CN101609561A - A kind of method that realizes smooth transition among animated cartoons - Google Patents

Abstract

The invention discloses a kind of method that realizes smooth transition among animated cartoons, comprise step: (a) obtain the last posture matrix of previous action and the beginning posture matrix of a back action respectively; (b) posture matrix of above-mentioned two actions is disassembled respectively be convergent-divergent, rotation, three components of translation; (c) above-mentioned convergent-divergent, rotation, three components of translation are carried out interpolation arithmetic respectively, obtain new convergent-divergent, rotation, translational component; (d) convergent-divergent, rotation, the translational component that obtains behind the above-mentioned interpolation arithmetic is integrated into the posture matrix of middle action; (e) posture matrix with above-mentioned middle action is applied to action, seamlessly transits.Animation can distortion when distinguishing feature of the present invention was middle transition, had coherent, level and smooth transition effect.

Description

A kind of method that realizes smooth transition among animated cartoons

Technical field

The present invention relates to computer image processing technology, particularly a kind of method of seamlessly transitting between the animation of realizing.

Background technology

In the animation process, we can regard role animation as the sequence of a role's key operations, and the key operations of making by motion capture or staff, their initial posture and recovery all are not quite similar.Therefore, the technology of seamlessly transitting between the animation is exactly can realize the level and smooth transition effect that links up between the key operations in order to make.Prior art can utilize computing machine according to the beginning of role's key operations, last posture, calculates two transition cartoon between the action, thereby realizes seamlessly transitting between animation.

Be smoothly transitted into another animation by an animation if desired, by interpolation arithmetic is carried out in the bone position of current action and the bone position of next action, then when upgrading animation, go out two interpolation between the position according to Time Calculation, utilize the value of calculating to upgrade the position of bone at last, just can realize two transition between animation.But if directly the matrix of the position of expression role's key operations is carried out interpolation arithmetic (as shown in Figure 1), the animation effect that draws will distortion.With the linear interpolation is example, directly each numerical value in the matrix is carried out interpolation arithmetic, and is not equal to the result to the interpolation arithmetic of each components such as convergent-divergent, rotation, translation of action.Though convergent-divergent, rotation, translation have been represented in the matrix unification, but matrix rotates with cosine function Cosine value representation, and general rotational component is represented with angle, because the exchange of angle and Cosine value is not linear, so direct interpolation can cause the distortion of transition between animation.

For example, in disclosed Chinese invention patent application CN 101223555A on July 16th, 2008, smooth transient method between a kind of animation is disclosed, adopt wherein said " snapshot and replacement " transfer behavior, make second animation just in time at that place " beginning " that first animation finishes, thereby realize the transition between first and second animations.Starting and ending action between common two different animations is different, if adopt above-mentioned " snapshot and replacement " transfer behavior, directly transit to the origination action of second animation, do not have the middle transition action, occur discontinuous between the action easily by the tenth skill of first animation.

Summary of the invention

Based on the defective that exists in the prior art, the method that the object of the present invention is to provide a kind of employing that relevant action is carried out intermediate interpolated realizes the transition between animation, have motion transition level and smooth, be connected characteristics such as link up.

The technical solution adopted in the present invention: a kind of method that realizes smooth transition among animated cartoons may further comprise the steps:

(a) obtain the last posture matrix of previous action and the beginning posture matrix of a back action respectively;

(b) posture matrix of above-mentioned two actions is disassembled respectively be convergent-divergent, rotation, three components of translation;

(c) above-mentioned convergent-divergent, rotation, three components of translation are carried out interpolation arithmetic respectively, obtain new convergent-divergent, rotation, translational component;

(d) convergent-divergent, rotation, the translational component that obtains behind the above-mentioned interpolation arithmetic is integrated into the posture matrix of middle action;

(e) posture matrix with above-mentioned middle action is applied to action, seamlessly transits.

The posture matrix of the middle action in the above-mentioned steps (d) is with the sequential combination of convergent-divergent (S) * rotation (R) * translation (T), and wherein convergent-divergent (S), rotation (R), translation (T) are respectively convergent-divergent, rotation, translational component.

Above-mentioned rotational component is expressed as $Q=\{x\sin \frac{\mathrm{\θ}}{2},y\sin \frac{\mathrm{\θ}}{2},z\sin \frac{\mathrm{\θ}}{2},\cos \frac{\mathrm{\θ}}{2}\},$ Wherein: x, y, z are vector of unit length, and θ is the anglec of rotation.The matrix representation of described rotational component is

$R(V,\mathrm{\θ})=\left[\begin{array}{ccc}\cos \mathrm{\θ}+(1-\cos \mathrm{\θ})x^2& (1-\cos \mathrm{\θ})\mathrm{yx}-\left(\sin \mathrm{\θ}\right)z& (1-\cos \mathrm{\θ})\mathrm{zx}+\left(\sin \mathrm{\θ}\right)y\\ (1-\cos \mathrm{\θ})\mathrm{xy}+\left(\sin \mathrm{\θ}\right)z& \cos +(1-\cos \mathrm{\θ})y^2& (1-\cos \mathrm{\θ})\mathrm{zy}-\left(\sin \mathrm{\θ}\right)x\\ (1-\cos \mathrm{\θ})\mathrm{xz}-\left(\sin \mathrm{\θ}\right)y& (1-\cos \mathrm{\θ})\mathrm{yz}+\left(\sin \mathrm{\θ}\right)x& \cos \mathrm{\θ}+(1-\cos \mathrm{\θ})z^2\end{array}\right],$ Wherein: x, y, z are vector of unit length, and θ is the anglec of rotation.

Above-mentioned convergent-divergent representation in components is S={S _x, S _y, S _z, wherein: S _x, S _y, S _zBe tri-vector.The matrix representation of described convergent-divergent component is

$S=\left[\begin{array}{ccc}{S}_x& 0& 0\\ 0& S_y& 0\\ 0& 0& S_z\end{array}\right],$ Wherein: S _x, S _y, S _zBe tri-vector.

Above-mentioned translational component is expressed as T={T _x, T _y, T _z, wherein: T _x, T _y, T _zBe tri-vector.The matrix representation of described translational component is

$T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ T_x& T_y& T_z& 1\end{array}\right],$ Wherein: T _x, T _y, T _zBe tri-vector.

The present invention is by extracting the bone positional value of key operations in the animation, its matrix disassembled be convergent-divergent, rotation, three components of translation, then these three components are calculated its interpolation respectively, be incorporated into an intermediary matrix at last again, again this intermediary matrix is applied in the animation, thereby seamlessly transitting between the realization animation, animation can distortion when its distinguishing feature was middle transition, had coherent, level and smooth transition effect.

Description of drawings

Fig. 1 be the direct interpolation that adopts of prior art process flow diagram;

Fig. 2 is a schematic flow sheet of the present invention.

Embodiment

Below in conjunction with accompanying drawing concrete structure of the present invention is further described.

Smooth transient method between animation of the present invention is meant in animation process, realizes the last posture (recovery) of previous action and the beginning posture (initial posture) of a back action are linked up, and makes between two actions to seamlessly transit.

As shown in Figure 2, smooth transient method of the present invention is realized by following steps:

(a) obtain the bone positional value of the last posture of previous action respectively, atrix1 represents with matrix M; And the bone positional value of the beginning posture of a back action, atrix2 represents with matrix M;

(b) the posture matrix Matrix1 of above-mentioned two actions and Matrix2 are disassembled respectively into convergent-divergent (Scaling1, Scaling2), rotation (Rotation1, Rotation2), translation (Translate1, Translate2) three components;

(c) to above-mentioned convergent-divergent (Scaling1, Scaling2), rotation (Rotation1, Rotation2), translation (Translate1, Translate2) three components carry out interpolation arithmetic respectively, obtain new convergent-divergent (Scaling), the rotation (Rotation), translation (Translate) component;

(d) convergent-divergent (Scaling) that obtains behind the above-mentioned interpolation arithmetic, rotation (Rotation), translation (Translate) component are integrated into the posture matrix Matrix of middle action;

(e) the posture matrix Matrix with above-mentioned middle action is applied to action, seamlessly transits.

Further introduce fractionation and conversion mutually between transformation matrix (posture matrix of middle action) and convergent-divergent, rotation, three components of translation below.In the present embodiment, transformation matrix gets up with convergent-divergent (S) * this sequential combination of rotation (R) * translation (T).

1, rotation matrix

Along X, Y, the matrix of Z axle rotation can be expressed as:

$R\left({\mathrm{\θ}}_x\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\θ}}_x& \sin {\mathrm{\θ}}_x\\ 0& -\sin {\mathrm{\θ}}_x& \cos {\mathrm{\θ}}_x\end{array}\right]$

$R\left({\mathrm{\θ}}_y\right)=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_y& 0& -\sin {\mathrm{\θ}}_y\\ 0& 1& 0\\ \sin {\mathrm{\θ}}_y& 0& \cos {\mathrm{\θ}}_y\end{array}\right]$

$R\left({\mathrm{\θ}}_z\right)=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_z& \sin {\mathrm{\θ}}_z& 0\\ -\sin {\mathrm{\θ}}_z& \cos {\mathrm{\θ}}_z& 0\\ 0& 0& 1\end{array}\right]$

Rotation arbitrarily can represent that the present invention represents rotation matrix with angle-axle form by above-mentioned these three combinations of matrices in the space.{ z} and an anglec of rotation θ represent for x, y just to use a vector of unit length.It is positive dirction that θ is defined as with the vector of unit length, along the number of degrees that are rotated counterclockwise.

Rotation matrix is expressed as

$R(V,\mathrm{\θ})=\left[\begin{array}{ccc}\cos \mathrm{\θ}+(1-\cos \mathrm{\θ})x^2& (1-\cos \mathrm{\θ})\mathrm{yx}-\left(\sin \mathrm{\θ}\right)z& (1-\cos \mathrm{\θ})\mathrm{zx}+\left(\sin \mathrm{\θ}\right)y\\ (1-\cos \mathrm{\θ})\mathrm{xy}+\left(\sin \mathrm{\θ}\right)z& \cos +(1-\cos \mathrm{\θ})y^2& (1-\cos \mathrm{\θ})\mathrm{zy}-\left(\sin \mathrm{\θ}\right)x\\ (1-\cos \mathrm{\θ})\mathrm{xz}-\left(\sin \mathrm{\θ}\right)y& (1-\cos \mathrm{\θ})\mathrm{yz}+\left(\sin \mathrm{\θ}\right)x& \cos \mathrm{\θ}+(1-\cos \mathrm{\θ})z^2\end{array}\right];$

Rotational component can be expressed as by the plain Q of quaternary

$Q=\{x\sin \frac{\mathrm{\θ}}{2},y\sin \frac{\mathrm{\θ}}{2},z\sin \frac{\mathrm{\θ}}{2},\cos \frac{\mathrm{\θ}}{2}\},$ Wherein: x, y, z are vector of unit length, and θ is the anglec of rotation.

By the plain Q generator matrix of quaternary M, can calculate θ by last component, and then obtain x, y, three components of z.Extract the plain Q of quaternary by matrix M, can just obtain matrix trace earlier, draw 1+2cos θ, thereby try to achieve θ, and then diagonal line both sides element is subtracted each other, obtain x, y, z respectively earlier with the element addition on the diagonal line.

2, convergent-divergent component and matrix

The convergent-divergent component can be expressed as S={S by a tri-vector _x, S _y, S _z; Scaled matrix can be expressed as $S=\left[\begin{array}{ccc}{S}_x& 0& 0\\ 0& S_y& 0\\ 0& 0& S_z\end{array}\right],$ Wherein: S _x, S _y, S _zBe tri-vector.

The exchange of convergent-divergent component and scaled matrix is fairly simple, but needs to consider to represent simultaneously when a matrix situation of convergent-divergent and rotation.Here the R{ θ that introduced with the front _xBe example, the situation of having integrated convergent-divergent and rotation when transformation matrix is described:

$M=S\×R=\left[\begin{array}{ccc}{S}_x& 0& 0\\ 0& S_y& 0\\ 0& 0& S_z\end{array}\right]\×\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\θ}}_x& \sin {\mathrm{\θ}}_x\\ 0& -\sin {\mathrm{\θ}}_x& \cos {\mathrm{\θ}}_x\end{array}\right]=\left[\begin{array}{ccc}{S}_x& 0& 0\\ 0& S_y\cos {\mathrm{\θ}}_x& S_y\sin {\mathrm{\θ}}_x\\ 0& -S_z\sin {\mathrm{\θ}}_x& S_z\cos {\mathrm{\θ}}_x\end{array}\right].$

As can be seen, the length of the row vector of M is exactly the value of corresponding zoom factor.Equally, the rotation matrix with angle-axle expression becomes to have identical feature.

So when splitting convergent-divergent and rotational component, need calculate scale value earlier, with each capable scale value of matrix, calculate rotation matrix more again divided by correspondence.

3, translational component and matrix

{ z} can not be finished by one 3 * 3 matrix for x, y owing to a three-dimensional coordinate.Needs use homogeneous coordinates x, and y, z, 1}, translation matrix is expressed as:

$T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ T_x& T_y& T_z& 1\end{array}\right],$ Wherein: T _x, T _y, T _zBe tri-vector.

The component of translation also can be represented by a tri-vector: T={T _x, T _y, T _z, the exchange of translational component and scaled matrix also is fairly simple.

Compare with the transition method of the direct interpolation shown in Fig. 1, the present invention is by extracting the bone positional value of key operations in the animation, its matrix disassembled be convergent-divergent, rotation, three components of translation, then these three components are calculated its interpolation respectively, be incorporated into an intermediary matrix at last again, again this intermediary matrix be applied in the animation, thereby realize seamlessly transitting between animation, animation can distortion when its distinguishing feature was middle transition, had coherent, level and smooth transition effect.

Claims (8)

1. a method that realizes smooth transition among animated cartoons is characterized in that, may further comprise the steps:

(a) obtain the last posture matrix of previous action and the beginning posture matrix of a back action respectively;

(b) posture matrix of above-mentioned two actions is disassembled respectively be convergent-divergent, rotation, three components of translation;

(c) above-mentioned convergent-divergent, rotation, three components of translation are carried out interpolation arithmetic respectively, obtain new convergent-divergent, rotation, translational component;

(d) convergent-divergent, rotation, the translational component that obtains behind the above-mentioned interpolation arithmetic is integrated into the posture matrix of middle action;

(e) posture matrix with above-mentioned middle action is applied to action, seamlessly transits.

2. according to the method for the described realization smooth transition among animated cartoons of claim 1, it is characterized in that, the posture matrix of the middle action in the described step (d) is with the sequential combination of convergent-divergent (S) * rotation (R) * translation (T), and wherein convergent-divergent (S), rotation (R), translation (T) are respectively convergent-divergent, rotation, translational component.

3. according to the method for the described realization smooth transition among animated cartoons of claim 2, it is characterized in that described rotational component is expressed as $Q=\{x\sin \frac{\mathrm{\θ}}{2},y\sin \frac{\mathrm{\θ}}{2},z\sin \frac{\mathrm{\θ}}{2},\cos \frac{\mathrm{\θ}}{2}\},$ Wherein: x, y, z are vector of unit length, and θ is the anglec of rotation.

4. according to the method for claim 2 or 3 described realization smooth transition among animated cartoons, it is characterized in that the matrix representation of described rotational component is

$R(V,\mathrm{\θ})=\left[\begin{array}{ccc}\cos \mathrm{\θ}-(1-\cos \mathrm{\θ})x^2& (1-\cos \mathrm{\θ})\mathrm{yx}-\left(\sin \mathrm{\θ}\right)z& (1-\cos \mathrm{\θ})\mathrm{zx}+\left(\sin \mathrm{\θ}\right)y\\ (1-\cos \mathrm{\θ})\mathrm{xy}-\left(\sin \mathrm{\θ}\right)z& \cos \mathrm{\θ}+(1-\cos \mathrm{\θ})y^2& (1-\cos \mathrm{\θ})\mathrm{zy}-\left(\sin \mathrm{\θ}\right)x\\ (1-\cos \mathrm{\θ})\mathrm{xz}-\left(\sin \mathrm{\θ}\right)y& (1-\cos \mathrm{\θ})\mathrm{yz}+\left(\sin \mathrm{\θ}\right)x& \cos \mathrm{\θ}+(1-\cos \mathrm{\θ})z^2\end{array}\right],$

Wherein: x, y, z are vector of unit length, and θ is the anglec of rotation.

5. according to the method for the described realization smooth transition among animated cartoons of claim 2, it is characterized in that described convergent-divergent representation in components is S={S _x, S _y, S _z, wherein: S _x, S _y, S _zBe tri-vector.

6. according to the method for claim 2 or 5 described realization smooth transition among animated cartoons, it is characterized in that the matrix representation of described convergent-divergent component is

$S=\left[\begin{array}{ccc}{S}_x& 0& 0\\ 0& S_y& 0\\ 0& 0& S_z\end{array}\right],$ Wherein: S _x, S _y, S _zBe tri-vector.

7. according to the method for the described realization smooth transition among animated cartoons of claim 2, it is characterized in that described translational component is expressed as T={T _x, T _y, T _z, wherein: T _x, T _y, T _zBe tri-vector.

8. according to the method for claim 2 or 7 described realization smooth transition among animated cartoons, it is characterized in that the matrix representation of described translational component is

$T=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ T_x& T_y& T_z& 1\end{array}\right],$ Wherein: T _x, T _y, T _zBe tri-vector.

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