CN103325086A - Deformation method of three-dimensional figure based on tetrahedron coordinate system - Google Patents

Abstract

The invention discloses a deformation method of a three-dimensional figure based on a tetrahedron coordinate system. The deformation method comprises the following steps of: inputting the three-dimensional figure, calibrating the top point of the tetrahedron; obtaining a tetrahedron coordinate value of each point of the three-dimensional figure in the tetrahedron; dragging the top point of the tetrahedron to deform the tetrahedron; and obtaining the deformed three-dimensional figure. A mesh is automatically generated to envelope the whole three-dimensional figure by labeling a small quantity of feature points on the input three-dimensional figure, and the final deformation effect is obtained by directly dragging the position change of the features points to perform once interpolation. The deformation method disclosed by the invention can be realized by parallel computing, and has the advantages of being simple in operation, small in calculated quantity, real time in view effect and easy to control. Furthermore, the deformation method belongs to linear deformation, so that the before conversion and after conversion are invertible; the specific properties of the plane and the straight line in the deformation can be maintained, and the deformation from plane to camber can be realized by using a feature point encryption method, and the method is flexible and multipurpose.

Description

A kind of deformation method of the three-dimensional picture based on tetrahedral coordinate system

Technical field

The present invention relates to the computer graphic image processing technology field; More particularly, the deformation method that relates to a kind of three-dimensional picture based on tetrahedral coordinate system.

Background technology

Development and three-dimensional (Three Dimensions along with computer graphics, 3D) the progress of object data acquisition technique, the three-dimensional body data generate with the 3 D graphic data treatment technology and are well developed in the short time, wherein, the three-dimensional picture treatment technology has merged the multi-subject knowledges such as computational mathematics, image processing, computer graphics, has very widely at aspects such as film advertisement, game animation, medical analysis, geographic patterns and uses.The important component part that the deformation technology of three-dimensional picture is processed as three-dimensional picture, between the computer animation key frame, play a part very crucially in the dynamic design such as continuous smooth gradual change and special effect making or role's attitude expression, also can be applied to simultaneously the aspects such as advertisement game making.

Present topmost 3D transform technology is the Free Transform technology, Free Transform technology based on SPL and spline surface is to be proposed by first official the eighties in 20th century, although in 20 years development, obtain many improvement, but essence all is: master pattern is embedded in the comparison easy to handle parameter space, obtain the Parametric Representation of master pattern in this space, when distortion, only need to operate this parameter space, and utilize model after between the two relation calculates distortion.This technology is widely used in the main flow 3D design softwares such as Maya, 3DMax.The 3D transform technology also comprises axial deformation in addition, is mainly used in the aspects such as skin deformation.

Although having very widely at present, the Free Transform technology uses, but because the Free Transform technology generally is by regulating the position at reference mark, interpolation calculation obtains the position of other net point on the grid surface again, again each grid is carried out a texture interpolation and obtain final model deformation effect, need twice interpolation just can obtain net result, time cost is high like this.Although and the reference mark number of Free Transform is to have lacked manyly with respect to the net point number of grid surface, number is still many, causes computation complexity high.At last and since the reference mark of Free Transform technology not direct effect to figure, so can not accurately control the position that unique point will be deformed in the figure, be difficult to keep the geometric detail of tablet pattern, it generally is only applicable to the distortion of smooth figure.

Summary of the invention

The problem that exists in order to solve above-mentioned prior art, the present invention disclose a kind of deformation method of the three-dimensional picture based on tetrahedral coordinate system, and described deformation method comprises step: a) input three-dimensional picture; B) demarcate tessarace; C) the tetrahedron coordinate figure of each point in tetrahedron on the acquisition three-dimensional picture; D) drag tessarace, so that the tetrahedron distortion; E) three-dimensional picture after the acquisition distortion.

In addition, when the distortion of described three-dimensional picture is based on a plurality of tetrahedral coordinate system, in step b), by demarcating a plurality of tessaraces, divide described three-dimensional picture is carried out tetrahedral grid, the division methods of described tetrahedral grid comprises the steps: b1) set up a rectangular parallelepiped; B2) order marks n unique point on described three-dimensional picture, and any four unique points are not coplanar, and wherein, n is positive integer; B3) according to the order of the described unique point of mark, generate a plurality of tetrahedrons as tetrahedral grid.

In addition, described tetrahedral grid is with the complete envelope of described three-dimensional picture.

In addition, described rectangular parallelepiped is with the complete envelope of described three-dimensional picture.

In addition, at step b3) in, the concrete methods of realizing that generates described tetrahedral grid comprises the steps: b31) first unique point in the described n unique point is divided into 12 tetrahedrons with described rectangular parallelepiped; B32) second unique point in the described n unique point is divided into four new tetrahedrons with the tetrahedron under it, then with the deletion of the tetrahedron under described second unique point, keep and divide four new tetrahedrons that form, and then in described rectangular parallelepiped, form 15 tetrahedrons; B33) the 3rd unique point from a described n unique point is to n unique point, according to step b32) in described second unique point mode that the tetrahedron under it is divided their tetrahedrons under are separately divided, then with they tetrahedron deletions under separately, and then in rectangular parallelepiped, forming 3n-9 tetrahedron, this 3n-9 tetrahedron forms described tetrahedral grid.

In addition, at step b31) in, described first unique point is divided into 12 tetrahedral concrete methods of realizings with described rectangular parallelepiped: each face of described rectangular parallelepiped is divided into two triangles by any diagonal line of this face, described first unique point and each triangle consist of a tetrahedron, and then described rectangular parallelepiped is divided into 12 tetrahedrons.

In addition, in step c), obtain each some tetrahedron coordinate figure in the tetrahedron under it on the described three-dimensional picture, wherein, the affiliated tetrahedron of this each point is step b33) in 3n-9 the tetrahedron forming one.

In addition, in step d), with step b33) in the tessarace that forms move so that step b33) in the tetrahedron that forms be deformed into new tetrahedron.

In addition, in step e), Cartesian coordinates value according to the new tessarace that the tetrahedron under each point of the tetrahedron coordinate figure in the tetrahedron and this forms in step d) under it of each point on the described three-dimensional picture of trying to achieve in the step c), try to achieve the Cartesian coordinates value of each point on the three-dimensional picture after the distortion, and then obtain the three-dimensional picture after the distortion.

In addition, do not intersect and do not break away between a plurality of tetrahedrons before the distortion, and do not intersect and do not break away between a plurality of tetrahedrons after the distortion.

In addition, when the distortion of described three-dimensional picture is based on a tetrahedral coordinate system, in step b), by demarcate in described three-dimensional picture four not the unique point on same consist of a tetrahedron.

In addition, in step c), according to the Cartesian coordinates value of each point on the described three-dimensional picture and the Cartesian coordinates value of described tessarace, obtain the tetrahedron coordinate figure of each point in tetrahedron on the described three-dimensional picture.

In addition, in step e), Cartesian coordinates value according to the tessarace after the distortion that forms in the tetrahedron coordinate figure of each point on the described three-dimensional picture of trying to achieve in the step c) and the step d), try to achieve the Cartesian coordinates value of each point on the three-dimensional picture after the distortion, and then obtain the three-dimensional picture after the distortion.

The deformation method of the three-dimensional picture based on tetrahedral coordinate system of the present invention, by a small amount of unique point of three-dimensional picture mark in input, automatically the generating mesh envelope is lived whole three-dimensional picture, and interpolation once obtains final deformation effect by the change in location that directly drags unique point again.And deformation method of the present invention can realize with parallel computation, thus have easy and simple to handle, calculated amount is little, real-time viewing effect, is easy to the advantages such as control.In addition, deformation method of the present invention belongs to linear deformation, therefore before and after conversion reversible, both can in distortion, can keep plane, special properties that straight line has constant, also can utilize the unique point enciphered method to realize that the plane to the distortion of curved surface, has flexible multi-purpose characteristics.

Description of drawings

Fig. 1 is the tetrahedral schematic diagram that is used for defining according to an embodiment of the invention tetrahedral coordinate system.

Fig. 2 is according to an embodiment of the invention based on the process flow diagram of the deformation method of the three-dimensional picture of tetrahedral coordinate system.

Embodiment

Now embodiments of the invention are described in detail, its example shown in the accompanying drawings, wherein, identical label represents same parts all the time.Below with reference to the accompanying drawings embodiment is described to explain the present invention.In the accompanying drawings, for clarity, can exaggerate the layer and the zone thickness.In the following description, obscuring of the present invention's design that causes for fear of the unnecessary detailed description of known configurations and/or function can be omitted the unnecessary detailed description of known configurations and/or function.

In the reality, usually utilize cartesian coordinate system to describe the position of a point, a kind of new coordinate system---tetrahedral coordinate system is described the position of a point but the present invention proposes, in this coordinate system, can be easy to realize the topology distortion of three-dimensional picture, therefore, this method can be applied in the three-dimensional picture distortion.

Below will the tetrahedral coordinate system that the present invention proposes be described in detail.Fig. 1 is the tetrahedral schematic diagram that is used for defining according to an embodiment of the invention tetrahedral coordinate system.

As shown in Figure 1, there is a some P tetrahedron ABCD inside.Under cartesian coordinate system, the Cartesian coordinates value of gauge point P, A, B, C and D is respectively (Px, Py, Pz), (Ax, Ay, Az), (Bx, By, Bz), (Cx, Cy, Cz) and (Dx, Dy, Dz), then under the tetrahedral coordinate system of tetrahedron ABCD, the tetrahedron coordinate figure of some P is (Pa, Pb, Pd), wherein, the value of Pa, Pb and Pd is defined by following formula (1).

$\left\{\begin{array}{c}\mathrm{Pa}=\frac{V_{\mathrm{PBCD}}}{V_{\mathrm{ABCD}}}=\frac{\stackrel{\→}{\mathrm{CP}\·}(\stackrel{\→}{\mathrm{CB}}\×\stackrel{\→}{\mathrm{CD}})*\frac{1}{6}}{\stackrel{\→}{\mathrm{CD}}\·(\stackrel{\→}{\mathrm{CA}}\×\stackrel{\→}{\mathrm{CB}})*\frac{1}{6}}=\frac{\stackrel{\→}{\mathrm{CP}\·}(\stackrel{\→}{\mathrm{CB}}\×\stackrel{\→}{\mathrm{CD}})}{\stackrel{\→}{\mathrm{CD}}\·(\stackrel{\→}{\mathrm{CA}}\×\stackrel{\→}{\mathrm{CB}})}\\ \mathrm{Pb}=\frac{V_{\mathrm{PDAC}}}{V_{\mathrm{ABCD}}}=\frac{\stackrel{\→}{\mathrm{CP}}\·(\stackrel{\→}{\mathrm{CD}}\×\stackrel{\→}{\mathrm{CA}})*\frac{1}{6}}{\stackrel{\→}{\mathrm{CD}}\·(\stackrel{\→}{\mathrm{CA}}\×\stackrel{\→}{\mathrm{CB}})*\frac{1}{6}}=\frac{\stackrel{\→}{\mathrm{CP}}\·(\stackrel{\→}{\mathrm{CD}}\×\stackrel{\→}{\mathrm{CA}})}{\stackrel{\→}{\mathrm{CD}}\·(\stackrel{\→}{\mathrm{CA}}\×\stackrel{\→}{\mathrm{CB}})}\\ \mathrm{Pd}=\frac{V_{\mathrm{PABC}}}{V_{\mathrm{ABCD}}}=\frac{\stackrel{\→}{\mathrm{CP}}\·(\stackrel{\→}{\mathrm{CA}}\×\stackrel{\→}{\mathrm{CB}})*\frac{1}{6}}{\stackrel{\→}{\mathrm{CD}}\·(\stackrel{\→}{\mathrm{CA}}\×\stackrel{\→}{\mathrm{CB}})*\frac{1}{6}}=\frac{\stackrel{\→}{\mathrm{CP}}\·(\stackrel{\→}{\mathrm{CA}}\×\stackrel{\→}{\mathrm{CB}})}{\stackrel{\→}{\mathrm{CD}}\·(\stackrel{\→}{\mathrm{CA}}\×\stackrel{\→}{\mathrm{CB}})}\end{array}\right.---\left(1\right)$

Wherein, V _PBCD, V _PDCA, V _PABCAnd V _ABCDThe volume that represents respectively tetrahedron PBCD, PDCA, PABC and ABCD; The multiplication cross of ' * ' expression vector; The dot product of ' ' expression vector.

With hereinafter, will the inverse transformation of above-mentioned tetrahedral coordinate system be described.The inverse transformation of tetrahedral coordinate system refers to tetrahedral coordinate system is transformed into cartesian coordinate system.Specifically: under cartesian coordinate system, when being moved, the position of four summit A, B, C and the D of tetrahedron ABCD becomes summit A ', B ', C ' and D ', the position of point P is moved too and becomes a P ', but the tetrahedron that each face of some P ' and tetrahedron A ' B ' C ' D ' forms after mobile and the volume ratio of tetrahedron A ' B ' C ' D ' with mobile before put the tetrahedron of each face formation of P and tetrahedron ABCD and the volume ratio of tetrahedron ABCD remains unchanged, the tetrahedron coordinate of namely putting P does not change with the variation of the Cartesian coordinates of place tetrahedron top.The Cartesian coordinates of some P ' after the movement just can draw by following formula (2).

$\left\{\begin{array}{c}{P}^{\′}x=\mathrm{Pa}*A^{\′}x+\mathrm{Pb}*B^{\′}x+\mathrm{Pd}*D^{\′}x+(1-\mathrm{Pa}-\mathrm{Pb}-\mathrm{Pd})*C^{\′}x\\ P^{\′}y=\mathrm{Pa}*A^{\′}y+\mathrm{Pb}*B^{\′}y+\mathrm{Pd}*D^{\′}y+(1-\mathrm{Pa}-\mathrm{Pb}-\mathrm{Pd})*C^{\′}y\\ P^{\′}z=\mathrm{Pa}*A^{\′}z+\mathrm{Pb}*B^{\′}z+\mathrm{Pd}*D^{\′}z+(1-\mathrm{Pa}-\mathrm{Pb}-\mathrm{Pd})*C^{\′}z\end{array}\right.---\left(2\right)$

Herein: $P^{\′}=\left(\begin{array}{c}{P}^{\′}x\\ P^{\′}y\\ P^{\′}z\end{array}\right),$ $O=\left(\begin{array}{cccc}{A}^{\′}x& B^{\′}x& D^{\′}x& C^{\′}x\\ A^{\′}y& B^{\′}y& D^{\′}y& C^{\′}y\\ A^{\′}z& B^{\′}z& D^{\′}z& C^{\′}z\end{array}\right),$ $W=\left(\begin{array}{c}\mathrm{Pa}\\ \mathrm{Pb}\\ \mathrm{Pd}\\ 1-\mathrm{Pa}-\mathrm{Pb}-\mathrm{Pd}\end{array}\right)$

Then formula (2) can be expressed as following formula (3).

P′=OW （3）

Can be found out by formula (2) and formula (3), the conversion between cartesian coordinate system and the tetrahedral coordinate system is linear transformation.Therefore, the character that has of above-mentioned tetrahedral coordinate system comprise following some:

(1) translation, rotation, convergent-divergent unchangeability.In tetrahedral coordinate system, the translation along with the coordinate system summit of the position of a point, rotation, scaling.

(2) in tetrahedral coordinate system, line segment is still line segment along with coordinate origin after the topology distortion.

(3) in tetrahedral coordinate system, the plane is still the plane along with coordinate origin after the topology distortion.

(4) continuity of topology distortion.The topology distortion of geometric figure in 2 adjacent tetrahedral coordinate systems is continuous, and this has guaranteed the continuity of topological distortion.

Below will the deformation method based on the three-dimensional picture of tetrahedral coordinate system be described in detail.Fig. 2 is according to an embodiment of the invention based on the process flow diagram of the deformation method of the three-dimensional picture of tetrahedral coordinate system.

As shown in Figure 2, comprise step based on the deformation method of the three-dimensional picture of tetrahedral coordinate system according to an embodiment of the invention:

S1: input three-dimensional picture;

S2: demarcate tessarace;

S3: obtain the tetrahedron coordinate figure of each point in tetrahedron on the three-dimensional picture;

S4: drag tessarace, so that the tetrahedron distortion;

S5: the three-dimensional picture after obtaining to be out of shape.

Since based on the deformation method of the three-dimensional picture of single tetrahedral coordinate system and based on the deformation method of the three-dimensional picture of a plurality of tetrahedral coordinate systems in the implementation procedure of above-mentioned steps and incomplete same, therefore following we will be described respectively the two.At first, the deformation method based on the three-dimensional picture of single tetrahedral coordinate system is described.

For the deformation method based on the three-dimensional picture of single tetrahedral coordinate system, in step S1, the three-dimensional picture of input can be produced by 3D design software designs more of the prior art, for example, 3DMax or Maya software, also can be by being similar to OpenGL(Open Graphics Library) etc. the developing instrument exploitation produce, no longer elaborate at this.

In step S2, can demarcate four not unique points on same in the three-dimensional picture of input, consist of a tetrahedron.In addition, also can around three-dimensional picture, demarcate four not unique points on same.

In step S3, try to achieve the tetrahedron coordinate figure of each point on the three-dimensional picture according to above-mentioned formula (1).

In step S4, the tessarace (being above-mentioned unique point) that forms among the step S2 can be moved, so that the tetrahedron that forms among the step S2 is changed into a new tetrahedron.In addition, in this step, can the tetrahedron that form among the step S2 be changed into new tetrahedron by tetrahedral any one summit that forms among the mobile step S2, any two summits, any three summits or four summits.

In step S5, in the formula (2) that the Cartesian coordinates value substitution of the new tessarace that forms among the tetrahedron coordinate figure of each point on the three-dimensional picture of trying to achieve according to formula (1) among the step S3 and the step S4 is above-mentioned, in the hope of the Cartesian coordinates value of each point on the three-dimensional picture after the distortion, the three-dimensional picture after then obtaining to be out of shape.

In addition, the line between new tetrahedral each summit after the distortion does not intersect.

Owing to can only simply be out of shape based on the three-dimensional picture of single tetrahedral coordinate system, for example, in the design of expression design, face exaggerated deformation or other continuous modifications of cartoon role, in the time need to carrying out comparatively complicated distortion to three-dimensional picture, just need to set up a plurality of tetrahedral coordinate systems (namely forming the tetrahedral coordinate system grid).Below will the deformation method based on the three-dimensional picture of a plurality of tetrahedral coordinate systems be described.

For for the deformation method of the three-dimensional picture of a plurality of tetrahedral coordinate systems, in step S1, the three-dimensional picture of input can be produced by 3D design software designs more of the prior art, for example, 3DMax or Maya software, also can be by being similar to OpenGL(Open Graphics Library) etc. the developing instrument exploitation produce, also no longer elaborate at this.

In step S2, by demarcating a plurality of tessaraces, divide three-dimensional picture is carried out tetrahedral grid.Herein, the division methods that three-dimensional picture is carried out tetrahedral grid has determined the quality of the deformation effect of three-dimensional picture to a great extent, for so that the deformation effect of three-dimensional picture is good, the present embodiment provides a kind of division methods of three-dimensional picture being carried out automatically tetrahedral grid, but the present invention is not limited to this division methods, because the deformation effect in order to realize that nature is continuous in practice, three-dimensional picture for different structure, need to set up different tetrahedral grids covers and divides, sphere tetrahedral grid for example: namely all tetrahedrons have a common summit (being the centre of sphere), all tetrahedral other three summits all on sphere, require the sphere tetrahedral grid non-cross, do not break away from mutually (herein do not break away from mutually to refer to have and only have 1 common sides between the adjacent tetrahedron), complete envelope three-dimensional picture.Equally, also can be the external rectangular parallelepiped grid of sphere tetrahedral grid, namely outside the sphere tetrahedral grid, add again a rectangular parallelepiped, need to satisfy above-mentioned condition equally.。Division methods that the present embodiment provides requires three-dimensional picture with the complete envelope of tetrahedral grid, and its concrete methods of realizing comprises the steps:

S21: set up a rectangular parallelepiped.Wherein, this rectangular parallelepiped needs the complete envelope of whole three-dimensional picture;

S22: on three-dimensional picture the order mark n unique point as feature point set (P1, P2 ..., Pn), and any four unique points are not coplanar, and wherein, n is positive integer;

S23: by the order of mark during unique point, generate a plurality of tetrahedrons as the tetrahedron collection (T1, T2 ..., Tm), namely generate tetrahedral grid.

In step S23, generate a plurality of tetrahedral concrete methods of realizings and comprise the steps:

S231: first unique point P1 in the feature point set among the step S22 is divided into 12 tetrahedrons with the rectangular parallelepiped of setting up among the step S21;

S232: second unique point P2 in the feature point set among the step S22 is divided into four new tetrahedrons with the tetrahedron under it, then the tetrahedron under second unique point P2 is deleted, keep and divide four new tetrahedrons that form, and then in rectangular parallelepiped, form 15 tetrahedrons.

S233: from described the 3rd unique point to n unique point, the mode of the tetrahedron under it being divided according to second unique point among the step S232 is divided their tetrahedrons under separately, then with they tetrahedron deletions under separately, and then in rectangular parallelepiped, form 3n-9 tetrahedron, be among the step S23 the tetrahedron collection (T1, T2 ... Tm) m in is 3n-9, and this 3n-9 tetrahedron forms tetrahedral grid.

First unique point P1 among the step S23 is divided into 12 tetrahedral concrete methods of realizings with the rectangular parallelepiped of setting up among the step S21: each face of rectangular parallelepiped is divided into two triangles by any diagonal line of this face, first unique point P1 and each triangle consist of a tetrahedron, and then rectangular parallelepiped is divided into 12 tetrahedrons.

In step S3, try to achieve each point on three-dimensional picture tetrahedron coordinate figure in tetrahedron (tetrahedron is in 3n-9 the tetrahedron that forms among the step S233 one under this) under it according to above-mentioned formula (1).

In step S4, the tessarace that forms among the step S233 (being 8 summits of the rectangular parallelepiped set up among above-mentioned unique point and the step S21) can be moved, so that the tetrahedron that forms among the step S233 is changed into new tetrahedron.In this step, demand according to the three-dimensional picture distortion, any amount tessarace in 3n-9 the tetrahedron that forms in can mobile step S233, and for a tetrahedron in 3n-9 the tetrahedron, can move this tetrahedral any one summit, any two summits, any three summits or four summits.

In step S5, in the formula (2) that the Cartesian coordinates value substitution of the new tessarace that the tetrahedron under each point of the tetrahedron coordinate figure in the tetrahedron and this forms in step S4 under it of each point on the three-dimensional picture of trying to achieve according to formula (1) among the step S3 is above-mentioned, in the hope of the Cartesian coordinates value of each point on the three-dimensional picture after the distortion, the three-dimensional picture after then obtaining to be out of shape.

In addition, the topological structure of tetrahedral grid remains unchanged in distortion.This has just guaranteed the continuously consistent validity before and after the three-dimensional picture distortion.In other words, before distortion, do not intersect and do not break away between the 3n-9 that forms among the step S233 tetrahedron; After distortion, also do not intersect and do not break away between the 3n-9 that forms among the step S233 tetrahedron, and the annexation between each summit does not change in the tetrahedral grid (being 3n-9 tetrahedron) before and after the distortion.

In sum, according to an embodiment of the invention based on the deformation method of the three-dimensional picture of tetrahedral coordinate system, by a small amount of unique point of three-dimensional picture mark in input, automatically the generating mesh envelope is lived whole three-dimensional picture, and interpolation once obtains final deformation effect by the change in location that directly drags unique point again.And deformation method of the present invention can realize with parallel computation, thus have easy and simple to handle, calculated amount is little, real-time viewing effect, is easy to the advantages such as control.In addition, deformation method of the present invention belongs to linear deformation, therefore before and after conversion reversible, both can in distortion, can keep plane, special properties that straight line has constant, also can utilize the unique point enciphered method to realize that the plane to the distortion of curved surface, has flexible multi-purpose characteristics.

Although specifically shown with reference to its exemplary embodiment and described the present invention, but it should be appreciated by those skilled in the art, in the situation that does not break away from the spirit and scope of the present invention that claim limits, can carry out various changes on form and the details to it.

Claims (13)

1. the deformation method based on the three-dimensional picture of tetrahedral coordinate system is characterized in that, described deformation method comprises step:

A) input three-dimensional picture;

B) demarcate tessarace;

C) the tetrahedron coordinate figure of each point in tetrahedron on the acquisition three-dimensional picture;

D) drag tessarace, so that the tetrahedron distortion;

E) three-dimensional picture after the acquisition distortion.

2. deformation method according to claim 1, it is characterized in that, when the distortion of described three-dimensional picture is based on a plurality of tetrahedral coordinate system, in step b), by demarcating a plurality of tessaraces, divide described three-dimensional picture is carried out tetrahedral grid, the division methods of described tetrahedral grid comprises the steps:

B1) set up a rectangular parallelepiped;

B2) order marks n unique point on described three-dimensional picture, and any four unique points are not coplanar, and wherein, n is positive integer;

B3) according to the order of the described unique point of mark, generate a plurality of tetrahedrons as described tetrahedral grid.

3. deformation method according to claim 2 is characterized in that, described rectangular parallelepiped is with the complete envelope of described three-dimensional picture.

4. deformation method according to claim 3 is characterized in that, described tetrahedral grid is with the complete envelope of described three-dimensional picture.

5. deformation method according to claim 4 is characterized in that, at step b3) in, the concrete methods of realizing that generates described tetrahedral grid comprises the steps:

B31) first unique point in the described n unique point is divided into 12 tetrahedrons with described rectangular parallelepiped;

B32) second unique point in the described n unique point is divided into four new tetrahedrons with the tetrahedron under it, then with the deletion of the tetrahedron under described second unique point, keep and divide four new tetrahedrons that form, and then in described rectangular parallelepiped, form 15 tetrahedrons;

B33) the 3rd unique point from a described n unique point is to n unique point, according to step b32) in described second unique point mode that the tetrahedron under it is divided their tetrahedrons under are separately divided, then with they tetrahedron deletions under separately, and then in rectangular parallelepiped, forming 3n-9 tetrahedron, this 3n-9 tetrahedron forms described tetrahedral grid.

6. deformation method according to claim 5, it is characterized in that, at step b31) in, described first unique point is divided into 12 tetrahedral concrete methods of realizings with described rectangular parallelepiped: each face of described rectangular parallelepiped is divided into two triangles by any diagonal line of this face, described first unique point and each triangle consist of a tetrahedron, and then described rectangular parallelepiped is divided into 12 tetrahedrons.

7. according to claim 5 or 6 described deformation methods, it is characterized in that, in step c), obtain each some tetrahedron coordinate figure in the tetrahedron under it on the described three-dimensional picture, wherein, the affiliated tetrahedron of this each point is step b33) in 3n-9 the tetrahedron forming one.

8. deformation method according to claim 7 is characterized in that, in step d), with step b33) in the tessarace that forms move so that step b33) in the tetrahedron that forms be deformed into new tetrahedron.

9. deformation method according to claim 8, it is characterized in that, in step e), Cartesian coordinates value according to the new tessarace that the tetrahedron under each point of the tetrahedron coordinate figure in the tetrahedron and this forms in step d) under it of each point on the described three-dimensional picture of trying to achieve in the step c), try to achieve the Cartesian coordinates value of each point on the three-dimensional picture after the distortion, and then obtain the three-dimensional picture after the distortion.

10. deformation method according to claim 8, it is characterized in that, do not intersect and do not break away between 3n-9 the tetrahedron before the distortion, do not intersect and do not break away between 3n-9 after the distortion tetrahedron, and the annexation between each summit does not change in the described tetrahedral grid before and after the distortion.

11. deformation method according to claim 1, it is characterized in that, when the distortion of described three-dimensional picture is based on a tetrahedral coordinate system, in step b), by demarcate in described three-dimensional picture four not the unique point on same consist of a tetrahedron.

12. deformation method according to claim 11, it is characterized in that, in step c), according to the Cartesian coordinates value of each point on the described three-dimensional picture and the Cartesian coordinates value of described tessarace, obtain the tetrahedron coordinate figure of each point in tetrahedron on the described three-dimensional picture.

13. deformation method according to claim 12, it is characterized in that, in step e), Cartesian coordinates value according to the tessarace after the distortion that forms in the tetrahedron coordinate figure of each point on the described three-dimensional picture of trying to achieve in the step c) and the step d), try to achieve the Cartesian coordinates value of each point on the three-dimensional picture after the distortion, and then obtain the three-dimensional picture after the distortion.

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