JP4996275B2 - Difficulty determination method, device, program - Google Patents

Description

  The present invention is a shooting game in which a player and an enemy aircraft are displayed on a screen, and the player moves the enemy aircraft for a predetermined time by W types of actions to fight an enemy aircraft that attacks the enemy aircraft. The present invention relates to a difficulty determination method, apparatus, and program.

Hereinafter, the difficulty level determination method described in Non-Patent Document 1 will be described. Let D be a predetermined number of time steps. In this case, each time step d (d = 1, ..., D) the total number of the movement path apparatus itself can take to move in W type behavior for each is W ^D. For each path of movement of the ship, it is assumed that the movement path of the enemy also exist as W ^D. Assume that your aircraft is destroyed by the enemy aircraft when it touches the enemy aircraft. Let _ND be the number of movement paths (death behavior patterns) in which the own aircraft is destroyed by enemy aircraft. At this time, the self-shooting probability PD in the period of the predetermined time step _D is given by the following equation.

P _D = N _D / W ^D
The ship shoot probability P _D, the difficulty and definition in the period of the predetermined time step.
An example of all action patterns in the case of W = 3 and D = 3 is shown in FIG. In FIG. 5, it is assumed that a collision occurs at * 1, * 2, and * 3. In FIG. 5, the solid line represents the trajectory drawn by the own device when the action of w = 1 is selected at each time step d. A broken line represents a trajectory drawn by the own device when an action of w = 2 is selected at each depth d. An alternate long and short dash line represents a trajectory drawn by the own device when an action of w = 3 is selected at each depth d. A pattern with a cross at the end of a branch is a death behavior pattern. Assuming that a movement route that is not destroyed by an enemy aircraft is a safe behavior pattern, a safety behavior pattern is indicated by a circle at the end of the branch. At this _time, an N D = ^13, since a W D = 27, difficulty is ship shoot probability _{P D} is
P _D = 13/27
It becomes.
Hiroshi Kawano, “Study on Algorithms for Shooting Enemy Attack Bullet for Shooting Games”, Information Processing Society of Japan Research Report [Game Informatics], June 30, 2006, vol. 2006, no. 70, p. 61-68

The above Non-Patent Document 1, a specific method for determining the total number N _D of the path the apparatus itself is destroyed is not disclosed. That is, no specific technique (hardware configuration, flowchart, etc.) for calculating the difficulty level is shown.

  According to the first aspect of the present invention, the own aircraft and the enemy aircraft are displayed on the screen, and the own aircraft is moved by an operation of selecting an action of W (W is an arbitrary natural number) type to attack the own aircraft. In the method of determining the difficulty level of a shooting game that fights against enemy aircraft that add swords, the self-behavior pattern generation means performs each action at each time step d (d = 1,..., D, D are arbitrary natural numbers). All or some of the own device action patterns that perform an operation of moving for a predetermined time T according to w (w = 1,..., W) are generated. The own machine position calculation means obtains the position at each time step d of the own machine that moves according to each of the generated own machine action patterns. The enemy aircraft position calculation means obtains the position at each time step d of the enemy aircraft moving according to a predetermined enemy aircraft action pattern. The first area calculation means includes a predetermined first shape including the obtained position at the time step d of the own machine moving according to the generated own machine action pattern, and each cell s constituting a grid obtained by dividing the screen. Calculate the area of overlap with. The second area calculation means calculates the area of the overlapping portion between the predetermined second shape including the obtained position of the enemy aircraft at each time step d and each cell s. The collision probability calculating means calculates a collision probability by calculating a value obtained by dividing the area of the overlapping portion between the second shape and each cell s by the area of the cell s. The own device existence probability calculation means calculates the probability Ps (s ′, d−1) that the own device is located in the cell s ′ at time step d−1, 1 / W, the first shape, and each cell s. In time step d, the sum of the value obtained by dividing the area of the overlapping portion by the area of the first shape and the value obtained by subtracting the collision probability from 1 for all the cells s ′ is obtained. By sequentially repeating the process of obtaining the probability Ps (s, d) that the machine is located in the cell s, the probability Ps (s, D) that the machine is located in each cell s is obtained at time step D. The difficulty level determination means outputs a value obtained by adding the probability Ps (s, D) that the own device is present in the cell s at time step D for all or some cells.

  According to the second aspect of the present invention, the own aircraft and the enemy aircraft are displayed on the screen, and the own aircraft is moved by an operation of selecting an action of W (W is an arbitrary natural number) type to attack the own aircraft. In the method of determining the difficulty level of a shooting game that fights against enemy aircraft that add swords, the self-behavior pattern generation means performs each action at each time step d (d = 1,..., D, D are arbitrary natural numbers). All or some of the own device action patterns that perform an operation of moving for a predetermined time T according to w (w = 1,..., W) are generated. The own machine position calculation means obtains the position at each time step d of the own machine that moves according to each of the generated own machine action patterns. The enemy aircraft attack bullet position calculation means obtains the position at each time step d of the enemy aircraft attack bullet moving according to a predetermined enemy aircraft attack bullet action pattern. The first area calculation means includes a predetermined first shape including the obtained position at the time step d of the own machine moving according to the generated own machine action pattern, and each cell s constituting a grid obtained by dividing the screen. Calculate the area of overlap with. The third area calculating means calculates the area of the overlapping portion between the predetermined third shape including the position of the obtained enemy aircraft attack bullet at each time step d and each cell s. The collision probability calculation means calculates a collision probability by calculating a value obtained by dividing the area of the overlapping portion between the third shape and each cell s by the area of the cell s. The own device existence probability calculation means calculates the probability Ps (s ′, d−1) that the own device is located in the cell s ′ at time step d−1, 1 / W, the first shape, and each cell s. In time step d, the sum of the value obtained by dividing the area of the overlapping portion by the area of the first shape and the value obtained by subtracting the collision probability from 1 for all the cells s ′ is obtained. By sequentially repeating the process of obtaining the probability Ps (s, d) that the machine is located in the cell s, the probability Ps (s, D) that the machine is located in each cell s is obtained at time step D. The difficulty level determination means outputs a value obtained by adding the probability Ps (s, D) that the own device is present in the cell s at time step D for all or some cells.

  According to the seventh aspect of the invention, the first shape is a shape in which each side of the cell s where the player's own machine is located at time step d is widened by an expected operation error of the player.

A specific method for obtaining the difficulty level according to the present invention has been shown. Also, by introducing probabilities such as the existence probability of the own aircraft and calculating the sum of the continuous values of the existence probability of the own aircraft instead of the discrete values of the number of paths where the own aircraft is destroyed by the enemy aircraft, It is possible to capture continuously. For this reason, the reliability index according to the present invention is further reliable.
According to the seventh aspect of the present invention, it is possible to obtain a degree of difficulty that sufficiently considers human operation accuracy by using a shape that is widened by the player's operation error.

  Furthermore, according to the present invention, it is possible to quantitatively determine the attack strength of enemy aircraft in the shooting game in consideration of the operation position information of the player, and the difficulty level of the game can be set accurately and easily. . When a shooting game is used as a psychophysical experiment tool when investigating the influence of the game on the human brain, it is possible to give an index of the difficulty level of the game.

  FIG. 6 illustrates a shooting game that is a target of the processing of the present invention. On the screen, the own aircraft 1 'and the attack bullet 3' of the own aircraft 1 ', and the enemy aircraft 2' and the attack bullet 4 'of the enemy aircraft 2' are displayed. There may be a plurality of attack bullets 3 ′, enemy aircraft 2 ′, and attack bullets 4 ′. When there are a plurality of enemy aircrafts 2 ′, it is assumed that these enemy aircrafts are assigned different numbers i (i = 1,..., I, I are arbitrary natural numbers). Similarly, when there are a plurality of enemy bullets 4 ′, the enemy bullets 4 ′ have different numbers k (k = 1,..., K, K are arbitrary natural numbers). It is assumed that is attached. Also, it is assumed that the own aircraft 1 ′, enemy aircraft 2 ′, attack bullet 3 ′, and attack bullet 4 ′ are located on a two-dimensional plane composed of the X axis and the Y axis.

  The player operates its own aircraft 1 'to fight the enemy aircraft 2'. The player can move his / her own machine for the action unit time τ with W types of movement speeds (direction and speed) in one operation. W types of movement speeds (Vxs (w), Vys (w)) that can be taken by the own aircraft 1 'are determined in advance, and different movement speeds (Vxs (w), Vys (w)) have different movements. It is assumed that a speed number w (w = 1,..., W) is assigned. Hereinafter, the action of selecting the movement speed number w is referred to as action w. In addition, the player can perform an operation of firing an attack bullet 3 ′ for attacking the enemy aircraft 2 ′ at the same time as moving at the W speeds. The attack bullet 3 'moves according to a predetermined trajectory. The trajectory drawn by the attack bullet 3 'is called the own ray.

For example, when W = 9, the moving speed that the aircraft 1 'can take is
(Vxs (1), Vys (1)) = (V, 0)
(Vxs (2), Vys (2)) = (V, V)
(Vxs (3), Vys (3)) = (0, V)
(Vxs (4), Vys (4)) = (− V, V)
(Vxs (5), Vys (5)) = (− V, 0)
(Vxs (6), Vys (6)) = (− V, −V)
(Vxs (7), Vys (7)) = (0, −V)
(Vxs (8), Vys (8)) = (V, −V)
(Vxs (9), Vys (9)) = (0, 0)
It can be.

  The enemy aircraft 2 'can move at a moving speed (Vxei (a), Vyei (a)). A type of movement speeds (Vxei (a), Vyei (a)) that the enemy aircraft 2 'can take are determined in advance, and different movement speeds (Vxei (a), Vyei (a)) have different movements. Assume that a speed number a (a = 1,..., A) is assigned. The enemy aircraft 2 'can fire the attack bullet 4' at an arbitrary speed (direction and speed) in order to attack the own aircraft. The fired attack bullet 4 ′ moves at a predetermined moving speed (Vxbk, Vybk), for example.

  When the own aircraft 1 ′ collides with the enemy aircraft 2 ′ and the attack bullet 4 ′ fired by the enemy aircraft 2 ′, the own aircraft 1 ′ is destroyed and the game is over there. On the contrary, when the attack bullet 3 'of the own aircraft 1' collides with the enemy aircraft 2 ', the enemy aircraft 2' is destroyed. When all the enemy aircraft 2 'are destroyed by the attack bullet 3' of the own device 1 ', the player wins the game.

  The game screen is divided into grids, and the unit of the grid is called a grid. For example, the coordinate of the lower left cell of the screen is (0, 0), and the coordinates of the cell of (0, 0) that are X right and Y above are ( X, Y). Here, X and Y are integers of 0 or more.

  It should be noted that the length S of one side of the square is a value obtained by multiplying the speed V of the aircraft traveling in the direction parallel to the side by a predetermined time T, that is, S = VT. Divide the game screen into grids. By setting the length of one side of the cell in this way, no matter which moving speed (Vxs (w), Vys (w)) the aircraft in the certain cell s moves, after a predetermined time T Will always exist in a certain cell s with a probability of 100%. For this reason, a calculation burden can be reduced. Here, the predetermined time T is a time length of 0.3 seconds to 1 second when the action unit time τ is 0.03 seconds to 0.1 seconds.

In addition, if the length of one side of the mesh is large, the processing of the present invention becomes rough, and it may not be possible to properly control the own device. Therefore, the length S of one side of the square is less than one third of the length of half the sum of the diameter of the circle inscribed in the shape of the own aircraft and the diameter of the circle inscribed in the shape of the attacking bullet of the enemy aircraft. It is preferable to determine the predetermined time T and the speed V of the own machine so as to become values.
The coordinates (X, Y) expressed in capital letters are the coordinates of the cells. On the other hand, coordinates (x, y) expressed in small letters represent coordinate positions in real number expression on the game screen. Arbitrary coordinates (x, y) can be converted into coordinates (X, Y) of a grid including the coordinates (x, y).
The positions of the own aircraft, enemy aircraft, and enemy aircraft attack bullets mean, for example, the center of a circle inscribed in the shape of the own aircraft, enemy aircraft, and enemy aircraft attack bullet, the center of gravity of the shape, and the like.

[First embodiment]
<Functional configuration>
FIG. 1 illustrates a functional configuration of a difficulty level determination device 1000 according to the first embodiment. The difficulty level determination device 1000 includes, for example, an own aircraft presence probability calculation unit 1, an own aircraft existence probability storage unit 2, a difficulty level determination unit 3, an own aircraft position calculation unit 4, an enemy aircraft position calculation unit 5, an enemy aircraft attack bullet position It has the calculation part 6, the position memory | storage part 7, the error memory | storage part 8, the own machine action pattern production | generation part 9, the own machine action pattern storage part 91, the control part 10, and the memory | storage part 101.

FIG. 2 illustrates a functional configuration of the own device existence probability calculation unit 1. The own aircraft existence probability calculation unit 1 includes, for example, a position acquisition unit 11, an area calculation unit 12, an addition unit 13, a division unit 14, a probability calculation unit 15, an area calculation unit 17, a collision probability calculation unit 18, and a subtraction unit 19. Have. The probability calculation unit 15 includes, for example, a multiplication unit 151 and an addition unit 152.
Each part of these difficulty level determination apparatuses 1000 is implement | achieved by performing the process according to the flowchart shown by FIG. 3, FIG. 4, for example.

≪Own machine action pattern generator≫
The own machine action pattern generation unit 9 (see FIG. 1) performs each action w (w = 1,..., W) for each time step d (d = 1,..., D is an arbitrary natural number). All the own behavior patterns of the own device that performs an operation of moving for a predetermined time T according to the above are generated. The generated own behavior pattern is stored in the own behavior pattern storage unit 91.

  The own behavior pattern is a permutation w (d, de, j) of the moving speed number w (w = 1,..., W) generated for each time step d (d = 1,..., D). . For example, when D = 3, the own device action pattern generation unit 9 sets the permutation w (1, de, j) of the movement speed number w when d = 1 and the movement speed number w when d = 2. A permutation w (2, de, j) and a permutation (3, de, j) of the moving speed number w when d = 3 are generated.

  For example, the permutation w (1, de, j) of the movement speed number w in the case of d = 1 is composed of the following 9 (= 9 to the 1st power) permutations.

j = 1: {w (1, 1, 1) = 1}
j = 2: {w (1, 1, 2) = 2}
...
j = 8: {w (1, 1, 2) = 8}
j = 9: {w (1,1,9) = 9}
Further, for example, the permutation w (2, de, j) of the movement speed number w in the case of d = 2 is composed of the following 81 (= 9 squared) permutations.
j = 1: {w (2, 1, 1) = 1, w (2, 2, 1) = 1}
j = 2: {w (2, 1, 2) = 1, w (2, 2, 2) = 2}
...
j = 80: {w (2,1,80) = 9, w (2,2,80) = 8}
j = 81: {w (2,1,81) = 9, w (2,2,81) = 9}
Further, for example, the permutation w (3, de, j) of the moving speed number w in the case of d = 3 is composed of 729 (= 9 to the third power) permutations as follows.
j = 1: {w (3, 1, 1) = 1, w (3, 2, 1) = 1, w (3, 3, 1) = 1}
j = 2: {w (3, 1, 2) = 1, w (3, 2, 2) = 1, w (3, 3, 2) = 2}
...
j = 728: {w (3,1,728) = 9, w (3,2,728) = 9, w (3,3,728) = 8}
j = 729: {w (3,1,729) = 9, w (3,2,729) = 9, w (3,3,729) = 9}

A certain own machine action pattern (permutation) w (d, de, j) = {w (d, 1, j) = w ₁ ,..., W (d, de, j) = w _de ,. When d, j) = w _d } is given, the own machine moves according to the own action pattern, and the own machine moves for a predetermined time T according to the movement speed number w _{1 at} time step d = 1. In the time step d = de, the own device moves for a predetermined time T according to the moving speed number w _de . In the time step d = d, the own device moves in the moving speed number w _d. This means that an operation of moving for a predetermined time T is performed.

  The self-machine action pattern generation unit 9 generates a part of the self-machine action patterns instead of all of the self-machine action patterns, and applies the difficulty level determination method based on the part of the self-machine action patterns. Also good. For example, in the above-described embodiment, the own device can move according to nine types of movement speed numbers. However, for example, when moving according to only eight types of movement speed numbers (for example, the action of the own device stopping) If not, each of the own machine action patterns is generated, and the above-described difficulty determination method is applied based on the generated own machine action patterns. Moreover, although the self-machine action pattern production | generation part 9 produces | generates all the self-machine action patterns, you may apply the said difficulty level determination method based on a part of the produced | generated self-machine action pattern. By applying the difficulty level determination method to some of the own machine action patterns, it is possible to obtain a limited difficulty level when the action of the own machine is restricted.

≪Own machine position calculation part≫
The own machine position calculation unit 4 (see FIG. 1) obtains the position (xs, ys) at each time step d of the own machine that moves according to each own machine action pattern generated by the own machine action pattern generation unit 9. The obtained position (xs, ys) is stored in the position storage unit 7. As described above, a certain own-machine action pattern (permutation) w (d, de, j) = {w (d, 1, j) = w ₁ ,..., W (d, de, j) = w _de ,. , W (d, d, j) = w _d } is given, the self-machine moves according to the self-behavior pattern. At time step d = 1, the self-machine follows a predetermined speed according to the movement speed number w ₁ . An operation of moving for a time T, and at time step d = de, the own device operates for a predetermined time T according to the moving speed number w _de. means that the operation of moving a predetermined time T in accordance with the moving speed number w _d. Therefore, the position (xs, ys) at each time step d of the own machine that moves according to the own machine action pattern w (d, de, j) can be calculated by the following equation, for example.

(Xs, ys) = (xs0 + Σ k = 1 d Vxs (w k) × T, ys0 + Σ k = 1 d Vys (w k) × T)
Here, (Vxs (w), Vys (w)) is a predetermined moving speed vector corresponding to the moving speed number w, and Vxs (w) and Vys (w) are respectively the moving speed vectors. x component and y component.

  It is to be noted that an enemy aircraft position calculation unit 5 or an enemy aircraft attack bullet position calculation unit 6 which will be described later determines an enemy aircraft position (xei, yei) or an enemy aircraft attack bullet position (xes, ys) or an enemy aircraft attack bullet position ( When obtaining xbk, ybk), the own device position calculation unit 4 calculates the position (xs, ys) of the own device for each behavior unit time τ as necessary.

≪Enemy aircraft position calculation part≫
The enemy aircraft position calculation unit 5 (see FIG. 1) obtains the position (xei, yei) at each time step d (d = 1,..., D) of the enemy aircraft moving according to a predetermined enemy aircraft action pattern. The obtained position (xei, yei) of the enemy aircraft is stored in the position storage unit 7.

The action pattern of a predetermined enemy aircraft is, for example, an action pattern that continues to take a predetermined movement speed (Vxei ^* , Vyei ^* ), an action pattern that moves randomly regardless of the position or time of the own machine, or a movement unit time τ Each time, a moving speed vector (Vxei (a), Vyei (a)) that maximizes the inner product with the vector drawn from the position of the enemy aircraft to the position of the own aircraft is selected and moved according to the selected moving speed vector. It is an action pattern to do. As described above, the predetermined enemy aircraft action pattern may be anything that moves regardless of the position and time of the own aircraft, or that moves depending on the position and time of the own aircraft. When calculating the position of the enemy aircraft according to the position of the own aircraft, the position (xs, ys) of the own aircraft calculated by the own aircraft position calculation unit 4 is used.
When there are a plurality of enemy aircraft, the positions (xei, yei) of each enemy aircraft i (i = 1,..., I) at each time step d are calculated and stored in the position storage unit 7.

≪Enemy aircraft attack bullet position calculation part≫
The enemy aircraft attack bullet position calculation unit 6 (refer to FIG. 1) calculates the position (xbk,...) Of the enemy aircraft attack bullets moving according to a predetermined enemy aircraft attack bullet action pattern at each time step d (d = 1,. ybk). The obtained position (xbk, ybk) of the enemy aircraft is stored in the position storage unit 7.

The action pattern of a predetermined enemy aircraft attack bullet is, for example, an action pattern that continues to take a predetermined movement speed (Vxbk ^* , Vybk ^* ), an action pattern that moves randomly regardless of the position and time of the own aircraft, and an action unit At each time τ, a movement speed vector (Vxbk (c), Vybk (c)) that maximizes the inner product with the vector drawn from the position of the enemy attack bullet to the position of the own aircraft is selected, and this selected movement An action pattern that moves according to a velocity vector. As described above, the predetermined enemy aircraft attacking bullet action pattern may be anything such as one that moves regardless of its own position and time, and one that moves depending on its own position and time. When calculating the position of an enemy aircraft attack bullet according to the position of the own aircraft, the position (xs, ys) of the own aircraft calculated by the own aircraft position calculation unit 4 is used.
When there are a plurality of enemy bullets, the positions (xbk, ybk) of the attack bullets k (k = 1,..., K) of all enemy aircraft at each time step d are calculated, and the position storage unit 7 To store.

≪Own machine existence probability calculation part≫
The own machine existence probability calculation unit 1 (see FIG. 1), each cell s constituting a grid dividing the game screen without being destroyed at time step d-1 by the own machine moving according to each of the generated own machine action patterns. From the probability Ps (s ', d-1) located at', the process of obtaining the probability Ps (s, d) that the own machine moving according to each own machine action pattern is located at each cell s without being destroyed at time step d. By repeating, the probability Ps (s, D) that the own device is located at each cell s at time step D is obtained. As a result of moving according to each own device action pattern with reference to FIG. 2 and FIG. How to determine the probability Ps (s, d) that the aircraft that exists in the cell s ′ with the probability of Ps (s ′, d−1) is located in the cell s at the time step d as a result of following each device action pattern Explain. FIG. 2 is a diagram illustrating a functional configuration of the own device existence probability calculation unit 1, and FIG. 7 is a diagram that assists in explaining how to obtain the probability Ps (s, d).

Consider a cell se in which the side of the cell s where the machine is located at time step d is expanded by ex in the positive and negative directions of the x axis and by ey in the positive and negative directions of the y axis. ex and ey are expected player operation errors. The cell se is a cell indicated by a broken line in FIG. In FIG. 7, the centers of the meshes se and the meshes s overlap, but this is not a limitation. As the cell se, an arbitrary shape including the position of the own device at the time step d and considering the operation error of the player may be used. The position calculated by the own position calculation unit 4 (see FIG. 1) is used as the position of the own apparatus. The position acquisition unit 11 (see FIG. 2) acquires the position of the own device and outputs it to the area calculation unit 12. In addition,
Also, consider a cell scei centered on the position of the enemy aircraft at time step d and a cell scbk centered on the position of the enemy aircraft attack bullet at time step d. The length of one side of the cell scei is, for example, a value obtained by dividing the sum of the diameter of the circle inscribed in the shape of the enemy aircraft and the diameter of the circle inscribed in the shape of the own aircraft by 2, and the length of one side of the cell scbk This is, for example, a value obtained by dividing the sum of the diameter of a circle inscribed in the shape of an enemy aircraft attack bullet and the diameter of a circle inscribed in the shape of the own aircraft by two. As the position of the enemy aircraft and the position of the enemy aircraft attack bullet at time step d, those calculated by the enemy aircraft position calculation unit 5 and the enemy aircraft attack bullet position calculation unit 6 are used. The position acquisition unit 11 acquires the position of the enemy aircraft and the position of the enemy aircraft attack bullet, and outputs them to the area calculation unit 17.

  Instead of the square screen that centers on the position of the enemy aircraft, any shape that reflects the shape of the enemy aircraft and the shape of the hit determination, including the position of the enemy aircraft, can be used. Further, in place of the square scbk centered on the position of the enemy attacking bullet, any shape reflecting the shape of the enemy attacking bullet or the shape of the hit determination including the position of the enemy attacking bullet can be used.

  The area calculation unit 12 (corresponding to the first area calculation means) calculates the area of the overlapping portion between the cell se and each cell s. In the example shown in FIG. 7, the cell se overlaps each cell at the portions of s00, s01, s02, s10, s11, s12, s20, s21, and s22. Hereinafter, a cell including an overlapping portion smn (m = 0, 1, 2, n = 0, 1, 2) is referred to as a cell smn. The area of the overlapping portion smn is expressed as an area Smn. The area calculation unit 12 calculates each area Smn (m = 0, 1, 2, n = 0, 1, 2) and outputs it to the addition unit 13 and the division unit 14, respectively.

The adder 13 calculates the sum of the areas Smn. This sum is expressed as Sall. That is, the adder 13 calculates a value Sall determined by Σ _m Σ _n Smn. Sall is output to the division unit 14.
Dividing unit 14 divides each Smn by Sall, so that the own machine located in cell s ′ at time step d−1 moves according to a certain own machine action pattern w (d, de, j). The probability Ptr (w, m, n) of moving to each cell smn at time step d is obtained. Ptr (w, m, n) is a value determined by Smn / Sall. The calculated Ptr (w, m, n) is output to the probability calculation unit 15.

  The area calculation unit 17 (corresponding to the second area calculation unit and the third area calculation unit) calculates the area Scm of the union of the overlapping portion of the cell mesh and the overlapping region of the cell cell smn and the overlapping portion of the cell cell scbk and the cell cell smn. It calculates | requires for every smn and outputs it to the collision probability calculation part 18. FIG. For example, in FIG. 7, the meshes sei overlap with the cells s11 and sei11, the cells s12 and sei12, the cells s21 and sei21, and the cells s22 and sei22. The cell scbk overlaps with the cells s20 and sbk20, and overlaps with the cells s21 and sbk21. For the cell s11, the area of the sei11 portion is Sc12, for the cell s12, the area of the sei12 portion is Sc12, for the cell 20, the area of the sbk20 portion is Sc20, and for the cell 22 the area of the sei22 portion is Sc22. It becomes. The grid 21 where the sei21 portion and the sbk21 portion overlap is indicated by a vertical stripe pattern from the sum of the area of the sei21 portion and the sbk21 portion, that is, the sum of the sei21 area and the sbk21 area. The area obtained by subtracting the area of the region (see FIG. 7) is Sc21.

  In addition, when there are a plurality of enemy aircraft and enemy aircraft attack bullets, the area calculation unit 17 obtains an overlapping portion between the square mesh Sei and the square s for each of the plurality of enemy aircrafts, and calculates an overlapping portion between the square scbk and the square s. The area Scm is calculated by obtaining for each of the plurality of enemy aircraft attack bullets and calculating the area of the union of the overlapping portions for each square s.

  The collision probability calculation unit 18 divides each area Scmn by the area of the cell smn, thereby obtaining a probability Pcmd that the enemy aircraft and the attacking bullet of the enemy aircraft exist in each cell smn at time step d. The calculated Pcmn is output to the subtractor 19. Pcmn represents the probability that the enemy aircraft and the attacking bullets of the enemy aircraft will collide with the enemy aircraft located in the square smn and destroy the enemy aircraft.

The subtractor 19 calculates a value obtained by subtracting Pcmn from 1 for each cell smn, and outputs the result to the probability calculator 15.
The probability calculation unit 15 calculates the probability Ps (s ′, d−1) that the time is located in the cell s ′ at the time step d−1 and the probability that the moving speed w is selected at the time step d−1 (for example, 1 / W), Ptr (w, m, n), and a value obtained by multiplying the value obtained by subtracting the collision probability from 1 for all the cells s ′, the aircraft can obtain the cell at time step d. A probability Ps (s, d) located at s is obtained.

That is, by calculating a value determined by Ps (s, d) = Σ _{s ′} (1 / W) · (1−Pcmn) · Ps (s ′, d−1) · Ptr (w, m, n) , Ps (s, d) is obtained. The calculated Ps (s, d) is stored in the own device existence probability storage unit 2.
The own device existence probability calculation unit 1 finally obtains a probability Ps (s, D) that the own device is located in each cell s at time step D by sequentially repeating the above-described processing.

  As described above, the functions of the own device existence probability calculation unit 1 are realized by performing processing according to the flowcharts shown in FIGS. 3 and 4.

≪Difficulty determination part≫
The difficulty level determination unit 3 (see FIG. 1) calculates a value obtained by adding the probability Ps (s, D) that the own device is located in each cell s at time step D for all cells s. Is the difficulty level of the shooting game. That is, the difficulty level determination unit 3 calculates a value determined by Σ _s Ps (s, D) as the difficulty level.

  Note that a value obtained by adding the probability Ps (s, D) of the player's own device to each cell s at time step D for some cells s is calculated, and the calculated value is used as the difficulty level of the shooting game. Also good. By setting the value obtained by adding Ps (s, D) for some of the cells s as the difficulty level, the limited difficulty level when the movement range of the own aircraft is limited to those partial cells s. Can be sought.

≪Storage section≫
In the storage unit 101, the time step d, the element number de of the permutation w, the number j of the permutation w, the time p, the predetermined time T, the number W of movement speed numbers of the own device, and the search depth D are stored in advance. It is assumed that D is a value that can be changed according to the accuracy of the required difficulty level or the performance of the hardware, and can be set to about 5 to 15, for example.

[Process flow]
With reference to FIG. 3, the flow of processing of each part of the difficulty level determination device 1000 will be described. FIG. 3 is a diagram illustrating the processing flow of the difficulty level determination device 1000. The processing flow illustrated in FIG. 3 is a so-called horizontal search. The horizontal search is a search method in which a search is started from a certain node, all nodes connected to the node are examined, and then the child nodes connected to the examined node are examined in order. For example, in the case of D = 3 and W = 3, as shown in FIG. 8, this is a method of searching each route in the order of the numbers given to the movement route for each action unit.

<Step S1>
The control unit 10 of the difficulty level determination apparatus 1000 stores d read from the storage unit 101 in the storage unit 101 as d = 1. Further, the control unit 10 sets the current time to time 0, the position of the own aircraft at time t = 0 (xs0, ys0), the position of the enemy aircraft at time t = 0 (xei0, yei0), and time t = 0. Information on the position (xbk0, ybk0) of the enemy aircraft attack bullet at is acquired and stored in the position storage unit 7. Further, the control unit 10 stores the cell including the position (xs0, ys0) of the own device at time t = 0 as s0 and stores it in the own device existence probability storage unit 2 as Ps (s0, 0) = 1. Here, the cell s0 is a cell including the position (xs0, ys0) of the own device at time t = 0.

<Step S2>
The own-machine action pattern generation unit 9 generates a permutation w (d, de, j) of the movement speed number w from the current value of d. As described above in the section of “Self Behavior Pattern”, for example, when d = 1, the following 9 (= 9 to the 1st power) permutations are created.

j = 1: {w (1, 1, 1) = 1}
j = 2: {w (1, 1, 2) = 2}
...
j = 8: {w (1, 1, 2) = 8}
j = 9: {w (1,1,9) = 9}
The created permutation is stored in the own device action pattern storage unit 91. Further, j read from the storage unit 101 is set to j = 1, and is stored in the storage unit 101 again.

<Step S3>
The control unit 10 stores de read from the storage unit 101 as de = d and stores the de in the storage unit 101 again.

<Step S4>
The control unit 10 determines whether d read from the storage unit is d = 1. If d = 1, the process of step S5 is performed. Otherwise, the process of step S14 is performed.

<Step S5>
If it is determined in step S4 that d = 1, the own device position calculation unit 4 uses (xs0, ys0) read from the position storage unit 7 and uses the position (xs, ys) = (xs0) of the own device. , Ys0). The enemy aircraft position calculation unit 5 uses the (xei0, yei0) read from the position storage unit 7 to set the enemy aircraft position (xei, yei) = (xei0, yei0). The enemy aircraft attack bullet position calculation unit 6 uses the (xbk0, ybk0) read from the position storage unit 7, and the enemy aircraft attack bullet position (xbk (t), ybk (t)) = (xbk0, ybk0) To do.

<Step S6>
The own device position calculation unit 4 reads the moving speed number w (d, de, j) corresponding to d, de, and j read from the storage unit 101 from the own device action pattern storage unit 91. In addition, the control unit 10 stores p read from the storage unit 101 in the storage unit 101 again as p = 0.

<Step S7>
The own device position calculation unit 4 determines the position (xs, ys) of the own device as a moving speed vector (Vsx (w (d, de, j)), Vsy corresponding to the moving speed number w (d, de, j). (W (d, de, j))) is moved by the action unit time τ, and the position of the own device is updated. That is, it is assumed that its own position (xs, ys) = (xs + τ × Vsx (w (d, de, j)), ys + τ × Vsy (w (d, de, j))).

  The enemy aircraft position calculation unit 5 obtains the position of the enemy aircraft after τ time from the position of the enemy aircraft (xei, yei) using a predetermined enemy aircraft action pattern. Then, the position of the enemy aircraft is updated by setting the position (xei, yei) of the enemy aircraft as the position of the enemy aircraft after τ time. When the predetermined enemy aircraft action pattern depends on the position (xs, ys) of the own machine, the position (xs, ys) of the own machine calculated by the own machine position calculation unit 4 is used. When there are a plurality of enemy aircraft, the enemy aircraft positions are updated for all enemy aircraft i (i = 1,..., I).

The enemy aircraft attack bullet position calculation unit 6 obtains the position of the enemy aircraft attack bullet after τ time from the position (xbk, ybk) of the enemy aircraft attack bullet using a predetermined enemy aircraft attack bullet action pattern. Then, the position of the enemy aircraft attack bullet is updated by setting the position (xbk, ybk) of the enemy aircraft attack bullet as the position of the enemy aircraft attack bullet after τ time. When the predetermined enemy aircraft attack bullet behavior pattern depends on the position (xs, ys) of the own machine, the position (xs, ys) of the own machine calculated by the own machine position calculation unit 4 is used. When there are a plurality of enemy aircraft attack bullets, the positions of the enemy aircraft attack bullets are updated for all enemy aircraft attack bullets k (k = 1,..., K).
The control unit 10 increments p read from the storage unit 101 by 1 and stores it in the storage unit 101.

<Step S8>
The control unit 10 determines whether p × τ = T by using p, τ, and T read from the storage unit 101. Otherwise, the process of step S7 is performed.

<Step S8 '>
If it is determined in step S8 that p × τ = T, the position (xs, ys) of the aircraft at that time is set to (xs (d, de, j), ys (d, de, j)). The position (xei, yei) of the enemy aircraft at that time is set as (xei (d, de, j), yei (d, de, j)), and the position of the enemy aircraft attacking bullet (xbk, ybk) at that time (Xbk (d, de, j), ybk (d, de, j)) are stored in the position storage unit 7 respectively.

  In this way, every time p × τ = T, the current position is stored in the position storage unit 7, so that the own aircraft position calculation unit 4, enemy aircraft position calculation unit 5, enemy aircraft attack bullet position calculation The unit 6 obtains the position (own aircraft, enemy aircraft, enemy aircraft attack bullet) at each time step d when moving according to each (own aircraft, enemy aircraft, enemy aircraft attack bullet) action pattern.

<Step S9>
The own aircraft existence probability calculation unit 1 calculates a probability that the own aircraft moving according to the current moving speed number w (d, de, j) is located in each cell s without being destroyed by an enemy aircraft. Hereinafter, the process of step S91-step S98 which comprises step S9 is demonstrated. For details on se, sei, scbk, smm, Smm, Sall, Ptr (w, m, n), Pcm, and the like, see the description of the above “Own-machine existence probability calculation unit” and FIG.

<< Step S91 (FIG. 4) >>
The position acquisition unit 11 (see FIG. 2) of the own device existence probability calculation unit 1 at the time step d moved according to the permutation w (d, de, j) of the own device action pattern calculated by the own device position calculation unit 4. The position (xs (d, de, j), ys (d, de, j)) of the own machine is read from the position storage unit 7, and a cell s corresponding to this position is obtained and output to the area calculation unit 12. .

<< Step S92 >>
The area calculation unit 12 calculates the area Smn of the overlapping part of each cell smn and the cell se that is the same as the cell s or expanded by the errors ex and ey, and outputs them to the addition unit 13 and the division unit 14. To do. The errors ex and ey are read from the error storage unit 8.

<< Step S93 >>
The adder 13 calculates the sum of the areas of smn Sall = ΣmΣnsmn and outputs it to the divider 14.

<< Step S94 >>
The division unit 14 obtains a probability Ptr (w, m, n) = smn / Sall for moving to the cell smn at time step d and outputs the probability Ptr (w, m, n) for each cell smn to the probability calculation unit 15.

<< Step S95 >>
The area calculation unit 17 obtains the area Scmn of the overlapping part of the cell mesh and the overlapping part of the cell scbk and the cell smn for each cell smn, and outputs it to the collision probability calculation unit.

<< Step S96 >>
The collision probability calculation unit 18 obtains a probability Pcmn = Scmn / Smn that the enemy aircraft and the enemy aircraft attack bullets are located in the cell smn at the time step d for each cell and outputs it to the subtraction unit 19.

<< Step S97 >>
The subtracting unit 19 subtracts Pcmn from 1, and obtains a probability 1-Pcmn for each square smn that destroys the enemy aircraft and enemy aircraft attack bullets located in the square smn at time step d. The result is output to the calculation unit 15.

<< Step S98 >>
The probability calculation unit 15 adds (1 / W) · (1−Pcmn) · Ptr (w, m, n) · Ps (s ′,) to Ps (smn, d) read from the own device existence probability storage unit 2. By performing the process of adding d-1) for each cell smn, the probability Ps (s, d) existing in the cell s without being destroyed by the enemy aircraft at the time step d is updated, and the own device exists. Store in the probability storage unit 2. W is read from the storage unit 101, and Ps (s ′, d−1) is read from the own device existence probability storage unit 2.

<Step S10>
The control unit 10 increments the permutation number j read from the storage unit 101 by 1 and stores it again in the storage unit 101.

<Step S11>
The control unit 10 determines whether j−1 = W to the d power using j, W, and d read from the storage unit 101. If j−1 = W is not the d-th power, the process of step S4 is performed. If j-1 = W to the power of d, the process of step S12 is performed.

<Step S12>
The control unit 10 increments the time step d read from the storage unit 101 by 1 and stores it again in the storage unit 101.

<Step S13>
The control unit 10 determines whether d = D + 1 using d and D read from the storage unit 101. If d = D + 1 is not satisfied, the process of step S2 is performed. If d = D + 1, the process of step S15 is performed.

<Step S14>
If it is determined in step S4 that d = 1 is not satisfied, the control unit 10 determines the d-1th of the permutation w (d, de, j) of the own behavior pattern of d and j currently being evaluated. Are searched for from the own action pattern storage unit 91 for the permutation w (d-1, d-1, j ′) of the own action patterns of d−1 and j ′. Information about the permutation w (d−1, d−1, j ′) of the own aircraft action pattern is output to the own aircraft position calculation unit 4, the enemy aircraft position calculation unit 5, and the enemy aircraft attack bullet position calculation unit 6. .

  For example, as shown in FIG. 9A, the permutation of the own action pattern of d = 2, j = 1 is {w (2,1,1) = 1, w (2,2,1) = 1}. Yes, if the permutation of the own action pattern of d = 1, j = 1 is {w (1,1,1) = 1}, w (2,1,1) = 1 and w (1, 1, 1) = 1, the permutation elements of the own behavior pattern match. Therefore, the elements up to d−1 about the permutation {w (2,1,1) = 1, w (2,2,1) = 1} of the own behavior pattern of d = 2 and j = 1 are obtained. The permutation of the same own behavior pattern is the permutation {w (1, 1, 1) = 1} of the own behavior pattern of d = 1, j = 1.

Further, as shown in FIG. 9B, for example, the permutation of the own action pattern of d = 3, j = 3 is {w (3,1,3) = 1, w (3,2,3) = 1. , W (3, 3, 3) = 3}, and the permutation of the own action pattern of d = 2, j = 1 is {w (2, 1, 1) = 1, w (2, 2, 1). = 1}, {w (3, 1, 3) out of the permutation of the own behavior pattern of d = 3, j = 3 and the permutation of the own behavior pattern of d = 2, j = 1. = 1, w (3, 2, 3) = 1} and {w (2, 1, 1) = 1, w (2, 2, 1) = 1}, the permutation elements of the own machine action pattern Match. Therefore, the permutation of the own behavior pattern of d = 3, j = 3 {w (3,1,1) = 1, w (3,2,1) = 1, w (3,3,1) = 3} The permutation of the self-behavior action pattern with the same elements up to the (d-1) th is {w (2,1,1) = 1, w (2, 2, 1) = 1}.
The own-machine position calculation unit 4 includes the position (xs (d-1, d-1, j ′)) of the own machine corresponding to the permutation w (d−1, d−1, j ′) of the own machine action pattern. ys (d−1, d−1, j ′)) is read from the position storage unit 7 and the position (xs, ys) = (xs (d−1, d−1, j) of the own machine currently evaluated '), Ys (d-1, d-1, j')).

  Similarly, the enemy aircraft position calculation unit 5 determines the position (xei (d-1, d-1, j) of the enemy aircraft corresponding to the permutation w (d-1, d-1, j ') of the own aircraft action pattern. '), Yei (d-1, d-1, j')) are read out from the position storage unit 7, and the position (xei, yei) = (xei (d-1, d-) of the enemy aircraft currently being evaluated. 1, j ′), yei (d−1, d−1, j ′)).

  Similarly, the enemy aircraft attack bullet position calculation unit 6 calculates the position (xbk (d-1, d) of the enemy aircraft attack bullet corresponding to the permutation w (d-1, d-1, j ') of the own machine action pattern. −1, j ′), ybk (d−1, d−1, j ′)) from the position storage unit 7 and the position (xbk, ybk) = (xbk ( d-1, d-1, j '), ybk (d-1, d-1, j')).

<Step S15>
The difficulty level determination unit 3 (see FIG. 1) calculates a value obtained by adding the probability Ps (s, D) that the own device is located in each cell s at time step D for all cells s. Is the difficulty level of the shooting game. That is, the difficulty level determination unit 3 calculates a value determined by Σ _s Ps (s, D) as the difficulty level.

[How to find errors ex and ey]
Hereinafter, an example of how to obtain the errors ex and ey will be described. First, the target point that the player should follow is displayed on the game screen. It is assumed that the target point is moved by a predetermined algorithm and at which time and at which position is determined. Let the player operate his / her own machine and follow the target point. Then, at each time, the difference between the x coordinate of the own machine and the x coordinate of the target point (hereinafter referred to as a tracking error in the x-axis direction) is measured. Similarly, the difference between the y coordinate of the own device and the y coordinate of the target point (referred to as a tracking error in the y-axis direction) at each time is measured. An example of the measurement result is shown in FIG. FIG. 10 is a diagram showing the follow-up error in the x-axis direction at each time, the vertical axis is the follow-up error in the x-axis direction, and the horizontal axis is the time.

  In general, the position of the player's own machine is discretely defined by the dots that make up the game screen. For example, it is difficult to discuss how much follow-up error appears when the own machine advances by one dot. For this reason, it is necessary to consider how much time and how much the error is expanded. This is important in determining the size of the grid used for the difficulty determination of the present invention and how much T should be set.

Here, it is considered that the player operates his / her own device to reduce the tracking error as in feedback control. For this reason, it is considered that the maximum value of the absolute value of the following error does not increase so much after a certain time T ^* has elapsed. Therefore, in the present invention, for example, the time after the certain time T ^* is set to T and the time T after the self-machine is operated in the same state (position error 0 state) as that of the self-machine. ^* The maximum absolute value of the tracking error until a certain time after that is used as the error. Thereby, the time T at which the tracking error is stabilized and the stable tracking error can be used, and the accuracy of the difficulty determination method according to the present invention is improved. For reference, the maximum value of the absolute value of the follow-up error in the x-axis direction shown in FIG. The thin line in FIG. 11 is the tracking error in the x-axis direction shown in FIG. 10, and the dotted line is the absolute value of the tracking error in the x-axis direction shown in FIG.

Thus, for example, in the present invention, the time after the time T ^{* at which} the increase in the maximum value of the absolute value of the follow-up error in the x-axis direction and the y-axis direction almost stops at that time is T, and the x-axis direction The maximum value of the absolute value of the following error up to a certain time after time T ^* is used as ex, and the maximum value of the absolute value of the tracking error in the y-axis direction up to that time is used as ey.

In addition, the distance (following error) at each time t between the position of the own machine and the position of the target point is measured without dividing into the x-axis direction and the y-axis direction, and the maximum absolute value of the following error does not increase greatly. The time after time T ^* may be T, and the maximum absolute value of the tracking error up to time T may be ex and ey, respectively.

Also, instead of setting the time after the time T ^{* at} which the maximum absolute value of the tracking error does not increase significantly to T, an arbitrary time is set as T, and the maximum absolute value of the tracking error up to the time T is set as an error. It may be used.

  Prior to the determination of the difficulty level, the error calculation unit 82 calculates these errors and stores them in the error storage unit 8. Further, an input unit 81 may be provided so that an error can be set freely.

  The error may be estimated during the shooting game. For example, if you display an image that moves according to a predetermined algorithm on the screen and the player follows the image, a bonus stage that gives a higher score as the tracking accuracy is higher Set in. In such a bonus stage, the error calculator 82 estimates the error by the method described above.

[Modifications, etc.]
In the above embodiment, the case where both enemy aircraft and enemy aircraft attack bullets exist is described as an example, but the same applies even when only one of the enemy aircraft and enemy aircraft attack bullets exists. Furthermore, the difficulty level determination method according to the present invention can be realized. Further, even if there is only one enemy aircraft and one enemy aircraft attacking bullet, the difficulty level determination method according to the present invention can be realized even if there are a plurality of enemy aircraft.

  The difficulty level determination method and apparatus of the shooting game can be realized by a computer. In this case, the enemy machine operation control method and apparatus contents of the shooting game are described by a program. Then, by executing this program on a computer as shown in FIG. 12, the functions of each part of the difficulty level determination device for the shooting game are realized on the computer.

  The program describing the processing contents can be recorded on a computer-readable recording medium. As the computer-readable recording medium, for example, any recording medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory may be used. Specifically, for example, as a magnetic recording device, a hard disk device, a flexible disk, a magnetic tape or the like, and as an optical disk, a DVD (Digital Versatile Disc), a DVD-RAM (Random Access Memory), a CD-ROM (Compact Disc Read Only). Memory), CD-R (Recordable) / RW (ReWritable), etc., magneto-optical recording medium, MO (Magneto-Optical disc), etc., semiconductor memory, EEP-ROM (Electronically Erasable and Programmable-Read Only Memory), etc. Can be used.

  The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. When executing the process, the computer reads a program stored in its own recording medium and executes a process according to the read program. As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. It is good. Note that the program in this embodiment includes information that is provided for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer).
In this embodiment, a method and apparatus for determining the difficulty level of a shooting game are configured by executing a predetermined program on a computer. However, at least a part of these processing contents is realized by hardware. It is good as well.

  In addition to the above embodiments, the method, apparatus, and program for determining the difficulty level of a shooting game according to the present invention are not limited to the above-described embodiments, and can be changed as appropriate without departing from the spirit of the present invention. is there.

The figure which illustrated the functional structure of the difficulty determination apparatus 1000. The figure which illustrated the functional composition of self-machine existence probability calculation part 1. The figure which illustrated the flow of the process of the difficulty determination apparatus 1000. The figure which illustrated the flow of processing of Step S9 and own machine existence probability calculation part 1. The figure which assists the description about the difficulty determination method by background art. A conceptual diagram of a shooting game. The figure which assists description of how to obtain | require probability Ps (s, d). The figure which assists description of a horizontal type | mold search. The permutation w (d−1, j ′) of the own behavior pattern of d−1 and j ′, where the elements up to d−1 of the permutation w (d, de, j) of the permutation pattern of d and j are the same. The figure which illustrated d-1, j '). The figure which illustrated the follow-up error of the x-axis direction in each time. The figure which showed the maximum value of the absolute value until the time of the tracking error of a x-axis direction. The figure which illustrated the functional composition when performing the difficulty determination apparatus with a computer.

Claims (10)

A shooting game in which the player and enemy aircraft are displayed on the screen, and the player moves the aircraft by selecting an action of W (W is an arbitrary natural number). The degree of difficulty of the aircraft is determined by the own aircraft action pattern generation means, the own aircraft position calculation means, the enemy aircraft position calculation means, the first area calculation means, the second area calculation means, the collision probability calculation means, In the difficulty level determination method performed by the computer including the machine presence probability calculation means and the difficulty level determination means ,
The self-behavior pattern generation means performs a predetermined time T according to each action w (w = 1,..., W) for each time step d (d = 1,..., D, D is an arbitrary natural number). A self-machine action pattern generation step for generating all or a part of the self-machine action pattern of the self-machine that performs the moving action;
The own machine position calculating means obtains the position at each time step d of the own machine that moves according to each of the generated own machine action patterns;
An enemy aircraft position calculating step in which the enemy aircraft position calculating means calculates a position at each time step d of an enemy aircraft moving according to a predetermined enemy aircraft action pattern;
Each above first area calculation means, constitute a predetermined first shape containing the Motoma' position at time step d of own apparatus to move according to their machine behavior patterns the generated, a grid obtained by dividing the screen grids a first area calculating step of calculating an area of an overlapping portion with s;
The second area calculation means, and a predetermined second shape including the position at each time step d above Motoma' enemy machine, and a second area calculation step of calculating the area of overlap between each square s,
By the collision probability calculating means calculates the area divided by the area of the square s the overlapping portion between each square s calculated in the second area calculation step, the collision probability calculating step of obtaining the collision probability When,
The own device existence probability calculating means is calculated in the first area calculating step, the probability Ps (s ′, d−1) that the own device is located in the cell s ′ at time step d−1, 1 / W, and The sum of the value obtained by dividing the area of the overlapping portion with each cell s by the area of the first shape and the value obtained by subtracting the collision probability from 1 for all the cells s ′ The probability Ps (s, D) that the own device is located in each cell s in time step D is sequentially repeated by repeating the process of obtaining the probability Ps (s, d) that the own device is located in the cell s at time step d. The step of calculating the existence probability of the aircraft to be obtained,
A difficulty level determination step in which the difficulty level determination means outputs a value obtained by adding the probability Ps (s, D) of the aircraft in the grid s at time step D to all or some of the grids;
A difficulty determination method having A shooting game in which the player and enemy aircraft are displayed on the screen, and the player moves the aircraft by selecting an action of W (W is an arbitrary natural number). The determination of the difficulty level is performed by: own-machine action pattern generation means, own-machine position calculation means, enemy aircraft attack bullet position calculation means, first area calculation means, third area calculation means, and collision probability calculation means; In the difficulty determination method performed by a computer having own machine existence probability calculation means and difficulty determination means ,
The self-behavior pattern generation means performs a predetermined time T according to each action w (w = 1,..., W) for each time step d (d = 1,..., D, D is an arbitrary natural number). A self-machine action pattern generation step for generating all or a part of the self-machine action pattern of the self-machine that performs the moving action;
The own machine position calculating means obtains the position at each time step d of the own machine that moves according to each of the generated own machine action patterns;
The enemy aircraft attack bullet position calculation means for calculating the position of each enemy step attack bullet that moves in accordance with a predetermined enemy aircraft attack bullet action pattern at each time step d;
Each above first area calculation means, constitute a predetermined first shape containing the Motoma' position at time step d of own apparatus to move according to their machine behavior patterns the generated, a grid obtained by dividing the screen grids a first area calculating step of calculating an area of an overlapping portion with s;
The third area calculation means, and a predetermined third shape including a location at each time step d above Motoma' enemy machine attacking bullets, and a third area calculation step of calculating the area of overlap between each square s ,
By the collision probability calculating means calculates the area divided by the area of the square s the overlapping portion between each square s calculated in the third area calculation step, the collision probability calculating step of obtaining the collision probability When,
The own device existence probability calculating means is calculated in the first area calculating step, the probability Ps (s ′, d−1) that the own device is located in the cell s ′ at time step d−1, 1 / W, and The sum of the value obtained by dividing the area of the overlapping portion with each cell s by the area of the first shape and the value obtained by subtracting the collision probability from 1 for all the cells s ′ The probability Ps (s, D) that the own device is located in each cell s in time step D is sequentially repeated by repeating the process of obtaining the probability Ps (s, d) that the own device is located in the cell s at time step d. The step of calculating the existence probability of the aircraft to be obtained,
A difficulty level determination step in which the difficulty level determination means outputs a value obtained by adding the probability Ps (s, D) of the aircraft in the grid s at time step D to all or some of the grids;
A difficulty determination method having In the difficulty level determination method according to claim 1,
The computer further includes an enemy aircraft attack bullet position calculation means,
further,
An enemy aircraft attack bullet position calculation step in which the enemy aircraft attack bullet position calculation means obtains a position at each time step d of an enemy aircraft attack bullet moving according to a predetermined enemy aircraft attack bullet action pattern;
Have
In the second area calculating step, the overlapping portion between the predetermined second shape including the position of the obtained enemy aircraft at the time step d and the mesh s and the position of the obtained enemy aircraft attack bullet at the time step d are determined. Calculating the area of the union of the predetermined third shape and the overlapping portion of the cell s for each cell s,
The collision probability calculating step calculates a value obtained by dividing the area of the union of overlapping portions with the cell s calculated for each cell s in the second area calculating step by the area of the cell s. A step for determining the probability,
The difficulty determination method characterized by the above. In the difficulty level determination method according to claim 1, there are a plurality of enemy aircraft,
The enemy aircraft position calculation step is a step of obtaining the position at each time step d of the enemy aircraft moving according to a predetermined enemy aircraft action pattern for each of the plurality of enemy aircraft.
In the second area calculating step, an overlapping portion between the predetermined second shape including the obtained position of the enemy aircraft at the time step d and the mesh s is obtained for each of the plurality of enemy aircrafts, and a union of those overlapping portions Calculating the area of each square s,
The collision probability calculating step calculates a value obtained by dividing the area of the union of overlapping portions with the cell s calculated for each cell s in the second area calculating step by the area of the cell s. A step for determining the probability,
The difficulty determination method characterized by the above. In the difficulty determination method according to claim 2, there are a plurality of enemy aircraft attack bullets,
The enemy aircraft attack bullet position calculating step is a step of obtaining, for each of a plurality of enemy aircraft attack bullets, a position at each time step d of an enemy aircraft attack bullet moving according to a predetermined enemy aircraft attack bullet action pattern.
In the third area calculating step, an overlapping portion between the predetermined third shape including the position of the obtained enemy aircraft attack bullet at the time step d and the square mesh s is obtained for each of the plurality of enemy aircraft attack bullets, and their overlap. Calculating the area of the union of the parts for each cell s;
The collision probability calculating step, by calculating the value of the area of union, divided by the area of the square s of the overlapped portion of the square s calculated for each square s in the third area calculation step, A step of determining the collision probability,
The difficulty determination method characterized by the above. In the difficulty level determination method according to claim 3, there are a plurality of enemy aircraft and enemy aircraft attack bullets,
The enemy aircraft position calculation step is a step of obtaining the position at each time step d of the enemy aircraft moving according to a predetermined enemy aircraft action pattern for each of the plurality of enemy aircraft.
The enemy aircraft attack bullet position calculating step is a step of obtaining, for each of a plurality of enemy aircraft attack bullets, a position at each time step d of an enemy aircraft attack bullet moving according to a predetermined enemy aircraft attack bullet action pattern.
In the second area calculating step, an overlapping portion between the predetermined second shape including the obtained position of the enemy aircraft at the time step d and the mesh s is obtained for each of the plurality of enemy aircraft, and the obtained enemy aircraft attack bullet is obtained. A step of calculating an overlapping portion of the predetermined third shape including the position at time step d and the mesh s for each of the plurality of enemy aircraft attack bullets, and calculating an area of the union of these overlapping portions for each of the cells s Is,
The difficulty determination method characterized by the above. In the difficulty determination method in any one of Claims 1-6,
The first shape is a shape in which each side of the cell s where the player is located at time step d is widened by an expected operation error of the player.
The difficulty determination method characterized by the above. In the difficulty level determination method according to claim 7,
The expected operation error of the player is the target position obtained at each time until a predetermined time and moved by a predetermined algorithm, and the player's own operation when the player operates the target position to follow the target position. The maximum value of the absolute value of the distance to the position up to that predetermined time,
The difficulty determination method characterized by the above. A shooting game in which the player and enemy aircraft are displayed on the screen, and the player moves the aircraft by selecting an action of W (W is an arbitrary natural number). In the difficulty level determination device,
All of the devices that perform the movement for a predetermined time T according to each action w (w = 1,..., W) for each time step d (d = 1,..., D, D is an arbitrary natural number). Self-action pattern generation means for generating a part or a part of the self-action pattern;
A ship position calculation means for determining a position at each time step d of own apparatus to move according to their machine behavior patterns the generated,
And enemy position calculation means for determining a position at each time step d of enemy moving in accordance with a predetermined enemy action pattern,
The area of the overlapping portion between the predetermined first shape including the obtained position at the time step d of the own machine moving according to the generated own machine action pattern and each cell s constituting the grid dividing the screen. A first area calculating means for calculating;
A second area calculating means for calculating an area of an overlapping portion between the predetermined second shape including the position of each enemy step obtained at each time step d and each cell s;
A collision probability calculating means for calculating a collision probability by calculating a value obtained by dividing the area of the overlapping portion with each cell s calculated by the second area calculating means by the area of the cell s;
The probability Ps (s ′, d−1) that the own device is located in the cell s ′ at time step d−1, 1 / W, and the overlapping portion of each cell s calculated by the first area calculating means By taking the sum of the value obtained by dividing the area by the area of the first shape and the value obtained by subtracting the collision probability from 1 for all cells s ′, the aircraft at time step d self-machine existence probability calculating means for determining the probability Ps (s, D) at which the own machine is located at each cell s at time step D by sequentially repeating the process of obtaining the probability Ps (s, d) located at s;
Difficulty level determination means for outputting a value obtained by adding the probability Ps (s, D) of the own machine in the cell s at time step D for all or some of the cells;
A difficulty determination device having A shooting game in which the player and enemy aircraft are displayed on the screen, and the player moves the aircraft by selecting an action of W (W is an arbitrary natural number). It is a difficulty determination program for determining the difficulty level of
All of the devices that perform the movement for a predetermined time T according to each action w (w = 1,..., W) for each time step d (d = 1,..., D, D is an arbitrary natural number). A self-behavior pattern generation step for generating a self-behavior pattern of a part of or
A self-machine position calculating step for obtaining a position at each time step d of the self-machine moving according to each of the generated self-machine action patterns;
An enemy aircraft position calculating step for obtaining a position at each time step d of an enemy aircraft moving according to a predetermined enemy aircraft action pattern;
The area of the overlapping portion between the predetermined first shape including the obtained position at the time step d of the own machine moving according to the generated own machine action pattern and each cell s constituting the grid dividing the screen. A first area calculation step to calculate;
A second area calculating step for calculating an area of an overlapping portion between the predetermined second shape including the position of each enemy step obtained at each time step d and each cell s;
A collision probability calculating step for determining a collision probability by calculating a value obtained by dividing the area of the overlapping portion with each cell s calculated in the second area calculating step by the area of the cell s;
The probability Ps (s ′, d−1) that the own device is located in the cell s ′ at time step d−1, 1 / W, and the overlapping portion of each cell s calculated in the first area calculation step By taking the sum of the value obtained by dividing the area by the area of the first shape and the value obtained by subtracting the collision probability from 1 for all cells s ′, the aircraft at time step d an own machine existence probability calculating step for obtaining a probability Ps (s, D) at which the machine is located at each cell s at time step D by sequentially repeating a process for obtaining a probability Ps (s, d) located at s;
A difficulty level determination step of outputting a value obtained by adding the probability Ps (s, D) of the own machine in the cell s in time step D for all or some cells;
Is a difficulty determination program for causing a computer to execute.

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