CN103325086B - A kind of deformation method of the three-dimensional picture based on tetrahedral coordinate system - Google Patents

Abstract

The present invention discloses a kind of deformation method of the three-dimensional picture based on tetrahedral coordinate system, and it comprises step: input three-dimensional picture; Demarcate tessarace; Obtain the tetrahedron coordinate figure of each point in tetrahedron in three-dimensional picture; Drag tessarace, be out of shape to make tetrahedron; Obtain the three-dimensional picture after distortion.The present invention by marking a small amount of unique point in the three-dimensional picture of input, and automatic generating mesh envelope lives whole three-dimensional picture, then interpolation once obtains final deformation effect by directly dragging the change in location of unique point.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, and therefore, conversion is reversible, both can plane, special properties that straight line has can be kept in distortion constant, also unique point enciphered method can be utilized to realize the distortion of plane to curved surface, there is flexible multi-purpose feature.

Description

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

Technical field

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

Background technology

Along with development and the three-dimensional (ThreeDimensions of computer graphics, 3D) the progress of object data acquisition technique, three-dimensional body data genaration and 3 D graphic data treatment technology are well developed in the short time, wherein, the three-dimensional graph process technological incorporation multi-subject knowledges such as computational mathematics, image procossing, computer graphics, have and apply very widely in film advertisement, game animation, medical analysis, geographic pattern etc.The deformation technology of three-dimensional picture is as an important component part of three-dimensional graph process, play a part very crucial between computer animation key frame in continuous and derivable gradual change and the dynamic design such as special effect making or role's attitude expression, also can be applied to the aspects such as ad game making simultaneously.

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

Apply very widely although Free Transform technology has at present, but due to the position that Free Transform technology is generally by regulable control point, interpolation calculation obtains the position of other net point on grid surface again, again a texture interpolation is carried out to each grid and obtain final model deformation effect, need twice interpolation just can obtain net result, such time cost is high.Although and the reference mark number of Free Transform is lacked many relative to the net point number of grid surface, number is still many, causes computation complexity high.Finally, because the reference mark of Free Transform technology is not applied directly on figure, so can not accurately control the position that in figure, unique point will be deformed to, be difficult to the geometric detail keeping tablet pattern, it is generally only applicable to the distortion of smooth figure.

Summary of the invention

In order to solve above-mentioned prior art Problems existing, the present invention discloses 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) tessarace is demarcated; C) the tetrahedron coordinate figure of each point in tetrahedron in three-dimensional picture is obtained; D) drag tessarace, be out of shape to make tetrahedron; E) three-dimensional picture after distortion is obtained.

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

In addition, described tetrahedral grid is by complete for described three-dimensional picture envelope.

In addition, described rectangular parallelepiped is by complete for described three-dimensional picture envelope.

In addition, in step b3) in, the concrete methods of realizing generating described tetrahedral grid comprises the steps: b31) described rectangular parallelepiped is divided into 12 tetrahedrons by first unique point in a described n unique point; Tetrahedron belonging to it is divided into four new tetrahedrons by second unique point b32) in a described n unique point, then the tetrahedron belonging to described second unique point is deleted, retain four the new tetrahedrons dividing and formed, and then form 15 tetrahedrons in described rectangular parallelepiped; B33) from the unique point of the 3rd a described n unique point to the n-th unique point, according to step b32) in the tetrahedron of described second feature point pairs belonging to it carry out the mode that divides to they separately belonging to tetrahedron divide, then their tetrahedrons affiliated are separately deleted, and then in rectangular parallelepiped, forming 3n-9 tetrahedron, this 3n-9 tetrahedron forms described tetrahedral grid.

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

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

In addition, in step d), by step b33) in formed tessarace move, make step b33) in formed tetrahedron be deformed into new tetrahedron.

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

In addition, do not intersect between the multiple tetrahedrons before distortion and do not depart from, and not intersecting and do not depart between multiple tetrahedrons after distortion.

In addition, when the distortion of described three-dimensional picture is based on a tetrahedral coordinate system, in step b), by demarcating four not unique points on the same face and form a tetrahedron in described three-dimensional picture.

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

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

The deformation method of the three-dimensional picture based on tetrahedral coordinate system of the present invention, by marking a small amount of unique point in the three-dimensional picture of input, automatic generating mesh envelope lives whole three-dimensional picture, then interpolation once obtains final deformation effect by directly dragging the change in location of unique point.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, and therefore, conversion is reversible, both can plane, special properties that straight line has can be kept in distortion constant, also unique point enciphered method can be utilized to realize the distortion of plane to curved surface, there is flexible multi-purpose feature.

Accompanying drawing explanation

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

Be described in detail embodiments of the invention now, its sample table shows in the accompanying drawings, and wherein, identical label represents same parts all the time.Be described to explain the present invention to embodiment below with reference to the accompanying drawings.In the accompanying drawings, for clarity, the thickness in layer and region can be exaggerated.In the following description, obscuring of the present invention's design that the unnecessary detailed description in order to avoid known features and/or function causes, can omit the unnecessary detailed description of known features and/or function.

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

Below the tetrahedral coordinate system proposed the present invention is described in detail.Fig. 1 is according to an embodiment of the invention for defining the tetrahedral schematic diagram of 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, and (Dx, Dy, Dz) Cz), 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 define by formula (1) below.

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

Wherein, V _pBCD, V _pDCA, V _pABCand V _aBCDrepresent the volume of tetrahedron PBCD, PDCA, PABC and ABCD respectively; ' × ' represents the multiplication cross of vector; ' ' represents the dot product of vector.

With hereinafter, be described to the inverse transformation of above-mentioned tetrahedral coordinate system.The inverse transformation of tetrahedral coordinate system refers to and tetrahedral coordinate system is transformed into cartesian coordinate system.Specifically: under cartesian coordinate system, summit A ', B ', C ' and D ' is become when the position of four summits A, B, C and D of tetrahedron ABCD is moved, the position of some P is moved too and becomes a P ', but put P ' after mobile to remain unchanged with mobile front point each the tetrahedron formed of P and tetrahedron ABCD and the volume ratio of tetrahedron ABCD with each the tetrahedron formed of tetrahedron A ' B ' C ' D ' and the volume ratio of tetrahedron A ' B ' C ' D ', the tetrahedron coordinate namely putting P does not change with the change of the Cartesian coordinates of place tetrahedron top.The Cartesian coordinates of the some P ' after movement just can be drawn by formula (2) below.

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

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 formula (3) below.

P′=OW（3）

As can be seen from formula (2) and formula (3), the conversion between cartesian coordinate system and tetrahedral coordinate system is linear transformation.Therefore, the character that above-mentioned tetrahedral coordinate system has comprise following some:

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

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

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

(4) continuity of topology distortion.The topology distortion of geometric figure in adjacent 2 tetrahedral coordinate systems is continuous print, which ensure that the continuity of topology distortion.

Be described in detail to the deformation method of the three-dimensional picture based on tetrahedral coordinate system below.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, step is comprised 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 in three-dimensional picture;

S4: drag tessarace, be out of shape to make tetrahedron;

S5: obtain the three-dimensional picture after distortion.

Deformation method due to the three-dimensional picture based on single tetrahedral coordinate system and the deformation method based on the three-dimensional picture of multiple tetrahedral coordinate system are incomplete same in the implementation procedure of above-mentioned steps, therefore following we will be described respectively the two.First, the deformation method of the three-dimensional picture based on single tetrahedral coordinate system is described.

For the deformation method of the three-dimensional picture based on single tetrahedral coordinate system, in step sl, the three-dimensional picture of input can be designed by 3D design software more of the prior art and produce, such as, 3DMax or Maya software, also can by being similar to OpenGL(OpenGraphicsLibrary) etc. developing instrument exploitation and producing, no longer elaborate at this.

In step s 2, four not unique points on the same face can be demarcated in the three-dimensional picture of input, form a tetrahedron.In addition, four not unique points on the same face also can be demarcated around three-dimensional picture.

In step s3, the tetrahedron coordinate figure of each point in three-dimensional picture is tried to achieve according to above-mentioned formula (1).

In step s 4 which, the tessarace formed in step S2 (namely above-mentioned unique point) can be moved, make the tetrahedron formed in step S2 change into a new tetrahedron.In addition, in this step, by any one summit tetrahedral formed in mobile step S2, any two summits, any three summits or four summits, the tetrahedron formed in step S2 can be changed into new tetrahedron.

In step s 5, the Cartesian coordinates value of the new tessarace formed in tetrahedron coordinate figure of each point in the three-dimensional picture of trying to achieve according to formula (1) in step S3 and step S4 is substituted in above-mentioned formula (2), in the hope of the Cartesian coordinates value of each point in the three-dimensional picture after distortion, then obtain the three-dimensional picture after distortion.

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

Because the three-dimensional picture based on single tetrahedral coordinate system can only be simply out of shape, such as, in the expression design of cartoon role, the design of face exaggerated deformation or other continuous modifications, when needing to carry out comparatively complicated distortion to three-dimensional picture, just need to set up multiple tetrahedral coordinate system (namely forming tetrahedral coordinate system grid).Be described to the deformation method of the three-dimensional picture based on multiple tetrahedral coordinate system below.

For the deformation method of the three-dimensional picture based on multiple tetrahedral coordinate system, in step sl, the three-dimensional picture of input can be designed by 3D design software more of the prior art and produce, such as, 3DMax or Maya software, also can by being similar to OpenGL(OpenGraphicsLibrary) etc. developing instrument exploitation and producing, also no longer elaborate at this.

In step s 2, by demarcating multiple tessarace, so that three-dimensional picture is carried out tetrahedral grid division.Herein, the division methods of carrying out tetrahedral grid to three-dimensional picture determines the quality of the deformation effect of three-dimensional picture to a great extent, in order to make the deformation effect of three-dimensional picture good, present embodiments provide a kind of division methods of three-dimensional picture being carried out automatically to tetrahedral grid, but the present invention is not limited to this division methods, due in practice in order to realize nature continuous print deformation effect, for the three-dimensional picture of different structure, need to set up different tetrahedral grids to cover and divide, such as sphere tetrahedral grid: namely all tetrahedrons have a common summit (i.e. the centre of sphere), all other three summits tetrahedral are all on sphere, require that sphere tetrahedral grid is non-cross, do not depart from mutually (not departing from mutually herein refers to be had between neighboring tetrahedra and to only have 1 common sides), complete envelope three-dimensional picture.Equally, also can be sphere tetrahedral grid circumscribed rectangular volume mesh, namely add a rectangular parallelepiped outward again at sphere tetrahedral grid, the above-mentioned condition of same demand fulfillment.。The division methods that the present embodiment provides requires complete for three-dimensional picture tetrahedral grid envelope, and its concrete methods of realizing comprises the steps:

S21: set up a rectangular parallelepiped.Wherein, this rectangular parallelepiped need by complete for whole three-dimensional picture envelope;

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

S23: by mark unique point time order, generate multiple tetrahedron as tetrahedron collection (T1, T2 ..., Tm), namely generate tetrahedral grid.

In step S23, generate multiple tetrahedral concrete methods of realizing and comprise the steps:

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

Tetrahedron belonging to it is divided into four new tetrahedrons by S232: second unique point P2 in the feature point set in step S22, then the tetrahedron belonging to second unique point P2 is deleted, retain four the new tetrahedrons dividing and formed, and then form 15 tetrahedrons in rectangular parallelepiped.

S233: from described 3rd unique point to the n-th unique point, carry out according to the tetrahedron of the feature point pairs of second in step S232 belonging to it mode that divides to they separately belonging to tetrahedron divide, then their tetrahedrons affiliated are separately deleted, and then in rectangular parallelepiped, form 3n-9 tetrahedron, tetrahedron collection namely in step S23 (T1, T2 ... Tm) m in is 3n-9, and this 3n-9 tetrahedron forms tetrahedral grid.

The rectangular parallelepiped set up in step S21 is divided into 12 tetrahedral concrete methods of realizings by first unique point P1 in step S23: be divided into two triangles by each of rectangular parallelepiped by any diagonal line in this face, first unique point P1 and each triangle form a tetrahedron, and then rectangular parallelepiped are divided into 12 tetrahedrons.

In step s3, the tetrahedron coordinate figure in each some tetrahedron (this affiliated tetrahedron is in 3n-9 the tetrahedron formed in step S233) belonging to it in three-dimensional picture is tried to achieve according to above-mentioned formula (1).

In step s 4 which, the tessarace formed in step S233 (8 summits of the rectangular parallelepiped set up in namely above-mentioned unique point and step S21) can be moved, make the tetrahedron formed in step S233 change into new tetrahedron.In this step, according to the demand of three-dimensional picture distortion, the any amount tessarace in 3n-9 the tetrahedron formed in step S233 can be moved, and for a tetrahedron in 3n-9 tetrahedron, this any one summit tetrahedral, any two summits, any three summits or four summits can be moved.

In step s 5, the Cartesian coordinates value of the new tessarace tetrahedron coordinate figure in each some tetrahedron belonging to it in the three-dimensional picture of trying to achieve according to formula (1) in step S3 and the tetrahedron belonging to this each point formed in step s 4 which substitutes in above-mentioned formula (2), in the hope of the Cartesian coordinates value of each point in the three-dimensional picture after distortion, then obtain the three-dimensional picture after distortion.

In addition, the topological structure of tetrahedral grid remains unchanged in distortion.This guarantees the continuous uniformly valid before and after three-dimensional picture distortion.In other words, before being deformed, do not intersect between 3n-9 the tetrahedron formed in step S233 and do not depart from; After deformation, also do not intersect between 3n-9 the tetrahedron formed in step S233 and do not depart from, and the annexation in the tetrahedral grid (i.e. 3n-9 tetrahedron) of distortion front and back between each summit does not change.

In sum, according to an embodiment of the invention based on the deformation method of the three-dimensional picture of tetrahedral coordinate system, by marking a small amount of unique point in the three-dimensional picture of input, automatic generating mesh envelope lives whole three-dimensional picture, then interpolation once obtains final deformation effect by directly dragging the change in location of unique point.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, and therefore, conversion is reversible, both can plane, special properties that straight line has can be kept in distortion constant, also unique point enciphered method can be utilized to realize the distortion of plane to curved surface, there is flexible multi-purpose feature.

Although specifically show with reference to its exemplary embodiment and describe the present invention, but it should be appreciated by those skilled in the art, when not departing from the spirit and scope of the present invention that claim limits, the various changes in form and details can be carried out to it.

Claims (13)

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

A) input three-dimensional picture, and form tetrahedron in described three-dimensional picture;

B) tessarace is demarcated;

C) the tetrahedron coordinate figure of each point in tetrahedron in three-dimensional picture is obtained; Wherein, described tetrahedron coordinate figure is the tetrahedron that each point in three-dimensional picture is formed with corresponding tetrahedral three summits and the tetrahedral volume ratio formed in described three-dimensional picture;

D) drag tessarace, be out of shape to make tetrahedron;

E) three-dimensional picture after distortion is obtained.

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

B1) rectangular parallelepiped is set up;

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

B3) according to the order of the described unique point of mark, multiple tetrahedron is generated as described tetrahedral grid.

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

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

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

Described rectangular parallelepiped is divided into 12 tetrahedrons by first unique point b31) in a described n unique point;

Tetrahedron belonging to it is divided into four new tetrahedrons by second unique point b32) in a described n unique point, then the tetrahedron belonging to described second unique point is deleted, retain four the new tetrahedrons dividing and formed, and then form 15 tetrahedrons in described rectangular parallelepiped;

B33) from the unique point of the 3rd a described n unique point to the n-th unique point, according to step b32) in the tetrahedron of described second feature point pairs belonging to it carry out the mode that divides to they separately belonging to tetrahedron divide, then their tetrahedrons affiliated are separately deleted, 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, in step b31) in, described rectangular parallelepiped is divided into 12 tetrahedral concrete methods of realizings by described first unique point: be divided into two triangles by each of described rectangular parallelepiped by any diagonal line in this face, described first unique point and each triangle form a tetrahedron, and then described rectangular parallelepiped is divided into 12 tetrahedrons.

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

8. deformation method according to claim 7, is characterized in that, in steps d) in, by step b33) in formed tessarace move, make step b33) in formed tetrahedron be deformed into new tetrahedron.

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

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

11. deformation methods 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) in, by demarcating four not unique points on the same face and form a tetrahedron in described three-dimensional picture.

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

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