KR100445429B1 - Method for deformable object animation - Google Patents

Abstract

The present invention relates to a method of animation of atypical objects.

The present invention includes an initialization step of modeling a structure of an atypical object using a point-3D spring model; Force acting on the material point, initialization, calculation and integration of torque; Displaying the location, velocity, posture, angular velocity update, and the result of the vaginal point on the screen; And termination check phase,

Accordingly, the mass-spring model used for the animation of the conventional atypical object by the three-dimensional spring model and the quality and the feature that the user can select a large number of elements compared to the existing mass-spring model. More intuitive and simple structure enables structural representation and animation of atypical objects.

Description

{Method for deformable object animation}

The present invention relates to an atypical object animation method, and more particularly, to an atypical object animation method for modeling and animate an atypical object with a quality point and a three-dimensional spring.

Recently, 3D animation is becoming more common due to improved performance and lower prices of computer and 3D graphics accelerator cards. In the three-dimensional game, realistic and natural animation of human body using motion capture technology is widely used, and recently, effects using atypical object animation such as hair of the main character's hair blowing or fluttering clothes are basically used. This is a trend included in game content.

An animation of an atypical object, which is distinguished from a structured or rigid animation, literally refers to an animation of an object whose shape is not fixed. Representative examples include two-dimensional objects such as cloth, clothes, and flags, and three-dimensional objects such as jelly and tubes.

Mass-spring models are widely used in current unstructured object animation. After modeling an atypical object as a set of spring-connected mass points, it calculates the force acting on the mass point by the spring and integrates it to find the new position of the mass points. The spring used here is located in three-dimensional space, but its motion is one-dimensional.

Mathematically, The force acting when a spring with a spring constant k is deformed by length x is expressed as F = -k * x. If the two mass points are connected by springs, then each mass point is subject to the same magnitude and opposite direction by the law of action reaction. In the above equation, the force acting on the mass point is proportional to the change of spring length and is not related to the spring position in space.

FIG. 1 shows the results of modeling a two-dimensional amorphous object such as cloth in a lattice form using a mass-spring model. However, if the simulation by connecting the mass points 101 only in the shape of a checkerboard does not show the same result as the actual cloth. This is because, as described above, the operation characteristic of the one-dimensional spring is operated in fact against torsion or folding. In order to compensate for this, in general, in addition to the basic expansion spring 102, the structural spring of the atypical object uses a tension spring 103 and a folding spring 104 to prevent the twist.

The pull spring 103 is connected in a diagonal direction to prevent torsion, and the folding spring 104 is connected by jumping across one mass point to provide resistance to folding.

However, in the conventional non-structured object animation using the mass-spring model, there is a disadvantage in that a spring for preventing torsion or tilting should be added to the intuitive structure, and the more complicated the structure of the atypical object, the more complicated the spring structure. There is a problem that the user is not easy to set the structure.

Accordingly, an object of the present invention is to overcome the above-mentioned problems, and an object of the present invention is to model an amorphous object as a material point-three-dimensional spring model, which is a structure of material points connected by a three-dimensional spring having resistance to pulling and folding. Afterwards, the present invention relates to an atypical object animation method in which a user can intuitively model and animate an atypical object by calculating a force and torque acting on the material by a three-dimensional spring, and integrating it to obtain a new position and attitude of the material. .

An atypical object animation method for achieving the object of the present invention comprises: an initialization step of modeling the structure of the atypical object using a material point-3D spring model; Force acting on the material point, initialization, calculation and integration of torque; Displaying the location, velocity, posture, angular velocity update, and the result of the vaginal point on the screen; And a termination check step.

1 is a block diagram for explaining a conventional mass-spring model,

2 is a block diagram for explaining a material point-three-dimensional spring model according to the present invention,

3 is a block diagram for explaining a three-dimensional amorphous object in the form of a cube according to the present invention,

4 is a flowchart illustrating a method of animation of an atypical object according to the present invention.

<Description of the symbols for the main parts of the drawings>

101: mass 102: expansion spring

103: pull spring 104: folding spring

201: Point a 202: Point b

203: three-dimensional spring 204: reference vector of material point a

205: reference vector of material point b 206: axis of rotation of material point a

207: spring expansion force acting on material point a

208: reaction force by spring expansion force

209: Torque acting on material point a

210: The force acting on the point b by the torque acting on the point a

211: reaction force due to the force acting on the material point b

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 shows a mass 101 point, an expansion spring 102, a pull spring 103 and a folding spring 104 as a schematic diagram illustrating a conventional mass-spring model.

As mentioned in the prior art, the grating structure connected only by the expansion spring 102 is easy to think intuitively, but when the square grating is deformed into a rhombus, there is no restoring force due to the operation characteristic of the one-dimensional spring. It doesn't work. A spring added to compensate for this is the pull spring 103. In addition, even when the minimum square lattice is folded as a unit, only the expansion spring 102 or the pull spring 103 has no resistance. A spring added to compensate for this is the folding spring 104. The addition of a spring to complement the structure is formalized in the two-dimensional form of atypical object, but a lot of experience or trial and error is required to supplement the structure of the three-dimensional or arbitrary atypical object.

2 is a configuration diagram for explaining the material point-three-dimensional spring model according to the present invention, and the material point a 201 and the material point b 202 are connected by a three-dimensional spring 203.

The point-three-dimensional spring model has a restoring force determined from a length vector and a point reference vector of the spring, and the reference vector of the point of the spring is set to have resistance to pull and folding in addition to the expansion force of the existing spring. An angular acceleration of the material point is formed by the restoring force, and has an expansion force by the length of the spring.

Three-dimensional spring refers to a spring that is resistant to pull and folding unlike conventional spring. For this resistance, each material point has a reference vector corresponding to the spring connected thereto. In FIG.

The force acting by the three-dimensional spring proposed by the present invention is divided into two components: expansion force and restoring force. In this case, the expansion force represents a force proportional to the length deformation of the spring, as in the conventional one-dimensional spring, and the restoring force refers to the force proportional to the difference between the reference vector having the quality point and the longitudinal vector of the spring. Resilience is a force that makes it resistant to pull and folding.

Force 207 represents the expansion force acting on the material point a, and force 208 represents the reaction force against force 207. If the spring constant is k, the expansion force is expressed as F = -k * x.

206 represents the axis of rotation of the material point a used to express the restoring force, which is a straight line passing through the center of the material point a perpendicular to the expansion vector acting on the reference vector of the material point a and the material point a. The restoring force is generated by the difference between the reference vector and the spring length vector, and the torque 209 acting on the double material point a becomes a function of the reference vector of the material point a and the spring length vector.

As a simple example, 209 acts in the spring length vector direction at 204 and may be a force proportional to the angle between the two vectors. In response to 209, the material point b acts on a reaction force 210 perpendicular to the axis of rotation 206 and the spring longitudinal vector. 210 is inversely proportional to the distance between materials a and b. For equilibrium of force, reaction force about 210 should be applied to point a and 211 represents this force.

Table 1 below is an example of force and torque calculations acting on the material point by the spring.

In Table 1, the position vectors of the material points a and b are Pa and Pb, the velocity vectors are Va and Vb, the reference vectors are Da and Db, the angular velocity vectors are Wa and Wb, the spring constant is Kp, and the springs. When the damping constant is Kd, the restoring force constant is Jp, the restoring force damping constant is Jd, and the steady state spring length is L, the force vector Fa and the angular acceleration vector Ra acting on the material point a and the force vector Fb acting on b Is a hypothetical code for a function that calculates the angular acceleration vector Rb.

function [Fa, Ra, Fb, Rb] = spring (Pa, Va, Da, Wa, Pb, Vb, Db, Wb, Kp, Kd, Jp, Jd, L) vec_ab = Pb-Pa; // vector from material a to b, i.e. vector abd = norm (vec_ab); // norm of vector ab, i.e. distance between materials a and bvec_tm = Da-vec_ab / d; // approximate equation for torque vector acting on material point a = (0, -9.8, 0); // gravitational acceleration vector Fb = Kp * vec_tm / d when positive y-axis is in the sky direction; // force acting on material b by restoring force Fa = -Fb; // reaction force to the above forces (same magnitude, opposite direction) Ra = Jp * (-vec_tm)-Jd * Wa; // torque vector acting on mass a + damping force vec_tm = Db + vec_ab / d; // approximated equation for torque vector acting on material point b tm = Kp * vec_tm / d; // force acting on quality a by restoring force Fa = Fa + tm + Kp * vec_ab / d * (d-L)-Kd * Va + g; // force acting on the material a by restoring force + expansion force + damping force + gravity Fb = Fb-tm-Kp * vec_ab / d * (d-L)-Kd * Vb + g; // reaction force of force acting on material point a by restoring force + expansion force + damping force + gravity Rb = Jp * (-vec_tm)-Jd * Wb; // torque vector acting on material point b + damping force

In Table 1, the angular velocity vector represents the speed at which the reference vector rotates by changing the attitude of the material, and the angular acceleration vector is a derivative of the angular velocity vector with respect to time. In order to solve the numerical instability that may occur during integration for position calculation, damping force is generally applied. The damping force is a force that is proportional to the magnitude of the velocity of the object and opposite in direction. The damping constant is a constant used to calculate this damping force.

One of ordinary skill in the art may prepare a more physically accurate formula based on the force and torque calculation examples shown in Table 1 above, and change the atypical object by varying the recovery coefficient according to the coordinate axis. It is possible to set various structural characteristics of. This enables the representation of atypical objects having various characteristics as compared with the conventional methods.

Figure 3 is a block diagram showing the structure of a three-dimensional amorphous object in the form of a cube. If each vertex is made of a vertex and each corner is composed of three-dimensional springs, it is possible to construct and animate structurally stable atypical cube objects.

On the other hand, if the configuration of Fig. 3 with a conventional one-dimensional spring is structurally unstable and collapsed when a force such as torsion from the outside.

4 is an overall flowchart for explaining atypical object animation in the present invention.

Referring to FIG. 4, in the atypical object animation method according to the present invention, first, the atypical object is modeled as a quality point-3D spring model and various spring constants are initialized (S10).

Subsequently, after initializing the force and torque acting on the material point by deleting the previously calculated result to calculate the expansion force and the restoring force by the three-dimensional springs (S20), the force and torque calculations shown in Table 1 above are performed. In the same manner as in the example to calculate the cumulative force and torque acting on the material point for all springs (S30).

Next, by using the cumulative calculation results of the forces and torques are numerically integrated to calculate a new position and posture of the quality point (S40). In this case, any method commonly used for numerical integration may be used, and one of ordinary skill in the art may easily apply it, and Euler's method may be applied as a simple embodiment.

After calculating the new position and attitude of the material as described above, the resulting values are updated by replacing the existing values with the existing position, speed, attitude, and angular velocity (S50).

Finally, after displaying the atypical object on the screen from the position of the quality point updated as described above or storing the position for later playback (S60). Initializing the force and torque acting on the material point by checking whether the end condition of the atypical object animation is satisfied and deleting the previously calculated result to calculate the expansion force and the restoring force by the three-dimensional springs if the end condition is not satisfied. Returning to step S20, the calculation continues and the animation ends when the end condition is satisfied (S70).

As described above, the atypical object animation method according to the present invention is a new three-dimensional method instead of the existing method which is difficult to check the stability of the structure in the atypical object animation using the material and the spring model and is complicated by adding a pull spring or a folding spring. The advantage of using springs is that it allows intuitive modeling of atypical structures of structures, and in particular, it is possible to animate atypical objects with various characteristics because users can apply various deformations to force and torque calculations. As a result, the computing performance is expected to be widely used in 3D animation and special effects in the future.

What has been described above is only one embodiment for implementing the atypical object animation method according to the present invention, and the present invention is not limited to the above-described embodiment, and the gist of the present invention as claimed in the following claims. Without departing from the scope of the present invention, any person having ordinary skill in the art will have the technical spirit of the present invention to the extent that various modifications can be made.

Claims (3)

An initialization step of modeling a structure of the atypical object using a quality point three-dimensional spring model; Force acting on the material point, initialization, calculation and integration of torque; Displaying the location, speed, posture, angular velocity update, and the result of the quality point on the screen; And Check if the end condition of the atypical object animation is satisfied, and if the end condition is not satisfied, return to the step of initializing the force and torque acting on the material point, continue the calculation, and end the animation if the end condition is satisfied. Atypical object animation method, characterized in that consisting of. The method of claim 1, wherein the initialization step for modeling the structure of the atypical object In addition to the expansion force of the existing spring, the reference vector of the material point for the spring is set to have resistance to pull and folding, and has a restoring force determined from the length vector of the spring and the reference vector of the material point. And a spring-three-dimensional spring model having expansion force by the length of the spring. An initialization step of modeling a structure of the atypical object using a quality point three-dimensional spring model; Force acting on the material point, initialization, calculation and integration of torque; Displaying the location, velocity, posture, angular velocity update, and the result of the vaginal point on the screen; And Check if the end condition of the atypical object animation is satisfied, and if the end condition is not satisfied, return to the step of initializing the force and torque acting on the material point, continue the calculation, and end the animation if the end condition is satisfied. A computer-readable recording medium having a program for executing atypical object animation.