163] The vanishing point can also be restricted so that the user cannot move beyond the 180-degree circle.

[0164] Furthermore, the camera's orientation in virtual 3D space is not necessarily parallel to the ground. Therefore, the preferred line-of-sight level 260 can be freely set according to the user's intended purpose.

[0165] In addition, the lens circle can also be displayed on the canvas. In the case of a lens circle with a fisheye lens having a field of view of more than 180 degrees, two pairs of vanishing points can be made to exist within the lens circle.

[0166] Figure 2B This indicates that, based on the user's instructions, the building's shape 280A was depicted along each fisheye perspective ruler.

[0167] Figure 2C This illustration depicts the completed building 280B and the roads surrounding it. For example, when the user is drawing a curve, lines can be drawn at the positions of each fisheye perspective ruler. Alternatively, when the user is drawing a line in a location separate from the fisheye perspective rulers, an invisible fisheye perspective ruler can be selected at a position on the canvas indicated by a pointing device, and the curve can be drawn along the selected fisheye perspective ruler based on the user's instructions. By reducing the number of fisheye perspective rulers displayed, obstruction during user drawing is prevented, and the computer can draw an illustration with appropriate fisheye lens representation based on the user's instructions.

[0168] Figure 3 This diagram shows the setup of a fisheye perspective ruler in conjunction with a reference image.

[0169] The multiple fisheye perspective rulers 342 converging at vanishing point 340 and the multiple fisheye perspective rulers 352 converging at vanishing point 350 are fisheye perspective rulers along the edges of tables, the boundaries of walls and floors, and the horizontal frames of window frames that are considered to be straight lines parallel to the ground.

[0170] In canvas 300, multiple fisheye perspective rulers 322 converging at vanishing point 320 are fisheye perspective rulers along the legs of a table, the boundaries between walls, and the vertical window frame, which are considered to be straight lines perpendicular to the ground.

[0171] In this way, by using reference images, users can easily set multiple fisheye perspective rulers.

[0172] Figure 4 This is a diagram showing the state of drawing curve 410 along a fisheye perspective ruler.

[0173] By having the user move the pointing device along the fisheye perspective ruler on the canvas, the computer is able to draw curve 410.

[0174] Figure 5 This is a diagram showing the state where the view of the reference image is turned off. The drawn curve 410 is displayed along with the fisheye perspective ruler. In addition, the quadrilateral 500 is a diagram for conveniently showing the position of the reference image.

[0175] Figure 6 and Figure 7 This is a graph representing an example of the function f(θ, k) used to generate a fisheye perspective ruler. Figure 6 This is the graph for the case where 0 ≦ θ < π / 2. Figure 7 This is the diagram for the case where π / 2 ≦ θ ≦ π. Let θ be the angle formed by point O on canvas 610, point P on a line V passing through point O and orthogonal to the plane of the canvas, and point W existing in three-dimensional space. Let the distance between point O and point P be 1. Then, place point S, which exists on line V, on the opposite side of point O relative to point P, at a distance k from point P.

[0176] Additionally, consider a surface G with the line V as its axis of symmetry. An example of surface G is a sphere of radius 1 centered at point P. However, surface G is not limited to such a sphere.

[0177] Let point Q be the point where the line connecting points P and W intersects surface G. Let point D be the point where the line connecting points S and Q intersects canvas 610. Let n be the distance from point O to point D.

[0178] When surface G is a sphere of radius 1 centered at point P, the distance n is expressed as follows:

[0179] n=(k+1)*sin(θ) / (k+cos(θ))(Formula 1),

[0180] Wherein, 0≦k≦∞.

[0181] If the scaling factor is set to R, then the function f(θ, k) is expressed as follows:

[0182] f(θ,k)=R*(k+1)*sin(θ) / (k+cos(θ)) (Formula 2).

[0183] Furthermore, k is a parameter representing the intensity of distortion in the fisheye lens representation, and the scaling factor R is a parameter that is the overall transformation multiplied by a scale. f(θ, k) is shown below, and depending on the value of k, it is consistent with or approximates various projection methods.

[0184] k = 0: Consistent with perspective projection (f(θ, k) = R*tan(θ)) (Equation 3-1),

[0185] k=1: Consistent with stereographic projection (f(θ, k) = 2*R*tan(θ / 2))

[0186] (Equation 3-2)

[0187] k = 1.8: Approximates equidistant (f(θ, k) ≒ R*θ) (Equation 3-3),

[0188] k = 2.5: Approximates the equisolid projection (f(θ, k) ≒ 2*R*sin(θ / 2)) (Equation 3-4),

[0189] k = ∞: consistent with the stereographic (f(θ, k) = R*sin(θ)) (Equation 3-5).

[0190] In this way, by appropriately setting the deformation parameter k and the scaling factor R, it is possible to define a fisheye perspective scale corresponding to the fisheye lens performance of various properties.

[0191] Furthermore, the radius of the 180-degree circle is the value of the function f(θ, k) when θ = π / 2, i.e., f(π / 2, k).

[0192] The function f(θ, k) has the following properties.

[0193] Within the range of θ used for transformation, 0 ≤ θ < π / 2.

[0194] Satisfy 0≦f(θ,k)≦R*tan(θ) (Equation 4),

[0195]

[0196] and satisfy

[0197] When the range of θ includes the region greater than π / 2, and within the range of θ where π / 2 ≤ θ ≤ π,

[0198] Satisfying f(θ, k)>0 (Equation 5-3),

[0199]

[0200] Equation 4 indicates that, compared to the transformation using perspective projection (and the same scaling), the coordinates of the transformed point move towards point O.

[0201] Equation 5-1 indicates that, compared to the transformation using perspective projection (and the same scaling), the portion corresponding to the result of the transformation using the function f(θ, k) shrinks in the radial direction centered at point O.

[0202] Equation 5-2 indicates that near point O, the scaling is roughly the same as that using perspective projection transformation (and the same scaling).

[0203] Based on the above conditions Equations 4, 5-1, and 5-2, it can be seen that near point O, the transformation using perspective projection is roughly the same, with contraction towards O. As the distance from point O increases, the degree of contraction in the radial direction centered on point O becomes stronger.

[0204] Furthermore, it can also be used as The function f(θ, k) is determined in a monotonically decreasing manner relative to θ. The transformation using the function f(θ, k) relative to the transformation using perspective projection (and the same scaling), the degree of contraction of the part corresponding to the result of the transformation becomes stronger (contracting in a smaller way) the further away from point O.

[0205] like Figure 7 As shown, a fisheye perspective ruler can also be defined when θ exceeds π / 2 (90°). However, depending on the value of k, sometimes the value of f(θ, k) becomes infinite or does not satisfy Equation 5-4. Therefore, it is preferable to limit the range of θ to the range where the value of f(θ, k) does not become infinite and satisfies Equation 5-4.

[0206] Furthermore, if the value of k is set to -1 < k < 0, then the coil-like deformation can be represented. Point S is located on the same side as point O relative to point P.

[0207] The function f(θ, k) is used to transform a straight line on the canvas or a graphic existing in three-dimensional space to obtain a curve with the same shape as the curve obtained by transforming the straight line using the function f(θ, k), and then a fisheye perspective ruler with the obtained curve is displayed.

[0208] For a straight line L existing in three-dimensional space, there exists a graph F that satisfies the following conditions.

[0209] Condition: The graph F exists in three-dimensional space, and the curve obtained by transforming graph F using the function f(θ, k) is the same as the curve obtained by transforming line L using the function f(θ, k).

[0210] Using this, we can also use the function f(θ, k) to transform the line L instead of the line L, and use the function f(θ, k) to transform the figure F to obtain the curve of the fisheye perspective ruler.

[0211] Here is an example of such a figure F. The plane containing point P and line L is defined as plane E.

[0212] • The line of intersection between plane E and surface G.

[0213] • A curve on plane E.

[0214] • A planar figure on plane E.

[0215] The above application of the graph F also applies to other instances of the function f(θ, k) described below.

[0216] Alternatively, when determining the coordinates of point B, a fisheye perspective ruler can be defined as follows: By setting an orthogonal coordinate system (denoted as X and Y coordinates) with point O as the origin on the plane of the canvas (not shown), and applying a function f(θ, k) with different parameters on the X and Y coordinates of point B, the coordinates of point B on the canvas can be determined to define the fisheye perspective ruler.

[0217] By defining such a fisheye perspective ruler, it is possible to obtain fisheye perspective rulers with different fisheye lens performance in the X-axis and Y-axis directions.

[0218] The above application of different parameters in the X and Y coordinates also applies to other instances of the function f(θ, k) described below.

[0219] Figure 8 and Figure 9 This is a graph representing other examples of the function f(θ, k) used when generating a fisheye perspective ruler. Figure 8 This is the graph for the case where 0 ≦ θ < π / 2. Figure 9 The graph shows the case where π / 2 ≦ θ ≦ π.

[0220] Let the value of the angle ∠OPW formed by point O on canvas 810, point P on a straight line V that passes through point O and is orthogonal to the plane of the canvas, and point W existing in three-dimensional space be θ.

[0221] Set the distance between point O and point P to 1.

[0222] A surface G is formed with the straight line V as the axis of axis symmetry.

[0223] Let point Q be the point where the line connecting point P and point W intersects the surface G, and let α be the angle between the plane of canvas 810 and vector OQ. Let point C be the point placed on the line connecting point P and point W, and let β be the angle between the plane of canvas 810 and vector OC.

[0224] k is defined as follows:

[0225] k = β / α (Equation 6).

[0226] Let the distance from point O to point C be m.

[0227] When surface G is a sphere of radius 1 centered at point P, the distance m is expressed as follows:

[0228] m=sin(θ) / cos(θ-θ*k / 2)(Formula 7),

[0229] Where 0≦k≦2.

[0230] If the scaling factor is set to R, then the function f(θ, k) is expressed as follows:

[0231] f(θ,k)=R*sin(θ) / cos(θ-θ*k / 2) (Equation 8).

[0232] Furthermore, k is a parameter representing the intensity of distortion in the fisheye lens representation, and the scaling factor R is a parameter that is the overall transformation multiplied by a scale. f(θ, k) is shown below, and depending on the value of k, it is consistent with or approximates various projection methods.

[0233] k = 0: Consistent with perspective projection (f(θ, k) = R*tan(θ)),

[0234] k = 0.655: Approximates stereographic.

[0235] k = 0.875: Approximates equidistant.

[0236] k=1: Consistent with equisolid projection (f(θ,k)=2*R*sin(θ / 2)), k=2: Consistent with stereographic projection (f(θ,k)=R*sin(θ)).

[0237] In this way, by appropriately setting the parameter k of the deformation intensity and the scaling factor R, it is possible to define a fisheye perspective ruler corresponding to the performance of fisheye lenses of various properties.

[0238] The function f(θ, k) has the properties shown in Equations 4, 5-1 to 5-4.

[0239] like Figure 9 As shown, a fisheye perspective ruler can be defined even when θ exceeds π / 2 (90°). However, depending on the value of k, sometimes the value of f(θ, k) becomes infinitely large or does not satisfy Equation 5-4. Therefore, it is preferable to limit the range of θ to the range where the value of f(θ, k) does not become infinitely large and satisfies Equation 5-4.

[0240] Furthermore, if the value of k is set to k < 0, then the coil-like deformation can be represented.

[0241] Furthermore, application examples have been omitted since they have already been explained.

[0242] By using the functions above, a fisheye perspective ruler can be defined.

[0243] Alternatively, the vanishing point can be set as the point where the two fisheye perspective rulers intersect.

[0244] The line of sight can also be a curve drawn using a function employed when generating a fisheye perspective ruler. Furthermore, the line of sight can also serve as one of the fisheye perspective rulers, causing the drawn lines to snap to the line of sight when the user draws the horizon, allowing the computer to draw the horizon based on the user's actions.

[0245] Figure 10 This is a diagram representing an example of a surface G that is not a sphere.

[0246] exist Figure 10 In this case, surface G1010 has a surface that resembles an inverted cone. The deformation in the region near point O is stronger than when the surface is a sphere. In this way, by changing the shape of surface G, various fisheye perspective rulers can be defined.

[0247] Figure 11 is a diagram illustrating an example of setting the deformation intensity and scaling factor R based on user instructions, as well as determining the vanishing point. Figures 11A to 11D This is an example of a user interface that allows users to intuitively manipulate the intensity of deformation, the scale factor R, the determination of the vanishing point, and the determination of the two fisheye perspective rulers.

[0248] exist Figure 11A In the process, based on the user's instructions (e.g., by dragging the mouse cursor to the starting point D of 1120), s 1122 and the finish line D e Draw a straight line 1110 on the screen (1124).

[0249] exist Figure 11B In the middle, the vector determined by the starting point and ending point of the next drag of the mouse cursor 1170 is set as vector 1171.

[0250] based on Figure 11A The length L of the drag 1120 in the middle d , Figure 11B The length t of the component of vector 1171 perpendicular to line 1110 can determine several parameters, including the intensity k of deformation, the scaling factor R, the center point O of the lens, and the radius Rp of the 180-degree circle.

[0251] Therefore, based on the determined parameters, a curve 1112 (the line that forms the basis of the fisheye perspective ruler) is drawn that causes the straight line 1110 to bend in a manner passing through the starting point 1122 and the ending point 1124. At this time, regarding the direction of bending of the straight line 1110, it is bent in a direction consistent with the direction of the vector 1171 to obtain the curve 1112.

[0252] The strength of the deformation can be set as k = t / L, for example. d Alternatively, a different formula could be used, but preferably k is 0 at t=0 and monotonically increasing relative to t. Preferably, k is 0 at t=L. d In the case that k=1.

[0253] The radius of a 180-degree circle can be, for example, Rp = L. d 2 / t. It could also be a different calculation formula, but it is preferable that it becomes infinitely large as t→0, and at t=L d In the case of becoming L d , which is monotonically decreasing relative to t.

[0254] The scaling factor R can be determined based on the deformation strength k and the radius Rp of the 180-degree circle (e.g., equations a-1 and a-2 described later).

[0255] The center point O of the lens is at the connecting point D. s and point D e On the perpendicular bisector of the line segment, the line passing through point D can be... s and point D e The distance between the straight line and O is set to -4(t-L). d / 2) 2 / L d +L d Preferably, this distance is at t=0, L d In the case of a minimum value of 0, it becomes an upwardly convex function.

[0256] exist Figure 11CThe parameters have already been determined, so for example, by drawing a curve 1113 (which becomes the basis for other fisheye perspective rulers) that is the starting point 1182 of the drag 1181 through the mouse cursor 1180 and the position determined by the ending point 1184 of the drag 1181, the intersection of curve 1112 and curve 1113 can be determined as the vanishing point 1130.

[0257] exist Figure 11D In the middle, it is preferable to delete those exceeding the vanishing point of 1130. Figure 11C Curves 1112A and 1113A are shown in the figure.

[0258] Alternatively, the line of sight can be appropriately depicted by creating a vanishing point of 1130. Additionally, a 180-degree circle can be drawn based on multiple parameters.

[0259] As shown above, it is possible to display at least one vanishing point and two fisheye perspective rulers on the screen through simple operation.

[0260] Furthermore, by drawing two curves, users can add two fisheye perspective rulers (not shown) with the intersection of the two curves as the vanishing point. Additionally, if the user draws a curve that passes through an already drawn vanishing point, a fisheye perspective ruler (not shown) can also be added passing through that vanishing point.

[0261] Figure 12 is an example of the migration of the fisheye perspective ruler display when the user changes the intensity of the deformation. Figure 12A The fisheye perspective ruler is displayed before the change in the strength of the deformation. Figure 12B This indicates the display of a fisheye perspective ruler after altering the intensity of the deformation without changing the scale factor.

[0262] Figure 12A In the diagram, a horizontal line of sight 1220A, a fisheye perspective ruler 1230A, and 1240A are displayed within a 180-degree circle 1210A. A user-indicated position 1222A is located on the horizontal line of sight. A user-indicated position 1232A is located on the fisheye perspective ruler 1230A. A user-indicated position 1242A is located on the fisheye perspective ruler 1240A. Furthermore, a vanishing point 1250A is located on the horizontal line of sight 1220A.

[0263] exist Figure 12B The image shows the intensity of the deformation exhibited by the fisheye lens as changed by the user, with the state of increased deformation intensity.

[0264] Due to the increased strength of the deformation, it is related to the following aspects: Figure 12A In comparison, Figure 12B Things have changed.

[0265] (1) The size of the 180-degree circle 1210A becomes smaller and becomes the 180-degree circle 1210B.

[0266] (2) The fisheye perspective rulers 1230A and 1240A are curved and shortened, becoming fisheye perspective rulers 1230B and 1240B respectively.

[0267] In addition, Figure 12A and Figure 12B By changing the deformation intensity k without changing the scaling factor R, the sizes of the 180-degree circles 1210A and 1210B change. Alternatively, the change in deformation intensity k can be linked to the change in the scaling factor R, thus altering the deformation intensity without changing the size of the 180-degree circle.

[0268] The following shows how to keep the radius of the 180-degree circle at R. p An example of how to link the strength of deformation with the scaling factor R.

[0269] (1) When the function f(θ, k) is defined by Equation 2

[0270] Let the radius of the 180-degree circle be R. p Then, based on Equation 2, the following equation is derived:

[0271] R p =f(π / 2, k) =R*(k+1) / k.

[0272] Based on the above formula, we can derive...

[0273] R = R p *k / (k+1)(a-1)

[0274] The relationship.

[0275] By using the formula a=1 to link the deformation intensity k with the scaling factor R, it is possible to maintain the radius of the 180-degree circle at a constant value R. p Under the condition of [condition], the strength k of the deformation is changed.

[0276] (2) When the function f(θ, k) is defined by Equation 8

[0277] Let the radius of the 180-degree circle be R. p Then, based on Equation 8, the following equation is derived:

[0278] R p =f(π / 2,k)=R*cos(π*(2-k) / 4).

[0279] Based on the above formula, we can derive...

[0280] R = R p / cos(π*(2-k) / 4)(a-2)

[0281] The relationship.

[0282] By using the formula a=2 to link the deformation intensity k with the scaling factor R, it is possible to maintain the radius of the 180-degree circle at a constant value R. p Under the condition of [condition], the strength k of the deformation is changed.

[0283] Despite the aforementioned changes, the positions 1222A and 1222B on the horizontal line of sight remain (x0, y0) on the canvas and have not moved. Similarly, the positions 1232A and 1232B on the fisheye perspective ruler 1230A remain (x2, y2) on the canvas and have not moved. Likewise, the positions 1242A and 1242B on the fisheye perspective ruler 1240A remain (x1, y1) on the canvas and have not moved.

[0284] As described above, the specified positions can also be set so that they remain on the canvas even if the intensity of the deformation changes. For example, the fisheye perspective rulers set by the user to match the edges of a table can be set such that by pre-setting the aforementioned specified positions near the center of the table's edges, the shape of the fisheye perspective rulers changes while maintaining the user-specified positions, even if the intensity of the deformation changes. In this way, since the user can fix the specified positions in the fisheye perspective rulers, it is possible to make the fisheye perspective rulers follow the intended image position for referencing the image, and simultaneously change the tilt or curvature of the fisheye perspective rulers, making it easier to set fisheye perspective rulers with the user's desired shape.

[0285] The aforementioned advantages also apply to the specified positions set at eye level. By changing the intensity of the deformation, it is possible to prevent the eye level and the position and shape of the fisheye perspective ruler from changing to positions or shapes that the user does not desire.

[0286] Figure 13 illustrates the movement of the vanishing point as the inclination of the fisheye perspective ruler changes. Figure 13A This indicates the state before the tilt of the fisheye perspective ruler was changed. Figure 13B This indicates the state after changing the tilt of the fisheye perspective ruler.

[0287] exist Figure 13AIn this design, the fisheye perspective ruler 1320A has a vanishing point 1370A and two handles 1324A for the user to adjust the tilt. Dragging either handle 1324A provides the user with the desired operation. Furthermore, the fisheye perspective ruler 1320A is set to a predetermined position 1322A. For example, when the user drags and moves one handle 1324A using the cursor 1370, the fisheye perspective ruler 1320A can rotate around the predetermined position 1322A in the direction of arrow 1350.

[0288] exist Figure 13B In the diagram, the fisheye perspective ruler 1320A, indicated by the dashed line, rotates and bends along the direction of arrow 1350 according to the user's dragging operation, reaching the state of fisheye perspective ruler 1320B. Based on this rotation and bending change, the vanishing point 1370A moves to the position of vanishing point 1370B. Accompanying this movement of the vanishing point, the fisheye perspective ruler 1310A extends only by the amount indicated by arrow 1360 to reach vanishing point 1370B.

[0289] As described above, based on the user's instructions, the specified position 1322A can be fixed, while the position of the vanishing point can be moved by changing the tilt of the fisheye perspective ruler 1320A.

[0290] Figure 14 shows an example of adding a fisheye perspective ruler. Figures 14A to 14C The image shows an example of adding a fisheye perspective ruler.

[0291] exist Figure 14A In the diagram, fisheye perspective rulers 1410 and 1420 share a vanishing point 1430. When the user presses the mouse button, for example, at cursor position 1450, line 1460A is displayed. While the user holds down the mouse button and drags cursor 1450, line 1460A rotates accordingly, for example, rotating to line B. Furthermore, in... Figure 14A Although it displays straight lines 1460A and 1460B, it can also display curves.

[0292] exist Figure 14B If the user continues to drag, the fisheye perspective ruler 1460C will snap to the vanishing point 1430.

[0293] exist Figure 14C In the process, when the user ends the drag (releases the mouse button), the curve 1460D, which protrudes beyond the vanishing point 1430 of the fisheye perspective ruler 1460C, disappears. Through this operation, a new fisheye perspective ruler 1460C is generated that shares the existing vanishing point 1430.

[0294] Alternatively, it can be omitted. Figure 14A The state is displayed when the user drags the mouse. Figure 14BThe fisheye perspective ruler 1460C is located at cursor 1450. If the user releases the mouse button, the curve 1460D, which protrudes beyond the vanishing point 1430 of the fisheye perspective ruler 1460C, disappears. This operation can also generate a new fisheye perspective ruler 1460C that shares the existing vanishing point 1430.

[0295] Additionally, when there are multiple vanishing points on the canvas, it is also possible to... Figure 14B In the process, based on the operation of the cursor 1450 as instructed by the user, the fisheye perspective ruler 1460C is made to snap to the vanishing point (not shown) closest to the position of the fisheye perspective ruler 1460C.

[0296] In this way, it is easy to add a new fisheye perspective ruler by passing through the desired vanishing point.

[0297] Figure 15 is a diagram showing the state when the fisheye perspective ruler is moved to a specified position based on the user's instructions. Figure 15A It indicates the state before the specified position is moved. Figure 15B This indicates the state after the specified position has been moved.

[0298] exist Figure 15A In the diagram, the fisheye perspective ruler 1520A has a vanishing point 1540. The user drags the specified position 1522A along the direction of arrow 1530 using the mouse cursor 1550.

[0299] exist Figure 15B The state after the above drag is shown. The specified position is moved from the specified position 1522A to the specified position 1522B according to the drag. Along with this movement, the curve of the fisheye perspective ruler is changed accordingly. In addition, the vanishing point 1540 and other fisheye perspective rulers 1510 may remain unchanged.

[0300] Figure 16 shows an example of the handle display when the user provides an indication of the location of a fixed vanishing point. Figure 16A This indicates the state before the user provides an indication of the location of the fixed vanishing point. Figure 16B This indicates the status after the user provides an indication of the location of the fixed vanishing point.

[0301] exist Figure 16A In the image, since the vanishing point 1610 is allowed to move, four handles 1624 are displayed to change the tilt of the fisheye perspective ruler. In this state, the user can change the tilt of the fisheye perspective ruler by manipulating any one of the four handles 1624 using a mouse or similar device. Along with this change, the vanishing point 1610 moves.

[0302] exist Figure 16BIf the vanishing point 1610 is in a state where movement is not allowed, the four handles 1624 for changing the tilt of the fisheye perspective ruler may not be displayed. In this way, the user cannot operate the tilt of the fisheye perspective ruler, thus preventing movement of the vanishing point 1610 corresponding to this operation.

[0303] Alternatively, it can be set so that even if the user drags the vanishing point 1610 with the cursor, the vanishing point 1610 will not move. Furthermore, it is preferable that even if the user moves the specified position, the position of the vanishing point will not move.

[0304] Furthermore, regarding the vanishing point, which is not permitted to be moved, it is preferable not to move it even if the user changes the intensity of the deformation. However, in cases where the vanishing point's position fails due to changes in the intensity of the deformation or the scaling factor R, such as when attempting to move the vanishing point beyond the lens circle, the vanishing point can be moved.

[0305] Figure 17 is a diagram showing the state transition when the point O (the center point O of the lens) where the straight line V of the central axis of the virtual lens intersects the canvas is moved. Figure 17A This is the diagram before the center point O of the lens was moved. Figure 17B This is the diagram after the center point O of the lens has been moved.

[0306] Figure 17A The position of the lens center point O (1710A) is moved along the direction of arrow 1730. Figure 17B Move the lens to the center point O (1710B). Figure 17A The coordinates (x5, y5) of the specified position 1750A and the coordinates (x6, y6) of the specified position 1760A are in Figure 17B The coordinates (x5, y5) of the designated position 1750B and the coordinates (x6, y6) of the designated position 1760B are also not moved on the canvas. Furthermore, the 180-degree circle and the vanishing point move with the movement of the lens center point O. Accompanying this, the shapes of the fisheye perspective rulers 1752A and 1762A in Figure 17 change to fisheye perspective rulers 1752B and 1762B, respectively. Preferably, the line-of-sight levels 1790A and 1790B, and the designated positions existing on the line-of-sight line, move with the movement of the lens center point O.

[0307] In this way, when displaying reference images in an overlapping manner, it is possible to ensure that the reference images do not shift from the specified positions.

[0308] Figure 18 is a diagram illustrating the state transition when the vanishing point is moved. Figure 18A This is the graph before the vanishing point is moved. Figure 18B This is the graph after the vanishing point has been moved.

[0309] exist Figure 18AIn this case, the vanishing point 1820A is moved in the direction of arrow 1850. Figure 18B The image shows the location of the vanishing point 1820B after the movement. In this case... Figure 18A The coordinates (x7, y7) of the specified position 1870A and the coordinates (x8, y8) of the specified position 1880A are in Figure 18B The coordinates of positions 1870B (x7, y7) and 1880B (x8, y8) are respectively, and they do not move on the canvas. As the vanishing point 1820A in Figure 18 moves towards the vanishing point 1820B, the shapes of the fisheye perspective rulers 1872A and 1882A change to fisheye perspective rulers 1872B and 1882B, respectively.

[0310] Regarding the behavior when the vanishing point is dragged, it can be set as follows: The behavior can differ depending on whether the vanishing point is on the line of sight. Furthermore, even when it is on the line of sight, the behavior can differ depending on whether the vanishing point is the first vanishing point or a subsequent vanishing point.

[0311] (1) The vanishing point is the first vanishing point on the horizontal line of sight, and the horizontal line of sight is fixed:

[0312] • The location of the vanishing point moves along a line horizontal to the line of sight.

[0313] Even if the vanishing point is moved, the horizontal line of sight does not change.

[0314] (2) The vanishing point is the first vanishing point on the line of sight horizontal, and the line of sight horizontal is not fixed:

[0315] There are no restrictions on the location of the vanishing point.

[0316] • As the vanishing point moves, the horizontal line of sight will change.

[0317] (3) The vanishing point is either the second or subsequent vanishing point on the line of sight, or a vanishing point not on the line of sight:

[0318] • The location of the vanishing point is not limited (but it can also be set to adhere to the line-of-sight level).

[0319] Even if the vanishing point is moved, the horizontal line of sight does not change.

[0320] In this way, when displaying reference images in an overlapping manner, it is possible to ensure that the reference images do not shift from the specified positions.

[0321] Figure 19 is a diagram showing the state transition when the strength of the deformation is changed. Figure 19A It is a diagram showing the state before the deformation strength is changed. Figure 19B It is a diagram showing the state after the strength of the deformation has been changed.

[0322] When the vanishing point 1950A is fixed, it is preferable to maintain the coordinates of that fixed vanishing point. Unless otherwise indicated, it is preferable to maintain all coordinates of the specified positions.

[0323] exist Figure 19A The diagram illustrates a case where no indication is given of fixing the position of the vanishing point 1950A. In this case, Figure 19A The coordinates of positions 1930A and 1940A as specified in the code are respectively in Figure 19B The coordinates of the positions 1930B and 1940B are the same as those specified.

[0324] In contrast, Figure 19A In the context of providing the coordinates of the fixed vanishing point 1950A, it is preferable not to... Figure 19B The position of the vanishing point 1950B changes. In this case, the coordinates of the specified positions 1930A and 1940A are respectively in... Figure 19B The coordinates may not be the same as the specified positions 1930B and 1940B.

[0325] In this way, when the strength of the deformation is changed, the user can choose to fix the position of the vanishing point or fix a specified position.

[0326] Figure 20 is a diagram showing the state transition when the scaling factor R is changed. Figure 20A This is a diagram showing the state before the scaling factor R was changed. Figure 20B This is a diagram showing the state after changing the scaling factor R.

[0327] If vanishing point 2022A is fixed, it is preferable to maintain the coordinates of that fixed vanishing point. If no indication is given that all vanishing points are fixed, it is preferable to maintain all coordinates of the specified positions.

[0328] exist Figure 20A The diagram illustrates a case where no indication is given of fixing the position of vanishing point 2022A. In this case, Figure 20A The coordinates of positions 2030A and 2040A as specified in the code are respectively in Figure 20B The coordinates of the positions 2030B and 2040B are the same as those specified.

[0329] In contrast, Figure 20A In the context of providing the coordinates of the fixed vanishing point 2022A, it is preferable not to... Figure 20BThe position of the vanishing point 2022B changes. In this case, the coordinates of the specified positions 2030A and 2040A are respectively in... Figure 20B The coordinates of the specified positions 2030B and 2040B may not be the same.

[0330] In this way, when the scaling factor R is changed, the user can choose to fix the vanishing point position or a fixed, predetermined position.

[0331] Figure 21 is a diagram showing the changes in the display of the fisheye perspective ruler. Figure 21A It is a diagram showing the state before the deformation strength is changed. Figure 21B It is a diagram showing the state after the strength of the deformation has been changed.

[0332] about Figure 21A The fisheye perspective ruler 2150A in the text, when giving an indication of the increased strength of deformation, such as... Figure 21B The fisheye perspective ruler 2150B is shown as having been modified. Regarding other fisheye perspective rulers and the shape of the line-of-sight level, similarly, an indication of the increased intensity of the distortion is given. Figure 21A and Figure 21B The display has been changed as shown.

[0333] Figure 22 is a diagram showing the changes made to the curve already drawn along the fisheye perspective ruler as the display changes. Figure 22A It is a diagram showing the state before the deformation strength is changed. Figure 22B It is a diagram showing the state after the strength of the deformation has been changed.

[0334] exist Figure 22A The display of the fisheye perspective ruler (e.g., fisheye perspective ruler 2250A) shown has been changed to... Figure 22B In the case of the fisheye perspective ruler shown (e.g., fisheye perspective ruler 2250B), Figure 22A The previously drawn curve 2210A has been changed to Figure 22B The curve shown is 2210B.

[0335] As the intensity of the deformation changes, the display of the fisheye perspective ruler 2250A changes to the fisheye perspective ruler 2250B. Accompanying this change, the curve 2210A, which has been drawn along the fisheye perspective ruler, also changes to the curve 2210B.

[0336] In this way, it is also possible to adapt to changes in the intensity of specific deformations, thereby changing the fisheye perspective ruler and also changing the already drawn curves.

[0337] In this way, even if the fisheye perspective ruler is changed, the user does not need to start drawing again from scratch.

[0338] Figure 23 shows a change that occurs with the display of the fisheye perspective ruler, where not only is the curve drawn along the fisheye perspective ruler changed, but the reference image is also changed. Figure 23A It is a diagram showing the state before the deformation strength is changed. Figure 23B It is a diagram showing the state after the strength of the deformation has been changed.

[0339] In this way, even if the fisheye perspective ruler is changed, the user does not need to start redrawing from the beginning. And since the reference image itself is also deformed as a reference for drawing, it is easy to refer to the changes in details of the reference image when continuing to draw in more detail, so it is easier to continue drawing.

[0340] Figure 24 is a diagram showing how the reference image is changed along with the change in the display of the fisheye perspective ruler. Figure 24A It is a diagram representing the state before the change. Figure 24B It is a diagram representing the changed state.

[0341] Figure 24A The shape of either the fisheye perspective ruler 2420A or the fisheye perspective ruler 2430A is changed, respectively, to... Figure 24B Fisheye perspective rulers 2420B, 2430B, or Figure 24A The vanishing point 2450A has been changed to Figure 24B The vanishing point 2450B is located at this position, and the referenced image is also distorted accordingly. The depicted image (not shown) can also be modified to accommodate this change.

[0342] In this way, the fisheye perspective ruler can adapt to changes in curvature, changes in the position of the vanishing point, etc., based on the user's instructions, so that the drawn image and / or the referenced image can also be easily deformed to adapt to the changes.

[0343] <Implementation Method 2>

[0344] Figure 25 This is a flowchart for generating the curves of a fisheye perspective ruler used for depicting fisheye lenses. The following is a summary of... Figure 25 The steps are explained below.

[0345] [Step S2502] Determine the function f(θ, k).

[0346] Here, regarding the function f(θ, k),

[0347] Within the range of θ used for transformation, 0 ≤ θ < π / 2.

[0348] Satisfy 0≦f(θ,k)≦R*tan(θ) (Equation 9),

[0349]

[0350] and satisfy

[0351] When the range of θ includes the region greater than π / 2, and within the range of θ where π / 2 ≤ θ ≤ π,

[0352] Satisfying f(θ, k)>0 (Equation 11),

[0353]

[0354] The meanings of Equations 9, 10-1, and 10-2 are the same as those already explained regarding Equations 4, 5-1, and 5-2.

[0355] Regarding Equation 11, when θ exceeds π / 2 (90°), tan(θ) becomes negative in Equation 9, so tan(θ) is omitted from the condition.

[0356] Equation 12 indicates that the function is also a monotonically increasing function when θ exceeds π / 2 (90°).

[0357] Using a function that meets the above conditions, for example, when transforming a straight line on a canvas, a curve approximating the curve obtained by photographing a straight line with a fisheye lens can be obtained. By using this obtained curve on a fisheye perspective ruler, according to perspective projection, the line drawn by the straight line can be drawn using the curve approximating the image taken with a fisheye lens.

[0358] [Step S2504] The function f(θ, k) is used to transform the straight line on the canvas or the graphic existing in the three-dimensional space to obtain a curve with the same shape as the curve obtained by transforming the straight line using the function f(θ, k), and a fisheye perspective ruler with the obtained curve is displayed.

[0359] Through this step S2504, a fisheye perspective ruler with curves capable of depicting the appearance of a fisheye lens can be overlaid and displayed on the canvas.

[0360] By using the fisheye perspective ruler to draw on the canvas, users can create illustrations that resemble fisheye lenses.

[0361] Furthermore, for example, if the trajectory of a circle is converted to generate the curve of a fisheye perspective ruler, the user can easily draw the curve captured when the circle is photographed with a fisheye lens on the canvas using the fisheye perspective ruler with that curve.

[0362] Figure 26 It means to use in Figure 6 and Figure 7 The flowchart illustrates the processing of the functions described in the document.

[0363] [Step S2602] This step indicates that as Figure 25 The subroutine of step S2502 performs its function.

[0364] [Step S2604] As a function f(θ, k), apply

[0365] f(θ,k)=R*(k+1)*sin(θ) / (k+cos(θ)),

[0366] Here, 0≦k≦∞.

[0367] Regarding this function, use Figure 6 and Figure 7 An explanation was provided.

[0368] Figure 27 It means to use in Figure 8 and Figure 9 The flowchart illustrates the processing of the functions described in the document.

[0369] [Step S2702] This step indicates that as Figure 25 The subroutine of step S2502 performs its function.

[0370] [Step S2704] As a function f(θ, k), apply

[0371] f(θ,k)=R*sin(θ) / cos(θ-θ*k / 2),

[0372] Here, 0≦k≦2.

[0373] Regarding this function, use Figure 8 and Figure 9 An explanation was provided.

[0374] Figure 28 This is a flowchart showing how to display a fisheye perspective ruler on a canvas.

[0375] The following is a description of each step.

[0376] [Step S2802] Based on the user's instructions, determine the rules for converting straight lines on the canvas or virtual straight lines in three-dimensional space into curves on the canvas that are adapted to the fisheye lens display.

[0377] Specific examples of this rule have already been given, so we will avoid repeating them here.

[0378] [Step S2804] Generate a fisheye perspective ruler, which is determined by a rule-based curve and by a curve at a specified position on the canvas specified by the user.

[0379] [Step S2806] Determine the locations of the points where the curves of multiple fisheye perspective rulers converge, i.e., the vanishing points, on the plane including the canvas, so that the user can identify them.

[0380] [Step S2808] Display the fisheye perspective ruler on the canvas.

[0381] Through the above processing, a fisheye perspective ruler can be displayed on the canvas.

[0382] Figure 29A and Figure 29B This is a flowchart illustrating an example of a subroutine for steps S2802 and S2804 described above.

[0383] [Step S2902] indicates that the process following step S2902 is a subroutine of step S2802.

[0384] [Step S2904] Check if the user's instruction is a change in the strength of the deformation. If the check result is affirmative (yes), proceed to step S2906. If the check result is negative (no), return.

[0385] [Step S2906] Change the rules in response to changes in the strength of the deformation.

[0386] Figure 29B The following processing flow is executed after the above processing.

[0387] [Step S2910] indicates that the process following step S2910 is a subroutine of step S2804.

[0388] [Step S2912] Change the fisheye perspective ruler generated before the rule change to a fisheye perspective ruler determined by a curve, which is a curve based on the changed rule and is located at a position specified by the user before the rule change.

[0389] Through the above processing, along with the changes in deformation, the curve of the fisheye perspective ruler is appropriately modified.

[0390] Figure 30 This describes the process related to the determination of rules.

[0391] [Step S3002] indicates that the process following step S3002 is a subroutine of step S2802.

[0392] [Step S3004] The rule is determined based on at least one of the intensity of the deformation represented by the fisheye lens, the scaling factor, and the position of the virtual lens center point represented by the fisheye lens, as specified by the user.

[0393] Parameters not specified by the user can be predetermined.

[0394] Figure 31 This refers to other processes related to the determination of rules.

[0395] [Step S3102] indicates that the process following step S3102 is a subroutine of step S2802.

[0396] [Step S3104] Determine the curves of the two fisheye perspective rulers by drawing two curves on the canvas based on the user's instructions.

[0397] [Step S3106] Take the intersection of the two curves as the vanishing point.

[0398] [Step S3108]

[0399] The intensity of the deformation exhibited by the fisheye lens is determined based on at least the degree of curvature of at least one of the two curves.

[0400] Figure 32 This is a flowchart illustrating an example of the process for generating a fisheye perspective ruler.

[0401] [Step S3202] indicates that the process following step S3202 is a subroutine of step S2804.

[0402] [Step S3204] Check if the user's instruction is a change in the tilt of the fisheye perspective ruler. If the check result is affirmative (yes), proceed to step S3206. If the check result is negative (no), proceed to step S3208.

[0403] [Step S3206] Change the position of the vanishing point of the specified fisheye perspective ruler and return.

[0404] [Step S3208] Check if the user's instruction is a change of the specified location. If the check result is affirmative (yes), proceed to step S3210. If the check result is negative (no), proceed to step S3212.

[0405] [Step S3210] Without changing the position of the vanishing point, modify the curve of the specified fisheye perspective ruler that passes through the changed specified position, and return.

[0406] [Step S3212] Check whether the position of the specified vanishing point is fixed and whether the specified position of the fisheye perspective ruler converging at the specified vanishing point is changed. If the result of the check is affirmative (yes), proceed to step S3214. If the result of the check is negative (no), return.

[0407] [Step S3214] Set the fisheye perspective ruler to not be changed and return.

[0408] Figure 33 This is a flowchart illustrating other examples of the processing flow for generating a fisheye perspective ruler.

[0409] [Step S3302] indicates that the process following step S3302 is a subroutine of step S2804.

[0410] [Step S3304] Check whether the strength of the deformation has been changed by the user. If the result of the check is positive (yes), proceed to step S3306. If the result of the check is negative (no), proceed to step S3308.

[0411] [Step S3306] Change the curve of the perspective ruler without moving the specified position, and return. By not changing the specified position, the position of the fisheye perspective ruler at the specified position of interest to the user can be kept still.

[0412] [Step S3308] Check whether the vanishing point position has been changed according to the user's instructions. If the check result is affirmative (yes), proceed to step S3310. If the check result is negative (no), return.

[0413] [Step S3310] Change the curve of the fisheye perspective ruler and return.

[0414] Figure 34 This is a flowchart showing an example of a fisheye perspective ruler.

[0415] [Step S3402] indicates that the process following step S3402 is a subroutine of step S2808.

[0416] [Step S3404] Check if the display of the fisheye perspective ruler has been changed. If the result of the check is affirmative (yes), proceed to step S3406. If the result of the check is negative (no), return.

[0417] [Step S3406] Adapt to the changes of each of the multiple fisheye perspective rulers, and change the image drawn according to the user's instructions along the multiple fisheye perspective rulers respectively.

[0418] Figure 35 This is a flowchart showing other examples of fisheye perspective rulers.

[0419] [Step S3502] indicates that the process following step S3502 is a subroutine of step S2808.

[0420] [Step S3504] Check if the display of the fisheye perspective ruler has been changed. If the result of the check is yes, proceed to step S3506. If the result of the check is no, return.

[0421] [Step S3506] Adapt to the changes of each of the multiple fisheye perspective rulers, and change the image on the canvas that the user uses as a draft.

[0422] This process adapts the image used by the user as a reference image to the way the fisheye perspective ruler changes.

[0423] Figure 36 This is a hardware configuration diagram of the implementation method.

[0424] The hardware configuration of this embodiment includes a CPU 4001, a ROM 4002 capable of storing the program and data of this embodiment, a RAM 4003, a network interface 4005, an input interface 4006, a display interface 4007, and an external memory interface 4008. These hardware components are interconnected via a bus 4004.

[0425] Network interface 4005 is connected to network 4015. Network 4015 can be wired LAN, wireless LAN, Internet, telephone network, etc. Input interface 4006 is connected to input unit 4016. Display interface 4007 is connected to display unit 4017. Display unit 4017 can be implemented by multiple display devices. External memory interface 4008 is connected to storage medium 4018. Storage medium 4018 can be RAM, ROM, CD-ROM, DVD-ROM, hard disk, memory card, USB memory, etc.

[0426] <Variation Example 1>

[0427] With point W present on the canvas, by transforming the variables by setting the distance between point O and point W to r, an equivalent representation can be achieved using distance r instead of angle θ. The function g(r, k) is used to convert the coordinates of point W to the coordinates of point B on the canvas, which is separated from point O by a distance g(r, k). The relationship between distance r and angle θ is expressed by the following formula.

[0428] r = tan(θ) (Equation 13).

[0429] Since point W exists on the canvas, the range of θ is 0 ≤ θ < π / 2. The function g(r, k) equivalent to function f(θ, k) is obtained through the following transformation.

[0430] g(r, k) = f(tan -1 (r), k)(Equation 14).

[0431] The condition 0≦f(θ,k)≦R*tan(θ) is replaced by the condition 0≦g(r,k)≦R*r.

[0432] Conditional expression Replaced with conditional expression Conditional expression Replaced with conditional expression

[0433] Therefore, the conditional expressions of equations 4, 5-1, and 5-2 are equivalent to the following equation.

[0434] 0≦g(r, k)≦R*r (Equation 15)

[0435]

[0436] in addition, The condition that θ is monotonically decreasing is replaced by This is in contrast to the condition that r is monotonically decreasing.

[0437] As Figure 6 A variation of the embodiment shown will be described. By transforming Equation 2 using Equation 14, the following equation, which is equivalent to Equation 2, is obtained.

[0438] g(r, k) = R*(k+1)*sin(tan) -1 (r)) / (k+cos(tan -1 (r)))(Form 17).

[0439] As Figure 8 A variation of the embodiment shown will be described. By transforming Equation 8 using Equation 14, the following equation, which is equivalent to Equation 8, is obtained.

[0440] g(r, k) = R * m = sin(tan -1 (r)) / cos(tan -1 (r)-tan -1 (r)*k / 2)

[0441] (Equation 18).

[0442] Figure 37 This is a diagram showing how the position of point B is obtained without using θ, based on the position of point W existing on canvas 3710.

[0443] Using the function g(r, k) shown in Equation 17 or Equation 18, the coordinates of point W are converted to the coordinates of point B on the canvas 3710, which is separated from point O by a distance g(r, k). That is, the relationship between distance r and angle θ is given by g(r, k) = f(tanθ). -1 (r), k) represent.

[0444] <Variation Example 2>

[0445] Figure 38 This is a diagram showing the user interface for easily setting up multiple orthogonal fisheye perspective rulers.

[0446] Multiple fisheye perspective rulers (e.g., fisheye perspective rulers 3912 and 3914, fisheye perspective rulers 3922 and 3924) that share a common vanishing point on the canvas correspond to sets of lines parallel to each other in three-dimensional space. It can also be configured to impose constraints such that the sets of lines in three-dimensional space corresponding to one set of fisheye perspective rulers on the canvas plane are orthogonal to the sets of lines in three-dimensional space corresponding to the other set of fisheye perspective rulers.

[0447] Figure 38 Specific examples are shown. For instance, imagine the top surface of a table with a rectangular shape, where a rectangle parallel to the ground in three-dimensional space is the object being depicted. Figure 38 In the diagram, the deformed rectangle 3930 surrounded by thick lines is, for example, the upper surface of a table. The set of curves of multiple fisheye perspective rulers 3912 and 3914 passing through the vanishing point 3910 should be orthogonal to each other in three-dimensional space with the set of curves of multiple fisheye perspective rulers 3922 and 3924 passing through the vanishing point 3920.

[0448] Therefore, for example, it can be set such that if the user determines the position of the vanishing point 3910 on the line of sight 3902, the position of the vanishing point 3920 is automatically determined in a manner that satisfies the above-mentioned orthogonal condition in three-dimensional space.

[0449] Furthermore, it can be set such that when the user moves the position of the vanishing point 3910 along the line of sight, the position of the vanishing point 3920 is automatically moved along the line of sight in conjunction with this, satisfying the above-mentioned orthogonal condition in three-dimensional space.

[0450] In this way, it is easy to set up mutually orthogonal fisheye perspective rulers, and when the user changes the position or vanishing point of one fisheye perspective ruler, the other fisheye perspective ruler can be easily maintained in a mutually orthogonal setting accordingly.

[0451] Such a setting can be achieved, for example, by allowing the user to specify a pair of two vanishing points with mutually orthogonal fisheye perspective scales.

[0452] The order of the steps in the illustrated flowchart can be changed as long as there are no contradictions. Furthermore, as long as there are no contradictions, the illustrated flowchart can be executed multiple times at different time points. Additionally, as long as there are no contradictions, multiple steps can be executed simultaneously. Moreover, not all steps are necessary; some steps may be omitted or not executed, provided there are no contradictions.

[0453] The above aspects also apply to the constituent elements of the methods specified in the protection scheme. That is, the order of the constituent elements can be changed as long as there is no contradiction. In addition, multiple constituent elements can be implemented simultaneously as long as there is no contradiction. Furthermore, the implementation of these constituent elements also falls within the technical scope specified in the protection scheme.

[0454] Alternatively, each step can be executed by the operating system or hardware. Furthermore, the program can be distributed while stored on a non-transitory medium.

[0455] The program and method for implementing the above embodiments can be provided by a person possessing Figure 36 The computer, configured with the hardware shown, executes the program. That is, the program of the implementation method can also be implemented as a method for causing the computer to execute.

[0456] The program can also be stored on storage medium 4018, ROM 4002 or RAM 4003.

[0457] Each implementation can also be implemented as a device with hardware that has the program installed.

[0458] The term "fisheye perspective ruler" as used in this instruction manual is synonymous with "perspective ruler" in the scope of protection and the accompanying drawings.

[0459] The scaling factor R is an example of a parameter that represents the overall scaling of a fisheye perspective ruler.

[0460] Explanation of reference numerals in the attached figures

[0461] 4004 bus

[0462] 4005 Network Interface

[0463] 4006 Input Interface

[0464] 4007 Display Interface

[0465] 4008 External Memory Interface

[0466] 4015 Network

[0467] 4016 Input Section

[0468] 4017 Display Department

[0469] 4018 Storage Media

Claims

1. A method for displaying a perspective ruler, wherein the perspective ruler is placed on a planar canvas existing in a virtual three-dimensional space, and a computer displays the perspective ruler according to instructions from a user to depict a fisheye lens effect, so as to draw lines along the perspective ruler on the canvas. The perspective ruler display method includes the following steps: A function f(θ, k) is defined, wherein the angle ∠OPW formed by point O on the canvas, point P on a straight line V passing through point O and orthogonal to the plane of the canvas, and point W existing in the three-dimensional space is set to θ; the distance between point O and point P is set to 1; and the coordinates of point W are converted to the coordinates of point B on the canvas, which is separated from point O by a distance f(θ, k). Furthermore, the function f(θ, k) satisfies the following conditions: Within the range of θ used for transformation, 0 ≤ θ < π / 2. satisfy , ， and satisfy , When the range of θ includes the region greater than π / 2, and within the range of θ where π / 2 ≤ θ ≤ π, Satisfying f(θ, k) > 0, ;as well as The function f(θ, k) is used to transform the straight lines on the canvas or the graphics existing in the three-dimensional space to obtain a curve with the same shape as the curve obtained by transforming the straight lines using the function f(θ, k), and a perspective ruler with the obtained curve is displayed. Here, k is a parameter representing the intensity of the deformation exhibited by the fisheye lens in the perspective ruler. R is a parameter representing the overall scaling of the perspective ruler centered at point O.

2. The perspective ruler display method as described in claim 1, Point B lies on a straight line that is perpendicularly projected onto the plane of the canvas by the line connecting point O and point W.

3. The perspective ruler display method as described in claim 1, The point W is a point existing on the canvas, and the perspective ruler refers to the perspective ruler that displays the curve obtained by transforming the straight line on the canvas using the function f(θ, k).

4. The perspective ruler display method as described in claim 3, Point B exists on the straight line connecting point O and point W.

5. The perspective ruler display method as described in claim 1, A surface G is formed with the straight line V as the axis of axis symmetry. Let point Q be the point where the line connecting point P and point W intersects the surface G. Let point D be the point where the line connecting point S and point Q intersects the canvas. Point S exists on the line V and is located on the opposite side of point O relative to point P. The value of k is proportional to the distance between point P and point S. The value of the function f(θ, k) is proportional to the distance between point O and point D.

6. The perspective ruler display method as described in claim 1, A surface G is formed with the straight line V as the axis of axis symmetry. Let point Q be the point where the line connecting point P and point W intersects the surface G; let point C be the point on the line connecting point P and point W; let α be the angle between the plane of the canvas and vector OQ; and let β be the angle between the plane of the canvas and vector OC. The value of k is proportional to the value of β / α. The value of the function f(θ, k) is proportional to the distance between point O and point C.

7. The perspective ruler display method as described in claim 1, The function f(θ, k) is, when the intensity k of the deformation is a specified value, related to... Consistent or similar.

8. The perspective ruler display method as described in claim 1, The function f(θ, k) is defined when the intensity of the deformation k is a specified value. With as a stereoscopic projection , As an equidistant projection , As an equal solid angle projection as well as As a positive projection At least one of them is consistent or approximate.

9. The perspective ruler display method as described in claim 1, Determining the function f(θ, k) includes the following steps: When determining the coordinates of point B, different functions f(θ, k) are applied to the X-coordinate and Y-coordinate of point B on the mutually orthogonal coordinate axes (X-axis and Y-axis) with point O as the origin on the plane of the canvas to obtain the coordinates of point B on the canvas.

10. The perspective ruler display method as described in claim 1, Displaying the perspective ruler includes the following steps: The deformation intensity k and scaling factor R are set in such a way that the magnitude of the function f(π / 2, k) is kept constant.

11. The perspective ruler display method as described in claim 1, The function f(θ, k) is defined by the following equation: ， Here, 0≦k≦∞.

12. The perspective ruler display method as described in claim 1, The function f(θ, k) is defined by the following equation: ， Here, 0≦k≦2.

13. A method for displaying a perspective ruler, wherein the perspective ruler is placed on a planar canvas, and a computer displays the perspective ruler according to instructions from a user to depict a fisheye lens representation, so as to draw lines along the perspective ruler on the canvas. The perspective ruler display method includes the following steps: Define a function g(r, k). This function g(r, k) is used to convert the coordinates of point W to the coordinates of point B on the canvas, where the distance between point O and point W on the canvas is r, and the distance between point W and point O is g(r, k). The g(r, k) satisfies: ， ， ;as well as The function g(r, k) is used to transform the straight lines on the canvas to obtain curves, and a perspective ruler with the obtained curves is displayed. Here, k is a parameter representing the intensity of the deformation exhibited by the fisheye lens in the perspective ruler. R is a parameter representing the overall scaling of the perspective ruler centered at point O.

14. The perspective ruler display method as described in claim 13, The function g(r, k) is defined by the following equation: ， Here, 0≦k≦∞.

15. The perspective ruler display method as described in claim 13, The function g(r, k) is defined by the following equation: ， Here, 0≦k≦2.

16. A storage medium storing a program, The program causes the computer to perform the perspective ruler display method as described in any one of claims 1 to 15.

Images