JP2009020874A - Hair simulation method, and device therefor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a hair simulation method capable providing an animation image rich in reality, and capable of shortening extremely a processing time in simulation. <P>SOLUTION: This hair simulation method is provided with a hair master simulation step of constituting a hair bundle of hair members distributed in the periphery of one hair master, using a particle model as a model of each of the hair masters and hair members, including a hair master initialization step and a hair member initialization step, and for calculating positions of all the master particles constituting the hair master, and a hair member deformation step for changing relative coordinates among the respective member particles constituting the respective hair members, based on motion speed vectors of the master particles, and is provided further a hair member generation step for calculating a position of each member particle in each hair member, based on the positions of the master particles calculated in the hair master simulation step and based on a relative position of the member particle changed in the hair member deformation step. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a hair simulation method.

  Hair simulation is one of the important technologies in the field of computer animation, and methods related to modeling, simulation, rendering, etc. about hair have been researched and developed for many years.

However, human hair consists of 100,000 or more hairs, and in order to simulate this, it is necessary to process a large amount of data. For these reasons, it has been difficult to implement real-time simulations. Thus, much of the research so far has been aimed at so-called off-line animation.
From Ken Anjo et al., “A Simple Method for Extracting the Natural Beauty of Hair”, ACM Computer Graphic (SIGGRAPH 92), Vol. 26, No. 2, p. 111 120 pages, 1992 Yosuke Band et al., “Animating Hair with Loosely Connected Particles”, Computer Graphic Forum (Eurographic Bulletin 2003) Vol. 22, No. 3, pages 411-418 2003 F. Verteils et al., “Adaptive Wisp Tree-Amultiresolution control structure for simulating dynamic clustering in hairmotion”, ACM SIGGRAPH, Eurographic Symposium on Computer Animation 2003, 207-213, 2003 Kiran S. Bahat et al., “Estimating Cloth Simulation Parameters from Video”, ACM SIGGRAPH, Eurographic Symposium on Computer Animation 2003, 37-51, 2003 Johnny Tea. Chang et al., “APractical Model for Hair Mutual Interactions”, ACM SIGGRAPH, Eurographic Symposium on Computer Animation 2002, 73-80, July 2002 Byungwon Cho et al., “Statistical Wisp Model and Pseudo physical Approaches for Interactive Hairstyle Generation”, Volume 11 of the IEEE Bulletin on Imaging and Computer Graphics, Volume 11 , No. 2, pages 160-170, March 2005 Randima Fernando et al., "The Cg Tutorial: The Definitive Guide to Programmable Real-Time Graphics", Addition-Wesley Professional 2003 Live Gupta et al., “Optimized Framework for Real Time Hair Simulation”, Computer Graphic International (CGI 2006), pages 702-710, June 2006 Sunil Haddup and Nadia Magnenat-Salman, “Modeling Dynamic Hair as a Continuum”, Computer Graphic Forum (Eurographic 2001), Vol. 20, No. 3, 2001 James Tea. Kazuya et al., “Rendering Fur with Three Demensional Textures”, ACM SIGGRAPH, Computer Graphics (SIGGRAPH 89), Vol. 23, No. 3, pp. 271-280, 1989 Tee-Yong Kim and Ulrich Newman, “Interactive Multiresolution Hair Modeling and Editing”, ACM Bulletin on Graphics, (SIGGRAPH 2002), Vol. 21, No. 3, 620 -629, 2002 Tom Rocovic, et al., “Deep Shadow Maps”, SIGGRAPH 2000, pages 385-392, 2000 Mark Mayer et al., “Interactive Animation of Cloth-like Objects in Virtual Reality”, Magazine of Video and Computer Animation, Volume 12, 1st Edition, 1-12, May 2001 Hubert Nguyen and William Donnelly. "HairAnimation and Rendering in the Nalu Demo", GPU Gems2, 361-380, 2005 nVidia “Demonstration of clothing simulation using GPU (GPU Cloth)”, http: // developer. nvidia.com/, 2005 Sylvain Paris et al., “Capture of Hair Geometry from Multiple Images”, ACM Newsletter on Graphics, (SIGGRAPH 2004), Vol. 23, 3rd edition, pages 712-719, 2004 Pascal Borino et al., “Real-Time Animation of Complex Hairstyles”, IEEE newsletter on video and computer graphics, Vol. 12, No. 2, March-April 2006 Rodriguez Navarro J. et al., “FastCloth Simulation on Moving Humanoids”, Eurographic 2005 Short Presentation, pp. 85-88, 2005 Shu Dong Yang et al., “The Cluster Hair Model”, Graphic Model, Vol. 62, 2nd edition, pp. 85-103, March 2000 Izo Yu et al., “Modeling Realistic Virtual Hairstyles”, Pacific Graphics 2001, 295-304, 2001 Kelly Ward et al., “Modeling Hair Using Level-of-Detail Representations”, Computer Animation and Social Agents 2003, 41-47, 2003 Yashiko Watanabe et al., “Atrigonal Prism-Based Method for Hair Image Generation”, IEEE Computer Graphics and Applications, Vol. 12, 1st edition, pp. 47-53, 1992 1 Moon

  By the way, in recent years, real-time hair simulation is required in the field of computer games using online animation and virtual reality.

  As a general technique for realizing hair simulation, a method using a particle model is widely used. In this method, each hair constituting the hair is modeled as a connection of a large number of particles, and the movement of each particle is calculated based on the force acting on each particle, thereby simulating the movement of the hair.

  However, human hair as a whole is composed of as many as 10,000 to 100,000 hairs, so if you try to calculate the movement of all the hair using the particle model method, the latest hardware is used. However, it takes about several seconds to process each frame of animation, and real-time animation is unrealistic.

  Real-time simulation can be realized even with a method using a particle model by reducing the number of hairs or simplifying the simulation model. However, such a method has a problem that the animation lacks reality.

  For this reason, such a technique is currently used only in a few computer games. Many computer games still use hair with no movement represented by polygons.

  Thus, as a method for solving such a problem of the particle model, performing processing at high speed, and generating natural hair, a method of combining a rough hair model and a detailed hair model has been developed.

  In this method, first, hair movement is calculated by physical simulation using a rough hair model. Here, since a rough model is used, simulation can be realized at high speed. Thereafter, a natural hair is realized by dynamically generating a detailed hair model composed of a larger number of hairs from a rough hair model. In this process, a physical simulation is not usually used, and a large number of hairs are generated by a geometric process.

  However, in the conventional method, when a large number of hairs are generated, the hair is generated using fixed parameters, and thus there is a problem that the movement of the generated hair is unnatural.

  Further, as a simplest method for generating a detailed hair model from a rough hair model, there is a method using hair interpolation (Reference Documents 5 and 14).

  In this method, new hair is newly generated by interpolating surrounding hair between a small number of hairs. In such a method, when a large number of hairs are generated from a small number of hairs, a certain distance from the surrounding hair is maintained, and hair having a uniform hair shape is generated.

  However, real human hair does not move independently of the surrounding hair, but moves while bundling nearby hairs influencing each other. Therefore, the method of simply interpolating hair cannot reproduce such human hair movement, and thus cannot generate natural hair movement.

  Another method for generating a detailed hair model from a rough hair model is to use a hair bundle.

  This considers each hair of a rough hair model as a single hair that represents a bundle of hairs, and produces a bundle of hairs from each hair, such as creating a certain number of hairs around each hair. It is a technique. Many of these methods are primarily intended to generate still images of hair, not hair animation.

  However, in these methods, since a hair bundle is generated from each hair according to a fixed parameter, the shape of the hair bundle generated from a certain hair is always the same. The shape of the actual human hair bundle naturally changes with the movement. Therefore, when these methods are simply applied to hair animation, there is a problem that unnatural hair is generated.

  In view of the problems of the conventional technique, an object of the present invention is to provide a hair simulation technique that can eliminate the unnaturalness of hair by a conventional real-time simulation at a low calculation cost.

  The invention according to claim 1 is a hair simulation method for simulating the movement of hair of a character appearing in a computer animation or a computer game and generating an animation by continuously displaying frame images. The character's hair is composed of a plurality of hair bundles dispersedly arranged, and each bundle has one master hair representing the bundle and member hairs scattered around the master hair. Each master hair is composed of a number of master particles, and each member hair is composed of a number of member particles to initialize the simulation. As a step for the position of the master particles constituting the master hair according to the predefined hair information A master hair initializing step for initializing, and a member hair initializing step for initializing the relative position of the member particles with respect to the corresponding master particles according to information on the shape of the bundle and the shape of the hair defined in advance, As a simulation step of generating and displaying a frame image, a master hair that simulates the movement of each master hair by a physical simulation using a particle model and calculates the positions of all the master particles constituting each master hair A simulation step, and a member hair deformation step for changing the relative coordinates of each member particle constituting each member hair with respect to the master particle corresponding to the member particle based on the motion velocity vector of the master particle for each bundle. , Master hair simulation step A member hair generation step for calculating the position of the member particles of the member hair scattered around each master hair from the calculated position of the master particles and the relative position of the member particles changed in the member hair deformation step; And a rendering step of generating a frame image by drawing all the member hairs based on the positions of the member particles calculated in the member hair generation step.

  The present invention includes a member hair deformation step. In the present invention, the shape of the hair bundle is changed by paying attention to the movement speed of the master hair (that is, rough model hair). The conventional method for generating a hair bundle is to generate a hair bundle having a fixed shape, and the generated animation is unnatural. Since a hair bundle whose shape changes dynamically according to the frequency is generated, a more natural hair animation can be generated.

  Invention of Claim 2 is the hair simulation method of Claim 1, Comprising: Each said member hair deformation | transformation step is carried out so that a bundle | flux may spread so that a speed | rate may become large according to the motion velocity vector of a master particle. In accordance with the bundle shape deformation step that changes the relative position of the member particle with respect to the corresponding master particle and the motion velocity vector of the master particle, the hair of each member particle is compressed in the horizontal direction as the velocity increases. And a hair shape deformation step of changing a relative position with respect to the corresponding master particle.

  According to the present invention, depending on the movement speed of the hair bundle in the horizontal direction, the effect that the hair bundle spreads backward and the effect that the individual hairs are crushed laterally due to air resistance are less calculated. Can be realized at a cost.

  The invention according to claim 3 is a hair simulation device for simulating the movement of the hair of a character appearing in a computer animation or a computer game, and generating an animation by continuously displaying frame images. The character's hair is composed of a plurality of hair bundles dispersedly arranged, and each bundle has one master hair representing the bundle and member hairs scattered around the master hair. Each master hair is composed of a number of master particles, and each member hair is composed of a number of member particles to initialize the simulation. As a means, the position of the master particles constituting the master hair is initialized according to the predefined hair information. Master hair initialization means, and member hair initialization means for initializing the relative position of the member particles with respect to the corresponding master particles in accordance with information on the shape of the bundle and the shape of the hair defined in advance. As a means for generating and displaying, a master hair simulation means for simulating the movement of each master hair by a physical simulation using a particle model and calculating the positions of all master particles constituting each master hair; Member hair deformation means for changing the relative coordinates of each member particle constituting each member hair with respect to the master particle corresponding to the member particle on the basis of the motion velocity vector of the master particle, and the master hair simulation. Master particle position calculated in step and member hair deformation Member hair generating means for calculating the position of the member particles of the member hair scattered around the respective master hairs from the relative positions of the member particles changed in step, and the member particles calculated in the member hair generating step And a rendering means for rendering a frame image by drawing all member hairs based on the position.

  The present invention is provided with member hair deformation means. In the present invention, the shape of the hair bundle is changed by paying attention to the movement speed of the master hair (that is, coarse model hair). An apparatus using a conventional method for generating a hair bundle generates a hair bundle having a fixed shape, and the generated animation is unnatural. Since a hair bundle whose shape dynamically changes according to the movement speed of the hair is generated, a more natural hair animation can be generated.

  According to a fourth aspect of the present invention, in the hair simulation apparatus according to the third aspect, the member hair deformation means is configured so that each member particle deforms such that the bundle spreads as the velocity increases according to the motion velocity vector of the master particle. In accordance with the bundle shape deforming means for changing the relative position of the corresponding master particle, and the movement speed vector of the master particle, each member particle corresponds so that the hair is compressed in the horizontal direction as the speed increases. Hair shape deformation means for changing the relative position to the master particle.

  According to the present invention, depending on the movement speed of the hair bundle in the horizontal direction, the effect that the hair bundle spreads backward and the effect that the individual hairs are crushed laterally due to air resistance are less calculated. Can be realized at a cost.

  According to the present invention, since a hair bundle whose shape dynamically changes according to the movement speed of the master hair is generated, a more natural hair animation can be generated. As a result, according to the present invention, the unnaturalness of the conventional real-time simulation can be solved and a natural hair animation can be generated in real time.

  Hereinafter, embodiments of a hair simulation method according to the present invention and a hair simulation device using the method will be described in detail with reference to the drawings.

  First, the hair simulation method according to the present invention will be described.

  As shown in FIG. 1, the hair simulation method includes two steps of “initialization step” and “simulation step” for simulating the hair generated by the initialization. Based on the result, the hair can be rendered to an output destination such as a screen.

  The initialization step includes an initialization step for a rough model of hair (see FIG. 3A) and an initialization step for a detailed model (see FIG. 3B). The rough model initialization step is a step of initializing the positions of master particles constituting the master hair described later (hereinafter referred to as “master hair initialization step”). The detailed model initialization step is a step of initializing the relative position between the member particles of the member hair described later and the corresponding master particles (hereinafter referred to as “member hair initialization step”).

  The simulation step is a “master hair simulation step” for simulating the movement of each master hair (hair constituting a rough model) generated by initialization and calculating the positions of all master particles constituting each master hair. The relative coordinate of each member particle constituting each member hair (hair constituting the detailed model) calculated in the member hair initialization step is changed based on the movement speed of the master particle corresponding to the member particle. Member hair deformation step ”and“ member hair generation step ”for calculating the position of the member particles of the member hair from the position of the master particle calculated in the master hair simulation step and the relative position of the member particle changed in the member hair deformation step And calculation results in the simulation step And it outputs the hair on a screen or the like based on and a "rendering step".

  As described above, the hair simulation method according to the present invention combines the physical simulation of hair using a rough model with the method of dynamically generating a large number of hair bundles (detailed models) based on the rough model. Realizes natural hair simulation at high speed.

  Next, the system configuration of the hair simulation method will be described in detail along the processing flow with reference to FIGS.

<<< Initialization step >>>
Prior to the simulation step, it is necessary to perform an initialization step. As described above, the initialization step is divided into a master hair initialization step and a member hair initialization step. Hereinafter, the processing of each step will be described in order.

<< Master hair initialization step >>
First, a master hair initialization step is executed. The master hair initialization step is a step of generating a rough model.

  The rough model is composed of a plurality of master hairs distributed on the head of a human (character). That is, the master hair initialization step is a step of generating a plurality of master hairs arranged in a distributed manner. Each master hair is modeled by a particle model. That is, each master hair is modeled as a continuous connected body of particles in which a plurality of master particles are continuously connected. Hereinafter, each particle constituting the master hair is referred to as master particle.

  In the master hair initialization step, a plurality of master hairs are distributed and arranged at appropriate positions on the head of the human body model in a state extending in a direction (normal direction) perpendicular to the scalp. Moreover, the master hair arrange | positioned in the step of initialization extends linearly. Accordingly, the plurality of master hairs are generated in a state of extending radially around the head.

With respect to which range of the human body model the master hair is to be generated, the user can specify an arbitrary range according to the hairstyle to be expressed. Similarly _, the length l _i of each master hair can be set arbitrarily by the user. That is, the initial state of the rough model can be determined based on the master hair initialization information such as the pre-defined hair generation range information and the master hair direction / length information at each point in the hair generation range. . By performing the above processing based on these pieces of information, the coordinates p _{i, k} of each master particle are initialized. Here, p _{i, k} represents the coordinates of the k th particle of the i th master hair.

  Note that the number of master hairs can be arbitrarily set by the user. In the hair simulation method, about 500 to several thousand master hairs are generated in the master hair initialization step.

  Further, the number of particles used for expressing each master hair is not particularly limited, but about 10 to 20 particles are used per hair. In this embodiment, 10 particles are used per hair.

<< Member hair initialization step >>
Next, a member hair initialization step is performed. The member hair initialization step is a step of initializing information (relative position of each member particle constituting the member hair with respect to the corresponding master particle) for generating a detailed model.

  The detailed model is composed of a plurality of collections of hair bundles (hereinafter simply referred to as “bundles”), and each bundle is a plurality of member hairs arranged around the master hair. It consists of The number of member hairs constituting each bundle is not particularly limited, but is about 10 to 20 hairs. In this embodiment, 10 to 20 member hairs are generated around each master hair. Therefore, it can be said that each master hair constituting the rough model is hair representative of a bundle of hairs of the detailed model. In this manner, a plurality of member hairs are generated in a state of being scattered around the master hair, thereby generating a hair bundle.

  Each member hair of the hair bundle is modeled by a particle model, similar to the coarse model master hair. Hereinafter, each particle constituting the member hair is referred to as a member particle. In the member hair initialization step, the relative positions of the member particles with respect to the corresponding master particles are initialized in accordance with information on the shape of the bundle and the shape of the hair defined in advance. In the subsequent simulation step, as will be described later, the relative coordinates of the member particles are changed so as to control the shape of the hair bundle and the shape of each hair based on the speed of the master particles constituting the master hair. (See FIG. 4C). Finally, a detailed model is generated by determining the position of each member particle based on the relative position of each member particle and the position of the corresponding master particle.

  There are various methods for generating a detailed model based on a rough model (see References 6, 5, 14, and 3). As described above, in the present invention, the master hair constituting the rough model is used. A method of generating a hair bundle model (detailed model, see FIGS. 4A and 4B) by generating a predetermined number of member hairs around the hair.

In other words, here, the basic shape of the hair bundle, which is a detailed model, is used to initialize the hair bundle, including predefined bundle shape information and hair shape information (such as hair length information and hair spread information). Information and hair shape initialization information). More specifically, the basic shape of the hair bundle is determined using a function representing the shape of the bundle such as a predetermined length and spread, and a parameter representing the shape of the hair such as amplitude, period and phase. That is, the relative coordinates of each member particle constituting each member hair with respect to the corresponding master particle are initialized using these functions and parameters.
Hereinafter, the procedure for calculating the relative coordinates of each member particle will be described more specifically.
The relative coordinates of each member particle include an offset (u _{i, j, k} , v _{i, j, k} , t _{i, j, k} ) representing the shape of the bundle, and an offset (cu _{i, j} ) representing the shape of the hair. _{, k} , cv _{i, j, k} ). That is, the member hair initialization step includes a “bundle shape initialization step” for calculating an offset representing the shape of the bundle, and a “hair shape initialization step” for calculating an offset representing the shape of the hair. Each step will be described later. The subscripts i, j, and k represent the k-th particle of the j-th member hair of the i-th master hair. u _{i, j, k} , v _{i, j, k} , t _{i, j, k} are horizontal directions with respect to the master hair (u _{i, j, k} , v _{i, j, k} ), vertical directions T _{i, j, k} is the offset of each member particle to represent the shape of the bundle, expressed in the local coordinate system of the master hair (FIG. 8). Further, (cu _{i, j, k} , cv _{i, j, k} ) is an offset of each member particle for representing the shape of the hair. It represents the change in the position of the member particles in the horizontal direction relative to the master hair with respect to the reference position. The relative coordinates q _{i, j, k} (= u ′ _{i, j, k} , v ′ _{i, j, k} , t ′ _{i, j, k} ) of each member particle with respect to the master particle are offsets representing the shape of the bundle. (U _{i, j, k} , v _{i, j, k} , t _{i, j, k} ), expressed by the sum of offsets (cu _{i, j, k} , cv _{i, j, k} ) representing the shape of the hair .

Here, the shape of the hair bundle is determined using functions such as the length assignment function D (l) and the radius function R (s), and the offset (u _{i, j} representing the shape of each master particle bundle is determined. _{, k} , v _{i, j, k} , t _{i, j, k} ). The length assignment function D (l) is a parameter representing the length of each master hair. The radius function R (s) is a parameter representing the maximum radius (maximum moving radius) of the bundle at a predetermined point (particle position) s (0 ≦ s ≦ 1) on the master hair. Here, s is a value that changes from the root of the master hair toward the tip, the point “s = 0” corresponds to the point (particle) at the root position of the master hair, and the point “s = 1” is the master hair. It shall correspond to the point (particle) at the tip position of the hair. As the mediation functions of the length assignment function D (l) and the radius function R (s), a user such as an animation creator can set a function corresponding to the shape of the hair bundle to be expressed for each master hair. it can. FIGS. 5 (a) and 5 (b) show examples of differences in the shape of the generated hair bundle when different length assignment functions D (l) and radius functions R (s) are used.

<Bundle shape initialization step>
Hereinafter, a procedure for determining the offset q _{i, j, k} (= u _{i, j, k} , v _{i, j, k} , t _{i, j, k} ) representing the shape of the bundle of each master particle will be described.

First, the horizontal offset (u _{i, j, 0} , v _{i, j, 0} ) of the member particle at the root of the member hair is determined using the following formula including the radius function R (s). In addition, the horizontal direction here is a direction (normal direction) orthogonal to the extending direction (tangential direction) of the master hair.

  The position (α, β) represents a position on a circular coordinate system (polar coordinate system) in a planar shape perpendicular to the master hair. Here, α represents a radius ratio from the center point, and represents an azimuth angle with respect to the β center point. α and β are determined by random numbers for each member hair. Rand () used in equation (1) is a random function, rand (0.0 to 1.0) is a random value between 0.0 and 1.0, and rand (0.0 to 2π) is 0.0 Randomly take an angle between ˜2π.

Then, the length l _{i, j} of each member hair is determined by the following equation (2) including the length assignment function D (l). The variable l _{i, j} represents the length of the j-th member hair of the bundle based on the i-th master hair of the coarse model. Note that rand (0.0 to 1.0) is a random function that randomly determines a number between 0.0 and 1.0. Integrate D (l) while gradually adding l _{i, j} until it matches a randomly determined number between 0.0 and 1.0, and stop when the values match Thus, the length l _{i, j} of the master hair is determined.

Finally, the horizontal relative position (u _{i, j, 0} , v _{i, j, 0} ) of the member particles at the base of each member hair determined so far, and the length l _i, Based on _j , the offset (u _{i, j, k} , v _{i, j, k} , t _{i, j, k} ) of each member particle of each member hair is calculated using the following equation (3).

<Hair shape initialization step>
Next, a procedure for determining an offset q _{i, j, k} (= u _{i, j, k} , v _{i, j, k} , t _{i, j, k} ) representing the shape of the hair of each master particle will be described. .

With the offset that represents the bundle shape of each master particle determined so far, it is possible to represent a straight hair with the position of the master hair moved in the horizontal direction. However, actual human hair is not necessarily straight, and there is hair that has a fine curve. Therefore, in order to represent such a hair shape, an offset (cu _{i, j, k} , cv _{i, j, k} ) representing the hair shape is used.
In the present embodiment, (cu _{i, j, k} , cv _{i, j, k} ) is determined using the coefficient of the sine curve as a parameter. As discussed in reference 20, various shapes of human hair can be represented by combinations of sine curves (sine waves) and radial functions. In this embodiment, since the radius function has already been applied to determine the shape of the bundle, a sine curve is used as an element for determining the shape of the hair as shown in the following equation (4).

(Α _u , α _v , f, θ) are parameters that change the shape of the sine curve, α _u , α _v are amplitudes in each direction (u direction and v direction), f is the period of the curve, θ represents the phase. The amplitude represents the size of the hair curve in the horizontal direction, and the larger the amplitude, the more the hair is bent. The period represents the distance between the curves, and the larger the period value, the narrower and narrower the hair between the curves. Further, the phase represents a deviation in the vertical direction of the curve.

  Thus, each member hair has an individual parameter (αu, αv, f, θ). These values can be set for each member hair by the user depending on the hairstyle desired to be expressed. However, it is difficult to set individual values for each member hair. Therefore, in the present embodiment, basically, a value is set for each master hair (each bundle), and the same parameter is set for all member hairs generated (belonging to the same bundle) based on the same master hair. use.

  However, if the same parameter is used for all hairs in the same bundle, a large number of hairs having exactly the same shape may be generated, and an image lacking reality may be generated. Therefore, a constant change is added to the parameter of each member hair by a random number. By using random numbers, non-uniform hair is generated, and the reality of the simulation is increased. FIGS. 6A, 6B and 6C show curves and twisted hair generated using the model of this embodiment.

<< Summary of Member Hair Initialization Step >> As described above, in the member hair initialization step, the k-th particle of the j-th member hair, which constitutes the bundle of the i-th master hair, has the above-described process. An offset (t _{i, j, k} , u _{i, j, k} , v _{i, j, k} ) representing the shape of the bundle and an offset (c _{i, j, k} , cv _{i, j, k} ) representing the shape of the hair ) Was calculated. In the simulation step described later, these offsets are changed according to the movement speed of the member particles, and member hair is generated based on the changed offset.

It should be noted that more complicated methods may be used for the calculation method of each offset used in the above processing and the equations (1), (3), and (4) used for the calculation. By using a more complicated model, it is considered that it is possible to set a finer hair shape instead of taking the effort of the setter.

Finally, as shown in the following equation (5), the offset (u _{i, j, k} , v _{i, j, k} , t _{i, j, k} ) representing the shape of the bundle and the shape of the hair are represented. By adding an offset (cu _{i, j, k} , cv _{i, j, k} ), the relative position q _{i, j, k} (= u ′ _{i, j, k} , v ′ _{i, j, k} ) of each member particle , T _{i, j, k} ).

Based on the relative value of each member particle and q _{i, j, k} = (u ′ _{i, j, k} , v ′ _{i, j, k} , t _{i, j, k} ) and the master hair, each member particle The absolute position of the member hair can be calculated.

<<< Simulation step >>>
After the initialization step is completed, a simulation step is performed to actually generate hair animation. As described above, the simulation step is divided into a master hair simulation step, a member hair simulation step, a member hair deformation step, and a rendering step. Hereinafter, the processing of each step will be described in order.

<< Master hair simulation step >>
First, a master hair simulation step is executed. In the master hair simulation step, the movement of each master hair generated in the master hair initialization step is calculated using a physical simulation, and the positions of all master particles are updated.

  The master hair simulation step of this embodiment uses a very small number (for example, about 200 to 1000) of master hair (coarse model). Such a physical simulation of a relatively small number of hairs can be simulated sufficiently efficiently using a current general computer or a physical simulation method.

  In general, in a physical simulation using a particle model, various forces acting on each particle are calculated according to the physical model, and how each particle moves based on the force is calculated based on numerical integration. The force applied to the hair particles includes the tension that acts to maintain a constant hair length between adjacent particles, the repulsive force from the human body and nearby hair that acts when the particles come into contact with the human body and other hair, gravity And air resistance (wind power).

  However, in this embodiment, in order to increase the speed, the motion calculation is performed using only gravity and wind force without considering the force between adjacent particles and the repulsive force from the human body. The distance between the particles and the repulsion from the human body achieve the same effect as considering these forces by correcting the position of the particles based on the constraint conditions. The particle model and physical simulation used in the present embodiment are almost the same as the conventional method (see References 1, 14, and 5), so only the outline will be described below.

  Verlet integration is used for the integration calculation for calculating the motion of particles. Verlet integration is relatively stable even when the simulation step interval is large (for example, it is more stable than the more commonly used Euler integration), and there is no need to store the velocity of each particle. Is excellent.

The position (latest position) of the k-th particle P _k is expressed by the following equation (6) based on the positions P _k ⁻¹ , P _k ⁻² , the gravitational acceleration g, and the wind force w at the previous (most recent) time. ) Is used to calculate and update.

Here, “w” is wind force and has a direction and a size. The acceleration of the wind forces on the each particle is considered the tangential direction (tangent vector) t _k at the position of the particle, and proportional to the magnitude of the angle between the direction of the wind force w.

  By the above formula, the motion of particles based on gravity and wind force is calculated. However, in this state, the length of the hair is not maintained, and the particles continue to fall, or the hair is sunk into the human body, resulting in an unnatural simulation. Therefore, these problems are prevented from occurring by directly correcting the position of the particles based on some constraints. This is a method similar to the conventionally used method (reference documents 13, 15, 18).

First, the position of the particle is updated using the following equation (7) so as to keep the distance between the adjacent particles P _k ⁻¹ constant.

Here, l _k is a length in an initial state between the particles P _k and the particles P _k ⁻¹ connected to each other.

Next, the positions of the particles are similarly updated so that they do not sink into the hair and the human body. Here, the human body is expressed as a collection of a small number of spheres for speeding up. Each sphere has a center position o _i and a radius r _i . At this time, when the particle is present inside a certain sphere (when the distance between the particle position and the center position of the sphere is equal to or less than the radius of the sphere), the following equation (8) is used, The position of the particle is corrected so that the distance between the position of and the center position of the sphere is equal to or larger than the radius of the sphere.

The user sets the center position and radius of each sphere representing the human body in advance. The center position o _{i of the} sphere is updated based on the human posture in each frame.

  In addition, the position of the particle is determined according to the movement of the head so that the position of the particle at the base of each hair is always fixed at the same position on the surface of the head.

  When the constraint condition is applied, it is sequentially applied from the particle at the root of the hair toward the particle at the tip.

  In addition, since it is difficult to calculate the interaction between hairs at high speed, it is not handled in the simulation of the master hair.

<< Member hair deformation step >>
Next, a member hair deformation step is executed in which the relative coordinates of each member particle constituting the member hair with respect to the master particle corresponding to the member particle are changed based on the motion velocity vector of the master particle.

  In general, hair undergoes movements such as deformation at various speeds due to movement and wind. For example, when the hair bundle moves at a high speed, a part of the hair moves with a delay due to the interaction between the hairs. Therefore, it is considered that the hair bundle spreads in the direction opposite to the movement direction. In order to reproduce such a phenomenon, in the present embodiment, the shape of the hair bundle is determined according to the horizontal velocity of the master particles constituting the master hair particle model (the velocity in the direction perpendicular to the tangential direction of the hair). Control to spread. That is, the relative position of the member particles with respect to the master particles (offset representing the shape of the bundle) is changed so that the hair bundle spreads according to the horizontal movement speed of the master particles of the master hair.

  Further, when individual hair moves at high speed, it is considered that the hair is compressed left and right by air resistance. In order to reproduce such a phenomenon, in the present embodiment, the shape of each hair is controlled such that the lateral spread decreases as the horizontal velocity of the master particles increases. That is, the relative position (offset representing the shape of the hair) of the member particles with respect to the master particles is changed so that the lateral spread of the hair is reduced according to the horizontal movement speed of the master particles of the master hair.

  In general, in order to reproduce realistic hair movements, it is very important not only to calculate individual hair movements independently, but also to consider the effects of each other's hair on each other during simulation. is there. However, in order to calculate the interaction between hairs, it is necessary to determine whether a certain hair and other hair are in contact with each other for the combination of all the hairs. Even if it is devised, it takes a lot of processing time. Therefore, the calculation of the interaction between hairs is omitted in the systems aiming at the real-time simulation so far. As a result, since the movement is not obstructed by other hairs, all the hairs move in the same way, resulting in an unnatural hair animation.

  Even in the hair simulation method of the present embodiment, accurate calculation of the interaction including the contact determination between the hairs is not performed. In other words, in the dynamic hair bundle deformation model (detailed model) according to this method, the deformation is not calculated by physically accurately calculating the mutual influence between the hairs, but simply according to the movement speed. The deformation is performed by performing a geometric deformation. By using this method, the result caused by the interaction between hairs in the hair bundle can be efficiently realized by a simple model. Therefore, according to the present invention, natural hair animation can be generated in real time.

The member hair deformation step is more specifically based on the offset (u _{i, j, k} , v _{i, j, k} , t _{i, j, k} ) representing the shape of the bundle based on the velocity of the corresponding master particle. A “bundle shape deforming step” for controlling, and an “hair shape deforming step” for controlling an offset (cu _{i, j, k} , cv _{i, j, k} ) _{representing the} hair shape based on the velocity of the master particle. ing. That is, the shape of the bundle and the shape of the member hair constituting the bundle are controlled based on the speed of the master particle to which each member particle corresponds. This velocity is calculated based on the previous particle position and the current particle position. In the following, in this chapter, q _{i, j, k} = (t _{i, j, k} , u _{i, j, k} , v _{i, j, k} ) is simply expressed as q = (t, u, v). To express.

<Bundle shape deformation step>
In the member hair deformation step, first, a bundle shape deformation step is executed. As described above, the bundle shape deformation step is a step of controlling the offset indicating the shape of the bundle based on the velocity of the corresponding particles of the master hair.

  As shown in FIG. 4 (c), it is generally considered that the shape of the hair bundle spreads as the movement of the bundle becomes faster. If all the hairs were each simulated using a particle system, all the hairs would move in the same way and the bundle size would not change at all. However, in actual human hair, the hairs interact with each other, and the movement of the hair is disturbed or flows backward. Here, in order to reproduce such deformation of the shape of the bundle, the offset q representing the shape of the bundle of each member particle is controlled according to the speed of the corresponding master particle of the master hair (FIG. 7 ( a) (b)).

  However, it is difficult to accurately model the relationship between the bundle speed and the shape of the bundle, which is how the spread of the bundle changes according to the bundle speed, because it is determined by the complex interaction between the hairs. . The relationship between the bundle speed and the bundle shape also varies depending on the quality and density of the hair. In the present embodiment, a simple deformation model is used in which the bundle width is determined linearly in proportion to the bundle speed.

As shown in FIG. 7B, the offset position q is moved based on the velocity vector s and the scaling parameter RS _k .
In order to determine the direction and size for changing the offset position according to the speed direction, the offset position represented by the uv coordinate system is converted into an sr coordinate system based on the direction of the speed vector s, and the sr coordinate system is used. Apply deformation.

  Therefore, first, the unit vector us is calculated. The unit vector us is parallel to the uv plane. Here, the unit vector us is calculated by projecting the velocity vector onto the uv plane.

  Next, the unit vector ur is calculated. This unit vector ur is perpendicular to the vector us and parallel to the uv plane.

  The horizontal offset (u, v) is converted into coordinates (r, s) in the sr coordinate system using the unit vector us, unit vector ur and the following equation (9) calculated in this way. .

The post-deformation offset position “s ′” is determined using the velocity vector magnitude | s | and the scaling factor RS _k .

As an intuitive method for determining RS _k , however, here, a radius function R ′ (t) representing a bundle shape when the hair bundle is most spread is used. The radius function R ′ (t) can be given an arbitrary function by the user in accordance with the hairstyle to be expressed, like the radius function R (t) used in the initialization of the bundle shape.

The scaling coefficient RS _k is calculated from R ′ (t) and R (t) for each master particle by the following equation (11).

  However, as described above, since this deformation is a simple linear deformation, if the speed | s | is too large, the width of the bundle becomes too wide, and an unnatural shape may occur. In order to avoid such a problem, | s | is limited here by the maximum speed Smax. That is, in Equation (10), when the magnitude of the velocity vector | s | is equal to or greater than Smax, Smax is used instead of | s |.

  Finally, the offset q = (u ′, v ′) representing the current bundle shape is obtained by returning the offset (S ′, r) calculated in the sr coordinate system to the offset (u ′, v ′) in the uv coordinate system. , T ′).

<Hair shape deformation step>
Next, a hair shape deformation step is executed. The hair shape deformation step is a step of controlling the offset representing the hair shape based on the velocity of the corresponding particles of the master hair.

When human hair moves at a high speed in the horizontal direction, it is considered that bent hair such as curly hair is compressed in the horizontal direction by air resistance, as shown in FIG. Therefore, in order to realize such deformation, the linear change model is also used here for the offset (cu _{i, j, k} , cv _{i, j, k} ) representing the shape of the hair, similar to the shape deformation of the bundle. Is introduced.

Here, (cu _{i, j, k} , cv _{i, j, k} ) is linearly changed according to the velocity of the master particle. By adding an offset (cu _{i, j, k} , cv _{i, j, k} ) representing the deformed hair shape to an offset (u ′, v ′, t ′) representing the shape of the bundle, the relative position of the particles Calculate That is, Expression (5) is replaced with the following Expression (13).

In Expression (13), calculation is performed such that the offset (cu _{i, j, k} , cv _{i, j, k} ) representing the shape of the hair decreases as the velocity | s | of the master particle increases. Here, CS is a value representing the maximum deformation and plays the same role as R ′ (t) in the equations (10) and (11). By using this, when the velocity of the particles is extremely large, the member hair is prevented from becoming straight by preventing the offset from becoming smaller than the value determined by CS.

<< Member Hair Generation Step >>
And a member hair production | generation step is performed. The member hair generation step is a step of calculating the position of the member particle of the member hair using the position of the master particle calculated in the master hair simulation step and the relative position of the member particle changed in the member hair deformation step. .

The member hair deformation step calculates the relative coordinates q _{i, j, k} = (u _{i, j, k} , v _{i, j, k} , t _{i, j, k} ) of each member particle. q _{i, j, k} represents the relative coordinates of the k th particle of the j th member hair of the i th master hair. q _{i, j, k} = (u _{i, j, k} , v _{i, j, k} , t _{i, j, k} ) indicates the direction horizontal to the master hair (u _{i, j, k} , v _{i , j, k} ), and is represented in the local coordinate system of the master particle p _{i, k , where} t _{i, j, k} is the vertical direction (see FIG. 8).

The unit vectors t _{i, k} , u _{i, k} , v _{i, k} for representing the local coordinate system (t _{i, k} , u _{i, k} , v _{i, k} ) are as follows for each master particle. Calculate with First, the tangential vector t _i of the _{hair, k} is the position p _i of the master _particles, and _k, the position p _i of the adjacent master _particles, the difference vector _k-1 is calculated and to normalize, be determined Can do. Next, the unit vector u _{i, k} , v _{i, k} representing the direction of the surface perpendicular to the hair is expressed by the following equation (14) using the tangential direction vector t _{i, k} and an arbitrary reference vector x: ). The reference vector is preferably orthogonal to the tangential direction vector t _{i, k} as much as possible. In this implementation, since the hair generally extends in the vertical direction, the x-axis of the head was used as the reference vector. In addition, the perpendicular direction here is a gravity direction.

In the member hair generation step, the position (absolute position) p _{i, j, k} of each member particle constituting the member hair is changed to q _{i, j, k} (= u _{i, j, k} , v _{i, j, k} , (t _{i, j, k} ) and the local coordinate system (t _{i, k} , u _{i, k} , v _{i, k} ) of the master particle p _{i, k} are used to calculate the following equation (15)

<< Rendering Step >>
One frame of hair simulation can be generated by drawing (rendering) individual member hair generated by the member hair generation step on the screen together with the human body model. An animation of hair simulation can be generated by repeating all the steps in the simulation step and continuously generating images of each frame while calculating changes in hair.

  The conventional technique was used for the technique of rendering the hair. In general, it is important in hair rendering to consider both individual hair shading models and self shadows. In the present embodiment, a widely known model is used as the shading model (see Reference Document 10), and a detailed description thereof will be omitted. In this implementation, this shading model is implemented as a vertex shader program, and can be calculated at high speed on a GPU (processor on graphic hardware) described below. Further, as a method for realizing self-shadowing, a deep shadow method (see reference document 12) can be used. This method is a general method for realizing self-shadowing, and can be executed at high speed using a GPU.

<< GPU implementation >>
In recent years, graphic hardware has greatly advanced. By using a programmable shader mechanism of graphic hardware, general processing other than graphics processing can be realized at high speed using a GPU. Yes. Therefore, a technology for realizing physical simulation at high speed by applying such graphic hardware has recently attracted much attention. The hair simulation method of the present embodiment models hair using a particle model and can be operated on a GPU. The particle model used in the hair simulation method according to the present invention is suitable for mounting using a GPU because each particle constituting the particle model can be processed in parallel (see References 14, 15, and 18). ).

  In the hair simulation method according to the present invention, not only a rough model physical simulation but also a detailed model deformation process can be executed on the GPU.

  In this embodiment, the simulation system as described so far is operated using a GPU. This embodiment is implemented using C ++ and OpenGL. The Cg Tutorial (Reference 7) was used to use the programmable shader.

  In addition, a simple hairstyle editor was implemented for users to set hairstyles. Use this editor to set a sphere for collision detection for the input human body model, the range of the head that generates the master hair, the length of the master hair at each position, and the hair It is possible to easily specify parameters such as parameters for generating bundles using a mouse and keyboard.

Thus, since the hair simulation method according to the present invention can be easily mounted on a GPU, real-time simulation can be realized by using the simulation method.

  Hereinafter, a method for mounting the present technique on the GPU will be described.

FIG. 9 summarizes the textures used for the input and output of the shader program.
First, the implementation of the master hair simulation on the GPU will be described.

  The physical simulation using the particle model as described above can be processed on the GPU. Here, the implementation on the GPU will be briefly described. The method used in the present embodiment is the same method as in the previous research (Reference Document 14).

As shown in FIG. 10, when processing by the GPU, the position of the particle is stored as color information in the texture image data. In the hair simulation method of the present embodiment, at least three textures for storing the respective data of the positions P, P ⁻¹ , and P ⁻² are necessary. All variables are stored in a video memory of graphic hardware including a GPU in the form of texture.

  The texture data array (array) in which the particle position information and the like are stored is sent to a fragment shader program (fragment shader program), which is a program in which processing in units of pixels is described.

A shader program that implements integration processing on the GPU outputs the current position P of the particle with the two most recent positions P ⁻¹ and P ⁻² as inputs.

  In order to simplify the implementation of the shader program, when the particle position data is stored in the texture, as shown in FIG. 10, the data on all the particles of one hair are stored in one data string. To do. In this way, the position data of the adjacent particles can be easily accessed by always referring to the adjacent pixels. In the shader program, since it is necessary to calculate the direction of the tangent from the difference vector with the position of the adjacent particle, such a data storage method is effective for performing this calculation in a shorter time.

Further, in the simulation of the present embodiment, dummy particles are added as a further base of the hair base particles in order to calculate t ₀ (see FIGS. 8 and 10). The position of the dummy particle is calculated based on the movement of the head as in the case of the base particle.

When the texture of the RGBA color model is used, the xyz coordinate value of the particle position P can be stored in RGB of each pixel, and the initial distance l _k can be stored in A.

A shader program that implements the application process of the constraint condition on the GPU outputs the position P ′ after applying the constraint condition, with the position P calculated by the integration as an input. At this time, since the position P ^-2 is not necessary, the number of necessary textures can be saved by using the texture for the position P ^-2 as the texture for the output position P '.

  In addition, after calculating the position change of the particle by integral calculation, the constraint condition is repeatedly applied. The process of applying the restriction on the length between particles and the process of applying the restriction on the penetration of particles into the human body are each implemented as different shader programs. Each shader program is repeatedly applied several times.

  Next, initialization of member hair and implementation of shape deformation on the GPU will be described.

The position P _{i, j, k} of the member hair of the member hair corresponds to the position P _{i, j} of the corresponding particle of the master hair, the position P _{i, j} ⁻¹ immediately before it, and the offset (t _{i, j, k} , u _{i, j, k} , v _{i, j, k} ) (cu _{i, j, k} , cv _{i, j, k} ) and deformation parameters (RS _k , CS, Smax). The immediately preceding position is used to calculate the velocity s _{i, j, k} for each particle. Since a maximum of four values (in the case of RGBA) can be stored in one texture, at least two textures are required to store these eight variables.

Here, the same deformation parameters (RS _k , CS, Smax) may be used for all hairs, or different parameters may be used. In the former case, the parameters (CS, Smax) can be directly passed to the shader program without using the texture. Even in this case, two textures are still needed for the five offset parameters and RS _k . Note that the offset amount and the parameter for deformation remain unchanged during the simulation. Therefore, these textures are initially initialized only once. These parameters are also required for all particles of the member hair.

  Here, assuming that there are N mass hairs and M member hairs are generated for each master hair, as shown in FIG. 9, the texture region for “N × M” hairs. is required. Then, in order to render “N × M” member hairs, it is necessary to repeat the process of calculating and rendering on the screen for each N master hairs M times. In order to perform such processing, it is necessary to give the shader program the texture address of the starting point in which the variables of the group of M member hairs to be processed this time are stored in each repeated processing.

  Instead of the processing in the previous paragraph, N × M points may be rendered simultaneously. In this case, all textures need to be given to the shader program, and a large texture for storing information about the output position and the texture coordinate system of the output particles are arranged in the texture coordinate system of the input particles. Additional texture is required.

<Experimental result>
The results of a hair simulation experiment using the hair simulation method described above will be described.

  In this hair simulation experiment, as the simulation apparatus 1, a personal computer main body 3 having a standard performance whose OS is Windows Vista (registered trademark) and a graphic card 4 mounted thereon was used. More specifically, the simulation apparatus 1 has a CPU 5 with an Intel (registered trademark) Core2 Duo E6600 2.4 GHz, a main memory 6 with 2 GB, a display 7, a hard disk 8 as an external storage device, A multi-drive 9 for a storage medium such as a CD-ROM, a sound card 10, a LAN card 11, an input / output interface such as a mouse 12 and a keyboard 13 are connected. Reference numeral “14” is a bus (see FIG. 11).

  The following table shows the calculation processing time under various conditions. FIG. 12 shows some drawing images.

  Here, in all experiments, the number of particles constituting each hair particle model was set to 10. The appropriate amount of hair (number of hairs) varies depending on the hairstyle and the size (diameter) of the hair bundle, but generally, at least about 10,000 to 20,000 hairs are required to cover the scalp of the character (person).

  In the detailed model, when 10,000 to 20,000 member hairs were used as the total number, the animation speed was about 40 fps (frames / second) to 50 fps (Experimental Examples 1, 2, 3 in Table 1 and FIG. 12 ( a) (b)). On the other hand, when a total of 50,000 member hairs were used, the speed decreased to about 30 fps (see Experimental Example 4 in Table 1).

  In addition, the calculation processing time in the conventional bundle model (static bundle model) in which the member hair does not move and the calculation processing time in the dynamic bundle model (detail model) used in this embodiment are almost the same. Met. And the dynamic bundle model could be executed as a real-time simulation. And as expected, the conventional static bundle model is unnatural because the shape of the bundle does not change (see FIG. 12C), and by using the dynamic bundle model of this embodiment, It became a natural simulation (see FIG. 12B).

  As described above, in this embodiment, a simple linear deformation model is used. This model does not guarantee physically correct movement. In addition, no constraint conditions are used at the time of producing member hair. Therefore, the length of the member hair may change during the animation, and the member hair may enter the human body. However, as far as the resulting animation is seen, the variation in the length of the member hair is generally very small and not noticeable at all.

  In this embodiment, attention is paid only to the speed in the horizontal direction, and the speed in the vertical direction is ignored. In general, the shape of the hair bundle should change not only in the horizontal direction but also in the vertical direction in response to changes in the velocity in the vertical direction. However, in order to change the position of the particles constituting the hair model in the vertical direction, it is necessary to convey the change along the hair from the root particle to the tip particle of the hair. For this purpose, in the calculation process for each particle, the result of the process for adjacent particles is required. Such processing has a problem that it is difficult to implement the program on the GPU.

  The main object of providing the method of the present embodiment is to provide a higher quality reality to a hair real-time simulation method that is currently feasible at a realistic calculation cost. Physical accuracy is less important, especially for online applications. An important feature of this method is that the introduction of a reasonable bundle deformation model has improved the problem of the conventional stationary bundle model. If more computation time is required, a physically more accurate model can be realized. However, this method meets the demand for a simulation that is as realistic as possible in as little time as possible. Is the best fit.

It is a flowchart figure which shows the outline | summary of the flow of a process of the hair simulation method of this embodiment. It is a block diagram which shows the outline | summary of the system of the hair simulation method of this embodiment. Regarding the hair simulation method of the present embodiment, (a) is one frame showing the state of a rough model simulated using particle model simulation, and (b) uses a dynamic bundle model. It is one frame which shows the state of the detailed model generated geometrically. The dynamic bundle model is shown, (a) is an explanatory view showing a state in which member hair is generated around the master hair, and (b) is an example in which a bundle having a static shape is generated. (C) is explanatory drawing which shows the example which produced | generated the bundle | flux from which a shape changes dynamically. (A) is an explanatory diagram showing examples of different bundle shapes by different radius functions, and (b) is a diagram of different bundle shapes by different length assignment functions. It is explanatory drawing which shows an example. FIG. 6 shows the results of generating various hair shapes by changing the parameters that define the hair shape, (a) is an explanatory diagram showing straight hair, and (b) FIG. 3 is an explanatory view showing a wavy hair, and FIG. 3C is an explanatory view showing a twisted hair. It is for demonstrating control of the shape of a bundle | flux, (a) is explanatory drawing for demonstrating the shape of the bunch of a stationary state, (b) demonstrates the shape of the bundle | flux of a motion state. It is explanatory drawing for. It is explanatory drawing which shows the spatial relationship between master hair and member hair. It is explanatory drawing which shows the texture used with a programmable shader. (A) is explanatory drawing which shows the state which stored the position of each particle | grain of each hair on a texture, (b) is explanatory drawing which shows the dummy particle added. It is a block diagram which shows the system configuration | structure of the simulation apparatus for performing the hair simulation method of this embodiment. (a)-(e) is explanatory drawing which shows the screenshot in the experiment on each experiment condition of Table 1, respectively.

Explanation of symbols

1 ... Hair simulation device 3 ... PC body 4 ... Graphic card
5 ... CPU, 6 ... Main memory, 7 ... Display,
8 ... Hard disk, 9 ... Multi drive, 10 ... Sound card,
11 ... LAN card, 12 ... mouse, 13 ... keyboard

Claims (4)

A hair simulation method for simulating the movement of the hair of characters appearing in computer animation and computer games and generating animation by continuously displaying frame images,
The character's hair is composed of a bundle of a plurality of dispersed hairs,
Each bundle is composed of one master hair representing the bundle and member hairs scattered around the master hair.
Each master hair is constituted by a connection of a large number of master particles, and each member hair is constituted by a connection of a large number of member particles,
As a step to initialize the simulation,
A master hair initialization step for initializing the position of the master particles constituting the master hair according to the predefined hair information;
A member hair initialization step that initializes the relative position of the member particles with respect to the corresponding master particles according to the information on the shape of the bundle and the shape of the hair,
As a simulation step of generating and displaying the frame image,
A master hair simulation step of simulating the movement of each master hair by a physical simulation using a particle model, and calculating the positions of all master particles constituting each master hair;
For each bundle, a member hair deformation step for changing the relative coordinates of each member particle constituting each member hair with respect to the master particle corresponding to the member particle based on the motion velocity vector of the master particle;
The member which calculates the position of the member particle of the member hair scattered around each master hair from the position of the master particle calculated in the master hair simulation step and the relative position of the member particle changed in the member hair deformation step A hair generation step;
A hair simulation method comprising: a rendering step of drawing a frame image by drawing all member hairs based on the positions of the member particles calculated in the member hair generation step. The member hair deformation step includes:
A bundle shape deformation step of changing the relative position of each member particle with respect to the corresponding master particle so that the bundle spreads as the velocity increases according to the motion velocity vector of the master particle;
A hair shape deformation step of changing the relative position of each member particle with respect to the corresponding master particle so that the hair is compressed in the horizontal direction as the velocity increases according to the motion velocity vector of the master particle. ,
The hair simulation method according to claim 1. A hair simulation apparatus for simulating the movement of hair of characters appearing in computer animation and computer games and generating animation by continuously displaying frame images,
The character's hair is composed of a bundle of a plurality of dispersed hairs,
Each bundle is composed of one master hair representing the bundle and member hairs scattered around the master hair.
Each master hair is constituted by a connection of a large number of master particles, and each member hair is constituted by a connection of a large number of member particles,
As a means to initialize the simulation,
Master hair initialization means for initializing the position of the master particles constituting the master hair according to the predefined hair information;
Member hair initialization means for initializing the relative position of the member particles with respect to the corresponding master particles in accordance with information on the shape of the bundle and the shape of the hair defined in advance,
As means for generating and displaying the frame image,
Master hair simulation means for simulating the movement of each master hair by a physical simulation using a particle model and calculating the positions of all master particles constituting each master hair;
Member hair deformation means for changing the relative coordinates of each member particle constituting each member hair with respect to the master particle corresponding to the member particle based on the motion velocity vector of the master particle for each bundle;
The member which calculates the position of the member particle of the member hair scattered around each master hair from the position of the master particle calculated in the master hair simulation step and the relative position of the member particle changed in the member hair deformation step Hair generation means;
Rendering means for rendering a frame image by drawing all member hairs based on the positions of the member particles calculated in the member hair generation step. The member hair deformation means includes
A bundle shape deforming means for changing the relative position of each member particle with respect to the corresponding master particle so that the bundle spreads as the velocity increases according to the motion velocity vector of the master particle;
Hair shape deformation means for changing the relative position of each member particle with respect to the corresponding master particle so that the hair is compressed in the horizontal direction as the velocity increases according to the motion velocity vector of the master particle. ,
The hair simulation apparatus according to claim 3.