Transition position calculation device and program thereof

Abstract

A transition position calculation device (1) includes: a time normalization unit (11) for normalizing a designated time from a start time and an end time; a time transition function calculation unit (12) for calculating a normalized position using a time transition function F (r0, r1, t) with respect to a first adjustment value r0 and second adjustment value r1(r0≧0, r1≧0, r0+r1≦1) and a normalized time t; and a position calculation unit (13) for calculating a transition position at the designated time from the normalized position, the start position and the end position.

Description

Transition position calculation device and its program

[0001] This invention relates to a transition position calculation device and its program.

[0002] Conventionally, a method for controlling camera work in CG animation involves setting keyframes, which are time points and represent the camera's pose, position, and field of view at those times, and controlling the camera work using a velocity curve between keyframes. This method is called easing. Easing smooths the start and / or end of a transition by suppressing the acceleration of the transition and setting the transition velocity to zero at one or both of the keyframes at the start and end of the transition. There are also information processing devices that have a function to edit the transition curve using a graph (see Patent Document 1).

[0003] Furthermore, when performing camera operations (panning, tilting, and zooming) with a pan-tilt-zoom camera, there are methods called triangular wave control and trapezoidal control, which control each operation angle by constant acceleration or constant velocity motion. In addition, in the camera operations of a pan-tilt-zoom camera, there is a method to achieve camera operations with a sense of dynamism and rhythm by modeling the camera operator's camera operations using a function and simulating the camera operations with the function (see Patent Document 2).

[0004] Japanese Patent Publication No. 2022-014358, Japanese Patent Publication No. 4441361

[0005] However, conventional easing can smooth the movement at the start and end of transitions, but since it only adjusts the acceleration, it results in mechanical movements at the start and end of transitions, giving the movement a rough impression. Triangular wave control and trapezoidal control also have the problem of resulting in mechanical movements at the start and end of transitions, since the acceleration or angular velocity is constant, giving the movement a rough impression.

[0006] Also, when editing the transition curve by a graph, it is possible to realize a soft start or end movement of the transition. However, there is a problem that it requires skill to appropriately adjust the graph shape for realizing camera work without a sense of incongruity. Also, the method of simulating the camera operation of a cameraman by a function can realize camera work with a sense of intonation and rhythm, but there is a problem that there is a difference in quality depending on the skill of the cameraman simulated at the time of modeling.

[0007] The present invention has been made in view of such problems, and an object thereof is to provide a transition position calculation device and a program thereof that can easily adjust the transition time and the transition position while ensuring the smoothness of the start and end movements of the transition without modeling the movements of a cameraman.

[0008] In order to solve the above problems, a transition position calculation device according to the present invention is a transition position calculation device that calculates a transition position at a specified time of an object that transitions from a start position to an end position from a start time to an end time, and includes a time normalization unit, a time transition function calculation unit, and a position calculation unit.

[0009] In such a configuration, the transition position calculation device normalizes the specified time from the start time and the end time by the time normalization unit. Then, the transition position calculation device calculates a normalized position by a time transition function F(r ０ and a second adjustment value r １ (r ０ ≧0, r １ ≧0, r ０ + r １ ≦1) and the normalized time t normalized by the time normalization unit. This time transition function F(r ０ , r １ , t) is ０ , r １ , t) is is.

[0010] For example, the time transition function F(r ０ , r １ , t) is is.

[0011] As a result, the time transition function calculation unit adjusts the value (r ０ ,r １ This allows for a smooth transition between the acceleration section from the starting position and the deceleration section to the ending position by controlling acceleration and jerk. The transition position calculation unit then uses the position calculation unit to calculate the actual transition position at a specified time from the normalized position normalized by the time transition function calculation unit, and from the starting and ending positions.

[0012] Also, the first adjustment value r ０ and the second adjustment value r １ har ０ = r1 = s / 2 (0 ≤ s ≤ 1), and the time transition function F(r ０ ,r １ F(s / 2,s / 2,t) is, That is also acceptable.

[0013] Furthermore, the transition position calculation device can be operated using a program that enables a computer to function as a transition position calculation device.

[0014] According to the present invention, by simply setting the time and position before and after the transition, as well as the adjustment value, it is possible to obtain a continuous acceleration curve with a constant jerk, and the movement of the object undergoing the transition can be controlled with a smooth acceleration curve.

[0015] This is a block diagram showing the configuration of a transition position calculation device according to the first embodiment of the present invention. ０ = 0.30, r １ This graph shows the relationship between the normalized time and the output (position) of the time transition function when r = 0.60. ０ = 0.30, r １ This graph shows the relationship between the normalized time and the first derivative (velocity) of the time transition function when r = 0.60. ０ = 0.30, r １ This graph shows the relationship between the normalized time and the second derivative (acceleration) of the time transition function when r = 0.60. ０ = 0.30, r １ This graph shows the relationship between the normalized time and the third derivative (jerk) of the time transition function when r = 0.60.０ > 0, r １ > 0, and r ０ +r １ This graph shows the relationship between the normalized time and the output of the time transition function when < 1. ０ > 0, r １ > 0, and r ０ +r １ This graph shows the relationship between the normalized time and the output of the time transition function when r = 1. ０ = 0, and 0 < r １ This graph shows the relationship between the normalized time and the output of the time transition function when < 1. ０ = 0, and r １ This graph shows the relationship between the normalized time and the output of the time transition function when 0 < r. ０ <1, and r １ This graph shows the relationship between the normalized time and the output of the time transition function when r = 0. ０ = 1, and r １ This graph shows the relationship between the normalized time and the output of the time transition function when r = 0. ０ = 0, and r １ This graph shows the relationship between the normalized time and the output of the time transition function when s = 0. This graph shows the relationship between the normalized time and the output of the time transition function when 0 < s < 1. This graph shows the relationship between the normalized time and the output of the time transition function when s = 1. This graph shows the relationship between the normalized time and the output of the time transition function when s = 0. This flowchart shows the operation of the transition position calculation device according to the first embodiment of the present invention. This is a block diagram showing the configuration of the transition position calculation device according to the second embodiment of the present invention.

[0016] Hereinafter, embodiments of the present invention will be described with reference to the drawings. <First Embodiment> [Configuration of the Transition Position Calculation Device] Referring to Figure 1, the configuration of the transition position calculation device 1 according to the first embodiment of the present invention will be described.

[0017] The transition position calculation device 1 calculates the transition position at a specified time for an object (hereinafter referred to as the transition object) that transitions from a start position to an end position between the start time and the end time. The transition object is not limited to any object that undergoes a transition. For example, one of the camera parameters related to the camera's position, orientation, or field of view can be the transition object. Specifically, this could be the camera's position coordinates, pan angle, tilt angle, focal length, etc. Furthermore, the transition object may also be, for example, the position of a character in a video.

[0018] The specified time is the time that identifies the transition position of the transition target, and is a time between the start time and the end time. For example, the transition position calculation device 1 receives the time from the start time to the end time as the specified time, at predetermined time intervals (for example, 10 ms). As shown in Figure 1, the transition position calculation device 1 comprises a path information setting unit 10, a time normalization unit 11, a time transition function calculation unit 12, and a position calculation unit 13.

[0019] The path information setting unit 10 pre-sets path information that specifies the route to be taken. The path information setting unit 10 sets the start time T as the path information. ０ And, end time T １ and two adjustment values ​​(r ０ ,r １ ) and starting position y ０ And, end position y １ The input is stored in memory, etc., which is not shown in the diagram. The individual path information will be explained in the sections 11, 12, and 13 below, which use each path information.

[0020] The time normalization unit 11 calculates the start time T ０ and end time T １ Therefore, the specified time T is normalized. Start time T ０ and end time T １ These are the start and end times for transitioning the target of the transition. Specifically, the time normalization unit 11 sets the start time T set in the path information setting unit 10. ０ and end time T １Based on the specified time T input from an external source, the normalized time t is calculated by performing the following equation (1).

[0021]

[0022] The time normalization unit 11 outputs the normalized time t to the time transition function calculation unit 12. The time transition function calculation unit 12 calculates two adjustment values ​​(r ０ ,r １ ) and normalized time t, the time transition function F(r ０ ,r １ The normalized position is calculated using t). That is, the time transition function calculation unit 12 sets the normalized position to an amplitude value of "0" or more and "1" or less as shown in the following equation (2).

[0023]

[0024] Note that the adjustment value r ０ The (first adjustment value) is a non-numeric value that represents the normalized duration of the acceleration interval starting from "0" at normalized time t. This adjustment value r ０ The larger the value of r, the smoother the transition will begin over time. １ The (second adjustment value) is a non-numeric value representing the normalized duration of the deceleration section ending at "1" in the normalized time t. This adjustment value r １ The larger the value of r, the smoother the transition will be over time. Here, the adjustment value (r) ０ ,r １ ) is r ０ ≥ 0, r １ ≥ 0, r ０ +r １ Assume that the condition ≤ 1. Also, the time transition function F(r ０ ,r １ ,t) is the function shown in equation (3) below.

[0025]

[0026] For example, the time transition function F(r ０ ,r １ ,t) are defined by the following equation (4).

[0027]

[0028] Here, the content of the time transition function F(r ０ , r １ , t) will be described. In Equation (4), when r ０ > 0 and the normalized time t is in the interval 0 < t < r ０ / 2 (when r ０ = 0, this interval does not exist), the third derivative of the time transition function F(r ０ , r １ , t) with respect to time is a positive constant (const.) as shown in the following Equation (5), and the second derivative is positive as shown in the following Equation (6). That is, in this interval, there is a positive constant jerk and a positive acceleration.

[0029]

[0030] In Equation (4), when r ０ > 0 and the normalized time t is in the interval r ０ / 2 < t < r ０ (when r ０ = 0, this interval does not exist), the third derivative of the time transition function F(r ０ , r １ , t) with respect to time is a negative constant as shown in the following Equation (7), and the second derivative is positive as shown in the following Equation (8). That is, in this interval, there is a negative constant jerk and a positive acceleration.

[0031]

[0032] In Equation (4), when r ０ [[ID=4|1]] + r １ < 1 and the normalized time t is in the interval r ０ < t < 1 - r １ (when r ０ + r １ = 1, then 1 - r １ = r ０ [[ID=|55]] and this interval does not exist), as shown in the following Equation (9), it has a constant velocity.

[0033]

[0034] |> In Equation (4), when r １ > 0 and the normalized time t is 1 - r １<t<1-r １ / interval (r １ When = 0, this interval does not exist.) In this interval, the time transition function F(r ０ ,r １ The third derivative of t) with respect to time is a negative constant, as shown in equation (10), and the second derivative is negative, as shown in equation (11). In other words, in this interval, the jerk is a constant negative and the acceleration is negative.

[0035]

[0036] In equation (4), r １ When > 0, the normalized time t is 1 - r １ / 2 < t < 1 interval (r １ When = 0, this interval does not exist.) In this interval, the time transition function F(r ０ ,r １ The third derivative of t) with respect to time is a positive constant, as shown in equation (12), and the second derivative is negative, as shown in equation (13). In other words, in this interval, the jerk is a constant positive and the acceleration is negative.

[0037]

[0038] Thus, the time transition function calculation unit 12 calculates the adjustment value (r ０ ,r １ The time transition function calculation unit 12 calculates the normalized position (amplitude value) for the transition in the acceleration section from the starting position and the transition in the deceleration section to the ending position. ０ ,r １ The position calculation unit 13 outputs ,t).

[0039] The position calculation unit 13 calculates the actual transition position at a specified time from the normalized position normalized by the time transition function calculation unit 12, the start position, and the end position. (Start position y) ０ and end position y １ The start time T of the transition target ０ Location and end time T １This is the position in the time transition function calculation unit 12. This position is, for example, a coordinate position such as x-coordinate value, y-coordinate value, angle when rotating from a certain start angle to a certain end angle, the focal length of the camera, etc. Specifically, the position calculation unit 13 calculates the normalized position F(r) output from the time transition function calculation unit 12. ０ ,r １ ,t) and the starting position y set in the path information setting unit 10. ０ and end position y １ Therefore, the actual position (transition position) y(T) corresponding to the specified time T is calculated using the following equation (14).

[0040]

[0041] In other words, the transition position y(T) can be determined from equation (1) above by the following equation (15).

[0042]

[0043] With the configuration described above, the transition position calculation device 1 can determine the position at a specified time according to the adjustment value, while ensuring smoothness, simply by setting the start time, end time, start position, end time, and adjustment value in advance, without having to model the cameraman's movements.

[0044] (Regarding transitions due to adjustments to the time transition function) Below, the normalized time and the transitions associated with it will be explained using the time transition function used in the time transition function calculation unit 12, which is a characteristic configuration of the present invention.

[0045] First, refer to Figures 2A to 2D, r ０ = 0.30, r １ Let's take the case where = 0.60 as an example, and consider the time transition function F(r ０ ,r １ , t) and the time transition function F(r ０ ,r １ This section explains the first to third derivatives (velocity, acceleration, and jerk) with respect to time (t).

[0046] Figure 2A shows the normalized time t and the time transition function F(r ０ ,r １ Figure 2B shows the relationship between the normalized time t and the output (position) of F(r).０ ,r １ The relationship between the first derivative (velocity) of t and the normalized time is shown in Figure 2B. Figure 2B shows the relationship between the normalized time t and the time transition function F(r ０ ,r １ The relationship between the first derivative (velocity) of t and the normalized time is shown in Figure 2C. Figure 2C shows the relationship between the normalized time t and the time transition function F(r ０ ,r １ The relationship between the second derivative (acceleration) of t and the normalized time is shown in Figure 2D. Figure 2D shows the relationship between the normalized time t and the time transition function F(r ０ ,r １ The relationship with the third derivative (rate of change) of t is shown.

[0047] As shown in Figure 2D, the jerk takes on a piecewise constant value. Because the jerk takes on a piecewise constant value, as shown in Figure 2C, the acceleration changes continuously in accordance with the magnitude of the jerk. As a result, the shock during transitions is less noticeable. Furthermore, as shown in Figure 2C, the acceleration is a piecewise linear curve. Also, as shown in Figure 2B, the velocity is a curve formed by smoothly connecting quadratic curves. Also, as shown in Figure 2A, the position is a curve formed by smoothly connecting three-dimensional curves, matching curvature and tangents. Thus, the time transition function calculation unit 12 calculates the normalized position (F(r) ０ ,r １ The position can be calculated by smoothly transitioning between "0" and "1" in t).

[0048] Next, refer to Figures 3A to 3G to determine the adjustment value (r ０ ,r １ The time transition function F(r) for various combinations of ) ０ ,r １ Let's explain the example of ,t).

[0049] Figure 3A shows r ０ > 0, r １ > 0, and r ０ +r １ This is an example where < 1. In this case, the normalized time t is 0 < t < r ０ At / 2, the acceleration is positive jerk, r ０ / 2 < t < r ０ In this case, negative acceleration, r ０ <t<1-r １ At constant speed, 1-r１ <t<1-r １ At / 2, deceleration due to negative jerk, and 1-r １ Smooth acceleration and deceleration, including constant velocity sections, are achieved through five modes: positive jerk deceleration in the range 2 < t < 1.

[0050] Figure 3B shows r ０ > 0, r １ > 0, and r ０ +r １ This is an example where = 1. In this case, the normalized time t is 0 < t < r ０ At / 2, the acceleration is positive jerk, r ０ / 2 < t < r ０ In this case, acceleration with negative jerk, 1-r １ <t<1-r １ At / 2, deceleration due to negative jerk, and 1-r １ In the case where / 2 < t < 1, smooth acceleration and deceleration are achieved without constant velocity sections through four modes of deceleration, including positive jerk.

[0051] Figure 3C shows r ０ = 0, and 0 < r １ This is an example where < 1. In this case, the normalized time t is 0 < t < 1 - r １ At constant speed, 1-r １ <t<1-r １ At / 2, deceleration due to negative jerk, and 1-r １ In the case where / 2 < t < 1, a smooth deceleration from the constant velocity section is achieved through three modes: positive jerk deceleration and deceleration.

[0052] Figure 3D shows r ０ = 0, and r １ This is an example where = 1. In this case, the normalized time t is smooth due to two modes of deceleration: negative jerk deceleration when 0 < t < 1 / 2, and positive jerk deceleration when 1 / 2 < t < 1.

[0053] Figure 3E shows that 0 < r ０ <1, and r １ This is an example where = 0. In this case, the normalized time t is 0 < t < r ０ At / 2, the acceleration is positive jerk, r ０ / 2 < t < r０ In this case, acceleration with negative jerk, and r ０ In the case where <t<1, the system achieves smooth acceleration into the constant-velocity section through three modes: constant velocity and constant velocity.

[0054] Figure 3F shows r ０ = 1, and r １ This is an example where = 0. In this case, the normalized time t is smooth due to two modes of acceleration: positive jerk acceleration when 0 < t < 1 / 2, and negative jerk acceleration when 1 / 2 < t < 1.

[0055] Figure 3G shows r ０ = 0, and r １ This is an example where = 0. In this case, the normalized time t becomes a single mode with constant velocity when 0 < t < 1. In this way, the time transition function calculation unit 12 can realize various transitions depending on the set adjustment value.

[0056] (Regarding variations of the adjustment value <Part 1>) Adjustment value (r ０ ,r １ Instead of ), two real values ​​such that 0 ≤ α ≤ 1 and 0 ≤ β ≤ 1 may be used as adjustment values ​​(α, β). In that case, the path information setting unit 10 sets the adjustment values ​​(r ０ ,r １ Instead of ), input the adjustment value (α, β). Note that the adjustment value (α, β) is the adjustment value (r ０ ,r １ The following relationships (17) and (18) apply to ).

[0057]

[0058] Then, the time transition function calculation unit 12 calculates the adjustment value (r) obtained by the calculations of equations (16) and (17). ０ ,r １ Using the above equation (4), the time transition function F(r ０ ,r １ We will perform the calculation t).

[0059] The adjustment value α (third adjustment value) is the time transition function F(r) within the time range 0 ≤ t ≤ 1. ０ ,r １,t) is the time ratio of the non-linear interval. That is, α = r ０ +r １ For example, at α = 0, the time transition function F(r ０ ,r １ The time transition function F(r) is a straight line throughout the entire interval. Also, at α=1, the time transition function F(r) ０ ,r １ t) is a curve throughout the entire section.

[0060] The adjustment value β (fourth adjustment value) is r ０ tor １ The ratio of r ０ :r １ = β: This is the value used to apportion (1-β). The larger β is, the gentler the acceleration near the start of the transition becomes, while the acceleration near the end of the transition becomes larger. For example, when β=0, the nonlinear interval near the start of the transition disappears. Also, when β=1, the nonlinear interval near the end of the transition disappears. Note that when α=0, the time transition function F(r) is not affected by the value of β. ０ ,r １ t) is a straight line throughout the entire section.

[0061] (Regarding variations of the adjustment value <Part 2>) Adjustment value (r ０ ,r １ ) is r ０ tor １ It is also acceptable to operate in such a way that and are always equal. For example, r ０ = r １ It may also be set to = s / 2 (where 0 ≤ s ≤ 1). In that case, the path information setting unit 10 adjusts the value (r ０ ,r １ Instead of ), an adjustment value s will be input. Then, the time transition function calculation unit 12 calculates the time transition function F(r ０ ,r １ The calculation is performed using F(s / 2, s / 2, t) as F(s / 2, s / 2, t). That is, the time transition function calculation unit 12 performs the calculation using the above equation (4) as the following equation (18).

[0062]

[0063] Next, with reference to Figures 4A to 4C, we will explain an example of the transition of the time transition function F(s / 2, s / 2, t) of equation (18) with respect to the adjustment value s.

[0064] Figure 4A shows an example where 0 < s < 1. In this case, the normalized time t is smooth, including a constant velocity section, through five modes: positive acceleration at 0 < t < s / 4, negative acceleration at s / 4 < t < s / 2, constant velocity at s / 2 < t < 1 - s / 2, negative deceleration at 1 - s / 2 < t < 1 - s / 4, and positive deceleration at 1 - s / 4 < t < 1.

[0065] Figure 4B shows an example where s = 1. In this case, the normalized time t is smooth and does not include a constant velocity section, with four modes: positive acceleration at 0 < t < s / 4, negative acceleration at s / 4 < t < s / 2, negative deceleration at 1 - s / 2 < t < 1 - s / 4, and positive deceleration at 1 - s / 4 < t < 1.

[0066] Figure 4C shows an example where s = 0. In this case, the normalized time t becomes a single mode with constant velocity when 0 < t < 1. In this way, the time transition function calculation unit 12 can realize various transitions depending on the set adjustment values.

[0067] [Operation of the Transition Position Calculation Device] Next, with reference to Figure 5 (and Figure 1 as appropriate for the configuration), the operation of the transition position calculation device 1 according to the first embodiment of the present invention will be described.

[0068] In step S1, the path information setting unit 10 specifies the start time T as path information that identifies the route to be transitioned. ０ And, end time T １ and two adjustment values ​​(r ０ ,r １ ) and starting position y ０ And, end position y １ This is entered and stored in memory, etc. (not shown in the diagram). This adjustment value (r ０ ,r １ ) is r ０ ≥ 0, r １ ≥ 0, r ０ +r １The condition ≤ 1 shall be satisfied. Note that the adjustment value (r ０ ,r １ ) is r ０ = r １ Alternatively, you could set it to = s / 2 (where 0 ≤ s ≤ 1) and input only one adjustment value s.

[0069] In step S2, the time normalization unit 11 receives a specified time T from an external source, which is the time at which the transition position is identified. In step S3, the time normalization unit 11 receives the start time T set in step S1. ０ and end time T １ Therefore, the specified time T entered in step S2 or step S7 described later is normalized and set as the normalized time t (see formula (1) above).

[0070] In step S4, the time transition function calculation unit 12 calculates the two adjustment values ​​(r) set in step S1. ０ ,r １ ) and the normalized time t normalized in step S3, the time transition function F(r ０ ,r １ The normalized position is calculated using the time transition function F(r ０ ,r １ The normalized position (amplitude value) at normalized time t can be determined by the two adjustment values ​​(r ０ ,r １ If a single adjustment value s is used instead of ), the calculation may be performed using the time transition function F(s / 2, s / 2, t) (see equation (18) above).

[0071] In step S5, the position calculation unit 13 calculates the normalized normalized position F(r) obtained in step S5. ０ ,r １ ,t) and the starting position y set in step S1 ０ and end position y １ From this, the transition position y(T) at the specified time T input in step S2 is calculated (see equation (14) above). In step S6, the position calculation unit 13 outputs the transition position y(T) obtained in step S5 to the outside.

[0072] In step S7, if the next specified time is entered (Yes in step S7), the time normalization unit 11 returns to step S3. On the other hand, if the next specified time is not entered (No in step S7), the transition position calculation unit 1 terminates its operation.

[0073] Through the above operations, the transition position calculation device 1 can calculate the position of sequentially input specified times while ensuring smoothness, simply by setting the start time, end time, start position, end time, and adjustment value in advance in step S1.

[0074] <Second Embodiment> [Configuration of Transition Position Calculation Device] Referring to Figure 6, the configuration of the transition position calculation device 1B according to the second embodiment of the present invention will be described.

[0075] The transition position calculation device 1B calculates the transition position of an object (hereinafter referred to as the transition object) at a specified time between the start time and the end time. Note that while the transition position calculation device 1 (Figure 1) specifies the transition using two points, the start position and the end position, the transition position calculation device 1B differs in that it specifies the transition using a transition function.

[0076] As shown in Figure 6, the transition position calculation device 1B comprises a path information setting unit 10B, a time normalization unit 11, a time transition function calculation unit 12, and a position calculation unit 13B. The time normalization unit 11 and the time transition function calculation unit 12 have the same configuration as the transition position calculation device 1 described in Figure 1, so they are given the same reference numerals and their description is omitted.

[0077] The path information setting unit 10B pre-sets path information that specifies the route to be taken. The path information setting unit 10B sets the start time T as the path information. ０ And, end time T １ and two adjustment values ​​(r ０ ,r １ The two adjustment values ​​(r ０ ,r １ ) is r ０ = r １It may also be a single adjustment value s = s / 2 (where 0 ≤ s ≤ 1). The path information other than the transition function G(f) is the same as the input to the path information setting unit 10 in Figure 1. The transition function G(f) (where 0 ≤ f ≤ 1) is a function that converts the normalized position (amplitude value) into a scalar value or vector value consisting of one or more components.

[0078] The position calculation unit 13B calculates the transition position at a specified time from the normalized position and the transition function. The position calculation unit 13B calculates the normalized position F(r) output from the time transition function calculation unit 12. ０ ,r １ From t) and the transition function G(f) set in the path information setting unit 10B, the actual position (transition position) y(T) corresponding to the specified time T is calculated using the following equation (19).

[0079]

[0080] In other words, the transition position y(T) can be determined from equation (1) above by the following equation (20).

[0081]

[0082] Each component of the transition position y(T) can be associated with parameters related to the camera position, camera orientation, or field of view. Below, we will explain with specific examples the case where the transition function G(f) is a scalar function that outputs a scalar value and the case where it is a vector function that outputs a vector value.

[0083] (Example of a scalar function as a transition function) An example of a scalar function whose transition function G(f) outputs a scalar value is a function that controls the focal length of a camera. For example, the focal length φ(T) is φ ０ From φ １ The transition function G(f) is controlled by proportional allocation using the harmonic mean by f. In this case, the transition position y(T) is the focal length φ(T) shown in equation (21) below.

[0084]

[0085] Then, the transition function G(f) can be given by the following equation (22).

[0086]

[0087] In this case, if the focal length φ is multiplied by m, the shooting range (tangent of the shooting angle of view) becomes 1 / m. In the above equation (14), the normalized position F(r ０ ,r １ While the imaging range changes non-linearly with respect to a linear change in t), according to equation (22), the normalized position F(r) is determined by equation (19). ０ ,r １ This makes it possible to change the shooting range linearly in response to a linear change in t. As a result, the transition position calculation device 1B can control the camera's focal length, which is a scalar value, at a specified time T.

[0088] (Example of a transition function being a vector function) An example of a function where the transition function G(f) outputs a vector value is a function that controls the camera position. For example, camera position [X(T), Y(T), Z(T)] ｔ (where t is the transpose) in the XY plane of three-dimensional space at coordinates [R, 0, 0] ｔ The starting position is [0, R, 0] ｔ Via [-R, 0, 0], the coordinates [0, 0, 0] are set to be the end position. ｔ This is the transition function G(f) that causes the orbit to be a circular arc with radius R centered at [point number].

[0089] In this case, the transition function G(f) is defined as equation (23) below.

[0090]

[0091] Furthermore, the transition position y(T) is defined as equation (24) below.

[0092]

[0093] As a result, the transition position calculation device 1B calculates the camera position [X(T), Y(T), Z(T)], which is a vector value, at the specified time T. ｔ This can be controlled. Another example of a vector function whose transition function G(f) outputs a vector value is a function that controls the camera position and focal length. For example, camera position [X(T), Y(T), Z(T)] ｔ(where t is the transpose) in the XY plane of cubic space, at coordinates [R, 0, 0] ｔ The starting position is [0, R, 0] ｔ Via [-R, 0, 0], the coordinates [0, 0, 0] are set to be the end position. ｔ While drawing a circular arc orbit with radius R centered at φ, the focal length φ(T) is set to φ ０ From φ １ The transition function G(f) is controlled by apportionment using the harmonic mean by f. In this case, the transition function G(f) is defined as equation (25) below.

[0094]

[0095] Furthermore, the transition position y(T) is defined as equation (26) below.

[0096]

[0097] As a result, the transition position calculation device 1B calculates the camera position [X(T), Y(T), Z(T)], which is a vector value, at the specified time T. ｔ Furthermore, the focal length φ(T) can be controlled. As described above, the transition position calculation device 1B can control the transition position by smoothly changing the parameter, using the value of the transition function G(f) as a parameter. The operation of the transition position calculation device 1B is the same as the operation of the transition position calculation device 1B described in Figure 5, except that the transition function is set in step S1 and the transition position is calculated using the transition function in step S5, so a diagrammatic explanation is omitted.

[0098] Furthermore, the transition position y(T) controlled by the transition position calculation unit 1,1B does not necessarily have to be a parameter relating to the actual camera position, camera orientation, or field of view; it may also be a parameter relating to the position, orientation, or field of view of a virtual camera in three-dimensional computer graphics (3DCG). In addition, the transition position y(T) may be the control target value of a pan-tilt-zoom (PTZ) camera equipped with actuators, or it may be the cropping position or size when extracting a partial image from a high-resolution image.

[0099] Although embodiments of the present invention have been described in detail above, the present invention is not limited to the embodiments described above, and includes design changes and the like that do not depart from the spirit of the present invention. Furthermore, although the transition position calculation devices 1 and 1B were described as independent hardware in the embodiments described above, the present invention is not limited thereto. For example, the present invention can also be realized by a program that causes hardware resources such as the CPU, memory, and hard disk of a computer to function as the transition position calculation devices 1 and 1B. This program may be distributed via a communication line, or it may be written to a recording medium such as a CD-ROM or flash memory and distributed.

[0100] 1, 1B Transition position calculation unit 10, 10B Path information setting unit 11 Time normalization unit 12 Time transition function calculation unit 13, 13B Position calculation unit

Claims

1. A transition position calculation device for calculating the transition position at a specified time for an object that transitions from a start position to an end position between a start time and an end time, comprising: a time normalization unit that normalizes the specified time from the start time and the end time; and a first adjustment value r ０ and the second adjustment value r １ (r ０ ≥ 0, r １ ≥ 0, r ０ +r １ ≤ 1) and the normalized time t normalized by the time normalization unit, the normalized position is given by the time transition function F(r ０ ,r １ The system comprises a time transition function calculation unit that performs calculations according to t, and a position calculation unit that calculates the transition position at the specified time from the normalized position normalized by the time transition function calculation unit, the start position, and the end position, wherein the time transition function F is A transition position calculation device characterized by being the same as above.

2. The time transition function F is, The transition position calculation device according to claim 1, characterized in that it is the same as described in claim 1.

3. The first adjustment value r ０ and the second adjustment value r １ are r ０ = r1 = s / 2 (0 ≤ s ≤ 1), and the time transition function F(r ０ , r １ , t), which is F(s / 2, s / 2, t), is The transition position calculation device according to claim 1, characterized in that it is as described above.

4. The transition position calculation device according to claim 1, characterized in that the position calculation unit calculates the transition position from the normalized position using a transition function that converts the transition position at the specified time into a scalar value or vector value consisting of one or more components, instead of the start position and the end position.

5. The transition position calculation device according to claim 1, characterized in that a third adjustment value α and a fourth adjustment value β (0 ≤ α ≤ 1 and 0 ≤ β ≤ 1) are set in advance, and the time transition function calculation unit performs calculations using αβ as the first adjustment value and α(1 - β) as the second adjustment value.

6. The transition position calculation device according to claim 1, characterized in that the transition position is a parameter relating to the camera's position, orientation, or field of view.

7. A program for causing a computer to function as a transition position calculation device according to any one of claims 1 to 6.

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