CN107392985A - Move controllable shape interpolation method - Google Patents
Move controllable shape interpolation method Download PDFInfo
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- CN107392985A CN107392985A CN201710511007.3A CN201710511007A CN107392985A CN 107392985 A CN107392985 A CN 107392985A CN 201710511007 A CN201710511007 A CN 201710511007A CN 107392985 A CN107392985 A CN 107392985A
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- triangular mesh
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T13/00—Animation
- G06T13/80—2D [Two Dimensional] animation, e.g. using sprites
Abstract
Controllable shape interpolation method is moved the invention discloses a kind of, the present invention gives a source shape and a target shape, initial shape transition sequence is generated using the shape interpolation method based on trigonometric ratio, user defines a part or global skeleton in source in shape, automatically corresponding frame position is derived for middle transition shape and target shape, user edits skeleton on any intermediate shape, skeleton change is applied to whole transitional sequence by algorithm automatically, so as to generate required motion dynamic.The invention provides a kind of motion attitude control method of simple, intuitive, it is allowed to which user is operated by simple skeleton, to edit the athletic posture in whole shape transition sequence, so as to generate more life-like lively animation sequence.
Description
Technical field
The present invention relates to two-dimensional character cartoon technique field, and controllable shape interpolation method is moved more particularly, to a kind of.
Background technology
Under the active support of the government, domestic animation industry is quickly grown in recent years, and animation yield is also substantially improved.So
And making 2 D animation by traditional Freehandhand-drawing mode needs plenty of time and great number cost of manufacture.It has developed perhaps both at home and abroad
More two-dimentional business animation software, such as Adobe Flash, Toon Boom Studio etc., with aided two-dimensional cartoon making.These
Business software mainly realizes so-called " paperless cartoon " function, i.e., drawing on traditional animation teacher's paper is switched to allow animation teacher to lead to
Cross Digitizing plate to paint on computers, to facilitate the editor of material and management.But animation teacher stills need on a frame-by-frame basis to draw
2 D animation sequence, workload are still very huge.
Two-dimensional shapes gradual change is an important technology in computer animation field, glossily one shape of transition can be arrived
Another shape.Two key frames for including two-dimensional vector shape are given, by the shape in one key frame of transition to another
Shape in individual key frame, the animation sequence between key frame can be automatically generated.Therefore, two-dimensional shapes transition techniques are extensive
Applied in two-dimentional key-frame animation system.In actual use, the motion that animation teacher is often desirable to adjust in animation sequence is moved
State, to produce more vivid animation sequence.Therefore, it is necessary to provide a kind of fortune of simple, intuitive during shape retrieval
Dynamic dynamic control method.
The content of the invention
The goal of the invention of the present invention is to overcome the shortcomings of that two-dimentional drawing amount of the prior art is big, there is provided one
Kind moves controllable shape interpolation method.
To achieve these goals, the present invention uses following technical scheme：
It is a kind of to move controllable shape interpolation method, it is characterized in that, comprise the following steps：
The isomorphism trigonometric ratio of (1-1) source shape and target shape generates
Give a source shape and a target shape, user place polygon edge respectively in source shape and target shape
Boundary, the use of isomorphism triangle algorithm is that source shape and target shape generate a pair of isomorphism trigonometric ratios, the isomorphism trigonometric ratio includes
The summit of source triangular mesh and target triangular mesh, triangular mesh and target triangular mesh corresponds, and has
In identical connection side structure；
Wherein, source triangular mesh covers source shape, and target triangular mesh covers target shape, therefore source shape
Can be as the texture of target triangular mesh as the texture of source triangular mesh, target shape.
The approximate rigid interpolation method of (1-2) based on disk；
(1-3) moves controllable shape transition
First, user defines a part or global skeleton in source in shape, and each point on skeleton all falls within source three
In one triangle of hexagonal lattice；According to the triangle one between source triangular mesh and target transition triangular mesh sequence
One corresponding relation, is mapped using center of gravity, and corresponding frame position is derived for transition triangular mesh and target triangular mesh；
User edits the skeleton on transition triangular mesh corresponding to any interpolation moment t, t ∈ (0,1), produces new bone
Frame posture, edited skeleton is set as " control skeleton "；By double-deck mechanism of transmission, the edit effect on skeleton will be controlled
Whole shape interpolation sequence is delivered to, produces required motion dynamic.
The present invention is a kind of controllable shape interpolation method of motion.Compared to existing shape interpolation method, the present invention carries
A kind of motion attitude control method of simple, intuitive is supplied, it is allowed to which user is operated by simple skeleton, to edit whole shape
Athletic posture in transitional sequence, so as to generate more life-like lively animation sequence.
Preferably, step (1-2) comprises the following steps：
(1-2-1) sets { piBe source triangular mesh in summit set, { qiBe target triangular mesh in summit collection
Close；Wherein, each source summit piWith representative points qiIt is corresponding, to each source summit p in the triangular mesh of sourcei, obtain its ring neighbour
Each neighbours summit in domain, each neighbours summit form Local Vertex set, claim Local Vertex collection to be combined into disk Pi；
(1-2-2) is for each source summit q in target triangular meshi, obtain each neighbours top in its ring neighborhood
Point, each neighbours summit form Local Vertex set, claim Local Vertex collection to be combined into disk Qi；
(1-2-3) sets pjFor disk PiIn a point, pjIn disk QiIn corresponding points be qj, with piAnd qiFor in rotation
The heart, define local linear transformation L(i, j), L(i, j)Including spin matrix RαWith scaling component s；Wherein, α is vectorial pj-piTo vector
qj-qiThe anglec of rotation, RαFor spin matrix corresponding to anglec of rotation α, s is vectorial qj-qiLength and vectorial pj-piLength
Ratio；
(1-2-4) utilizes formula qj-qi=Rα(pj-pi) s is by pjTransform to qj, in any interpolation moment t, calculate and obtain
Vectorial pj-piWith vectorial qj-qiMiddle transition vector Rtα(pj-pi) (1-t+ts), RtαFor spin moment corresponding to anglec of rotation ta
Battle array；
(1-2-5) is setIt is source triangular mesh summit and target triangular mesh summit in moment t interpolation position
Put, by minimizing second energy functionIt is calculatedIn each summit
Position；In j be withIn i effect identical subscript,WithRepresent setIn two different summits；
(1-2-6) basisObtain the transitional sequence of source triangular mesh summit and target triangular mesh；Successively by source
Shape and target shape are attached in transitional sequence line grain table of going forward side by side as texture, obtain source shape to target shape
Natural transition cartoon sequence.
Preferably, step (1-3) comprises the following steps：
Propagation of (1-3-1) frame to frame
Using source skeleton in shape, middle transition in shape control skeleton, the skeleton in target shape as crucial skeleton,
The inherent parameter of interpolation key skeleton is (i.e.：In skeleton in the length of joint segments, skeleton joint summit angle), obtain skeleton and insert
Value sequence；Each skeleton in interpolating sequence is associated with corresponding intermediate shape.
Propagation of (1-3-2) skeleton to triangular mesh
Intermediate shape at any interpolation moment t is associated with two skeletons, and one is gone out by shape transition sequential derivation
Skeleton S, S describe the posture of the intermediate shape in Interpolation Process, and another is to edit derivative skeleton S ' by user, and S ' is retouched
The intermediate shape has been stated in the posture needed for new motion dynamic.
If { JkAnd { J 'kIt is respectively joint summit in skeleton S and S ', the appearance of intermediate shape is adjusted as follows
Gesture, make the posture of intermediate shape consistent with the required posture that skeleton S ' is described：
If k1And k2It is two joints summit of each joint segments in skeleton, calculates vectorial Jk2-Jk1To vectorial J 'k2-
J′k1Anglec of rotation b, calculate vectorial J 'k2-J′k1Length and vectorial Jk2-Jk1Length between ratio, ratio is defined
For scaling c；
If the collection of the vertex position of transition triangular mesh corresponding with intermediate shape is combined intoEach grid vertex position
PutWith the joint summit { J in skeleton SkTo constrain, calculate each joint summit JkMediation with respect to the grid vertex position is sat
MarkIt is considered as joint summit JkWith respect to grid vertex positionInfluence weights.
For each grid vertex positionA joint segments are found in skeleton S, make two joints summit of joint segments
It is rightInfluence weights sum it is minimum in all joint segments；
WillIn t α be revised as t α+b, 1-t+ts and be revised as 1-t+ts+c；
Again minimizeThe new position of transition triangular mesh is obtained, and was obtained
The new posture of shape is crossed, new posture is consistent with the required posture that skeleton S ' is described.
The present invention has an advantageous effect in that compared with background technology：2 D animation sequence can be automatically generated, can be effective
The producing efficiency of 2 D animation is improved, its cost of manufacture is greatly reduced, there is important society and economic implications.
Therefore, the present invention has the advantages that：Provide a kind of motion attitude control method of simple, intuitive, it is allowed to
User is operated by simple skeleton, more life-like so as to generate to edit the athletic posture in whole shape transition sequence
Lively animation sequence.
Brief description of the drawings
Fig. 1 is an introduces a collection shape, target shape and the corresponding isomorphism trigonometric ratio figure of the present invention；
Fig. 2 is a kind of transitional sequence figure of the triangular mesh of the present invention；
Fig. 3 is the transitional sequence of the shape of the present invention and a kind of schematic diagram for being defined on the skeleton of source in shape；
Fig. 4 is the source shape, target shape and the frame sequence in intermediate shape and edited intermediate shape of the present invention
On skeleton a kind of schematic diagram；
Fig. 5 is a kind of caused new shape transition sequence chart after editing skeleton of the present invention；
Fig. 6 is a kind of flow chart of the present invention.
Embodiment
The present invention will be further described with reference to the accompanying drawings and detailed description.
Embodiment as shown in Figure 6 is a kind of controllable shape interpolation method of motion, is comprised the following steps：
Step 100, the isomorphism trigonometric ratio of source shape and target shape generates
A source shape as shown in Figure 1 and a target shape are given, user distinguishes in source shape and target shape
Polygonal Boundary is placed, the use of isomorphism triangle algorithm is that source shape and target shape generate a pair of isomorphism trigonometric ratios, isomorphism three
Angling includes source triangular mesh and target triangular mesh, a pair of the summit 1 of triangular mesh and target triangular mesh
Should, and with identical connection side structure；
Wherein, source triangular mesh covers source shape, and target triangular mesh covers target shape, therefore source shape
Can be as the texture of target triangular mesh as the texture of source triangular mesh, target shape.
Step 200, the approximate rigid interpolation method based on disk；
Step 210, if { piBe source triangular mesh in summit set, { qiIt is summit in target triangular mesh
Set；Wherein, each source summit piWith representative points qiIt is corresponding, to each source summit p in the triangular mesh of sourcei, obtain its ring
Each neighbours summit in neighborhood, each neighbours summit form Local Vertex set, claim Local Vertex collection to be combined into disk Pi；
Step 220, for each source summit q in target triangular meshi, obtain each neighbours top in its ring neighborhood
Point, each neighbours summit form Local Vertex set, claim Local Vertex collection to be combined into disk Qi；
Step 230, if pjFor disk PiIn a point, pjIn disk QiIn corresponding points be qj, with piAnd qiFor rotation
Center, define local linear transformation L(i, j), L(i, j)Including spin matrix RαWith scaling component s；Wherein, α is vectorial pj-piTo
Measure qj-qiThe anglec of rotation, RαFor spin matrix corresponding to anglec of rotation α, s is vectorial qj-qiLength and vectorial pj-piLength
The ratio of degree；
Step 240, formula q is utilizedj-qi=Rα(pj-pi) s is by pjTransform to qj, in any interpolation moment t ∈ [0,1], meter
Calculate and obtain vectorial pj-piWith vectorial qj-qiMiddle transition vector Rtα(pj-pi) (1-t+ts), RtαIt is corresponding for anglec of rotation ta
Spin matrix；
Step 250, setIt is source triangular mesh summit and target triangular mesh summit in moment t interpolation position
Put, by minimizing second energy functionIt is calculatedIn each summit
Position；In j be withIn i effect identical subscript,WithRepresent setIn two different summits；
Step according toObtain the transitional sequence of source triangular mesh summit as shown in Figure 2 and target triangular mesh；
Source shape and target shape are attached in transitional sequence line grain table of going forward side by side as texture successively, obtained as shown in Figure 3
Source shape to target shape natural transition cartoon sequence.
Step 300, controllable shape transition is moved
First, user defines a part as shown in Figure 3 or global skeleton in source in shape, each point on skeleton
All fall within a triangle of source triangular mesh；According between source triangular mesh and target transition triangular mesh sequence
Triangle one-to-one relationship, mapped using center of gravity, derived correspondingly for transition triangular mesh and target triangular mesh
Frame position as shown in Figure 4；
User edits the skeleton on transition triangular mesh corresponding to any interpolation moment t, t ∈ (0,1), produces new bone
Frame posture, edited skeleton is set as " control skeleton "；By following double-deck mechanism of transmission, the volume on skeleton will be controlled
Collect effect and be delivered to whole shape interpolation sequence, produce required motion dynamic as shown in Figure 5.
Step 310, propagation of the frame to frame
Using source skeleton in shape, middle transition in shape control skeleton, the skeleton in target shape as crucial skeleton,
The inherent parameter of interpolation key skeleton is (i.e.：In skeleton in the length of joint segments, skeleton joint summit angle), obtain skeleton and insert
Value sequence；Each skeleton in interpolating sequence is associated with corresponding intermediate shape.
Step 320, propagation of the skeleton to triangular mesh
Any interpolation moment t, the intermediate shape at t ∈ [0,1] place are associated with two skeletons, and one is by shape transition sequence
Derivative skeleton S, S describe the posture of the intermediate shape in Interpolation Process, and another is to edit derivative bone by user
Frame S ', S ' describe the intermediate shape in the posture needed for new motion dynamic.
If { JkAnd { J 'kIt is respectively joint summit in skeleton S and S ', the appearance of intermediate shape is adjusted as follows
Gesture, make the posture of intermediate shape consistent with the required posture that skeleton S ' is described：
If k1And k2It is two joints summit of each joint segments in skeleton, calculates vectorial Jk2-Jk1To vectorial J 'k2-
J′k1Anglec of rotation b, calculate vectorial J 'k2-J′k1Length and vectorial Jk2-Jk1Length between ratio, ratio is defined
For scaling c；
If the collection of the vertex position of transition triangular mesh corresponding with intermediate shape is combined intoEach grid vertex position
PutWith the joint summit { J in skeleton SkTo constrain, calculate each joint summit JkMediation with respect to the grid vertex position is sat
MarkIt is considered as joint summit JkWith respect to grid vertex positionInfluence weights.
For each grid vertex positionA joint segments are found in skeleton S, make two joints summit of joint segments
It is rightInfluence weights sum it is minimum in all joint segments；
WillIn t α be revised as t α+b, 1-t+ts and be revised as 1-t+ts+c；
Again minimizeThe new position of transition triangular mesh is obtained, and was obtained
The new posture of shape is crossed, as shown in figure 5, new posture is consistent with the required posture that skeleton S ' is described.
Minimize equation (1) and correspond to a linear least-squares Solve problems.By asking partially micro- to each known variables
Lead and set its value as 0, one group of linear equation can be obtained, the system of linear equations can pass through the numerical value side such as gaussian elimination or LU decomposition
Method solves to it.
It should be understood that the present embodiment is only illustrative of the invention and is not intended to limit the scope of the invention.In addition, it is to be understood that
After having read the content of the invention lectured, those skilled in the art can make various changes or modifications to the present invention, these etc.
Valency form equally falls within the application appended claims limited range.
Claims (3)
1. a kind of move controllable shape interpolation method, it is characterized in that, comprise the following steps：
The isomorphism trigonometric ratio of (1-1) source shape and target shape generates
Give a source shape and a target shape, user place Polygonal Boundary respectively in source shape and target shape,
The use of isomorphism triangle algorithm is that source shape and target shape generate a pair of isomorphism trigonometric ratios, the isomorphism trigonometric ratio includes source three
The summit of hexagonal lattice and target triangular mesh, triangular mesh and target triangular mesh corresponds, and with identical
Connection side structure in；
The approximate rigid interpolation method of (1-2) based on disk；
(1-3) moves controllable shape transition
First, user defines a part or global skeleton in source in shape, and each point on skeleton all falls within source triangle
In one triangle of grid；According to a pair of triangle 1 between source triangular mesh and target transition triangular mesh sequence
It should be related to, be mapped using center of gravity, corresponding frame position is derived for transition triangular mesh and target triangular mesh；
User edits the skeleton on transition triangular mesh corresponding to any interpolation moment t, t ∈ (0,1), produces new skeleton appearance
Gesture, edited skeleton is set as " control skeleton "；By double-deck mechanism of transmission, the edit effect transmission on skeleton will be controlled
To whole shape interpolation sequence, required motion dynamic is produced.
2. the controllable shape interpolation method of motion according to claim 1, it is characterized in that, step (1-2) includes following step
Suddenly：
(1-2-1) sets { piBe source triangular mesh in summit set, { qiBe target triangular mesh in summit set；
Wherein, each source summit piWith representative points qiIt is corresponding, to each source summit p in the triangular mesh of sourcei, obtain one ring neighbour
Each neighbours summit in domain, each neighbours summit form Local Vertex set, claim Local Vertex collection to be combined into disk Pi；
(1-2-2) is for each source summit q in target triangular meshi, each neighbours summit in one ring neighborhood is obtained,
Each neighbours summit forms Local Vertex set, claims Local Vertex collection to be combined into disk Qi；
(1-2-3) sets pjFor disk PiIn a point, pjIn disk QiIn corresponding points be qj, with piAnd qiIt is fixed for pivot
Adopted local linear transformation L(i, j), L(i, j)Including spin matrix RαWith scaling component s；Wherein, α is vectorial pj-piTo vectorial qj-qi
The anglec of rotation, RαFor spin matrix corresponding to anglec of rotation α, s is vectorial qj-qiLength and vectorial pj-piLength ratio
Value；
(1-2-4) utilizes formula qj-qi=Rα(pj-pi) s is by pjTransform to qj, in any interpolation moment t, calculate and obtain vector
pj-piWith vectorial qj-qiMiddle transition vector Rtα(pj-pi) (1-t+ts), RtαFor spin matrix corresponding to anglec of rotation ta；
(1-2-5) is setIt is source triangular mesh summit and target triangular mesh summit in moment t location of interpolation, leads to
Cross minimum second energy functionIt is calculatedIn each summit position
Put；In j be withIn i effect identical subscript,WithRepresent setIn two different summits；
(1-2-6) basisObtain the transitional sequence of source triangular mesh summit and target triangular mesh；Successively by source shape
Line grain table of going forward side by side is attached in transitional sequence as texture with target shape, obtains source shape to the nature of target shape
Transition cartoon sequence.
3. the controllable shape interpolation method of motion according to claim 2, it is characterized in that, step (1-3) includes following step
Suddenly：
Propagation of (1-3-1) frame to frame
Using source skeleton in shape, middle transition in shape control skeleton, the skeleton in target shape as crucial skeleton, interpolation
The inherent parameter of crucial skeleton, obtains skeleton interpolating sequence；Each skeleton in interpolating sequence is associated with corresponding transition shape
Shape.
Propagation of (1-3-2) skeleton to triangular mesh
Intermediate shape at any interpolation moment t is associated with two skeletons, and one is the skeleton gone out by shape transition sequential derivation
S, another is to edit derivative skeleton S ' by user；
If { JkAnd { J 'kIt is respectively joint summit in skeleton S and S ', the posture of intermediate shape is adjusted as follows, is made
The posture of intermediate shape is consistent with the required posture that skeleton S ' is described：
If k1And k2It is two joints summit of each joint segments in skeleton, calculates vectorial Jk2-Jk1To vectorial J 'k2-J′k1's
Anglec of rotation b, calculate vectorial J 'k2-J′k1Length and vectorial Jk2-Jk1Length between ratio, ratio is defined as scaling
Ratio c；
If the collection of the vertex position of transition triangular mesh corresponding with intermediate shape is combined intoEach grid vertex position
With the joint summit { J in skeleton SkTo constrain, calculate each joint summit JkWith respect to the harmonic coordinates of the grid vertex position
For each grid vertex positionA joint segments are found in skeleton S, make two joints summit pair of joint segments
Influence weights sum it is minimum in all joint segments, to make the anglec of rotation corresponding to the joint segments be b, scaling c；
WillIn t α be revised as t α+b, 1-t+ts and be revised as 1-t+ts+c；
Again minimizeThe new position of transition triangular mesh is obtained, and is obtained
The new posture of intermediate shape, new posture are consistent with the required posture that skeleton S ' is described.
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