CN107392985B - Motion-controllable shape interpolation method - Google Patents
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Abstract
The invention discloses a motion-controllable shape interpolation method, which gives a source shape and a target shape, generates an initial shape transition sequence by using a shape interpolation method based on triangulation, defines a local or global framework on the source shape by a user, automatically derives corresponding framework positions for a middle transition shape and the target shape, edits the framework on any transition shape by the user, and automatically applies framework change to the whole transition sequence by an algorithm so as to generate required motion dynamics. The invention provides a simple and visual motion gesture control method, which allows a user to edit the motion gestures in the whole shape transition sequence through simple skeleton operation, thereby generating a more vivid animation sequence.
Description
Technical Field
The invention relates to the technical field of two-dimensional character animation, in particular to a motion-controllable shape interpolation method.
Background
Under the strong support of the government, the domestic animation industry develops rapidly in recent years, and the animation yield is greatly improved. However, the two-dimensional animation by the conventional hand-drawing method requires a lot of time and a high production cost. Many two-dimensional commercial animation software such as Adobe Flash, Toon boot Studio, etc. are developed at home and abroad to assist two-dimensional animation production. These commercial software mainly implement the so-called "paperless cartoon" function, which turns the traditional paper-on-paper animators into a computer-on-paper animators through a digital tablet, to facilitate editing and managing of materials. However, the animators still need to draw two-dimensional animation sequences frame by frame, and the workload is still very large.
Two-dimensional shape morphing is an important technique in the field of computer animation to smoothly transition one shape to another. Given two key frames containing two-dimensional vector shapes, an animation sequence between key frames can be automatically generated by transitioning shapes in one key frame to shapes in another key frame. Therefore, two-dimensional shape morphing techniques are widely used in two-dimensional keyframe animation systems. In actual use, it is often desirable for an animator to adjust the dynamics of motion in an animation sequence to produce a more vivid animation sequence. Therefore, there is a need to provide a simple and intuitive method of dynamic control of motion during shape morphing.
Disclosure of Invention
The invention aims to overcome the defect of large workload of two-dimensional drawing in the prior art and provides a motion-controllable shape interpolation method.
In order to achieve the purpose, the invention adopts the following technical scheme:
a motion-controllable shape interpolation method is characterized by comprising the following steps:
(1-1) isomorphic triangularization generation of Source and target shapes
Giving a source shape and a target shape, respectively placing polygonal boundaries on the source shape and the target shape by a user, and generating a pair of isomorphic triangularization for the source shape and the target shape by using an isomorphic triangle algorithm, wherein the isomorphic triangularization comprises a source triangular mesh and a target triangular mesh, and the vertexes of the triangular meshes and the vertices of the target triangular mesh correspond to each other one by one and have the same connecting edge structure;
the source triangular mesh covers the source shape, and the target triangular mesh covers the target shape, so that the source shape can be used as the texture of the source triangular mesh, and the target shape can be used as the texture of the target triangular mesh.
(1-2) a disk-based approximate rigid interpolation method;
(1-3) motion-controllable shape transition
Firstly, a user defines a local or global framework on a source shape, and each point on the framework falls into one triangle of a source triangular mesh; according to the one-to-one correspondence relationship of the triangles between the source triangular mesh and the target transition triangular mesh sequence, using gravity mapping to derive corresponding skeleton positions for the transition triangular mesh and the target triangular mesh;
a user edits a framework on a transition triangular mesh corresponding to any interpolation time t, t ∈ (0, 1), a new framework posture is generated, the edited framework is set to be a 'control framework', and the editing effect on the control framework is transmitted to the whole shape interpolation sequence through a double-layer transmission mechanism to generate the required motion dynamic.
The invention relates to a motion-controllable shape interpolation method. Compared with the existing shape interpolation method, the invention provides a simple and visual motion posture control method, which allows a user to edit the motion posture in the whole shape transition sequence through simple skeleton operation, thereby generating a more vivid animation sequence.
Preferably, the step (1-2) comprises the steps of:
(1-2-1) is provided with { piIs the set of vertices in the source triangle mesh, { q }iThe vertex set in the target triangular mesh; wherein each source vertex piAnd target vertex qiCorrespondingly, for each source vertex p in the source triangular meshiObtaining each neighbor vertex in the ring neighborhood, each neighbor vertex forming a local vertex set, which is called as a disk Pi;
(1-2-2) for each source vertex q in the target triangular meshiObtaining each neighbor vertex in the ring neighborhood, each neighbor vertex forming a local vertex set, which is called as a disk Qi;
(1-2-3) setting pjIs a disc PiA point of (1), pjOn the disc QiThe corresponding point in (1) is qjWith piAnd q isiFor the center of rotation, a local linear transformation L is defined(i,j),L(i,j)Comprising a rotation matrix RαAnd a scaling component s, wherein α is a vector pj-piTo vector qj-qiAngle of rotation of (R)αIs a rotation matrix corresponding to the rotation angle α, s is a vector qj-qiLength of (d) and vector pj-piThe ratio of the lengths of (a);
(1-2-4) Using the formula qj-qi=Rα(pj-pi) s will be pjConversion to qjAt any interpolation time t, calculating and obtaining a vector pj-piSum vector qj-qiIntermediate transition vector R oftα(pj-pi)(1-t+ts),RtαA rotation matrix corresponding to the rotation angle ta;
(1-2-5) settingFor the interpolation positions of the vertex of the source triangular mesh and the vertex of the target triangular mesh at the moment t, by minimizing a quadratic energy functionIs calculated to obtainThe position of each vertex in the graph;j in (1) is andi in (a) acts as the same subscript,andrepresentation collectionTwo different vertices in (1);
(1-2-6) according toObtaining a transition sequence of a source triangular mesh vertex and a target triangular mesh; sequentially pasting the source shape and the target shape as textures to the transition sequence and performing linear texture fusion to obtain a natural transition animation sequence from the source shape to the target shapeAnd (4) columns.
Preferably, the step (1-3) comprises the steps of:
(1-3-1) frame-to-frame propagation
Interpolating the internal parameters of the key skeleton (namely the length of a joint section in the skeleton and the angle of a joint vertex in the skeleton) by taking the skeleton on the source shape, the control skeleton on the middle transition shape and the skeleton on the target shape as the key skeleton to obtain a skeleton interpolation sequence; each skeleton in the interpolated sequence is associated to a corresponding transition shape.
(1-3-2) propagation of skeletons to triangular meshes
The transition shape at any interpolation time t has associated with it two skeletons, one skeleton S derived from the shape transition sequence, S describing the pose of the transition shape during interpolation, and the other skeleton S ', S' derived from user editing describing the pose of the transition shape required in the new motion dynamics.
Let { JkAnd { J'kAdjusting the pose of the transition shape to conform to the desired pose described by the skeleton S' by:
let k1And k2Is the two joint vertices of each joint segment in the skeleton, and calculates the vector Jk2-Jk1To vector J'k2-J′k1The vector J 'is calculated as the rotation angle b of'k2-J′k1Length of (d) and vector Jk2-Jk1The ratio between the lengths of (a) and (b), the ratio being defined as the scaling c;
let the set of vertex positions of the transition triangular mesh corresponding to the transition shape beEach mesh vertex positionWith joint vertices { J ] in skeleton SkCalculating the vertex J of each joint for constraintkHarmonic coordinates relative to the mesh vertex positionCan be regarded as a joint vertex JkRelative mesh vertex positionInfluence of (2) on the weight.
For each mesh vertex positionFinding a joint segment in the skeleton S, and enabling two joint vertexes of the joint segment to be pairedThe sum of the influence weights of (a) is smallest in all joint segments;
will be provided withWherein t α is modified to t α + b, 1-t + ts is modified to 1-t + ts + c, and re-minimizationAnd obtaining a new position of the transition triangular mesh and a new posture of the transition shape, wherein the new posture is consistent with the required posture described by the skeleton S'.
Compared with the background technology, the invention has the following beneficial effects: the method can automatically generate the two-dimensional animation sequence, can effectively improve the production efficiency of the two-dimensional animation, greatly reduces the production cost of the two-dimensional animation, and has important social and economic significance.
Therefore, the invention has the following beneficial effects: a simple and intuitive motion gesture control method is provided, and a user is allowed to edit motion gestures in the whole shape transition sequence through simple skeleton operation, so that a more vivid and vivid animation sequence is generated.
Drawings
FIG. 1 is a diagram of a source shape, a target shape and corresponding isomorphic triangularization of the present invention;
FIG. 2 is a transition sequence diagram of the triangular mesh of the present invention;
FIG. 3 is a schematic diagram of a transition sequence of shapes and a skeleton defined over the source shape of the present invention;
FIG. 4 is a schematic diagram of the present invention of a sequence of skeletons on source shapes, target shapes and intermediate shapes and skeletons on edited intermediate shapes;
FIG. 5 is a diagram of a new shape transition sequence generated after editing the skeleton according to the present invention;
fig. 6 is a flow chart of the present invention.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
The embodiment shown in fig. 6 is a motion-controlled shape interpolation method, comprising the steps of:
Giving a source shape and a target shape as shown in FIG. 1, respectively placing polygonal boundaries on the source shape and the target shape by a user, and generating a pair of isomorphic triangularizations for the source shape and the target shape by using an isomorphic triangle algorithm, wherein the isomorphic triangularization comprises a source triangular mesh and a target triangular mesh, and the vertices of the triangular meshes and the vertices of the target triangular mesh correspond to each other one by one and have the same connecting edge structure;
the source triangular mesh covers the source shape, and the target triangular mesh covers the target shape, so that the source shape can be used as the texture of the source triangular mesh, and the target shape can be used as the texture of the target triangular mesh.
200, an approximate rigid interpolation method based on a disc;
step 210, set { piIs the set of vertices in the source triangle mesh, { q }iThe vertex set in the target triangular mesh; wherein each source vertex piAnd target vertex qiCorrespondingly, for each source vertex p in the source triangular meshiObtaining each neighbor vertex in the ring neighborhood, and each neighbor vertex forms a local vertex setThe local vertex of the scale is collected as a disc Pi;
Step 220, for each source vertex q in the target triangular meshiObtaining each neighbor vertex in the ring neighborhood, each neighbor vertex forming a local vertex set, which is called as a disk Qi;
Step 230, set pjIs a disc PiA point of (1), pjOn the disc QiThe corresponding point in (1) is qjWith piAnd q isiFor the center of rotation, a local linear transformation L is defined(i,j),L(i,j)Comprising a rotation matrix RαAnd a scaling component s, wherein α is a vector pj-piTo vector qj-qiAngle of rotation of (R)αIs a rotation matrix corresponding to the rotation angle α, s is a vector qj-qiLength of (d) and vector pj-piThe ratio of the lengths of (a);
step 240, using formula qj-qi=Rα(pj-pi) s will be pjConversion to qjAt any interpolation time t ∈ [0, 1]]Calculating and obtaining a vector pj-piSum vector qj-qiIntermediate transition vector R oftα(pj-pi)(1-t+ts),RtαA rotation matrix corresponding to the rotation angle ta;
step 250, settingFor the interpolation positions of the vertex of the source triangular mesh and the vertex of the target triangular mesh at the moment t, by minimizing a quadratic energy functionIs calculated to obtainThe position of each vertex in the graph;j in (1) is andi in (a) acts as the same subscript,andrepresentation collectionTwo different vertices in (1);
according to the steps ofObtaining a transition sequence of the source triangular mesh vertex and the target triangular mesh as shown in FIG. 2; and sequentially pasting the source shape and the target shape as textures on the transition sequence and performing linear texture fusion to obtain a natural transition animation sequence from the source shape to the target shape as shown in FIG. 3.
Firstly, a user defines a local or global skeleton as shown in fig. 3 on a source shape, and each point on the skeleton falls in one triangle of a source triangular mesh; according to the one-to-one correspondence relationship of the triangles between the source triangular mesh and the target transition triangular mesh sequence, using gravity mapping to derive corresponding skeleton positions as shown in FIG. 4 for the transition triangular mesh and the target triangular mesh;
the user edits the skeleton on the transition triangular mesh corresponding to any interpolation time t, t ∈ (0, 1), generates a new skeleton gesture, sets the edited skeleton as a 'control skeleton', and transmits the editing effect on the control skeleton to the whole shape interpolation sequence through the following double-layer transmission mechanism to generate the required motion dynamics as shown in fig. 5.
Frame-to-frame propagation, step 310
Interpolating the internal parameters of the key skeleton (namely the length of a joint section in the skeleton and the angle of a joint vertex in the skeleton) by taking the skeleton on the source shape, the control skeleton on the middle transition shape and the skeleton on the target shape as the key skeleton to obtain a skeleton interpolation sequence; each skeleton in the interpolated sequence is associated to a corresponding transition shape.
Step 320, propagation of skeleton to triangle mesh
The transition shape at any interpolation time t, t ∈ [0, 1] associates two skeletons, one skeleton S derived from the shape transition sequence, S describing the pose of the transition shape during interpolation, and the other skeleton S ', S' derived from user editing describing the pose of the transition shape required in the new motion dynamics.
Let { JkAnd { J'kAdjusting the pose of the transition shape to conform to the desired pose described by the skeleton S' by:
let k1And k2Is the two joint vertices of each joint segment in the skeleton, and calculates the vector Jk2-Jk1To vector J'k2-J′k1The vector J 'is calculated as the rotation angle b of'k2-J′k1Length of (d) and vector Jk2-Jk1The ratio between the lengths of (a) and (b), the ratio being defined as the scaling c;
let the set of vertex positions of the transition triangular mesh corresponding to the transition shape beEach mesh vertex positionWith joint vertices { J ] in skeleton SkCalculating the vertex J of each joint for constraintkHarmonic coordinates relative to the mesh vertex positionCan be regarded as a joint vertex JkRelative mesh vertex positionInfluence of (2) on the weight.
For each mesh vertex positionFinding a joint segment in the skeleton S, and enabling two joint vertexes of the joint segment to be pairedThe sum of the influence weights of (a) is smallest in all joint segments;
will be provided withWherein t α is modified to t α + b, 1-t + ts is modified to 1-t + ts + c, and re-minimizationA new position of the transition triangular mesh is obtained and a new pose of the transition shape is obtained, which, as shown in fig. 5, coincides with the desired pose described by the skeleton S'.
By solving the partial derivative for each unknown variable and setting its value to 0, a set of linear equations can be obtained, which can be solved by a numerical method such as gaussian elimination or L U decomposition.
It should be understood that this example is for illustrative purposes only and is not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
Claims (1)
1. A motion-controllable shape interpolation method is characterized by comprising the following steps:
(1-1) isomorphic triangulation generation of source and target shapes:
giving a source shape and a target shape, respectively placing polygonal boundaries on the source shape and the target shape by a user, and generating a pair of isomorphic triangularization for the source shape and the target shape by using an isomorphic triangle algorithm, wherein the isomorphic triangularization comprises a source triangular mesh and a target triangular mesh, and the vertexes of the triangular meshes and the vertices of the target triangular mesh correspond to each other one by one and have the same connecting edge structure;
(1-2) disk-based approximate rigid interpolation method:
(1-2-1) is provided with { piIs the set of vertices in the source triangle mesh, { q }iThe vertex set in the target triangular mesh; wherein each source vertex piAnd target vertex qiCorrespondingly, for each source vertex p in the source triangular meshiObtaining each neighbor vertex in the neighborhood of its ring, each neighbor vertex forming a local vertex set, called local vertex set as a disk Pi;
(1-2-2) for each source vertex q in the target triangular meshiObtaining each neighbor vertex in the neighborhood of the first ring, each neighbor vertex forming a local vertex set, which is called as a disk Qi;
(1-2-3) setting pjIs a disc PiA point of (1), pjOn the disc QiThe corresponding point in (1) is qjWith piAnd q isiFor the center of rotation, a local linear transformation L is defined(i,j),L(i,j)Comprising a rotation matrix RαAnd a scaling component s, wherein α is a vector pj-piTo vector qj-qiAngle of rotation of (R)αIs a rotation matrix corresponding to the rotation angle α, s is a vector qj-qiLength of (d) and vector pj-piThe ratio of the lengths of (a);
(1-2-4) Using the formula qj-qi=Rα(pj-pi) s will be pjConversion to qjAt any interpolation time t, calculating and obtaining a vector pj-piSum vector qj-qiIntermediate transition vector R oftα(pj-pi)(1-t+ts),RtαIs corresponding to the rotation angle taThe rotation matrix of (a);
(1-2-5) settingFor the interpolation positions of the vertex of the source triangular mesh and the vertex of the target triangular mesh at the moment t, by minimizing a quadratic energy functionIs calculated to obtainThe position of each vertex in the graph;j in (1) is andi in (a) acts as the same subscript,andrepresentation collectionTwo different vertices in (1);
(1-2-6) according toObtaining a transition sequence of a source triangular mesh vertex and a target triangular mesh; sequentially pasting the source shape and the target shape as textures to the transition sequence and performing linear texture fusion to obtain a natural transition animation sequence from the source shape to the target shape;
(1-3) motion-controllable shape transition:
firstly, a user defines a local or global framework on a source shape, and each point on the framework falls into one triangle of a source triangular mesh; according to the one-to-one correspondence relationship of the triangles between the source triangular mesh and the target transition triangular mesh sequence, using gravity mapping to derive corresponding skeleton positions for the transition triangular mesh and the target triangular mesh;
the method comprises the steps that a user edits a framework on a transition triangular mesh corresponding to any interpolation time t, t ∈ (0, 1), a new framework posture is generated, the edited framework is set to be a 'control framework', the editing effect on the control framework is transmitted to the whole shape interpolation sequence through a double-layer transmission mechanism, and the required motion dynamic state is generated;
(1-3-1) frame-to-frame propagation:
interpolating internal parameters of the key skeleton by taking the skeleton on the source shape, the control skeleton on the intermediate transition shape and the skeleton on the target shape as key skeletons to obtain a skeleton interpolation sequence; associating each skeleton in the interpolated sequence to a corresponding transition shape;
(1-3-2) propagation of the skeleton to the triangle mesh:
the transition shape at any interpolation time t is associated with two skeletons, one is a skeleton S derived from the shape transition sequence, and the other is a skeleton S' derived from the editing of a user;
let { JkAnd { J'kAdjusting the pose of the transition shape to conform to the desired pose described by the skeleton S' by:
let k1And k2Is the two joint vertices of each joint segment in the skeleton, and calculates the vector Jk2-Jk1To vector J'k2-J’k1The vector J 'is calculated as the rotation angle b of'k2-J’k1Length of (d) and vector Jk2-Jk1The ratio between the lengths of (a) and (b), the ratio being defined as the scaling c;
let the set of vertex positions of the transition triangular mesh corresponding to the transition shape beEach mesh vertex positionWith joint vertices { J ] in skeleton SkCalculating the vertex J of each joint for constraintkHarmonic coordinates relative to the mesh vertex position
For each mesh vertex positionFinding a joint segment in the skeleton S, and enabling two joint vertexes of the joint segment to be pairedThe sum of the influence weights of the joint segments is minimum in all the joint segments, and the corresponding rotation angle of the joint segment is b and the scaling ratio is c;
will be provided withWherein t α is modified to t α + b, 1-t + ts is modified to 1-t + ts + c, and re-minimizationAnd obtaining a new position of the transition triangular mesh and a new posture of the transition shape, wherein the new posture is consistent with the required posture described by the skeleton S'.
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