CN107392985B - Motion-controllable shape interpolation method - Google Patents

Abstract

The invention discloses a motion-controllable shape interpolation method. The invention gives a source shape and a target shape, and uses a shape interpolation method based on triangulation to generate an initial shape transition sequence. The user defines a local or The global skeleton automatically derives the corresponding skeleton position for the intermediate transition shape and the target shape. The user edits the skeleton on any transition shape, and the algorithm automatically applies the skeleton change to the entire transition sequence to generate the required motion dynamics. The invention provides a simple and intuitive motion gesture control method, which allows the user to edit the motion gestures in the entire shape transition sequence through simple skeleton operations, thereby generating a more realistic and vivid animation sequence.

Description

Motion Controlled Shape Interpolation Method

technical field

The invention relates to the technical field of two-dimensional character animation, in particular to a motion-controllable shape interpolation method.

Background technique

With the strong support of the government, the domestic animation industry has developed rapidly in recent years, and the output of animation has also increased significantly. However, making 2D animations by traditional hand-drawn methods requires a lot of time and high production costs. Many 2D commercial animation software has been developed at home and abroad, such as Adobe Flash, Toon Boom Studio, etc., to assist 2D animation production. These commercial software mainly realize the so-called "paperless cartoon" function, that is, the traditional animator's drawing on paper is converted into allowing the animator to draw on the computer through a digital tablet, so as to facilitate the editing and management of materials. However, animators still need to draw 2D animation sequences frame by frame, and the workload is still huge.

Two-dimensional shape gradients are an important technique in the field of computer animation, enabling smooth transitions from one shape to another. Given two keyframes containing 2D vector shapes, an animation sequence between keyframes can be automatically generated by transitioning the shape in one keyframe to the shape in the other keyframe. Therefore, 2D shape gradient technology is widely used in 2D keyframe animation systems. In practical use, animators often wish to adjust the motion dynamics in an animation sequence to produce a more vivid and realistic animation sequence. Therefore, it is necessary to provide a simple and intuitive motion dynamic control method in the shape gradient process.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a motion-controllable shape interpolation method in order to overcome the problem of large workload of two-dimensional rendering in the prior art.

In order to achieve the above object, the present invention adopts the following technical solutions:

A motion-controllable shape interpolation method, characterized in that it includes the following steps:

(1-1) Isomorphic triangulation generation of source shape and target shape

Given a source shape and a target shape, the user places polygon boundaries on the source and target shapes, respectively, using the isomorphic triangle algorithm to generate a pair of isomorphic triangulations for the source and target shapes that contain the source The triangle mesh and the target triangle mesh, and the vertices of the triangle mesh and the target triangle mesh correspond one-to-one, and have the same connecting edge structure;

Among them, the source triangle mesh covers the source shape, and the target triangle mesh covers the target shape, so the source shape can be used as the texture of the source triangle mesh, and the target shape can be used as the texture of the target triangle mesh.

(1-2) Approximate rigid interpolation method based on disk;

(1-3) Motion controllable shape transition

First, the user defines a local or global skeleton on the source shape, each point on the skeleton falls within a triangle of the source triangle mesh; one by one according to the triangles between the source triangle mesh and the target transition triangle mesh sequence Correspondence, using barycentric mapping to derive the corresponding skeleton positions for the transition triangle mesh and the target triangle mesh;

The user edits the skeleton on the transition triangle mesh corresponding to any interpolation time t, t∈(0, 1), to generate a new skeleton pose, and set the edited skeleton as the "control skeleton"; through the double-layer propagation mechanism, Pass the editing effects on the control armature to the entire shape interpolation sequence, producing the desired motion dynamics.

The present invention is a motion-controllable shape interpolation method. Compared with the existing shape interpolation method, the present invention provides a simple and intuitive motion gesture control method, allowing users to edit the motion gestures in the entire shape transition sequence through simple skeleton operations, thereby generating a more realistic and vivid image. animation sequence.

As preferably, step (1-2) comprises the steps:

(1-2-1) Let { _{pi } be the set of vertices in the source triangle mesh, and {q i } be} the set of vertices in the target triangle mesh; wherein, each source vertex p _i corresponds to the target vertex qi , for each source vertex pi in the source triangle _mesh , obtain each neighbor vertex in its ring neighborhood, each neighbor vertex forms a local vertex set, and the local vertex set is called a disk _Pi ;

( _1-2-2 ) For each source vertex qi in the target triangular mesh, obtain each neighbor vertex in its ring neighborhood, and each neighbor vertex forms a local vertex set, which is called a disk _Qi ;

(1-2-3) Let p _j be a point in the disk _Pi , the corresponding point of p _j in the disk Qi is _{q j ,} take p _i and qi as the rotation centers _, define the local linear transformation L _{(i, j)} , L _{(i, j)} includes the rotation matrix R _α and the scaling component s; wherein, α is the rotation angle from the vector p _{j -pi} to the vector q _j -q _i , and R _α is the corresponding rotation angle α The rotation matrix of , s is the ratio of the length of the vector q _j -q _i to the length of the vector p _{j -pi} ;

(1-2-4) Transform p _j to q _j using the formula q _j -q _i =R _α (p _{j -pi} )s, and at any interpolation time t, calculate and obtain the vector p _{j -pi} and the vector The intermediate transition vector R _tα (p _j -p _i )(1-t+ts) of q _j -q _i , R _tα is the rotation matrix corresponding to the rotation angle ta;

为源三角形网格顶点和目标三角形网格顶点在时刻t的插值位置，通过最小化二次能量函数

计算得到

中各顶点的位置；

中的j是和

中的i作用相同的下标，

和

表示集合

中的两个不同顶点；(1-2-5) Setting

is the interpolated position of the source triangle mesh vertex and the target triangle mesh vertex at time t, by minimizing the quadratic energy function

Calculated

the position of each vertex in ;

j in is and

The i in the function is the same subscript,

and

Represents a collection

two different vertices in ;

得到源三角形网格顶点和目标三角形网格的过渡序列；依次将源形状和目标形状作为纹理贴到过渡序列上并进行线性纹理融合，得到源形状到目标形状的自然过渡动画序列。(1-2-6) According to

Obtain the transition sequence of the vertices of the source triangle mesh and the target triangle mesh; paste the source shape and the target shape as textures on the transition sequence and perform linear texture fusion to obtain a natural transition animation sequence from the source shape to the target shape.

As preferably, step (1-3) comprises the steps:

(1-3-1) Frame-to-Frame Propagation

Taking the skeleton on the source shape, the control skeleton on the intermediate transition shape, and the skeleton on the target shape as the key skeleton, interpolate the intrinsic parameters of the key skeleton (ie: the length of the joint segment in the skeleton, the angle of the joint vertex in the skeleton), and get the skeleton Interpolation sequence; associates each armature in the interpolated sequence to the corresponding transition shape.

(1-3-2) Propagation of skeleton to triangle mesh

The transition shape at any interpolation time t is associated with two skeletons, one is the skeleton S derived from the shape transition sequence, S describes the pose of the transition shape during the interpolation process, and the other is the skeleton S derived from user editing ', S' describes the pose required for this transition shape in the new motion dynamics.

Let {J _k } and {J' _k } be the joint vertices in the skeleton S and S' respectively, and adjust the pose of the transition shape through the following steps, so that the pose of the transition shape is consistent with the desired pose described by the skeleton S':

Let k ₁ and k ₂ be the two joint vertices of each joint segment in the skeleton, calculate the rotation angle b from the vector J _k2 -J _k1 to the vector J' _k2 -J' _k1 , and calculate the vector J' _k2 -J' _k1 The ratio between the length of the vector J _k2 -J _k1 and the length of the vector J k2 -J k1, the ratio is defined as the scaling ratio c;

每个网格顶点位置

以骨架S中的关节顶点{J_k}为约束，计算各个关节顶点J_k相对该网格顶点位置的调和坐标

可以看作关节顶点J_k相对网格顶点位置

的影响权值。Let the set of vertex positions of the transition triangle mesh corresponding to the transition shape be

each mesh vertex position

Taking the joint vertices {J _k } in the skeleton S as constraints, calculate the harmonic coordinates of each joint vertex J _k relative to the position of the mesh vertex

It can be regarded as the position of joint vertex J _k relative to the mesh vertex

influence weight.

在骨架S中找到一条关节段，使关节段的两个关节顶点对

的影响权值之和在所有关节段中最小；for each mesh vertex position

Find a joint segment in the skeleton S, so that the two joint vertices of the joint segment are paired

The sum of the influence weights is the smallest among all joint segments;

中的tα修改为tα+b，1-t+ts修改为1-t+ts+c；重新最小化

得到过渡三角形网格的新位置，并得到过渡形状的新姿势，新姿势与骨架S′所描述的所需姿势一致。Will

The tα in is modified to tα+b, and 1-t+ts is modified to 1-t+ts+c; re-minimize

The new position of the transition triangle mesh is obtained, and the new pose of the transition shape is obtained, which corresponds to the desired pose described by the skeleton S'.

Compared with the background technology, the present invention has the beneficial effects of automatically generating a two-dimensional animation sequence, effectively improving the production efficiency of the two-dimensional animation, greatly reducing the production cost, and having important social and economic significance.

Therefore, the present invention has the following beneficial effects: a simple and intuitive motion gesture control method is provided, allowing users to edit the motion gestures in the entire shape transition sequence through simple skeleton operations, thereby generating a more realistic and vivid animation sequence.

Description of drawings

1 is a source shape, a target shape and a corresponding isomorphic triangulation diagram of the present invention;

Fig. 2 is a kind of transition sequence diagram of triangular mesh of the present invention;

3 is a schematic diagram of a transition sequence of shapes of the present invention and a skeleton defined on a source shape;

4 is a schematic diagram of the skeleton sequence on the source shape, the target shape and the intermediate shape and the skeleton on the edited intermediate shape of the present invention;

Fig. 5 is a kind of new shape transition sequence diagram produced after editing skeleton of the present invention;

Figure 6 is a flow chart of the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

The embodiment shown in FIG. 6 is a motion-controllable shape interpolation method, which includes the following steps:

Step 100, isomorphic triangulation generation of the source shape and the target shape

Given a source shape and a target shape as shown in Figure 1, the user places polygon boundaries on the source shape and the target shape respectively, and uses the isomorphic triangle algorithm to generate a pair of isomorphic triangulations for the source shape and the target shape, isomorphic Triangulation includes the source triangle mesh and the target triangle mesh, and the vertices of the triangle mesh and the target triangle mesh correspond one-to-one, and have the same connecting edge structure;

Among them, the source triangle mesh covers the source shape, and the target triangle mesh covers the target shape, so the source shape can be used as the texture of the source triangle mesh, and the target shape can be used as the texture of the target triangle mesh.

Step 200, a disc-based approximate rigid interpolation method;

Step 210, let { _{pi } be the set of vertices in the source triangle mesh, and {q i }} be the set of vertices in the target triangle mesh; wherein, each source vertex _pi corresponds to the target vertex qi _, and the source triangle For each source vertex p _i in the grid, each neighbor vertex in its ring neighborhood is obtained, and each neighbor vertex forms a local vertex set, which is called a disk _Pi ;

Step 220, for each source vertex qi in the target triangular _mesh , obtain each neighbor vertex in its ring neighborhood, each neighbor vertex forms a local vertex set, and the local vertex set is called a disk _Qi ;

Step 230, let p _j be a point in the disk _Pi , the corresponding point of p _j in the disk Qi is _{q j ,} take p _i and q _i as the rotation centers, define a local linear transformation L _{(i, j )} , L _{(i, j)} includes the rotation matrix R _α and the scaling component s; where α is the rotation angle from the vector p _{j -pi} to the vector q _j -q _i , R _α is the rotation matrix corresponding to the rotation angle α, s is the ratio of the length of the vector q _j -q _i to the length of the vector p _{j -pi} ;

Step 240, transform p _j into q _j using the formula q _j -q _i =R _α (p _j -p _i )s, and at any interpolation moment t∈[0,1], calculate and obtain the vector p _j -p _i and the intermediate transition vector R _tα (p _j -p _i )(1-t+ts) of the vector q _j -q _i , R _tα is the rotation matrix corresponding to the rotation angle ta;

为源三角形网格顶点和目标三角形网格顶点在时刻t的插值位置，通过最小化二次能量函数

计算得到

中各顶点的位置；

中的j是和

中的i作用相同的下标，

和

表示集合

中的两个不同顶点；Step 250, set

is the interpolated position of the source triangle mesh vertex and the target triangle mesh vertex at time t, by minimizing the quadratic energy function

Calculated

the position of each vertex in ;

j in is and

The i in the function is the same subscript,

and

Represents a collection

two different vertices in ;

得到如图2所示的源三角形网格顶点和目标三角形网格的过渡序列；依次将源形状和目标形状作为纹理贴到过渡序列上并进行线性纹理融合，得到如图3所示的源形状到目标形状的自然过渡动画序列。steps according to

Obtain the transition sequence of the source triangle mesh vertices and the target triangle mesh as shown in Figure 2; paste the source shape and the target shape as textures on the transition sequence and perform linear texture fusion to obtain the source shape shown in Figure 3 Natural transition animation sequence to target shape.

Step 300, motion controllable shape transition

First, the user defines a local or global skeleton on the source shape as shown in Figure 3, each point on the skeleton falls within a triangle of the source triangle mesh; according to the source triangle mesh and the target transition triangle mesh sequence The one-to-one correspondence between the triangles, using the center of gravity mapping, derives the corresponding skeleton position as shown in Figure 4 for the transition triangle mesh and the target triangle mesh;

The user edits the skeleton on the transition triangle mesh corresponding to any interpolation time t, t ∈ (0, 1), to generate a new skeleton pose, and set the edited skeleton as the "control skeleton"; propagate through the following two layers Mechanism that passes the editing effects on the control armature to the entire shape interpolation sequence, producing the desired motion dynamics as shown in Figure 5.

Step 310, frame-to-frame propagation

Taking the skeleton on the source shape, the control skeleton on the intermediate transition shape, and the skeleton on the target shape as the key skeleton, interpolate the intrinsic parameters of the key skeleton (ie: the length of the joint segment in the skeleton, the angle of the joint vertex in the skeleton), and get the skeleton Interpolation sequence; associates each armature in the interpolated sequence to the corresponding transition shape.

Step 320, Propagation of Skeleton to Triangle Mesh

The transition shape at any interpolation time t, t ∈ [0, 1] is associated with two skeletons, one is the skeleton S derived from the shape transition sequence, S describes the pose of the transition shape during the interpolation process, and the other is The derived skeleton S' is edited by the user, and S' describes the required pose of the transition shape in the new motion dynamics.

Let {J _k } and {J' _k } be the joint vertices in the skeleton S and S' respectively, and adjust the pose of the transition shape through the following steps, so that the pose of the transition shape is consistent with the desired pose described by the skeleton S':

Let k ₁ and k ₂ be the two joint vertices of each joint segment in the skeleton, calculate the rotation angle b from the vector J _k2 -J _k1 to the vector J' _k2 -J' _k1 , and calculate the vector J' _k2 -J' _k1 The ratio between the length of the vector J _k2 -J _k1 and the length of the vector J k2 -J k1, the ratio is defined as the scaling ratio c;

每个网格顶点位置

以骨架S中的关节顶点{J_k}为约束，计算各个关节顶点J_k相对该网格顶点位置的调和坐标

可以看作关节顶点J_k相对网格顶点位置

的影响权值。Let the set of vertex positions of the transition triangle mesh corresponding to the transition shape be

each mesh vertex position

Taking the joint vertices {J _k } in the skeleton S as constraints, calculate the harmonic coordinates of each joint vertex J _k relative to the position of the mesh vertex

It can be regarded as the position of joint vertex J _k relative to the mesh vertex

influence weight.

在骨架S中找到一条关节段，使关节段的两个关节顶点对

的影响权值之和在所有关节段中最小；for each mesh vertex position

Find a joint segment in the skeleton S, so that the two joint vertices of the joint segment are paired

The sum of the influence weights is the smallest among all joint segments;

中的tα修改为tα+b，1-t+ts修改为1-t+ts+c；重新最小化

得到过渡三角形网格的新位置，并得到过渡形状的新姿势，如图5所示，新姿势与骨架S′所描述的所需姿势一致。Will

The tα in is modified to tα+b, and 1-t+ts is modified to 1-t+ts+c; re-minimize

The new position of the transition triangle mesh is obtained, and the new pose of the transition shape is obtained, as shown in Figure 5, the new pose is consistent with the desired pose described by the skeleton S'.

Minimizing equation (1) corresponds to a linear least squares solution problem. By taking the partial derivative of each unknown variable and setting its value to 0, a set of linear equations can be obtained, which can be solved by numerical methods such as Gaussian elimination or LU decomposition.

It should be understood that this embodiment is only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of the present application.

Claims (1)

1. a motion-controllable shape interpolation method, is characterized in that, comprises the steps: (1-1) Isomorphic triangulation generation of source shape and target shape: Given a source shape and a target shape, the user places polygon boundaries on the source and target shapes, respectively, using the isomorphic triangle algorithm to generate a pair of isomorphic triangulations for the source and target shapes that contain the source The triangle mesh and the target triangle mesh, and the vertices of the triangle mesh and the target triangle mesh correspond one-to-one, and have the same connecting edge structure; (1-2) Approximate rigid interpolation method based on disk: (1-2-1) Let { _{pi } be the set of vertices in the source triangle mesh, and {q i } be} the set of vertices in the target triangle mesh; wherein, each source vertex p _i corresponds to the target vertex qi , for each source vertex pi in the source triangular _mesh , obtain each neighbor vertex in its one-ring neighborhood, each neighbor vertex forms a local vertex set, and the local vertex set is called a disk _Pi ; ( _1-2-2 ) For each source vertex qi in the target triangular mesh, obtain each neighbor vertex in its one-ring neighborhood, and each neighbor vertex forms a local vertex set, which is called the disk _Qi ; (1-2-3) Let p _j be a point in the disk _Pi , the corresponding point of p _j in the disk Qi is _{q j ,} take p _i and qi as the rotation centers _, define the local linear transformation L _{(i, j)} , L _{(i, j)} includes the rotation matrix R _α and the scaling component s; wherein, α is the rotation angle from the vector p _{j -pi} to the vector q _j -q _i , and R _α is the corresponding rotation angle α The rotation matrix of , s is the ratio of the length of the vector q _j -q _i to the length of the vector p _{j -pi} ; (1-2-4) Transform p _j to q _j using the formula q _j -q _i =R _α (p _{j -pi} )s, and at any interpolation time t, calculate and obtain the vector p _{j -pi} and the vector The intermediate transition vector R _tα (p _j -p _i )(1-t+ts) of q _j -q _i , R _tα is the rotation matrix corresponding to the rotation angle ta; (1-2-5) Setting

is the interpolated position of the source triangle mesh vertex and the target triangle mesh vertex at time t, by minimizing the quadratic energy function

Calculated

the position of each vertex in ;

j in is and

The i in the function is the same subscript,

and

Represents a collection

two different vertices in ; (1-2-6) According to

Obtain the transition sequence of the vertices of the source triangle mesh and the target triangle mesh; paste the source shape and the target shape as textures on the transition sequence and perform linear texture fusion to obtain a natural transition animation sequence from the source shape to the target shape; (1-3) Motion controllable shape transition: First, the user defines a local or global skeleton on the source shape, each point on the skeleton falls within a triangle of the source triangle mesh; one by one according to the triangles between the source triangle mesh and the target transition triangle mesh sequence Correspondence, using barycentric mapping to derive the corresponding skeleton positions for the transition triangle mesh and the target triangle mesh; The user edits the skeleton on the transition triangle mesh corresponding to any interpolation time t, t∈(0, 1), to generate a new skeleton pose, and set the edited skeleton as the "control skeleton"; through the double-layer propagation mechanism, Pass edit effects on the control armature to the entire shape interpolation sequence, producing the desired motion dynamics; (1-3-1) Frame-to-frame propagation: Taking the skeleton on the source shape, the control skeleton on the intermediate transition shape, and the skeleton on the target shape as the key skeleton, interpolate the intrinsic parameters of the key skeleton to obtain the skeleton interpolation sequence; associate each skeleton in the interpolation sequence with the corresponding transition shape ; (1-3-2) Propagation of skeleton to triangle mesh: The transition shape at any interpolation time t is associated with two skeletons, one is the skeleton S derived from the shape transition sequence, and the other is the skeleton S' derived from user editing; Let {J _k } and {J' _k } be the joint vertices in the skeleton S and S' respectively, and adjust the pose of the transition shape through the following steps, so that the pose of the transition shape is consistent with the desired pose described by the skeleton S': Let k ₁ and k ₂ be the two joint vertices of each joint segment in the skeleton, calculate the rotation angle b from the vector J _k2 -J _k1 to the vector J' _k2 -J' _k1 , and calculate the vector J' _k2 -J' _k1 The ratio between the length of the vector J _k2 -J _k1 and the length of the vector J k2 -J k1, the ratio is defined as the scaling ratio c; Let the set of vertex positions of the transition triangle mesh corresponding to the transition shape be

each mesh vertex position

Taking the joint vertices {J _k } in the skeleton S as constraints, calculate the harmonic coordinates of each joint vertex J _k relative to the position of the mesh vertex

for each mesh vertex position

Find a joint segment in the skeleton S, so that the two joint vertices of the joint segment are paired

The sum of the influence weights of is the smallest among all joint segments, so that the rotation angle corresponding to the joint segment is b and the scaling ratio is c; Will

The tα in is modified to tα+b, and 1-t+ts is modified to 1-t+ts+c; re-minimize

Get a new position for the transition triangle mesh, and get a new pose for the transition shape that matches the desired pose described by the skeleton S'.

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