JPH0561961A - System and device for interactive processing of computer animation - Google Patents

Abstract

PURPOSE:To efficiently obtain realistic animation without depending on strict physical simulation by interpolating the motion of a hair curve obtained from the change of representative number of hair from initial shape. CONSTITUTION:Each of the hair is assumed as an elastic material, and the initial shape of the hair is defined, and an external force applied to the elastic material and the attribute of the hair are defined. The travel position in the lapse of time of the representative number of hair can be found from the initial shape of the hair by solving a dynamic equation representing the deformation of the elastic material based on the external force and the attribute. The preview of the animation obtained from the above result is performed, and such processing is repeated until a desired result can be obtained, and residual hair is generated by interpolating the motion of an obtained representative hair curve. In such a case, a means which inputs an external item and the attribute of the hair artificially, and interpolation algorithm for the attachment of the preview function of the motion with respect to the representative hair curve and the fast motion of the hair are introduced.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates mainly to computer graphics modeling and animation techniques, and more particularly to a method for defining human hair or animal body hair and hair, and a method for expressing movements due to external force.

[0002]

2. Description of the Related Art A conventional technique for realizing human hair movement by computer animation is IEICE Technical Report Vol. 89 IE89-60 "Representation of Hair Movement by Stochastic Model". In this method, the movement of a single curve under uniform wind force is measured, and based on the empirical rule obtained from this, all movements of hair under uniform wind force are reproduced.

[0003]

The manner in which the hair moves in response to an external force can be obtained, in principle, by regarding each hair as an elastic body and solving its dynamic equation to solve it. ..
In this case, the equation to consider is the Euler-Lagrange equation

[0004]

[Equation 1] ∂ (ρ∂r / ∂t) / ∂t + γ∂r / ∂t + δE (r) δ / r = f (r, t) (Equation 1). Here, r = r (a, t) is a function of the one-dimensional parameter a and the time parameter t, and represents a curve. Ρ = ρ (a) and γ = γ (a) on the left side of Equation 1 respectively represent the density and damping coefficient of the curve at point a, E (r) is the potential energy, and δE (r) / δr is the Represents a variation. F = f (r, t) on the right side represents the external force term. This is an equation for a single curve, but to treat n hairs, r = r ₁ , r ₂ ,. ． ． , Rn will solve the above equations simultaneously. In that case, since there is an interaction between the hairs in particular, the external force term f on the right side is a value that depends on r ₁ , r ₂ , ..., R _n , and n is usually a value of several tens of thousands to 100,000. Therefore, it is almost impossible to solve these equations numerically at the same time from the processing capability of a normal graphics workstation. Therefore, the conventional technique as described above has been able to obtain a simple motion expression under a very restricted condition.

However, the conventional techniques have not provided a method for easily inputting parameters for obtaining a desired motion and realizing various motion expressions. In the above-mentioned prior art, since the model is simple, only a state of fluttering in a steady state under uniform wind force can be obtained, while it is not realistic to solve the dynamic equation exactly.

It is an object of the present invention to provide an expression system for realistically reproducing the movement of head hair, animal body hair and the like depending on external force and material by a simple input operation.

[0007]

According to the present invention, a computer animation interactive processing method for displaying hair that is deformed by an external force is such that (a) each hair is regarded as an elastic body, and (b) the initial hair. The shape is defined, and (c) the user defines the external force acting on the elastic body and the attributes of the hair,
(D) For a typical number of hairs, a dynamic equation representing the deformation of the elastic body is solved based on the external force and the attribute to obtain a moving position with time from the initial shape of the hair, and (e) The animation obtained from the result is previewed, (f) the processes from (c) to (e) are repeated until the desired result is obtained, and (g) the obtained typical movement of the hair curve is interpolated. It is designed to generate the remaining hair.

Further, according to the present invention, there is provided a computer animation interactive processing apparatus for displaying hair deformed by an external force, an image display display, data defining contents to be displayed on the image display, and gravity acting on the hair. Input means for inputting external constraint conditions including wind force and wind force, and attribute conditions including hair material, calculation means for obtaining a positional change of the hair curve due to an external force for a representative number of hairs, and the means A preview means for previewing a change in the position of the hair curve and an interpolating means for interpolating other typical hairs to the representative number of hairs are provided.

[0009]

In the present invention, basically, a simulation is performed based on the above (Equation 1), and based on the result, the movement of the set of curves of the hair is realized. As described above, the external force term and the like become complicated in consideration of the mutual influence of hairs, and the calculation load becomes large. Therefore, (1) external force terms and hair attributes are artificially defined by the user, and (2) only typical tens to hundreds of hairs are calculated,
(3) Preview the animation obtained from the calculation result. (1) to (3) until the desired result is obtained
Repeat the procedure up to and then calculate again for all hair. At that time, the above-mentioned dynamic equation is not recalculated, but is calculated using an algorithm for interpolating the typical movement of the hair curve obtained in the processing from (1) to (3). That is, a means for artificially inputting an external force term or attributes of hair and a preview function of a movement related to a typical hair curve are added,
And introduce a fast hair movement interpolation algorithm.

By providing a means for artificially inputting the external force term and the attributes of the hair, the expression of the external force term and the like can be simplified, and therefore, the above mechanical equation can be numerically calculated. You can Also, by providing a preview function for representative hair curves of at most several hundred,
It is possible to reduce the number of trial and error for obtaining the desired motion. Further, the calculation of the movement of all the hairs is accelerated by introducing an interpolation algorithm based on the calculation result of the above-mentioned representative hair curve, and an animation showing a desired movement can be easily obtained at high speed.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to FIG. FIG. 1 shows a basic flow of a hair movement generating procedure according to the present invention. First, a three-dimensional CG model of a human head is defined, and then a hair generation region and a hairstyle are defined (1 in FIG. 1). Next, the initial values of various data for calculating the movement of hair are input (2 in FIG. 1). In this embodiment, a means of simplifying and solving the above-mentioned dynamic equation (Equation 1) in order to obtain a realistic motion is taken, and the data necessary for that is explained below.

First, for simplification, the equation (1) for one curve will be described more specifically. The potential energy term E (r) considers only the elastic deformation energy of the space curve, especially the energy associated with the change in curvature. In that case, the equation of the curve is

[0013]

[Equation 2] r = r (a, t) = (x (a, t), y (a, t), z (a, t))… (Equation 2)

[0014]

[Equation 3] E (r) = ∫ K (a) {(d ² x (a, t) / da ² ) ² + (d ² y (a, t) / da ² ) ² + (d ² z ( a, t) / da ² ) ² } da… (Equation 3) Here, the integral is related to the parameter a, and for simplicity, the curve is defined as 0 ≦ a ≦ 1. The function K (a) is hereinafter referred to as the curvature energy coefficient. Also, the second derivative appearing in the term of the integrand is related to the variable a, and the symbol ∂ of partial differential should be used originally, but it is d for simplicity. Next, the external force term f (r, t) is, for example, gravity g (r) and wind force w (r, t).
Considering the case of

[0015]

(4) g (r) = ρ (a) G, w (r, t) = fl (r, t) (Equation 4)

[0016]

F (r, t) = g (r) + w (r, t) (Equation 5) Of course, for external forces other than wind power,
It can be handled by the formulation by. For example, the user can specify w (r, t) even in a situation where the hair is shaken according to the movement of the body. In order to give a variety of ways to apply such external force, it is better to actually measure and input, or to make a database, if necessary.

Under the above conditions, the user uses the initial data of (2)-(5) in FIG. 2, that is, the curve density ρ (a), the curvature energy coefficient K (a), and the gravity vector. Input G, the wind force vector field fl (r, t), and the gravity control parameter φ (φk if the value changes for each curve). Of these input data, the curvature energy function K (a) is used as data relating to the physical properties and attributes of hair.
There is. Intuitively, this is considered to represent the hardness of the hair. In reality, it is often assumed that the hardness of hair is uniform, but at that time, the location (value of parameter a)
A constant value is given regardless of. Similarly, in reality, the hair density r (a) is a constant that does not depend on the value of a, and the gravity vector G does not depend on the location, and a constant value is input. The wind force takes the form of inputting the vector field fl (r, t) here, but this is a function of the coordinate values x, y, z of the position and the time t, and it is easy for the user to specify one by one. Not. Therefore, we will prepare a typical wind vector library and select from it.

Since the hairstyle (and thus all the hair curves) was defined in the previous step, the thinning number m of the hair (how many percent of the total hair curve should be calculated)
Is specified. That is, do not calculate for all hairs at a time, but calculate by spreading an appropriate number. At that time, in order to obtain an expression of the movement of the hair, the equation 1 is solved under the constraint that the length of the hair is constant over time. A well-known Lagrange's undetermined multiplier method or the like may be used as a numerical solution method by a computer for that purpose. When considering this equation for n curves, even if n is at most several hundreds, it will be very difficult to solve if the external force term includes unknown functions r ₁ r ₂ , ..., R _n . Therefore, as an auxiliary means for expressing the movement of about several hundred hairs, a method of defining so that other hair curves do not depend on the external force term is used. For example, as the external force, strictly speaking, the frictional force between hairs, the repulsive force, etc. should be taken into consideration, but the user defines it as a virtual force as follows.

[0019]

F (r, t) = φg (r) + w (r, t) (Equation 6) Here, φ is a real constant and the user inputs an appropriate value. For example, when φ is set to a value larger than 1, the magnitude of gravity becomes larger than that of the actual one, the movement of the hair becomes heavy, and the state in which the frictional force between the hairs is large and it is difficult to move can be reproduced.

If (Equation 6) is the definition of the external force term regarding the equation relating to the k-th curve r _k , more specifically,

[0021]

[Expression 7] f (r, t) = φ _k g (r) + w (r, t) (Expression 7) That is, the value of the coefficient φ in (Equation 6) may be a different value for each curve (φ _{k in the} above equation (Equation 7)). For example, when the wind is in front of the face, the value of φk for the hair group growing on the upper part of the head is set to 1 because the degree of freedom of movement of the hair in this portion is large. The portion near the neck is set to a value greater than 1 in consideration of the influence of the weight of the hair in the portion above it. As for what value the realistic movement can be obtained, a simulation of several hundred hairs or less was performed, and the animation image was confirmed via the preview system (3 in Fig. 1). Perform trial and error until it gets a movement (Fig. 1
4). As described above, the equation (Equation 1) for any hair curve r _{k is set} so that the external force term does not include any term other than r _k , so that all the curves to be handled can be calculated in parallel and the number of hairs is reduced. It can be processed at high speed by checking the preview. Therefore, although the method is unavoidable by trial and error, since it can be considerably reduced in the sense of its substantial required time, it provides a sufficiently realistic solution for creating a desired animation. In the above example,
Although the devising of the external force term has been described, the control for obtaining the effect of the material such as the hardness of the hair can be achieved by the user well defining the term of E (r).

Next, based on the result of the above preview, the entire curve of the hair is drawn. For that purpose, the movement of the previewed result of the hair curve thinned out as described above is propagated to the movement of the hair curve in the vicinity thereof with some randomness added. That is, the stochastic interpolation described later is performed. The degree σ of the randomness is input as a numerical value (5 in FIG. 1),
Calculate all hair movements (6 in Figure 1). Next, through time-lapse photography (7 in FIG. 1), an animation with a saturation close to the final animation is made, and the operation of interactively inputting the value of σ is repeated until the desired result is obtained (8 in FIG. 1). After that, the final image is created (9 in FIG. 1). For convenience,
Hereinafter, the curve used to obtain the preview result will be referred to as a preview curve.

Next, the stochastic interpolation method of the preview curve group will be described with reference to FIG. 2 showing FIG. 1 in more detail. In solving the equation of (Equation 1) and displaying the hair curve, each curve is represented as a connection of short line segments (shown by the wavy line in FIG. 5). 21, 2 in FIG.
As shown in 2, the number of interpolation curves generated between the preview curve groups is determined from the hair density (total number) specified in advance and the degree of thinning (designating one hair per m). .. In FIG. 4, in the case of m = 5, the generation points q ₁ , q ₂ , of the four adjacent preview curves (41 in FIG. 4) are
21 in total on and around the square with q ₃ and q ₄ as endpoints
There is a generation point (42 in FIG. 4) of the interpolation curve of the book. Even if it is an interpolation curve, the initial shape is defined at the definition stage of the hairstyle, so here the movement position resulting from movement due to changes in external force and attributes is obtained. As shown in FIG. 5, the interpolation curve is represented by a line segment sequence p ₀ p ₁ , p ₁ p ₂ , ..., P _n-1 p _n , and the standard position p ₀ 'of the end point sequence at the next time step. , P ₁ ', ..., P _n ' can be determined as follows. Since the end points are fixed, p ₀ '= p ₀ . If it is determined up to p _i 'sequentially, the next end point p _{i + 1} ' is p _i 'p _{i + 1} ' is Σ _k
d (q ₀ k, p ₀ ) q _i q _{i + 1} Be oriented so that it is parallel, and the length of the line segment of p _i 'p _{i + 1} ' is the same as p _i p _{i + 1} , The position of the end point p _{i + 1} 'is fixed. Here, d
(Q, p) represents an appropriate distance between the two points p and q. For example, a normal Euclidean distance or a Manhattan distance may be used. Next, this standard position and the degree of randomness σ
Based on (25 in FIG. 2), the actual position of the end point r ₀ ′,
Determine r ₁ ', ..., R _n '. This σ is a quantity that defines how far away from the previous standard position (43 in FIG. 4)
Then, the function σ = σ (i) of the end point number i that takes a smaller value as it gets closer to the generation point. A large value is usually taken at the end, that is, at a place where i is large. Since the end points are fixed, r ₀ '= r ₀ as before. If it is decided up to r _i 'sequentially, the next actual end point r _{i + 1} ' is the axis p _i '
It is defined (using a random number) as an arbitrary point on a disk centered at p _i ′, with a radius σ (i), orthogonal to p _{i + 1} ′. This allows the position of all hairs to be calculated (2 in Figure 2).
6). Processing after time-lapse shooting (27, 28, 29 in Fig. 2)
Is as described above.

Another embodiment will be described as a simple method using a formulation different from the above embodiment. First, each hair is represented as a set of broken lines as shown in FIG. 5, as in the previous embodiment. The time change of the hair position when an external force is applied can be calculated by the calculation in the following procedure. It is assumed that the position of the hair at time t = 0 has been input. Then, functionally t = n by the following procedure.
The position at t = (n + 1) Δτ can be determined from the position information at Δτ (where Δτ is the time step size). In the following, the time is described as n for simplicity.

(1) Every k = 1 to m (where m is the number of broken lines for one hair), the k-th broken line from the root (61 in FIG. 6)
On the other hand, taking the coordinate system as shown in FIG. 6, the y-axis (6 in FIG.
The angle between the positive direction of 2) and the polygonal line θ = θ _k (FIG. 63),
Further, an angle φ = φ _k (FIG. 65) formed by projecting this polygonal line on the zx plane (FIG. 64) and the positive direction of the z-axis is _obtained .
Here, for the angle at time n, θ _k (n), φ _k (n)
Is written.

(2) Next, by solving the equation shown below,
Based on the values of θ and φ at times n-1 and n, time n
Find the values of θ and φ at +1.

Θ _k (n + 1) -2θ _k (n) + θ _k (n-1) = (Δτ) ² c _k F _θ (Equation 8) φ _k (n + 1) -2 φ _k (n) + φ _k (n− 1) = (Δτ) ² d _k Fφ (Equation 9) where Fθ and Fφ are external force fields F (t, x) given as a function of time t and position x of the node p _k of the hair, respectively. It is a scalar field projected onto the θ plane and the φ plane shown in FIGS. 7 and 8. Further, c _k and d _k correspond to so-called moments of inertia, but here they are simplified and given by the following equations determined by the value of k.

C _k = d _k = Io / k (Equation 10) Here, the user inputs the constant Io, which is a value determined in proportion to the mass and the length of one hair. In (Equation 10),
Dividing this by k indicates that the end of the hair is touched better.

A method of determining Fθ and Fφ based on the input (or selected) previous external force field F will be described with reference to FIGS. 7 and 8.

In FIG. 7, the θ plane and Fθ are described. First, the θ plane is a plane formed by the y axis (62 in FIG. 7) and a vector x _k (FIG. 71) formed by translating the line segment p _k-1 p _k to the origin (FIG. 72). That is. The external force F () is applied to the vector vθ (FIG. 73) having a magnitude 1 which is on the θ plane and which is perpendicular to the vector x _k and is oriented in the direction in which the angle value θ increases (counterclockwise in FIG. 7). FIG. 7
The value obtained by taking the inner product with 4) is Fθ.

In FIG. 8, the θ plane and Fφ will be described. θ
The plane is the zx plane (81 in FIG. 8) in the figure. Projection vector xφ to φ plane vector x _k (Fig 82)
First, a vector Vφ of size 1 (FIG. 83) indicating the direction of rotation in the counterclockwise direction on the φ plane, which is perpendicular to, is obtained. Next, the inner product of F and Vφ is taken and the value is taken as Fφ.

In order to consider the softness of the hair, etc., the drag force term Rθ (or R) is included in the Fθ (or Fφ) term.
φ) should be added. For example, Rθ is the previous line segment p
_It may be a function of the difference between the angles θ _k-1 (n) and θ _k (n) of _k-2 p _k-1 .

Rθ = f (θ _k (n) -θ _k-1 (n)) (Equation 11) where f is the absolute value of the difference θ _k (n) -θ _k-1 (n). It is a constant value when it is larger than a certain threshold value, and becomes 0 when this value is sufficiently close to 0. This makes it possible to adjust the drag force to weaken the external force when the line segment is likely to bend extremely.

The above is the explanation of the principle of the calculation processing method in (2), but there is only one exception processing. that is,
This is processing when the value of φ becomes 0. In this case, since the y-axis and the line segment vector have the same direction, the above θ plane cannot be defined. Therefore, in this case, the plane defined by the y-axis and the external force field vector F is defined as the θ plane.

(3) After obtaining the value at time n + 1 obtained as in (2) above, check the interference with the head for each line segment so that it does not enter the head (if the hair is long,
If there is a possibility of contact with the body, check the interference with the body. Here, for the sake of simplicity, the check with the head is described, but the interference check with the body and the subsequent processing are the same as those in the case of the head). If the line segment obtained by the method (2) hits the head or enters the inside, the position is corrected. The correction method is disclosed in, for example, Japanese Patent Application No. 3-116209.
It is possible to deal with it by the method proposed in the issue.

(4) The above-mentioned processes (1), (2),
By repeatedly calculating (3) for all hairs, the positions of all hairs at time n + 1 can be obtained.

In the above-mentioned method, the cross-judgment of hairs is not taken into consideration as in the previous embodiment.

As can be seen by paying attention to the equations 8 to 10, after fixing the hair, not only the position information at the time n-1 and the time n but also the position information at the time n + 1, the specified time. The positions at each time up to m (m> n) are sequentially calculated. This enables high-speed calculation processing.

FIG. 3 shows an example of the system configuration for realizing the above embodiments. In this system, there is a display of computer graphics and a display (31 in FIG. 3) for guidance of the interactive input processing described above.
There may be more than one depending on the application. Activation of various data / time-lapse devices, issuance of graphics commands, etc. are performed by an input editing device (32 in FIG. 3) such as a keyboard. The computer processing unit (33 in FIG. 3) processes from solving the above-mentioned dynamic equation to generating image data. The time-lapse device (34 in FIG. 3) for animation preview and final version animation creation is also linked. Furthermore, for example, the curvature energy coefficient K in the first embodiment
Those that are difficult for the user to specify, such as (a), the wind vector field fl (r, t), and the function σ representing the degree of randomness, are made into a library and used as a database (35 in FIG. 3). By doing so, animation can be created efficiently.

[0040]

According to the present invention, the movement determined depending on the external force or material such as human hair or animal feather can be realized realistically and easily as an expression of computer graphics. In other words, it is possible to efficiently create realistic hair and feather animations by using interactive processing and high-speed algorithms without depending on strict physical simulation.

[Brief description of drawings]

FIG. 1 is a basic flow of a motion generation procedure of a hair model according to the present invention.

FIG. 2 is a basic flow of a motion generation procedure of a hair model according to an embodiment of the present invention.

FIG. 3 is an exemplary configuration of a computer graphics system for implementing the present invention.

FIG. 4 is a diagram showing how to give an interpolation curve in one embodiment of the present invention.

FIG. 5 is a diagram showing a method for approximating a broken line of a hair curve according to an embodiment of the present invention.

FIG. 6 is a diagram showing a way of using a spherical coordinate system in an embodiment of the present invention.

FIG. 7 is a diagram showing how to project onto a plane having an external force field according to an embodiment of the present invention.

FIG. 8 is a diagram showing a method of projecting an external force field onto a zx plane according to an embodiment of the present invention.

[Explanation of symbols]

1 ... Definition of initial shape (hairstyle), 2 ... Input of various data for movement definition, 3 ... Preview of movement related to thinning hair curve, 4 ... desired movement, 5 ... degree of randomness regarding movement of entire hair Designation, 6 ... Compute all hair movements by probabilistic interpolation method, 7 ... Time-lapse photography, 8 ... Desired movement, 9 ... Image output.

Claims (10)

[Claims] 1. A computer animation interactive processing method for displaying hair that is deformed by an external force, wherein (a) each hair is regarded as an elastic body, (b) an initial shape of the hair is determined, and (c) ) The user defines the external force acting on the elastic body and the attributes of the hair, and (d) for a typical number of hairs, by solving a mechanical equation expressing the deformation of the elastic body based on the external force and the attribute, The moving position from the initial shape of the hair is obtained over time, (e) the animation obtained from the result is previewed, and (f) the processes from (c) to (e) are performed until a desired result is obtained. Repeatedly, (g) a computer animation interactive processing method characterized by interpolating the movement of the obtained representative hair curve to generate the remaining hair. 2. The interactive processing method for computer animation according to claim 1, wherein the external force applied to one hair does not include the influence of other hair. 3. A virtual external force is applied to each hair instead of the influence of the other hair.
The computer animation interactive processing method described. 4. The computer animation interactive processing method according to claim 1, wherein a user gives randomness to the interpolation of the typical hair curve. 5. The computer animation interactive processing method according to claim 1, wherein the external force includes a gravity vector, and an arbitrary vector is given as the gravity vector. 6. The computer-animation interactive processing method according to claim 1, wherein the external force includes an external force generated along with the movement of the displayed target object. 7. The attribute includes the density of elastic deformation energy of hair, and the magnitude of the density of elastic deformation energy is given irrespective of the actual measurement value of actual hair. The computer animation interactive processing method described. 8. A computer-animated interactive processing device for displaying hair that is deformed by an external force, comprising an image display display, data defining contents to be displayed on the image display, gravity acting on the hair, and wind force. Input means for inputting an external constraint condition including a hair condition and an attribute condition including a hair material, a calculating means for calculating a positional change of the hair curve due to an external force for a typical number of hairs, and a hair curve obtained by the means 2. A dialogue processing apparatus for computer animation, comprising: a preview means for previewing a change in the position of 1., and an interpolating means for interpolating another typical number of hairs. 9. The computer animation dialogue processing apparatus according to claim 8, wherein said input means is capable of interactively inputting said external constraint condition and said attribute condition. 10. The computer animation dialogue processing apparatus according to claim 8, further comprising time-lapse photographing means for time-lapse photographing the state of the hair at each time, which is interpolated by the interpolation means.