JP4210293B2 - Simulation apparatus, simulation method, and program - Google Patents

Description

  The present invention realizes a simulation apparatus, a simulation method, and a computer suitable for easily simulating changes in the shape of a shape-variable object such as a flexible cloth or paper arranged in a virtual space. Regarding the program.

2. Description of the Related Art Conventionally, in computer graphics (CG), a technique for simulating a flexible cloth or paper having a variable shape such as a cloak or a skirt worn by a human character has been proposed. Character position and posture (generally, the position and posture of an object representing a member constituting the character in the virtual space. Here, “posture” refers to the character or the position of each coordinate axis in a reference coordinate system. This means that when the coordinate axis of the coordinate system fixed to the object is different, the shape of the cloth or the like whose edges are connected to the character also changes. Such a technique is disclosed in the following document.
JP-A-2005-099952

  [Patent Document 1] uses a model in which a flexible object such as cloth, clothes, and hair is composed of a plurality of quadrilateral polygons, the vertexes are virtual mass points, and adjacent mass points are connected by virtual springs. A cross-simulation related technique for obtaining the shape is disclosed. At this time, the differential equation is numerically integrated and solved every predetermined update interval time (typically, a vertical synchronization interrupt period).

  Here, the update interval time is also called “step time” or “time step size” in the field of numerical integration, and it is necessary to be a minute time, but the degree of “minute” depends on the application field. As the update interval time is shortened, the simulation error becomes smaller, but the calculation amount required for numerical integration increases.

  In cross simulations, it can be considered that the more the number of mass points, the more accurately the shape of the cloth can be simulated, but the more the number of mass points, the more computational complexity required for numerical integration. .

  However, when such a simulation is performed in an information processing apparatus with a slow calculation speed and limited calculation resources, the update interval time is made as long as possible and the number of mass points is made as small as possible to simplify the calculation. The desire to want is great.

  On the other hand, when the update interval time is lengthened or the number of mass points is decreased, and the object moved by the character etc. is connected to the character operated by the player etc. There is a problem that the length becomes excessively long, and the shape becomes far away from the shape of an actual cloth or the like.

  In CG movie production where there is no need to perform such simulation in real time, it is not impossible to solve this problem by shortening the update interval time or increasing the number of mass points. When performing, real time property is required, and therefore, it is not possible to adopt a method of shortening the update interval time or increasing the number of mass points, and a new technique is required.

  The present invention solves the above-described problems, and is a simulation device and simulation suitable for easily simulating changes in the shape of a shape-variable object such as a flexible cloth or paper arranged in a virtual space. It is an object of the present invention to provide a method and a program for realizing the method on a computer.

  In order to achieve the above object, the following invention is disclosed in accordance with the principle of the present invention.

  The simulation apparatus according to the first aspect of the present invention includes a storage unit, a support calculation unit, a support correction unit, a mass point calculation unit, a support update unit, and a mass point update unit, and is configured as follows.

  Here, the targets of the simulation are the position and orientation of the support object arranged in the virtual space, and the positions of the plurality of mass point objects. In the virtual space, each of the plurality of mass point objects is the support object or Among the plurality of mass point objects, they are connected to other mass point objects via virtual elastic bodies.

  In addition, the storage unit stores the position and orientation of the support object arranged in the virtual space, and the positions of the plurality of mass point objects.

  In a virtual space, an object such as a cloth representing a skirt is typically represented by a mass object that is two-dimensionally connected to each other by a virtual elastic body (virtual spring or the like), and a part of its edge is , Connected to a support object representing the character's torso.

  A skirt without a human being spreads as a two-dimensional plane, but when a human wears a skirt, the overall shape is roughly the shape of a truncated cone, resulting in wrinkles and folds and irregularities. Therefore, the position of the mass object actually exhibits a three-dimensional distribution.

  That is, “two-dimensional surface” here means that in a certain basic state, a certain mass point object is connected to a mass point object arranged around it by a virtual elastic body.

  Here, for the support object, it is necessary to store the position and orientation (orientation) in the virtual space, but for the mass object, it is often sufficient to know the position. Of course, depending on the type of object to be simulated, the posture information may be further managed for the mass object.

  On the other hand, the support calculation unit calculates a support change amount representing a change in the position and posture of the support object with the elapse of the update interval time.

  Here, parameters such as the external force applied to the support object and the type of instruction input from the user are taken into account, and a physical simulation is performed based on the law corresponding to the physical law of the real world, after the update interval time. Calculate the position and orientation of the support object. At this time, gravity, wind force, or the like may be assumed as the external force.

  Note that the elastic force generated by the virtual elastic body connecting the mass point object and the support object is generally considered to be small. Therefore, when calculating changes in the position and orientation of the support object, a method of ignoring the elastic force is used. It is often good to do.

  The amount of change in support is the amount of change in the position that indicates how much the origin of the coordinate system fixed to the support object moves in the global coordinate system, and the amount of change in the coordinate system fixed to the support object in the global coordinate system. Typically, it is assumed that the amount of change in posture that represents only the rotation amount.

  On the other hand, the support correction unit calculates a support correction amount in which the calculated support change amount is corrected so as not to exceed a predetermined threshold.

  When the magnitude of the support change amount exceeds a predetermined threshold value, the deformation amount of the virtual elastic body becomes extremely large, and there is a high possibility that a realistic simulation cannot be performed. Therefore, in order to suppress the deformation amount of the virtual elastic body, a support correction amount smaller than the support change amount is considered, and based on this, a cross simulation is performed as described later.

Further, the mass point calculation unit calculates the plurality of mass points from the position and posture moved by the support correction amount calculated from the stored position and posture of the support object and the stored positions of the plurality of mass point objects. For each of the objects
(A) calculating the force exerted on the mass point object by the virtual elastic body to which the mass point object is connected;
(B) A mass change amount representing the relative position of the mass object with respect to the support object after the update interval time has elapsed is calculated from the calculated force.

  In other words, changes in the position and orientation of the support object that should have changed greatly are appropriately corrected to suppress the size to a certain extent, and each mass point object, in particular, the support, based on the suppressed change in position and orientation. Calculate the change in position of the mass object connected to the object. When the position and orientation of the support object change, the length of the virtual elastic body that connects the support object and the mass point object also changes. Accordingly, an elastic force corresponding to the change in length is applied to the mass point object. At this time, the calculation can be performed in consideration of gravity and wind power. Further, it is desirable to adopt a coordinate system fixed to the support object as the coordinate system for calculating the mass change amount.

  On the other hand, the support update unit updates the position and posture of the support object with the position and posture moved by the support change amount calculated from the position and posture of the support object stored in the storage unit.

  For the support object, the position and orientation are updated based on the calculated support change amount.

  Further, the mass point updating unit converts each of the positions of the plurality of mass point objects stored in the storage unit from the position of the supporting object whose position and orientation are updated by the amount of mass point change calculated for the mass point object. The position of the mass point object is updated with the moved position.

  The mass point object is moved without changing the coordinates in the coordinate system fixed to the support object by first moving by the support change amount. Then, in the coordinate system fixed to the support object, the position of the mass point object is moved based on the mass point change amount calculated for the mass point object.

  According to the present invention, it is possible to prevent the simulation result from becoming unnatural due to the length of the virtual elastic body that connects the support object and the mass point object being too long, and the update interval time that is the time unit of the cross simulation is to some extent. Even at the longest, an appropriate cross simulation can be performed.

  In the simulation apparatus of the present invention, the support correction unit calculates the support correction amount by applying the calculated support change amount to an internal function whose monotonously increases and the limit is equal to or less than the predetermined threshold. Can be configured.

  For example, when considering the change amount related to the position among the support change amounts, the position that internally divides the current position of the support object and the position obtained by adding the change amount related to the position to the current position, The current position is matched with the position obtained by adding only the portion related to the position of the support correction amount.

  Further, when considering the change amount related to the posture among the support change amounts, the change amount is expressed as rotating around a certain axis by a certain rotation angle, but the rotation angle relating to the correction amount is set to 0. The internal division can be performed by setting the angle and the angle to internally divide the angle.

  The present invention relates to a preferred embodiment of the invention described above, and can be calculated so as not to exceed a predetermined threshold by selecting an appropriate function when determining the support correction amount from the support change amount. It becomes like this.

  In the simulation apparatus of the present invention, the internal division function in the support correction unit includes a position internal function applied to a position change amount among the support change amounts and a posture change amount among the support change amounts. The position internal function is a monotonically increasing function that multiplies the upper limit of the change amount of the position by a coefficient of 0 or more and 1 or less, and the position internal function Can be configured to be a monotonically increasing function by multiplying the upper limit value of the rotation angle around the axis related to the change in the posture by a coefficient of 0 or more and 1 or less.

  The present invention is according to a preferred embodiment of the invention described above, and by calculating a support correction amount by multiplying a support change amount by a coefficient between 0 and 1, the support correction amount is easily calculated. Will be able to.

  In the simulation device of the present invention, the mass point calculation unit calculates the amount of change in the mass point by multiplying the elastic coefficient of the virtual elastic body by the reciprocal of the coefficient relating to the position internal function or the square of the reciprocal of the coefficient. It can be constituted as follows.

  Depending on the field of application of the simulation, the above invention can often perform a simulation with sufficient accuracy. However, in the above invention, it is considered that the advance of the time for the movement of the mass object is delayed with respect to the simulation time. Therefore, by multiplying the external force applied to the mass object by the reciprocal of the coefficient for correction, the magnitude of the external force is increased, the movement of the mass object is accelerated, and the delay with respect to the simulation time is compensated. Is.

  As an external force, an elastic force due to a virtual elastic body is assumed, but when gravity or wind force is applied, the gravity and wind force are similarly multiplied by the inverse of the coefficient to compensate for the delay. Also good.

  According to the present invention, by multiplying the external force applied to the mass point object by the reciprocal of the coefficient or the like, it becomes possible to compensate for the time delay of the movement of the mass point object and to make a more realistic motion.

  The simulation apparatus according to the present invention further includes an image generation unit, and the image generation unit pastes a predetermined texture on a polygon having a plurality of stored mass point objects as vertices, and adds the support object and the support object. It can be configured to generate an image of a deformable object to be connected.

  The present invention relates to a preferred embodiment of the above invention, wherein a polygon having a mass point object as a vertex is defined in accordance with a shape such as a skirt, and a texture representing a texture of a surface such as a cloth is attached to the polygon. As a result, it becomes possible to generate a deformable object whose shape is softly changed.

  In the simulation method according to another aspect of the present invention, the position and orientation of the support object arranged in the virtual space and the positions of the plurality of mass point objects are to be simulated, and each of the plurality of mass point objects is the support object. Alternatively, it is connected to another mass point object among the plurality of mass point objects via a virtual elastic body.

  The simulation method includes a storage unit, a support calculation unit, a support correction unit, a mass point calculation unit, a support update unit, and a mass point update unit that store the position and orientation of the support object and the positions of a plurality of mass point objects. It is executed by the simulation apparatus and includes a support calculation process, a support correction process, a mass point calculation process, a support update process, and a mass point update process, and is configured as follows.

  That is, in the support calculation step, the support calculation unit calculates a support change amount representing a change in the position and posture of the support object with the elapse of the update interval time.

  On the other hand, in the support correction step, the support correction unit calculates a support correction amount in which the calculated support change amount is corrected so as not to exceed a predetermined threshold.

  Further, in the mass point calculation step, the mass point calculation unit is based on the position and posture moved by the support correction amount calculated for the stored position and posture of the support object, and the stored positions of the plurality of mass point objects. , For each of the plurality of mass point objects, the relative position of the mass point object with respect to the support object as a result of the lapse of the update interval time due to the force exerted on the mass point object by the virtual elastic body to which the mass point object is connected The change in mass point representing is calculated.

  Then, in the support update step, the support update unit updates the position and posture of the support object with the position and posture moved by the support change amount calculated from the position and posture of the support object stored in the storage unit.

  On the other hand, in the mass point updating step, the mass point updating unit moves to each of the positions of the plurality of mass point objects stored in the storage unit by the support change amount calculated from the position, and further to the mass point object. The position of the mass point object is updated at a position moved with reference to the support object whose position and orientation are updated by the calculated mass point change amount.

  A program according to another aspect of the present invention is configured to cause a computer to function as the simulation apparatus and to cause the computer to execute the simulation method.

  The program of the present invention can be recorded on a computer-readable information storage medium such as a compact disk, flexible disk, hard disk, magneto-optical disk, digital video disk, magnetic tape, and semiconductor memory.

  The above program can be distributed and sold via a computer communication network independently of the computer on which the program is executed. The information storage medium can be distributed and sold independently from the computer.

  According to the present invention, a simulation apparatus, a simulation method, and a computer suitable for easily simulating changes in the shape of a shape-variable object such as a flexible cloth or paper arranged in a virtual space, A program to be realized can be provided.

  Embodiments of the present invention will be described below. In the following, for ease of understanding, an embodiment in which the present invention is realized using a game information processing device will be described. However, the embodiment described below is for explanation, and the present invention is described. It does not limit the range. Therefore, those skilled in the art can employ embodiments in which each or all of these elements are replaced with equivalent ones, and these embodiments are also included in the scope of the present invention.

  FIG. 1 is a schematic diagram showing a schematic configuration of a typical information processing apparatus that functions as a simulation apparatus of the present invention by executing a program. Hereinafter, a description will be given with reference to FIG.

  The information processing apparatus 100 includes a CPU (Central Processing Unit) 101, a ROM (Read Only Memory) 102, a RAM (Random Access Memory) 103, an interface 104, a controller 105, an external memory 106, and an image processing unit 107. A DVD-ROM (Digital Versatile Disc ROM) drive 108, a NIC (Network Interface Card) 109, an audio processing unit 110, and a microphone 111.

  A DVD-ROM storing a game program and data is loaded into the DVD-ROM drive 108 and the information processing apparatus 100 is turned on to execute the program, thereby realizing the simulation apparatus of the present embodiment. The

  The CPU 101 controls the overall operation of the information processing apparatus 100 and is connected to each component to exchange control signals and data. Further, the CPU 101 uses arithmetic operations such as addition / subtraction / multiplication / division, logical sum, logical product, etc. using an ALU (Arithmetic Logic Unit) (not shown) for a storage area called a register (not shown) that can be accessed at high speed. , Logic operations such as logical negation, bit operations such as bit sum, bit product, bit inversion, bit shift, and bit rotation can be performed. In addition, the CPU 101 itself is configured so that saturation operations such as addition / subtraction / multiplication / division for multimedia processing, vector operations such as trigonometric functions, etc. can be performed at a high speed, and those provided with a coprocessor. There is.

  The ROM 102 records an IPL (Initial Program Loader) that is executed immediately after the power is turned on, and when this is executed, the program recorded on the DVD-ROM is read out to the RAM 103 and execution by the CPU 101 is started. The The ROM 102 stores an operating system program and various data necessary for operation control of the entire information processing apparatus 100.

  The RAM 103 is for temporarily storing data and programs, and holds programs and data read from the DVD-ROM and other data necessary for game progress and chat communication. Further, the CPU 101 provides a variable area in the RAM 103 and performs an operation by directly operating the ALU on the value stored in the variable, or temporarily stores the value stored in the RAM 103 in the register. Perform operations such as performing operations on registers and writing back the operation results to memory.

  The controller 105 connected via the interface 104 receives an operation input performed when the user executes the game.

  The external memory 106 detachably connected via the interface 104 stores data indicating game play status (past results, etc.), data indicating game progress, and log of chat communication in the case of a network match ( Data) is stored in a rewritable manner. The user can record these data in the external memory 106 as appropriate by inputting an instruction via the controller 105.

  A DVD-ROM mounted on the DVD-ROM drive 108 stores a program for realizing the game and image data and audio data associated with the game. Under the control of the CPU 101, the DVD-ROM drive 108 performs a reading process on the DVD-ROM loaded therein, reads out necessary programs and data, and these are temporarily stored in the RAM 103 or the like.

  The image processing unit 107 processes the data read from the DVD-ROM by an image arithmetic processor (not shown) included in the CPU 101 or the image processing unit 107, and then processes the processed data on a frame memory ( (Not shown). The image information recorded in the frame memory is converted into a video signal at a predetermined synchronization timing and output to a monitor (not shown) connected to the image processing unit 107. Thereby, various image displays are possible.

  The image calculation processor can execute a two-dimensional image overlay calculation, a transmission calculation such as α blending, and various saturation calculations at high speed.

  Also, polygon information arranged in the virtual three-dimensional space and added with various texture information is rendered by the Z buffer method, and the polygon arranged in the virtual three-dimensional space from the predetermined viewpoint position is determined in the direction of the predetermined line of sight It is also possible to perform high-speed execution of operations for obtaining rendered images.

  Further, the CPU 101 and the image arithmetic processor operate in a coordinated manner, so that a character string can be drawn as a two-dimensional image in a frame memory or drawn on the surface of each polygon according to font information that defines the character shape. is there.

  The NIC 109 is used to connect the information processing apparatus 100 to a computer communication network (not shown) such as the Internet, and is based on the 10BASE-T / 100BASE-T standard used when configuring a LAN (Local Area Network). To connect to the Internet using an analog modem, ISDN (Integrated Services Digital Network) modem, ADSL (Asymmetric Digital Subscriber Line) modem, or cable television line. A cable modem or the like and an interface (not shown) that mediates between these and the CPU 101 are configured.

  The audio processing unit 110 converts audio data read from the DVD-ROM into an analog audio signal and outputs the analog audio signal from a speaker (not shown) connected thereto. Further, under the control of the CPU 101, sound effects and music data to be generated during the progress of the game are generated, and sound corresponding to this is output from the speaker.

  When the audio data recorded on the DVD-ROM is MIDI data, the audio processing unit 110 refers to the sound source data included in the audio data and converts the MIDI data into PCM data. If the compressed audio data is in ADPCM format or Ogg Vorbis format, it is expanded and converted to PCM data. The PCM data can be output by performing D / A (Digital / Analog) conversion at a timing corresponding to the sampling frequency and outputting it to a speaker.

  Furthermore, a microphone 111 can be connected to the information processing apparatus 100 via the interface 104. In this case, the analog signal from the microphone 111 is subjected to A / D conversion at an appropriate sampling frequency so that processing such as mixing in the sound processing unit 110 can be performed as a PCM format digital signal.

  In addition, the information processing apparatus 100 uses a large-capacity external storage device such as a hard disk so as to perform the same function as the ROM 102, the RAM 103, the external memory 106, the DVD-ROM mounted on the DVD-ROM drive 108, and the like. You may comprise.

  The information processing apparatus 100 described above corresponds to a so-called “consumer video game apparatus”, but the present invention can be realized as long as it performs image processing to display a virtual space. Therefore, the present invention can be realized on various computers such as a mobile phone, a portable game device, a karaoke apparatus, and a general business computer.

  For example, a general computer, like the information processing apparatus 100, includes an image processing unit that includes a CPU, RAM, ROM, DVD-ROM drive, and NIC and has simpler functions than the information processing apparatus 100. In addition to having a hard disk as an external storage device, a flexible disk, a magneto-optical disk, a magnetic tape, and the like can be used. Further, not the controller 105 but a keyboard or a mouse is used as an input device.

  FIG. 2 is an explanatory diagram showing a relationship between a support object, a mass point object, a virtual elastic body, and each coordinate system arranged in the virtual space. Hereinafter, a description will be given with reference to FIG.

  As shown in the figure, one end of a virtual elastic body 211 is connected to a connection point 212 and the other end of the virtual elastic body 211 is connected to a mass point object 206 to the support object 201 corresponding to the character's body. . The mass point objects 206 are also connected to each other via the virtual elastic body 211. In this way, the mass point objects 206 form a shape like a skirt or a cloak as a whole.

  In the virtual space 231, in addition to the global coordinate system 236, a local coordinate system 241 fixed to the support object 201 is prepared, and conversion between the global coordinate system 236 and the local coordinate system 241 is performed at the origin. It can be reduced to two: movement and rotation of the coordinate system.

  The support object 201 corresponds to a character that moves based on a user's instruction input or the like, or that the information processing apparatus 100 controls based on a predetermined algorithm. Accordingly, it is possible to appropriately move in the virtual space 231 and change its posture (corresponding to how much the local coordinate system 241 rotates about which axis with respect to the global coordinate system 236). At this time, it is possible to model in accordance with the physical laws assumed in the virtual space 231 and to be influenced by gravity, wind force, frictional force, and the like.

  The mass point object 206 models the mass per unit area of the cloth. When the mass point objects 206 are evenly distributed, the mass obtained by dividing the mass of the entire cloth by the number of the mass point objects 206, respectively. Is assigned. However, the mass to be assigned can be appropriately changed according to characteristics such as the distribution density of the mass object 206 and the shape of the cloth to be modeled.

  A natural length is assigned to such a virtual elastic body 211. The natural length is the length of the most natural shape. When expressing a skirt cloth or the like, the distance between the mass point objects 206 when the cloth is evenly spread in a flat shape is represented by the mass point object. Generally, the natural length of the virtual elastic body 211 that connects the two 206 is used.

  When the length of the virtual elastic body 211 (the distance between the mass point objects 206 connected to the virtual elastic body 211) is longer than the natural length, the elastic force (mass point object) obtained by multiplying the long distance by a predetermined spring constant. (Attractive force in the direction of pulling 206 together) occurs. On the other hand, when the length becomes shorter than the natural length, an elastic force (repulsive force in a direction in which the mass object 206 is moved away) is generated by multiplying the shortened distance by a predetermined spring constant.

  The virtual elastic body 211 that connects the support object 201 and the mass point object 206 plays an important role in that it generates an elastic force for moving the mass point object 206 group as the support object 201 moves. On the other hand, if the time interval (update interval time) when simulating the physical law in the virtual space 231 is long, the length of the virtual elastic body 211 becomes abnormally long. In such a case, The expression of the modeled cloth becomes extremely unnatural. In the present embodiment, a method for easily suppressing such a situation is employed.

  In the example shown in the figure, the virtual elastic body 211 is connected in a fan shape to the mass point object 206 in order to express the skirt, but other connection methods may be used depending on the application field and shape.

  FIG. 3 is an explanatory diagram showing various connection states of the virtual elastic body and the mass point object. Hereinafter, a description will be given with reference to FIG.

  In the example shown in FIG. 4A, the mass point objects 206 are arranged in a lattice point shape, and the virtual elastic body 211 is arranged at the position of the square side having the mass point object 206 as a vertex so that the adjacent mass point objects 206 are arranged. It is connected. It is an example of the simplest connection method.

  In the example shown in this figure (b), in the example shown in this figure (a), the virtual elastic bodies 211 are also connected between diagonal vertices (diagonal lines) of the square. Compared to the connection method shown in FIG. 5A, the deformation in the oblique direction is more natural.

  The example shown in this figure (c) is such that the virtual elastic body 211 connecting the mass object 206 forms a triangular side, and is similar to the method of dividing the mesh in the finite element method. Since the shape is not limited to a square, the present invention can be applied to a case where the cloth has an arbitrary shape.

  Hereinafter, the physical models of the support object 201 and the mass point object 206 will be briefly described. FIG. 4 is an explanatory diagram showing a method for simulating changes in position and orientation of general objects such as the support object 201 and the mass point object 206. Hereinafter, a description will be given with reference to FIG.

At a certain point in time t, the object 401 having the mass m (t) is applied to a position away from the center of gravity 402 by the virtual elastic body 211 and the like in addition to the gravity 451 m (t) g applied to the center of gravity 402. The external force 452 f ₁ (t),..., F _N (t) has an influence.

The vector sum F (t) of these gravity 451 and a plurality of external forces 452 is
F (t) = m (t) g + Σ _{i = 1} ^N f _i (t)

Therefore, when this is divided by the mass m (t) of the object 401, the acceleration vector of the object 401 is
a (t) = F (t) / m (t)
Is required.

When the position vector r (t) (based on the reference point 403) and the velocity vector v (t) of the center of gravity 402 of the object 401 at a certain time t are known, the update interval time Δt is later than this. The velocity vector v (t + Δt) at time t + Δt of
v (t + Δt) = v (t) + a (t) Δt
Can be approximated. The position vector r (t + Δt) is
r (t + Δt) = (v (t) + v (t + Δt)) Δt / 2
Approximate calculation can be performed as follows. By repeating this calculation, the position r (t) of the center of gravity of the object 401 at an arbitrary time point r can be simulated.

  On the other hand, regarding the posture change, an external force 452 applied to a position away from the center of gravity is considered. That is, the angular velocity vector ω (t) of the object 401 at time t represents that the object 401 is about to rotate by an angle of | ω (t) | per unit time with the rotation vector ω (t) as an axis. . The posture vector θ (t) of the object 401 can be considered as an integration of the angular velocity vector ω (t).

  If the orientation of each axis of the local coordinate system 241 is made to coincide with the global coordinate system 236 and then rotated by the angle | θ (t) | about the orientation vector θ (t), the local coordinates at time t The posture of the system 241 is obtained.

On the other hand, a plurality of external forces 452 are set as vectors f ₁ (t),..., F _N (t), and a displacement 453 from the center of gravity 402 to a place where the external force 452 is applied is expressed as vectors s ₁ (t) _,. Assuming (t), the torque L (t) applied to the object 401 is
L (t) = Σ _{i = 1} ^N s _i (t) × f _i (t)
If the moment of inertia matrix of the object 401 is M (t),
L (t) = M (t) (ω (t + Δt)-ω (t)) / Δt
Because
ω (t + Δt) = ω (t) + M (t) ^-1 L (t) Δt
Can be approximated. Similarly, the posture vector n (t + Δt)
n (t + Δt) = (ω (t + Δt) + ω (t)) Δt / 2
Approximate calculation is possible.

In general, to obtain the result r ′ obtained by rotating the position vector r around the axis vector c = (c _x , c _y , c _z ) by an angle ψ, it is possible to use a quaternion or a rotation matrix. Is possible. Hereinafter, a method using quaternions will be described.

Now, the quaternion C representing this rotation is
C = (c _x sin (ψ / 2), _cy sin (ψ / 2), c _z sin (ψ / 2), cos (ψ / 2))
It can be expressed as

The quaternion R for the position vector r = (r _x , r _y , r _z ) is
R = (r _x , r _y , r _z , 0)
It can be expressed as

Then, the operation for rotating the quaternion R by the quaternion C is as follows:
R '= CRC ^*
Can be expressed as Where ^* is the quaternion conjugate.
R '= (r _x ', r _y ', r _z ', r _w ')
If,
r '= (r _x ', r _y ', r _z ')
It is. In addition, a method using a rotation matrix may be used.

  Hereinafter, an operation for rotating the vector r about the vector c by an angle | c | is expressed as spin (c, r).

  Now, FIG. 5 is an explanatory diagram showing a state when a change in position and posture is calculated according to the physical model as described above. Hereinafter, a description will be given with reference to FIG.

  This figure illustrates the relationship between the positions of the support object 201 and the mass point object 206. Here, for ease of understanding, only one of the mass point objects 206 that are directly connected to the support object 201 via the virtual elastic body 211 is illustrated, and the scale factor is appropriately changed and described in Oiso. ing.

  Further, for ease of understanding, the Z axis of the global coordinate system 236 and the z axis of the local coordinate system 241 are parallel, and the support object 201 has the XY plane of the global coordinate system 236 (the x of the local coordinate system 241). As an example, the position is changed by moving in the (−y plane) and rotated around the z axis (Z axis). Further, it is assumed that the connection point 212 is arranged on the x axis in the local coordinate system 241.

  As described above, if the situation at the time t + Δt is approximately calculated from the situation at the time t with respect to the support object 201, the position r (t) and the posture θ ( The position r (t + Δt) and the posture θ (t + Δt) at time t + Δt are found. These differences are the amount of support change.

  In this figure, the vector of the difference in position on the supporting object 201 at time t and time t + Δt is represented by Δr, and the vector of the difference in posture (represented by a rotation angle because it is a rotation vector) is represented by Δθ. ing.

Then, the position q (t + Δt) of the connection point 212 at time t + Δt is as follows from the origin of the local coordinate system 241 (position of the support object 201) at time t + Δt as follows. That is, a position rotated by Δθ around the origin of 241.
q (t + Δt) = r (t) + Δr + spin (Δθ, q (t) -r (t))

  Here, consider a situation where the position p (t + Δt) is obtained from the position p (t) of the mass point object 206. The magnitude and direction of the elastic force applied to the mass point object 206 is determined by the displacement vector (q (t) −p (t) from the mass point object 206 (position p (t)) to the connection point 212 (position q (t)). )) Is determined by the conventional simulation method.

  However, if this displacement vector differs greatly between time t and time t + Δt, that is, q (t + Δt) -p (t + Δt) and q (t) -p (t) differ greatly. The simulation becomes unnatural. As a case where such a situation occurs, a case where Δr and Δθ are large can be considered. Therefore, in this embodiment, the following method is adopted.

  First, an upper limit value R and an upper limit value Θ are determined for the magnitudes of | Δr | and | Δθ |, respectively. These values can be determined as appropriate values so that the simulation does not become unnatural, for example, by actually performing a simulation experiment.

Next, a function h (·) whose value range monotonously increases from 0 to 1 is prepared. That is, h (·) is a function that looks at the following properties.
h (0) = 0
lim _{x → ∞} h (x) = 1
a <b ⇒ h (a) ≦ h (b)

Such functions include:
h (x) = x (0 ≦ x ≦ 1)
= 1 (1 <x)
Or using an appropriate constant H
h (x) = 2 ・ arctan (H ・ x) / π
In addition to the above, it is also possible to adopt a function that changes stepwise.

Then, among the support correction amounts, the support correction amount Δs related to the position and the support correction amount Δψ related to the posture are expressed as Δs = R h (| Δr |) Δr / | Δr |
Δψ = Θ h (| Δθ |) Δθ / | Δθ |
It is determined as follows. Δs and Δψ are vectors that internally divide between Δr and Δθ and the origin, that is, Δr / | Δr | and Δθ / | Δθ | are upper limit values R and Θ, respectively. Multiplied by a coefficient of 0 or more and 1 or less.

Then, assuming that the support object 201 is at the position r (t) + Δs and the posture θ (t) + Δψ, the position Q (t) of the virtual connection point 501 at this time is obtained. That is,
Q (t) = r (t) + Δs + spin (Δψ, q (t) -r (t))
It becomes.

  The position Q (t) of the virtual connection point 501 is a position that internally divides the position of the connection point 212 at time t and the position of the connection point 212 at time t + Δt (in some cases, the position is divided internally on the line segment). Yes, it may be divided internally on the curve.)

  When the position p (t + Δt) at time t + Δt is obtained from the position p (t) at time t of the mass point object 206, the mass object 206 is connected to the virtual connection point 501 by the virtual elastic body 211. I think. That is, it is not q (t) -p (t) or q (t + Δt) -p (t), but based on Q (t) -p (t), the elastic force by the virtual elastic body 211 on the mass object 206 Is demanded.

  Since the position of Q (t) is closer to q (t) than the position of q (t + Δt), even if the position of the support object 201 has changed greatly, Q (t) -p (t) The change can be suppressed to some extent. Therefore, the situation where the virtual elastic body 211 extends unnaturally long can be prevented.

  Thus, the external force for the mass point object 206 is obtained based on the virtual connection point 501. In this figure, an external force 511 by the virtual elastic body 211 connected to the virtual connection point 501 and an external force 512, 513, 514 by the virtual elastic body 211 connected to another mass point object 206 are displayed.

  From the above physical model, the position p (t) of the mass point object 206, and these external forces, a virtual position at time t + Δt can be obtained. This corresponds to the movement destination of the mass point object 206 when it is virtually considered that the support object 201 is moving only a little. The virtual position 521 of the movement destination is u (t + Δt).

  However, considering the original movement of the support object 201, if the position u (t + Δt) is set to p (t + Δt) as it is, the support object 201 is too far away. Therefore, the following concept is adopted.

First, the position of the mass point object 206 with respect to the support object 201 (mass point change amount) is
u (t + Δt)-(r (t) + Δs)

  It can be expressed as

At time t + Δt, the center of gravity of the support object 201 itself is
r (t + Δt) = r (t) + Δr
Have moved to
Δθ
Because it ’s just spinning.
p (t + Δt) = r (t) + Δr + spin (Δθ, u (t + Δt)-(r (t) + Δs))
Is the position of the new mass point object 206. This is one of the features of this embodiment.

At this time, the speed of the mass object 206 after the update interval time is
(p (t + Δt) -p (t)) / Δt
What should I do?

  According to the present embodiment, a cross simulation that is not unnatural can be realized even when the update interval time Δt is a little long or the number of mass point objects 206 is small.

  In the present embodiment, the interaction between the mass point object 206 and the support object 201 is substantially reduced. Therefore, depending on the application, it may be desired to compensate for this easily.

In such a case, the virtual elastic body 211 is multiplied by h (| Δr |), h (| Δr |) ^2, etc., by the spring coefficient of the virtual elastic body 211 that connects the mass point object 206 and the support object 201. The elastic force 211 may be increased virtually.

  According to this method, it is possible to make up for the fact that the position of the support object 201 and the amount of change in the line of sight are virtually reduced by virtually increasing the spring constant.

  According to this embodiment, the calculation of physical models such as rigid bodies, mass points, and springs that have been widely used in the past can be easily corrected to reduce the number of mass points when the time increment is large. Even now, you will be able to perform realistic motion simulations. Hereinafter, a specific configuration of the simulation apparatus will be described.

  FIG. 6 is an explanatory diagram showing a schematic configuration of the simulation apparatus according to the present embodiment. Hereinafter, a description will be given with reference to FIG.

  A simulation apparatus 701 according to this embodiment includes a storage unit 702, a support calculation unit 703, a support correction unit 704, a mass point calculation unit 705, a support update unit 706, a mass point update unit 707, and an image generation unit 708.

Here, the storage unit 702 is realized by the RAM 103 or the like,
The position, velocity, posture, angular velocity, mass, moment of inertia of the support object 201 at the current time,
The position, speed, mass, and current position of the mass point objects 206 at the current time
The relationship between the mass object 206 connected to each of the plurality of virtual elastic bodies 211, or the position of the connection point between the mass object 206 and the support object 201;
Natural lengths, spring constants of a plurality of virtual elastic bodies 211,
Distribution of external forces such as gravity and wind power,
Current time, time increment (update interval time),
Information such as the polygons constituting the surface of the support object 201 and the mesh of the mass object 206 and the texture pasted on the polygons is stored.

  FIG. 7 is a flowchart showing a flow of control of simulation processing executed by the simulation apparatus 701. Hereinafter, a description will be given with reference to FIG.

  When the process is started, the CPU 101 initializes the storage unit 702 prepared in the RAM 103 and gives an appropriate initial value (step S801).

  Next, the support calculation unit 703 calculates the support change amounts Δr and Δθ based on the above calculation method from the current position r (t) and posture θ (t) of the support object 201, various external force conditions, and the like. Obtained (step S802). Therefore, the CPU 101 functions as the support calculation unit 703 in cooperation with the RAM 103.

  Further, the support correction unit 704 calculates the support correction amounts Δs and Δψ from the calculated Δr, Δθ, and the like based on the above calculation method (step S803). Therefore, the CPU 101 functions as the support correction unit 704 in cooperation with the RAM 103.

  Further, for each mass point object (step S804), the mass point calculation unit 705 determines the mass point change amount u (t) for each mass point object 206 based on the above calculation method from Δs, Δψ and the like obtained as described above. + Δt) (step S805) is repeated (step S806). At this time, for the mass object 206 that is connected only to the other mass point object 206 and not connected to the support object 201, the same method as the calculation by the normal cross simulation is adopted. Therefore, the CPU 101 functions as the mass point calculation unit 705 in cooperation with the RAM 103.

  Next, the support update unit 706 obtains information on the position, posture, speed, and angular velocity of the support object 201 stored in the storage unit 702 based on the obtained support change amounts Δr, Δθ, and the like by the above calculation. The values r (t + Δt), θ (t + Δt), v (t + Δt), and ω (t + Δt) are updated (step S807). Therefore, the CPU 101 functions as the support update unit 706 in cooperation with the RAM 103.

  The material point update unit 707 updates the position and speed information of the mass point object 206 stored in the storage unit 702 with respect to each of the mass point objects 206 (step S808). The subsequent position p (t + Δt) and the mass point object speed (p (t + Δt) −p (t)) / Δt are updated (step S809) repeatedly (step S810). Therefore, the CPU 101 functions as the mass point update unit 707 in cooperation with the RAM 103.

  Further, the image generation unit 708 pastes texture information on a polygon having the surface of the support object 201 or the mass point object 206 as a vertex based on the information in the RAM 103, and displays an image representing the state of the virtual space 231 in the RAM. The frame is generated in the frame buffer 103 (step S811). Therefore, the CPU 101 functions as the image generation unit 708 in cooperation with the image processing unit 107 and the RAM 103. Various three-dimensional graphics techniques can be applied to this processing.

  Then, the process waits until a vertical synchronization interrupt occurs (step S812). During this time, other processes can be executed in a coroutine manner.

  When the vertical synchronization interrupt occurs, the time in the virtual space 231 is increased by the update interval time (vertical synchronization interrupt cycle), and the time is updated (step S813). Note that image generation can be thinned out as appropriate. At this time, the update interval time in the time update is also adjusted in accordance with the thinned number.

  Then, under the control of the CPU 101, the image processing unit 107 transfers the contents of the frame buffer to the frame memory, displays the generated image on the screen (step S814), and returns to step S802.

  By performing such processing, the simulation apparatus 701 of the present embodiment performs cross simulation by simple calculation even when the width of the update interval time is long or the number of mass point objects 206 is reduced. Will be able to.

  In the above embodiment, when the support change amount is calculated (step S802), the support correction amount is always calculated (step S803), the position of the virtual connection point 501 is obtained, and the local coordinate system 241 reference is calculated. The mass point change amount is calculated (step S805), but such processing is not always performed, and it is possible to appropriately use the conventional method.

  That is, after calculating the support change amount, if the support change amount is larger than a predetermined threshold value, the process of the above embodiment is performed, but if not, the process of obtaining the position of the virtual connection point 501 is not performed. The conventional cross simulation technique is applied. That is, in the latter case, the elastic force by the virtual elastic body 211 is obtained from the difference between the current position of the mass point object 206 and the position of the connection point 212 after the update interval time has passed on the basis of the global coordinate system 236, and the mass point Update the position of the object 206. Here, the former process has a large amount of calculation, and the latter process has a small amount of calculation.

  Therefore, when such an aspect is adopted, it is assumed that the effect of shortening the update interval time or reducing the number of mass point objects 206 will increase (when the support change amount is larger than a predetermined threshold). Only the processing based on the local coordinate system 241 is performed, and otherwise, the processing based on the global coordinate system 236 based on a small amount of calculation is performed, so that the processing speed in the information processing apparatus 100 can be appropriately kept high. become.

  As described above, according to the present invention, a simulation device, a simulation method, and a simulation method suitable for easily simulating a change in shape of a shape-variable object such as a flexible cloth or paper arranged in a virtual space, and A program for realizing these by a computer can be provided.

It is a schematic diagram which shows the outline | summary structure of the typical information processing apparatus which performs the function of the simulation apparatus of this invention by running a program. It is explanatory drawing which shows the relationship between the support object, mass object, virtual elastic body, and each coordinate system which are arrange | positioned in virtual space. It is explanatory drawing which shows the mode of various connection of a virtual elastic body and a mass point object. It is explanatory drawing which shows the technique of simulating the change of the position and attitude | position regarding general objects, such as a support object and a mass point object. It is explanatory drawing which shows a mode when the change of a position or attitude | position is calculated according to a physical model. It is explanatory drawing which shows schematic structure of the simulation apparatus which concerns on this embodiment. It is a flowchart which shows the flow of a process of the simulation method performed with this simulation apparatus.

Explanation of symbols

100 Information processing apparatus 101 CPU
102 ROM
103 RAM
104 Interface 105 Controller 106 External Memory 107 Image Processing Unit 108 DVD-ROM Drive 109 NIC
DESCRIPTION OF SYMBOLS 110 Sound processing part 111 Microphone 201 Support object 206 Mass point object 211 Virtual elastic body 212 Connection point 231 Virtual space 236 Global coordinate system 241 Local coordinate system 401 Object 402 Center of gravity 403 Reference point 451 Gravity 452 External force 453 Displacement 501 Virtual connection point 511 External force 512 External force 513 External force 514 External force 701 Simulation device 702 Storage unit 703 Support calculation unit 704 Support correction unit 705 Mass point calculation unit 706 Support update unit 707 Mass point update unit 708 Image generation unit

Claims (7)

A simulation device for simulating the position and posture of a support object arranged in a virtual space and the positions of a plurality of mass point objects,
In the virtual space, each of the plurality of mass point objects is connected to the support object or another mass point object among the plurality of mass point objects via a virtual elastic body,
A storage unit for storing the position and orientation of the support object and the positions of the plurality of mass point objects;
A support calculation unit for calculating a support change amount representing a change in the position and posture of the support object with the elapse of the update interval time;
A support correction unit for calculating a support correction amount obtained by correcting the calculated support change amount so as not to exceed a predetermined threshold;
For each of the plurality of mass point objects, from the position and posture moved by the calculated support correction amount from the stored position and posture of the support object and the stored positions of the plurality of mass point objects ,
(A) calculating the force exerted on the mass point object by the virtual elastic body to which the mass point object is connected;
(B) a mass point calculation unit that calculates a mass change amount representing the relative position of the mass object relative to the support object after the update interval time has elapsed, from the calculated force;
A support update unit for updating the position and posture of the support object with the position and posture moved by the calculated support change amount from the position and posture of the support object stored in the storage unit;
Each of the positions of the plurality of mass point objects stored in the storage unit is moved from the position of the support object whose position and orientation are updated by the calculated mass point change amount with respect to the mass point object. And a mass point updating unit for updating the position of the mass point object. The simulation apparatus according to claim 1,
The support correction unit calculates the support correction amount by applying the calculated support change amount to an internal division function that monotonously increases and the limit is equal to or less than the predetermined threshold value. The simulation apparatus according to claim 2,
The internal division function in the support correction unit includes a position internal function applied to a position change amount of the support change amount, and a posture internal function applied to a posture change amount of the support change amount. A fractional function,
The position internal function is a monotonically increasing function that multiplies the upper limit value of the change amount of the position by a coefficient of 0 or more and 1 or less,
The posture internal function is a monotonically increasing function that multiplies the upper limit value of the rotation angle around the axis related to the change in the posture by a coefficient of 0 or more and 1 or less. The simulation apparatus according to claim 3,
The said mass point calculation part multiplies the elastic coefficient of the said virtual elastic body by the reciprocal number of the coefficient which concerns on the said position division function, or the square of the reciprocal number of the said coefficient, and calculates the said mass point change amount. The simulation apparatus according to any one of claims 1 to 4, wherein:
An image generation unit configured to generate an image of the support object and a deformable object connected to the support object by pasting a predetermined texture on the polygon having the plurality of mass point objects stored as vertices; A simulation apparatus characterized by that. A simulation method for simulating the position and orientation of a support object arranged in a virtual space and the positions of a plurality of mass point objects,
Executed by a simulation device including a storage unit, a support calculation unit, a support correction unit, a mass point calculation unit, a support update unit, and a mass point update unit that store the positions and postures of the support objects and the positions of the plurality of mass point objects And
In the virtual space, each of the plurality of mass point objects is connected to the support object or another mass point object among the plurality of mass point objects via a virtual elastic body,
A support calculation step in which the support calculation unit calculates a support change amount representing a change in the position and orientation of the support object with the lapse of the update interval time;
A support correction step of calculating a support correction amount in which the support correction unit corrects the calculated support change amount so as not to exceed a predetermined threshold;
The mass point calculation unit is configured to calculate a plurality of the plurality of mass point objects from the positions and postures moved by the calculated support correction amount from the stored positions and postures of the support objects, and the plurality of stored mass point objects. For each of the mass point objects
(A) calculating the force exerted on the mass point object by the virtual elastic body to which the mass point object is connected;
(B) a mass point calculating step of calculating a mass point change amount representing a relative position of the mass point object with respect to the support object after the update interval time has elapsed, from the calculated force;
A support update step in which the support update unit updates the position and posture of the support object at a position and posture moved by the calculated support change amount from the position and posture of the support object stored in the storage unit;
The mass point update unit calculates each of the positions of the plurality of mass point objects stored in the storage unit from the position of the support object whose position and orientation are updated, with respect to the calculated mass point change amount for the mass point object. And a mass point updating step of updating the position of the mass point object at a position that has been moved by a distance. A program for causing a computer to simulate the position and posture of a support object arranged in a virtual space and the positions of a plurality of mass point objects,
In the virtual space, each of the plurality of mass point objects is connected to the support object or another mass point object among the plurality of mass point objects via a virtual elastic body,
The program runs the computer
A storage unit for storing the positions and postures of the supporting objects arranged in the virtual space and the positions of the plurality of mass point objects;
A support calculation unit for calculating a support change amount representing a change in the position and posture of the support object with the elapse of the update interval time;
A support correction unit for calculating a support correction amount obtained by correcting the calculated support change amount so as not to exceed a predetermined threshold;
For each of the plurality of mass point objects, from the position and posture moved by the calculated support correction amount from the stored position and posture of the support object and the stored positions of the plurality of mass point objects ,
(A) calculating the force exerted on the mass point object by the virtual elastic body to which the mass point object is connected;
(B) a mass point calculation unit that calculates a mass change amount representing the relative position of the mass object relative to the support object after the update interval time has elapsed, from the calculated force;
A support update unit for updating the position and posture of the support object with the position and posture moved by the calculated support change amount from the position and posture of the support object stored in the storage unit;
Each of the positions of the plurality of mass point objects stored in the storage unit is moved from the position of the support object whose position and posture are updated by the calculated mass point change amount with respect to the mass point object. A program that functions as a mass point updating unit for updating the position of the mass point object.

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