CN102136158B - Parallel shape interpolation method based on pre-calculated velocity field - Google Patents
Parallel shape interpolation method based on pre-calculated velocity field Download PDFInfo
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- CN102136158B CN102136158B CN201110070292.2A CN201110070292A CN102136158B CN 102136158 B CN102136158 B CN 102136158B CN 201110070292 A CN201110070292 A CN 201110070292A CN 102136158 B CN102136158 B CN 102136158B
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Abstract
The invention discloses a parallel shape interpolation method based on a pre-calculated velocity field, which belongs to the field of computer cartoons. The invention provides a novel explicit calculation method for peak tracks during the interpolation deforming process of a network model, which can better describe nonlinear deforming process like large-extent rotation and the like. Meanwhile, the parallel shape interpolation method gets rid of the restriction that a traditional method needs to solve a large equations set, and can uses equipment like an graphics accelerator card and the like to implement parallel calculation, thus being capable of realizing extremely high calculation efficiency. By the parallel shape interpolation method, corresponding angular velocity-linear velocity parameter pairs are calculated and stored at each peak during the optimization process at pre-calculated stage according to a given model waiting for interpolation; and a velocity field in space is formed by the angular velocity-linear velocity parameter pairs; then the velocity field is used for independently calculating the tracks of each peak in parallel during the real time interpolation stage according to a displaying velocity integration. The interpolation model sequences of transition cartoons can be obtained by sampling the track parameters.
Description
Technical field
The present invention relates in computer animation field, in order to make fusion between two models and the three-dimensional model shape interpolation technology of distortion special efficacy, to relate in particular to a kind of efficient shape interpolation method walking abreast based on precomputation velocity field.
Background technology
The problem of three-dimensional model being carried out to shape interpolation can be described as: two three-dimensional models that given topology is consistent, and respectively as interpolation parameter
with
time shape, require to calculate
any corresponding interpolation model of interpolation parameter in interval, each summit is at this interval corresponding track.Can realize two fusion and distortion special efficacys between model by this technology, special, this track is sampled and can be obtained the transition shape animation in sequential.
Traditional method is directly carried out linear interpolation to the corresponding vertex coordinate of setting models, this method is calculated simple, but can not be fine for the situation that comprises larger rotational component, can cause the phenomenon of significantly collapsing, its essence is cannot describe and contain the deformation process that rotates this non-linear component due to the expression formula of linear track.
Another kind of method is the interpolation method based on differential attribute, and the differential attribute of descriptive model local feature is carried out to interpolation, obtains interpolation model optimum under least square meaning afterwards by overall Solving Linear.One of representative of these class methods is the people's such as Dong Xu method, the first Grad at the each triangle surface of interpolation place, and recycling solves overall Poisson equation and obtains interpolation model.Specifically can be referring to document [Dong2005] Dong Xu, Hongxin Zhang, Qing Wang, and Hujun Bao, Poisson shape interpolation, In SPM ' 05, pages 267 – 274,2005.The advantage of these class methods is to solve well rotation interpolation problem, thereby obtains high-quality interpolation result; Shortcoming is that Interpolation Process must solve large-scale system of equations, and the cost of its room and time is all higher.
Summary of the invention
The object of the invention is to for the deficiencies in the prior art, a kind of new walked abreast shape interpolation method based on precomputation velocity field is provided.
For realizing above-mentioned object, the technical solution used in the present invention is that the walked abreast shape interpolation method based on precomputation velocity field comprises the following steps:
(1) two three-dimensional grid models corresponding to summit that topology is consistent of input;
(2) respectively the summit of described two three-dimensional grid models between build the interpolation track in shape interpolation process, described interpolation track meets the relation shown in formula (1):
（1）
In formula (1),
it is the right index value in summit;
for summit pair
speed to parameter, wherein,
be respectively the right angular velocity in summit and linear velocity parameter;
it is summit pair
trajectory displacement function;
for interpolation parameter;
(3) described speed right all summits is arranged in to overall column vector as the formula (2) to parameter:
（2）
Wherein
refer to the right number in summit,
with
for the angular velocity on all summits and linear velocity parameter,
column vector parameter being arranged in for all speed,
Recycling formula (3) is right
carry out multiple-objection optimization and obtain the angular velocity-linear velocity parameter pair after each summit place optimizes;
（3）
Wherein,
the gross energy adopting for multiple-objection optimization,
,
,
correspond respectively to interpolation condition bound energy, rotation condition energy and gradient constraint energy;
,
,
for corresponding energy weight;
(4) to the angular velocity-linear velocity parameter after the optimization obtaining in step (3) to adjusting, make the position corresponding coincidence right with the summit of inputted three-dimensional grid model of the starting point of described interpolation track and terminal;
(5) all angular velocity-linear velocity parameters of obtaining after step (4) is adjusted, to storing, are obtained to precomputation velocity field;
(6) input default interpolation parameter, in conjunction with described precomputation velocity field, the velocity field that each summit is right is carried out to integration, obtain the corresponding interpolation apex coordinate of described default interpolation parameter; According to described interpolation apex coordinate output interpolation model.
Further, the present invention in the time that user has other different default interpolation parameter, repeating said steps (6).
Further, step of the present invention (4) be angular velocity-linear velocity parameter after utilizing formula (4) to the optimization obtaining in step (3) to adjusting:
（4）
Wherein,
for the angular velocity after the optimization obtaining in step (3);
for the final speed obtaining of adjusting is to parameter;
with
be the column vector that all apex coordinates are lined up, correspond respectively to given interpolation parameter
with
time model.
The present invention is compared with background technology, the beneficial effect having is: this method can solve rotation interpolation problem well, the phenomenon of collapsing of having avoided linear interpolation to cause, simultaneously in interpolation calculation process, the velocity field obtaining on the estimation and interpolation parameter, the track position on each summit independently parallel computation obtains, and can reach high counting yield.The invention solves the efficient shape interpolation problem of three-dimensional model, can be for making fusion distortion special efficacy and the transition cartoon between two models, computer animation is contained in its application, video display special efficacy, the numerous areas such as Entertainment.
Brief description of the drawings
Fig. 1 is process flow diagram of the present invention;
Fig. 2 is rate integrating track schematic diagram;
Fig. 3 is that the different attitudes of tatou model utilize linear interpolation and this method to carry out the effect contrast figure of interpolation;
Fig. 4 is the distortion special efficacy schematic diagram between different head portrait models;
Fig. 5 is the distortion special efficacy schematic diagram between lion and the cat model of different attitudes.
Embodiment
Below in conjunction with drawings and Examples, the invention will be further described, and it is more obvious that object of the present invention and effect will become.
As shown in Figure 1, a kind of walked abreast shape interpolation method based on precomputation velocity field that the present invention proposes is divided into five steps, can regard two stages as: the wherein expression of summit interpolation track, optimization, processing and storage, can complete in pre-computation phase; The calculation procedure of summit interpolation track below completes at real time phase, and user can adjust alternately to trajectory parameters, and watches in real time the result after adjustment.
The present invention is based on the walked abreast shape interpolation method of precomputation velocity field, comprise the following steps:
(1) two three-dimensional grid models corresponding to summit that topology is consistent of input.
(2) respectively the summit of described two three-dimensional grid models between build the interpolation track in shape interpolation process.Summit is to being made up of a pair of summit of correspondence position on two three-dimensional grid models herein.Described interpolation track meets the relation shown in formula (1):
（1）
In formula (1),
it is the right index value in summit;
for summit pair
speed to parameter, wherein,
be respectively the right angular velocity in summit and linear velocity parameter;
it is summit pair
trajectory displacement function;
for interpolation parameter; Whole integral process as shown in Figure 2.Rotation amount is launched to also integration and obtains the explicit expression of displacement function about speed parameter:
（5）
In formula (5),
for unit matrix.
, wherein
for vector of unit length,
for scalar.
representation unit vector
corresponding antisymmetric matrix.
(3) described speed right all summits is arranged in to overall column vector as the formula (2) to parameter:
（2）
Wherein
refer to the right number in summit,
with
for the angular velocity on all summits and linear velocity parameter,
column vector parameter being arranged in for all speed,
Recycling formula (3) is right
carry out multiple-objection optimization and obtain the angular velocity-linear velocity parameter pair after each summit place optimizes;
（3）
Wherein,
the gross energy adopting for multiple-objection optimization,
,
,
correspond respectively to interpolation condition bound energy, rotation condition energy and gradient constraint energy;
,
,
for corresponding energy weight;
,
,
for corresponding energy weight, can be regulated by user, generally, after energy is carried out to unit normalization, the default setting of energy weight can be
.This multiple-objection optimization can solve by numerical optimization such as Gauss's Newton methods, utilizes iterative strategy to try to achieve the optimum solution under convergence state.
Introduce the expression of each energy below.
A) interpolation condition bound energy
Its implication be the beginning of requirement interpolation track and terminating point must with given model vertices position consistency, expression formula is as follows:
Wherein
with
be the column vector that all apex coordinates are lined up, correspond respectively to given interpolation parameter
with
time model.
all
the diagonal matrix that submatrix corresponding to individual summit is arranged in.
B) rotation condition energy
Its implication is to require the rotation that angular velocity is expressed in interpolation deformation process unified with linear velocity as far as possible.Consider the triangle of an interpolation deformation
, establish
for its vertex position and corresponding linear velocity when static.Its rotational speed component can be used
approximate:
Wherein
,
.
The rotational speed component at each summit place on average obtains by adjacent triangle, and they are arranged in to a column vector, obtains the rotational speed component of corresponding whole model
, wherein
be by
the matrix that combines of item.Rotation condition form of energy is as follows:
C) gradient constraint energy
Its implication is the deformation gradient rigidity as far as possible requiring in interpolation deformation process midpoint.Consider above-mentioned triangle
, establish it corresponding to interpolation parameter
time apex coordinate value be
, its deformation gradient
, wherein
be called leg-of-mutton gradient operator, wherein
for the normal vector of triangle when static.Gradient operator is arranged and obtained overall operator
, whole model is in interpolation parameter
time gradient be
.
Compose the 4th summit to triangle:
.
also analogy obtains.Pass through triangle
position on setting models, can obtain its full rank deformation gradient in whole process
, wherein
Utilize full rank deformation gradient to calculate corresponding to interpolation parameter
the deformation gradient of " approximate rigidity interpolation ":
Wherein
for the utmost point decomposes,
for rotation interpolation.Further calculate the deformation gradient of removing normal direction
All leg-of-mutton normal direction arrangement of gradients of going are become to column vector
.
Gradient constraint form of energy is:
(4) to the angular velocity-linear velocity parameter after the optimization obtaining in step (3) to adjusting, make the position corresponding coincidence right with the summit of inputted three-dimensional grid model of the starting point of described interpolation track and terminal.Adjusting the formula adopting is:
（4）
Wherein,
for the angular velocity after the optimization obtaining in step (3);
for the final speed obtaining of adjusting is to parameter;
with
be the column vector that all apex coordinates are lined up, correspond respectively to given interpolation parameter
with
time model.
(5) all angular velocity-linear velocity parameters of obtaining after step (4) is adjusted, to storing, are obtained to precomputation velocity field;
(6) input default interpolation parameter, in conjunction with described precomputation velocity field, bring speed parameter and interpolation parameter calculating trajectory displacement at each summit place into according to formula (1), add reference position and can obtain the corresponding interpolation apex coordinate of this trajectory parameters, thereby obtain interpolation model.This process is independently calculated each summit, can walk abreast and carry out.For example can utilize the hardware such as graphics acceleration card to carry out parallel computation.In the time that user has other different default interpolation parameter, repeat this step (6) to calculate its corresponding interpolation model according to different interpolation parameter.
As shown in Figure 3, the different attitudes (as shown in (a) in Fig. 3, (e) model) of given two tatou models, utilize method of the present invention can produce good interpolation effect (as shown in (f) in Fig. 3, (g), (h) model, (f), result shown in (g), (h) model corresponds respectively to interpolation parameter
), and traditional linear interpolation method is in the shank of the tatou model result (as shown in (b), (c), (d) model in Fig. 3) that can cause significantly collapsing.
As shown in Figure 4, the head portrait model (as shown in (a) in Fig. 4, (e) model) that given two difference are larger, adopt the inventive method to carry out special efficacy that interpolation can obtain being out of shape transition (as shown in (b) in Fig. 4, (c), (d) model, (b), result shown in (c), (d) model corresponds respectively to interpolation parameter
).
As shown in Figure 5, the lion of given different attitudes and cat model (as shown in (a) in Fig. 5, (e) model), adopt the inventive method to carry out interpolation and can obtain the special efficacy transition result that lion model is deformed into cat model in the time taking a step forward simultaneously (as shown in Fig. 5 (b), (c), (d) model, (b), result shown in (c), (d) model corresponds respectively to interpolation parameter
).
Claims (3)
1. the walked abreast shape interpolation method of the three-dimensional model based on precomputation velocity field in a computer animation field, for making two fusion distortion special efficacy and transition cartoon between three-dimensional model, is characterized in that, said method comprising the steps of:
(1) two three-dimensional grid models corresponding to summit that topology is consistent of input;
(2) respectively the summit of described two three-dimensional grid models between build the interpolation track in shape interpolation process, described interpolation track meets the relation shown in formula (1):
In formula (1), i is the right index value in summit; (w
i, v
i) be summit to the speed of i to parameter, wherein, w
i, v
ibe respectively the right angular velocity in summit and linear velocity parameter; d
ithe trajectory displacement function of summit to i; T is interpolation parameter; I is unit matrix, w
i=θ
ir
i, wherein r
ifor vector of unit length, θ
ifor scalar, [r
i]
×representation unit vector r
icorresponding antisymmetric matrix;
(3) described speed right all summits is arranged in to overall column vector as the formula (2) to parameter:
Wherein n refers to the number that summit is right, w
1w
nand v
1v
nfor the angular velocity on all summits and linear velocity parameter, w, v is the column vector that all speed is arranged in parameter,
Recycling formula (3) is to w, and v carries out multiple-objection optimization and obtains the angular velocity-linear velocity parameter pair after each summit place optimizes;
E(w,v)=α
2E
pose+β
2E
rot+γ
2E
grad （3）
Wherein, the gross energy that E (w, v) adopts for multiple-objection optimization, E
pose, E
rot, E
gradcorrespond respectively to interpolation condition bound energy, rotation condition energy and gradient constraint energy; α, β, γ are corresponding energy weight;
Wherein,
p
0and P
1represent the column vector that in three-dimensional grid model, all apex coordinates are lined up, the model while corresponding respectively to given interpolation parameter t=0 and t=1,
represent the diagonal matrix that in three-dimensional grid model, submatrix corresponding to all n summit is arranged in;
E
rot=|| w-W
v||
2, in formula, W represents by W
athe matrix that combines of item, wherein, W
a=-K
-1([q
1]
×[q
2]
×[q
3]
×),
represent apex coordinate and corresponding linear velocity when triangle A in three-dimensional grid model is static, wherein i=1,2,3;
in formula,
for all triangles in three-dimensional grid model are removed the deformation gradient of normal direction
the column vector that arrangement forms;
represent the deformation gradient of " approximate rigidity interpolation " that interpolation parameter is t=0.5, n
arepresent normal vector when three-dimensional grid model intermediate cam shape A is static; P
0the column vector that in three-dimensional grid model, all apex coordinates are lined up, the model during corresponding to interpolation parameter t=0; G is by all leg-of-mutton gradient operators in three-dimensional grid model
permutation and combination obtains,
expression as follows:
wherein,
the coordinate figure of the summit i that represents three-dimensional grid model intermediate cam shape A during corresponding to interpolation parameter t, wherein i=1,2,3;
(4) to the angular velocity-linear velocity parameter after the optimization obtaining in step (3) to adjusting, make the position corresponding coincidence right with the summit of inputted three-dimensional grid model of the starting point of described interpolation track and terminal;
(5) all angular velocity-linear velocity parameters of obtaining after step (4) is adjusted, to storing, are obtained to precomputation velocity field;
(6) input default interpolation parameter t, in conjunction with described precomputation velocity field, the velocity field that each summit is right is carried out to integration, obtain the corresponding interpolation apex coordinate of described default interpolation parameter; According to described interpolation apex coordinate output interpolation model, obtain two transition cartoon between described three-dimensional grid model.
2. method according to claim 1, is characterized in that: in the time that user has other different default interpolation parameter, and repeating said steps (6).
3. method according to claim 1 and 2, is characterized in that: described step (4) be angular velocity-linear velocity parameter after utilizing formula (4) to the optimization obtaining in step (3) to adjusting:
Wherein, w
opfor the angular velocity after the optimization obtaining in step (3); W ', v ' is for the final speed obtaining of adjusting is to parameter; P
0and P
1the column vector that all apex coordinates are lined up, the model while corresponding respectively to given interpolation parameter t=0 and t=1.
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| CN108759827B (en) * | 2018-03-21 | 2022-11-25 | 千寻位置网络（浙江）有限公司 | Method and device for constructing velocity field model, positioning method and system |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5850463A (en) * | 1995-06-16 | 1998-12-15 | Seiko Epson Corporation | Facial image processing method and facial image processing apparatus |
| CN101833785A (en) * | 2010-05-11 | 2010-09-15 | 浙江大学 | Controllable dynamic shape interpolation method with physical third dimension |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5850463A (en) * | 1995-06-16 | 1998-12-15 | Seiko Epson Corporation | Facial image processing method and facial image processing apparatus |
| CN101833785A (en) * | 2010-05-11 | 2010-09-15 | 浙江大学 | Controllable dynamic shape interpolation method with physical third dimension |
Non-Patent Citations (2)
| Title |
|---|
| Dong Xu et al..Poisson Shape Interpolation.《Graphical Models》.2006,第68卷(第3期),268-281. |
| Poisson Shape Interpolation;Dong Xu et al.;《Graphical Models》;20060531;第68卷(第3期);268-281 * |
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