CN102306398A - Method for deforming global energy grid based on adjustable normal numbers - Google Patents
Method for deforming global energy grid based on adjustable normal numbers Download PDFInfo
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- CN102306398A CN102306398A CN201110231271A CN201110231271A CN102306398A CN 102306398 A CN102306398 A CN 102306398A CN 201110231271 A CN201110231271 A CN 201110231271A CN 201110231271 A CN201110231271 A CN 201110231271A CN 102306398 A CN102306398 A CN 102306398A
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Abstract
The invention discloses a method for deforming a global energy grid based on adjustable normal numbers. The method comprises the following steps of: S1, inputting a grid to be deformed; S2, determining a control vertex and the position of the control vertex on the grid; S3, inputting parameters which reflect object rigid body material properties of the grid; S4, generating an initial deformed grid by using Laplace deformation; S5, applying rigid body deformation in the neighborhood of each vertex on the initial deformed grid; S6, establishing an energy function which takes the input parameters as exponent numbers, optimizing the function to obtain a new position of each vertex and obtain a deformation result of the grid; and S7, judging whether the deformation result approaches constringency, if so, ending the S7, otherwise, returning to the S5. By using the method, the deformation of grid models of a variety of materials can be efficiently simulated.
Description
Technical field
The invention belongs to technical field of digital media, the particularly a kind of grid deforming method that can simulate the object material properties.
Background technology
A grid can be become multiple shape through distortion of the mesh, this can generate model or animation sequence that meets user's request.The key of distortion of the mesh is the visual effect that can produce and can makes the result of distortion meet the general physical rule.
A kind of direct method comes model is out of shape according to physics law exactly, and the method that Terzopoulos was proposed in 1987 " Elastically deformable models " just is based on the method for physics.These class methods often need be found the solution a partial differential equation, and to find the solution these partial differential equation equations be very complicated and calculated amount is huge.
Another kind of method is based on how much method, and these class methods reach deformation result preferably through in the process of distortion, keeping the details of model.In order to make grid in the process of distortion, keep local details, mainly contain two types of work.One type of work is based on the method in grid codifferential territory, and another kind of work is to make that model conversion partially is a rigidity.The work that people such as Sorkine were done in 2004 " Laplacian surface editing " comes the local details of encoding model through the differential coordinate of part.People such as Sorkine use rigid body translation in through each local neighborhood at model and reach the purpose that keeps model detail in the work of being done in 2007 " As-rigid-as-possible surface modeling ".Top these can not be simulated the distortion of the object of various material based on methods of how much.
Summary of the invention
(1) technical matters that will solve
The purpose of this invention is to provide a kind of method based on the multiple object material distortion of how much can simulate.
(2) technical scheme
In order to solve the problems of the technologies described above, the present invention provides a kind of global energy grid deforming method based on adjustable norm, comprises step:
S1 imports grid to be out of shape;
S2 confirms control vertex and the position of control vertex on the said grid;
S3, the parameter of the said mesh rigid body material properties of input reflection;
S4 uses Laplce to be out of shape and generates initial warp mesh;
S5 uses rigid body translation in the neighborhood to each summit on the initial warp mesh;
S6, the parameter of setting up with said input is the energy function of exponent number, optimizes the new position that this function obtains each summit, obtains the deformation result of grid; And
S7 judges whether said deformation result levels off to convergence; If then finish; If not, then return S5.
Preferably; Said step S4 comprises: the weighted sum that deducts the volume coordinate of adjacent vertex through the volume coordinate with each summit on the grid; Thereby obtain the differential coordinate on each summit; The error of the differential coordinate on each summit before and after the feasible distortion is minimum under the situation of 2 norms then, thereby obtains an initial warp mesh.
Preferably, said step S5 make each bar limit of this neighborhood before the distortion after using rigid body translation with distortion after error minimum under the corresponding situation of limit in this neighborhood at Euclidean distance.
Preferably, when said parameter is 1, this optimization is changed into the canonical form that awl is optimized among the said step S6.
Preferably, among the said step S7 when the tendency of changes of the locus, summit on the grid in zero the time, deformation result levels off to convergence.
(3) beneficial effect
The global energy grid deforming method that the present invention is based on adjustable norm is used rigid body translation partially and is kept details; On the overall situation,, can simulate the distortion of the model of various material efficiently through finding the solution the distortion that a protruding optimization problem of energy that can have different norms is simulated various material.
Description of drawings
Fig. 1 is the process flow diagram that the present invention is based on the global energy grid deforming method of adjustable norm;
Fig. 2 A-2D is the corresponding different deformation effect of different parameters in one embodiment of the invention.
Embodiment
Below in conjunction with accompanying drawing and embodiment, specific embodiments of the invention describes in further detail.Following examples are used to illustrate the present invention, but are not restriction scopes of the present invention.
As shown in Figure 1, the global energy grid deforming method based on adjustable norm of the present invention comprises step: S1, import grid to be out of shape; S2 confirms control vertex and the position of control vertex on the said grid; S3, the parameter of the said mesh rigid body material properties of input reflection; S4 uses Laplce to be out of shape and generates initial warp mesh; S5 uses rigid body translation in the neighborhood to each summit on the initial warp mesh; S6, the parameter of setting up with said input is the energy function of exponent number, optimizes the new position that this function obtains each summit, obtains the deformation result of grid; S7 judges whether said deformation result levels off to convergence; If then finish; If not, then return S5.
In an embodiment of the present invention, this flow process is operated according to the following steps: (a) import any one grid model; (b) through the mutual locus of confirming control vertex and changing control vertex; (c) user input shows the parameter of object material; (d) be out of shape the initial deformation result of generation with Laplce; (e) use rigid body translation in the neighborhood to each summit on the model; (f) find the solution the position that overall majorized function obtains each summit; (g) successively to (e), (f) two stepping row iterations level off to convergence until distortion.
For (c), the parameter of the expression object material of user's input is the exponent number of global energy function, and near 1, then expression treats that the rigidity of deformable object is strong more as if this more parameters, if this more parameters is big, then representes the soft more of this object.
For (d), deduct the weighted sum of the volume coordinate of adjacent vertex through volume coordinate, thereby obtain the differential coordinate on each summit each summit on the model.The error of the differential coordinate on each summit before and after the feasible distortion is minimum under the situation of 2 norms then, thereby obtains an initial deformation result.
For (e), in same neighborhood before and after the model deformation, need to calculate a rigid body translation, make each bar limit of this neighborhood before the distortion after using this rigid body translation with distortion after error minimum under the corresponding situation of limit in this neighborhood at Euclidean distance.We decompose through the covariance matrix that the limit induced in the neighborhood before and after the model deformation is carried out svd, just can obtain this rigid body translation.
For (f), confirm the exponent number of the norm of global energy function according to the specified parameter of user.We establish this parameter is p.When p=1, we change into the canonical form that awl is optimized with this optimization, thereby can use storehouse-sdpt3 that awl optimizes situation when finding the solution p=1 of finding the solution; When p＞1 (p!=2) time, we use backtracking line search method to come this optimization problem is found the solution.
For (g), the algorithm that we proposed is the algorithm of iteration, when the tendency of changes of the locus, summit on the caused model of each iteration in zero the time, this just illustrates that iteration levels off to convergence.
Come in this way grid model is out of shape, can simulate the distortion of the model of various material efficiently.
With reference to Fig. 2 A-2D, be the corresponding no deformation effect figure of different parameters, Fig. 2 A-2D corresponding respectively parameter be 1,1.5,2,6 o'clock deformation result.When parameter was 1, corresponding result be Fig. 2 A, when parameter than hour, the rigidity of this object is stronger.Along with the increase of parameter, rigidity weakens thereupon, and like Fig. 2 D, when parameter was 6, it is comparatively soft that the material of object seems.
The above only is a preferred implementation of the present invention; Should be pointed out that for those skilled in the art, under the prerequisite that does not break away from know-why of the present invention; Can also make some improvement and replacement, these improvement and replacement also should be considered as protection scope of the present invention.
Claims (5)
1. the global energy grid deforming method based on adjustable norm is characterized in that, comprises step:
S1 imports grid to be out of shape;
S2 confirms control vertex and the position of control vertex on the said grid;
S3, the parameter of the said mesh rigid body material properties of input reflection;
S4 uses Laplce to be out of shape and generates initial warp mesh;
S5 uses rigid body translation in the neighborhood to each summit on the initial warp mesh;
S6, the parameter of setting up with said input is the energy function of exponent number, optimizes the new position that this function obtains each summit, obtains the deformation result of grid; And
S7 judges whether said deformation result levels off to convergence; If then finish; If not, then return S5.
2. the global energy grid deforming method based on adjustable norm as claimed in claim 1; It is characterized in that; Said step S4 comprises: the weighted sum that deducts the volume coordinate of adjacent vertex through the volume coordinate with each summit on the grid; Thereby obtain the differential coordinate on each summit; The error of the differential coordinate on each summit before and after the feasible distortion is minimum under the situation of 2 norms then, thereby obtains an initial warp mesh.
3. the global energy grid deforming method based on adjustable norm as claimed in claim 1; It is characterized in that, said step S5 make each bar limit of this neighborhood before the distortion after using rigid body translation with distortion after error minimum under the corresponding situation of limit in this neighborhood at Euclidean distance.
4. the global energy grid deforming method based on adjustable norm as claimed in claim 1 is characterized in that, when said parameter is 1, this optimization is changed into the canonical form that awl is optimized among the said step S6.
5. the global energy grid deforming method based on adjustable norm as claimed in claim 1 is characterized in that, among the said step S7 when the tendency of changes of the locus, summit on the grid in zero the time, deformation result levels off to convergence.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101071514A (en) * | 2006-05-12 | 2007-11-14 | 中国科学院自动化研究所 | Method for directly transferring three-dimensional model attitude |
| CN101276481A (en) * | 2008-04-16 | 2008-10-01 | 清华大学 | Method for extracting multi-dimension curvature characteristic on triangle gridding |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101071514A (en) * | 2006-05-12 | 2007-11-14 | 中国科学院自动化研究所 | Method for directly transferring three-dimensional model attitude |
| CN101276481A (en) * | 2008-04-16 | 2008-10-01 | 清华大学 | Method for extracting multi-dimension curvature characteristic on triangle gridding |
Non-Patent Citations (1)
| Title |
|---|
| OLGA SORKINE ET AL: "As-Rigid-As-Possible Surface Modeling", 《EUROGRAPHICS SYMPOSIUM ON GEOMETRY PROCESSING》 * |
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