CN101894389A - Rotation angle interpolation-based three-dimensional model torsional deformation method - Google Patents

Abstract

The invention discloses a rotation angle interpolation-based three-dimensional model torsional deformation method. In the method, the speed and the three dimension of deformation can be improved by dividing a three-dimensional model into a deformation zone, a transition zone and a non-deformation zone according to deformation characteristics of a role model and applying different deformation methods to each zone of the three-dimensional model. In the deformation zone and the transition zone of the three-dimensional model, corresponding zones of the three-dimensional model can twist around a framework in torsional deformation; smooth and continuous transition is realized close to articulation points of the surfaces of the three-dimensional model; and in the non-deformation zone of the three-dimensional model, local coordinates of grid vertexes in the non-deformation zone after the torsional deformation can be obtained by performing corresponding Euclidean transformation on part of vertexes.

Description

A kind of three-dimensional model torsional deformation method based on rotation angle interpolation

Technical field

The present invention relates to a kind of three-dimensional model torsional deformation method, belong to computer graphics, virtual reality technology field based on rotation angle interpolation.

Background technology

In the distortion of three-dimensional model, following several deformation technology is arranged usually: Morphing method, FFD deformation method, based on the deformation method of bone.The Morphing method realizes distortion by interpolation method, and the control volume that the FFD deformation method surrounds the three-dimensional model surface by control is realized distortion, realizes distortion by the model surface grid vertex is set corresponding to the weights that influence of bone based on the deformation technology of bone.

For actor model, two parts packets of information is arranged usually with which, the model bone information of the surface mesh information of representation model geometric properties and representation model topological characteristic.The distortion of actor model has following characteristics usually: distortion occurs near the zone the articulation point, belongs to local deformation; Distortion causes that around an articulation point rotation therefore the model after the distortion is consistent with the motion conditions of bone by one section bone.

The Morphing method belongs to overall situation distortion, and can not combine with the motion of bone; The FFD deformation method is to each summit of three-dimensional model, all needs by calculating this summit to the polynomial expression of all control vertexs with the coordinate after obtaining this vertex deformation, and the The deformation calculation complexity can not reach the deformation velocity that meets the demands; Need the user to carry out repeatedly adjustment based on the deformation method of bone, increased the use difficulty influencing weights.

Deformation characteristics at actor model, the inventive method proposes a kind of three-dimensional model torsional deformation method based on rotation angle interpolation, this method is by to carrying out grid vertex that interpolation the obtains three-dimensional model articulation point near zone rotation angle with respect to bone in the torsional deflection process around the anglec of rotation of bone, and then tries to achieve the local coordinate of grid vertex after distortion.

Summary of the invention

The objective of the invention is to overcome the defective of prior art,, propose a kind of three-dimensional model torsional deformation method based on rotation angle interpolation in order to solve the problem of the quick distortion true to nature of actor model.

The present invention is achieved through the following technical solutions:

The skeletal structure of three-dimensional model is: articulation point A and O connect into bone OA, and articulation point B and O connect into bone OB, and bone OA and bone OB are positioned near the axis of three-dimensional model.

Use the local coordinate after following method is calculated three-dimensional model summit torsional deflection:

(1) near three-dimensional model surface mesh shangguan node O, selects two summit P ₁, P ₂,, should make plane OP as preferably ₁P ₂With bone OA and bone OB angle separately about equally;

(2) obtain plane OP according to following method ₁P ₂Equation coefficient,

1. calculate tri-vector

Wherein * the vectorial multiplication cross of expression;

2. n=n '/| n ' |, variable s=-n μ _oμ wherein _oThe vector representation of the coordinate of expression articulation point O in world coordinate system; The dot product of expression vector;

3. V=[n, s]; V has stored plane OP ₁P ₂Four coefficients of equation,

The coefficient of plane equation is meant A, B, C and the D among the Ax+By+Cz+D=0.

(3), judge its grid vertex and plane OP to each triangular mesh of three-dimensional model ₁P ₂Relation, if all summits of grid all with articulation point A at plane OP ₁P ₂The same side, judge that then this triangular mesh belongs to bone OA, otherwise judge that this triangular mesh belongs to bone OB; If all do not constitute in the master pattern, then need before judgement, regard non-triangular mesh as a plurality of triangles and form by triangular mesh.

Judge that summit and articulation point A are at plane OP ₁P ₂The same side method be:

To a summit in the grid, the vector representation of the coordinate in world coordinate system is P, and the vector representation of the coordinate of articulation point A in world coordinate system is μ _A,

Calculate f _P=nP+s, f _A=n μ _AIf+s is f _PWith f _AJack per line judges that then summit P and summit A are at plane OP ₁P ₂The same side, otherwise judge that summit P and summit A be not at plane OP ₁P ₂The same side;

(4) make the local coordinate of calculating the three-dimensional model correspondence with the following method be tied to the transformation matrix F of world coordinate system ₁:

F ₁Be 4 * 4 matrixes, $F_1=\left[\begin{array}{cccc}{{\mathrm{\α}}_1}^T& {{\mathrm{\β}}_1}^T& {{\mathrm{\γ}}_1}^T& {{\mathrm{\μ}}_o}^T\\ 0& 0& 0& 1\end{array}\right],$

Subscript T representing matrix matrix transpose operation wherein,

And, vector

Vector γ ₁=γ ₁'/| γ ₁' |,

Vector α ₁=β ₁* γ ₁

(5) make the local coordinate of calculating each grid vertex of three-dimensional model with the following method:

The local coordinate of grid vertex P is μ in the three-dimensional model _{P '}=μ _PF ₁ ^-T, μ wherein _PThe vector representation of the expression coordinate of summit P in world coordinate system, subscript-T represents earlier matrix is carried out matrix transpose operation again to finding the inverse matrix as a result.

(6) the local coordinate μ of articulation point B _{B '}=μ _BF ₁ ^-T, μ wherein _Bα=μ is calculated in the vector representation of the coordinate of expression articulation point B in world coordinate system _B/ | μ _B|.

(7) according to following method three-dimensional model is divided into distorted area, zone of transition and non-deformation zone,

1. set the maximal projection value d of vector on bone OA and bone OB that distorted area grid vertex and articulation point O constitute;

2. set the value L of minimum projection of vector on bone OA that non-deformation zone grid vertex and articulation point O constitute ₁, and the value L of the minimum projection on bone OB ₂Should guarantee when being provided with that d is less than L ₁, L ₂Among minimum value;

3. in three-dimensional model, belong to each grid vertex of bone OA, its local coordinate that obtains in step (5) is written as P=, and (x, y z), less than d, judge then that this summit belongs to the distorted area as if y; If y is greater than L ₁, judge that then this summit belongs to non-deformation zone; If y is more than or equal to d and smaller or equal to L ₁, judge that then this summit belongs to zone of transition;

4. in three-dimensional model,, use μ to belonging to each grid vertex of bone OB _{P '}The local coordinate of representing this summit is calculated l _P=μ _{P '}μ _{B '}/ | μ _{B '}|, if l _PLess than d, judge that then this summit belongs to the distorted area; If l _PGreater than L ₂, judge that then this summit belongs to non-deformation zone; If l _PMore than or equal to d and smaller or equal to L ₂, judge that then this summit belongs to zone of transition;

(8) for each grid vertex that belongs to bone OA in the three-dimensional model, the local coordinate on this summit is written as P ₁=(z), if z＞0, this summit is with respect to the deflection angle φ of plane AOB for x, y ₁=2 π-φ ' ₁, otherwise, φ ₁=φ ' ₁, wherein

(9) for each grid vertex that belongs to bone OB in the three-dimensional model, the local coordinate on this summit is written as P ₂=(z), if z＞0, this summit is with respect to the deflection angle φ of plane AOB for x, y ₂=2 π-φ ₂', otherwise, φ ₂=φ ₂', wherein

And P ₂'=(x, y, 0), P ₂"=(P ₂α) α;

(10) parameter N is set, the grid vertex of three-dimensional model is divided into N zone according to the deflection angle with respect to plane AOB, deflection angle is being numbered of zone of the grid vertex correspondence of φ

, φ=φ when the summit belongs to bone OA ₁, and φ=φ when belonging to bone OB ₂

(11) according to vector the projection value on corresponding bone of following each grid vertex of method calculating three-dimensional model with articulation point O formation,

1. for each grid vertex that belongs to bone OA in the three-dimensional model, the projection value of vector on bone OA that this grid vertex and articulation point O constitute equals y, and y is from the local coordinate P of this grid vertex ₁=(x, y, z);

2. for each grid vertex that belongs to bone OB in the three-dimensional model, the projection value of vector on bone OB that this grid vertex and articulation point O constitute is P ₂μ _{B '}/ | μ _{B '}|, P wherein ₂Be this grid vertex local coordinate;

(12) in the obtaining step (10) in each regional distorted area and the zone of transition and belong to the vector that the grid vertex of bone OA and articulation point O constitute, the minimum value l of the projection value on bone OA ₁And the minimum value l that belongs to the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂

(13) make deformed region and the summit in the transitional region local coordinate after torsional deflection of calculating three-dimensional model with the following method, wherein torsional deflection angle is w ₁,

1. for each grid vertex that belongs to bone OA in the distorted area of three-dimensional model and the zone of transition, its local coordinate is written as P ₁, from the result of calculation of step (11), obtain the projection value l of vector on bone OA that this grid vertex and articulation point O constitute _P1, from the result of calculation of step (12), obtain in the distorted area in zone of this grid vertex correspondence and the zone of transition and belong to the grid vertex of bone OA and the vector that articulation point O constitutes, the minimum value l of the projection value on bone OA ₁And belong to minimum value l in the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂, wherein the zone of this grid vertex correspondence obtains from the division result of step (10);

2. put P ₁Rotation angle θ around bone OA _P1=w ₁* (L ₁-l _P1)/(L ₁-l ₁+ L ₂-l ₂)-w ₁, summit P ₁The local coordinate P of corresponding point after the torsional deflection ₁'=P ₁R _P1 ^T, rotation matrix R wherein _P1For:

$R_{P1}=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_{P1}\right)& 0& \sin \left({\mathrm{\θ}}_{P1}\right)\\ 0& 1& 0\\ -\sin \left({\mathrm{\θ}}_{P1}\right)& 0& \cos \left({\mathrm{\θ}}_{P1}\right)\end{array}\right]$

3. for each grid vertex that belongs to bone OB in the distorted area of three-dimensional model and the zone of transition, its local coordinate is written as P ₂, from the result of calculation of step (11), obtain the projection value l of vector on bone OB that this grid vertex and articulation point O constitute _P2, from the result of calculation of step (12), obtain in the distorted area in zone of this grid vertex correspondence and the zone of transition and belong to the grid vertex of bone OA and the vector that articulation point O constitutes, the minimum value l of the projection value on bone OA ₁' and belong to minimum value l in the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂', wherein the zone of this grid vertex correspondence obtains from the division result of step (10);

4. put P ₂Rotation angle θ around bone OA _P2=w ₁* (L ₁-l ₁'+l _P2-l ₂')/(L ₁-l ₁'+L ₂-l ₂')-w ₁, summit P ₂The local coordinate P of corresponding point after the torsional deflection ₂'=P ₂R _P2 ^T, rotation matrix R wherein _P2For:

$R_{P2}=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_{P2}\right)& 0& \sin \left({\mathrm{\θ}}_{P2}\right)\\ 0& 1& 0\\ -\sin \left({\mathrm{\θ}}_{P2}\right)& 0& \cos \left({\mathrm{\θ}}_{P2}\right)\end{array}\right]$

(14) make the local coordinate of summit after torsional deflection in the non-deformation zone territory of calculating three-dimensional model with the following method, wherein torsional deflection angle is w ₁,

For each grid vertex that belongs to bone OA in the three-dimensional model non-deformation zone territory, local coordinate is P before its distortion, the local coordinate P ' after this vertex deformation=PR ₁ ^T, rotation matrix R wherein ₁For:

$R_1=\left[\begin{array}{ccc}\cos (-w_1)& 0& \sin (-w_1)\\ 0& 1& 0\\ -\sin (-w_1)& 0& \cos (-w_1)\end{array}\right]$

For each grid vertex that belongs to bone OB in the three-dimensional model non-deformation zone territory, its local coordinate is constant before and after distortion.

(15) make the local coordinate of calculating distortion back three-dimensional model correspondence with the following method be tied to the transformation matrix F of world coordinate system ₁':

F ₁' be 4 * 4 matrixes, ${F_1}^{\′}=\left[\begin{array}{cccc}{\mathrm{\α}}^{\′T}& {\mathrm{\β}}^{\′T}& {\mathrm{\γ}}^{\′T}& {{\mathrm{\μ}}_o}^{\′T}\\ 0& 0& 0& 1\end{array}\right],$

Subscript T representing matrix matrix transpose operation wherein,

And, vector

Vector γ '=γ "/| γ " |,

Vector α '=β ' * γ ', μ _o' be that articulation point O is out of shape the vector representation of the coordinate in world coordinate system afterwards, A ₂, O ₂, B ₂Be articulation point A, O, the coordinate of B distortion back in world coordinate system.

Obtained local coordinate after all grid vertexes distortion of three-dimensional model by said method, and local coordinate is tied to the transformation matrix of world coordinate system behind the three-dimensional model deformation.Be tied to the transformation matrix of world coordinate system according to local coordinate behind the local coordinate of each grid vertex of three-dimensional model and the three-dimensional model deformation, draw the three-dimensional model after the distortion.So far, finished the torsional deformation of three-dimensional model.

The contrast prior art, the beneficial effect of the inventive method is, according to the deformation characteristics of actor model, three-dimensional model is divided into distorted area, zone of transition and non-deformation zone, by the deformation method different, can improve the speed and the sense of reality of distortion to each area applications of three-dimensional model.In the distorted area and zone of transition of three-dimensional model, by after torsional deflection, grid vertex being carried out interpolation with respect to the rotation angle of bone, can be implemented in three-dimensional model respective regions in the torsional deflection around the reversing of bone, and make the three-dimensional model surface realize smooth, continuous transition at the articulation point near zone; In the non-deformation zone of three-dimensional model, by the part summit being carried out the local coordinate after corresponding European conversion obtains the torsional deflection of non-deformation zone grid vertex.

Description of drawings:

Fig. 1 is a synoptic diagram of three-dimensional model being divided distorted area, zone of transition and non-deformation zone;

Fig. 2 is to the synoptic diagram behind three-dimensional model division distorted area, zone of transition and the non-deformation zone of human body shank.

Embodiment:

Below in conjunction with drawings and Examples technical solution of the present invention is done further explanation, essence of the present invention is a kind of method of three-dimensional model being carried out torsional deflection.

Next be deformed into example with the three-dimensional model that the shank and the pin of human body are formed, the specific embodiment of the present invention is described.

The articulation point of this three-dimensional model correspondence is A, O, B, and wherein articulation point A and O connect into bone OA, and articulation point B and O connect into bone OB.

According to the technical program, the method for this three-dimensional model being carried out torsional deflection is as follows:

(1) near articulation point O, selects two summit P ₁, P ₂, wherein articulation point O coordinate is (0.053979,0.029863 ,-0.339496), some P ₁Coordinate is (0.0623082,0.0758197 ,-0.249175), some P ₂Coordinate is (0.0871224,0.0691930 ,-0.263863).Calculate plane OP ₁P ₂Equation V=(0.0288590 ,-0.891964,0.451185,0.178254).

(2) articulation point A coordinate is (0.099197,0.543307 ,-0.151083), to each grid of three-dimensional model, judge all grid vertexes of this grid whether with articulation point A at plane OP ₁P ₂The same side, if then this grid belongs to bone OA, otherwise this grid belongs to bone OB.

(3) local coordinate of calculating three-dimensional model is tied to the local coordinate of each grid vertex in the transformation matrix of world coordinate system and the three-dimensional model.

(4) articulation point B coordinate in world coordinate system is (0.0890980,0.0151050 ,-0.256083), calculates the local coordinate B ' of articulation point B, B '=(x, y, z)=(0.09,0.0177,0).

(5) L is set ₁=0.25, L ₂=0.16, d=0.125, use following method that three-dimensional model is divided into distorted area, zone of transition and non-deformation zone:

In three-dimensional model, belong to each grid vertex of bone OA, (z), less than d, then this summit belongs to the distorted area as if y for x, y, if y is greater than L to obtain its local coordinate P= ₁, then this summit belongs to non-deformation zone, if y is more than or equal to d and smaller or equal to L ₁, then this summit belongs to zone of transition; In three-dimensional model, belong to each grid vertex of bone OB, obtain its local coordinate P ', calculate

If l is less than d, then this summit belongs to the distorted area, and greater than L2, then this summit belongs to non-deformation zone as if l, if l is more than or equal to d and smaller or equal to L ₂, then this summit belongs to zone of transition.Divide the result as shown in Figure 2.

(6) calculate in the three-dimensional model each grid vertex with respect to the deflection angle φ of plane AOB.The user is provided with parameter N=20, and deflection angle is being numbered of zone of the grid vertex correspondence of φ , grid vertexes all in the three-dimensional model is divided into 20 zones according to deflection angle.

(7) calculate the projection value of vector on corresponding bone of each grid vertex of three-dimensional model and articulation point O formation.

(8) in the obtaining step (6) in each regional distorted area and the zone of transition and belong to the vector that the grid vertex of bone OA and articulation point O constitute, the minimum value l of the projection value on bone OA ₁And the minimum value l that belongs to the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂

(9) make deformed region and the summit in the transitional region local coordinate after torsional deflection of calculating three-dimensional model with the following method, wherein torsional deflection angle w ₁=-0.261803:

For each grid vertex that belongs to bone OA in the distorted area of three-dimensional model and the zone of transition, its local coordinate is written as P ₁From the result of calculation of step (7), obtain the projection value l of vector on bone OA that this grid vertex and articulation point O constitute, from the result of calculation of step (8), obtain in the distorted area in zone of this grid vertex correspondence and the zone of transition and belong to the grid vertex of bone OA and the vector that articulation point O constitutes, the minimum value l of the projection value on bone OA ₁And belong to minimum value l in the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂, wherein the zone of this grid vertex correspondence obtains from the division result of step (6), some P ₁Around bone OA rotation angle θ ₁=w ₁* (L ₁-l)/(L ₁-l ₁+ L ₂-l ₂)-w ₁, calculate rotation matrix R ₁, grid vertex P ₁The local coordinate P of corresponding point after the torsional deflection ₁'=P ₁R ₁ ^TFor each grid vertex that belongs to bone OB in the distorted area of three-dimensional model and the zone of transition, its local coordinate is written as P ₂From the result of calculation of step (7), obtain the projection value l ' of vector on bone OB that this grid vertex and articulation point O constitute, from the result of calculation of step (8), obtain in the distorted area in zone of this grid vertex correspondence and the zone of transition and belong to the grid vertex of bone OA and the vector that articulation point O constitutes, the minimum value l of the projection value on bone OA ₁' and belong to minimum value l in the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂', wherein the zone of this grid vertex correspondence obtains from the division result of step (6), some P ₂Around bone OA rotation angle θ ₂=w ₁* (L ₁-l ₁'+l '-l ₂')/(L ₁-l ₁'+L ₂-l ₂')-w ₁, calculate rotation matrix R ₂, grid vertex P ₂The local coordinate P of corresponding point after the torsional deflection ₂'=P ₂R ₂ ^T

(10) calculate rotation matrix R, wherein rotation angle w=-w ₁, turning axle direction vector ρ=(0,1,0); For each grid vertex that belongs to bone OA in the three-dimensional model non-deformation zone territory, its local coordinate is P, the local coordinate P '=PR after this summit torsional deflection ^TThe grid vertex distortion front and back local coordinate that belongs to bone OB in the three-dimensional model non-deformation zone territory is constant.

(11) the corresponding coordinate of articulation point in world coordinate system is A behind the three-dimensional model deformation ₂=(0.1508,0.4863 ,-0.0254), O ₂=(0.054,0.0399 ,-0.3295), B ₂=(0.1048 ,-0.0149 ,-0.2764) makes the local coordinate of calculating distortion back three-dimensional model correspondence with the following method be tied to the transformation matrix F of world coordinate system ₁':

F ₁' be 4 * 4 matrixes, ${F_1}^{\′}=\left[\begin{array}{cccc}{\mathrm{\α}}^{\′T}& {\mathrm{\β}}^{\′T}& {\mathrm{\γ}}^{\′T}& {{\mathrm{\μ}}_o}^{\′T}\\ 0& 0& 0& 1\end{array}\right],$

Subscript T representing matrix matrix transpose operation wherein,

And, vector

Vector γ '=γ "/| γ " |,

Vector α '=β ' * γ ', μ _o' be that articulation point O is out of shape the vector representation of the coordinate in world coordinate system afterwards.

Obtained local coordinate after all grid vertexes distortion of three-dimensional model by said method, and local coordinate is tied to the transformation matrix of world coordinate system behind the three-dimensional model deformation.Be tied to the transformation matrix of world coordinate system according to local coordinate behind the local coordinate of each grid vertex of three-dimensional model and the three-dimensional model deformation, can use OPENGL to draw three-dimensional model after function and model view matrix manipulation function are drawn distortion.So far, finished the torsional deformation of three-dimensional model.

Above-described specific descriptions; purpose, technical scheme and beneficial effect to invention further describe; institute is understood that; the above only is specific embodiments of the invention; and be not intended to limit the scope of the invention; within the spirit and principles in the present invention all, any modification of being made, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (3)

1. three-dimensional model torsional deformation method based on rotation angle interpolation, the skeletal structure of described three-dimensional model is: articulation point A and O connect into bone OA, and articulation point B and O connect into bone OB, and bone OA and bone OB are positioned near the axis of three-dimensional model; It is characterized in that, comprise the steps:

Use the local coordinate after following method is calculated three-dimensional model summit torsional deflection:

(1) near three-dimensional model surface mesh shangguan node O, selects two summit P ₁, P ₂

(2) obtain plane OP according to following method ₁P ₂Equation coefficient,

1. calculate tri-vector

Wherein * the vectorial multiplication cross of expression;

2. n=n '/| n ' |, variable s=-n μ _oμ wherein _oThe vector representation of the coordinate of expression articulation point O in world coordinate system; The dot product of expression vector;

3. V=[n, s]; V has stored plane OP ₁P ₂Four coefficients of equation;

(3), judge its grid vertex and plane OP to each triangular mesh of three-dimensional model ₁P ₂Relation, if all summits of grid all with articulation point A at plane OP ₁P ₂The same side, judge that then this triangular mesh belongs to bone OA, otherwise judge that this triangular mesh belongs to bone OB; If all do not constitute in the master pattern, then need before judgement, regard non-triangular mesh as a plurality of triangles and form by triangular mesh;

(4) make the local coordinate of calculating the three-dimensional model correspondence with the following method be tied to the transformation matrix F of world coordinate system ₁:

F ₁Be 4 * 4 matrixes, $F_1=\left[\begin{array}{cccc}{{\mathrm{\α}}_1}^T& {{\mathrm{\β}}_1}^T& {{\mathrm{\γ}}_1}^T& {{\mathrm{\μ}}_o}^T\\ 0& 0& 0& 1\end{array}\right],$

Subscript T representing matrix matrix transpose operation wherein,

And, vector

Vector γ ₁=γ ₁'/| γ ₁' |,

Vector α ₁=β ₁* γ ₁

(5) make the local coordinate of calculating each grid vertex of three-dimensional model with the following method:

The local coordinate of grid vertex P is μ in the three-dimensional model _{P '}=μ _PF ₁ ^-T, μ wherein _PThe vector representation of the expression coordinate of summit P in world coordinate system, subscript-T represents earlier matrix is carried out matrix transpose operation again to finding the inverse matrix as a result;

(6) the local coordinate μ of articulation point B _{B '}=μ _BF ₁ ^-T, μ wherein _Bα=μ is calculated in the vector representation of the coordinate of expression articulation point B in world coordinate system _B/ | μ _B|;

(7) according to following method three-dimensional model is divided into distorted area, zone of transition and non-deformation zone,

1. set the maximal projection value d of vector on bone OA and bone OB that distorted area grid vertex and articulation point O constitute;

2. set the value L of minimum projection of vector on bone OA that non-deformation zone grid vertex and articulation point O constitute ₁, and the value L of the minimum projection on bone OB ₂Should guarantee when being provided with that d is less than L ₁, L ₂Among minimum value;

3. in three-dimensional model, belong to each grid vertex of bone OA, its local coordinate that obtains in step (5) is written as P=, and (x, y z), less than d, judge then that this summit belongs to the distorted area as if y; If y is greater than L ₁, judge that then this summit belongs to non-deformation zone; If y is more than or equal to d and smaller or equal to L ₁, judge that then this summit belongs to zone of transition;

4. in three-dimensional model,, use μ to belonging to each grid vertex of bone OB _{P '}The local coordinate of representing this summit is calculated l _P=μ _{P '}μ _{B '}/ | μ _{B '}|, if l _PLess than d, judge that then this summit belongs to the distorted area; If l _PGreater than L ₂, judge that then this summit belongs to non-deformation zone; If l _PMore than or equal to d and smaller or equal to L ₂, judge that then this summit belongs to zone of transition;

(8) for each grid vertex that belongs to bone OA in the three-dimensional model, the local coordinate on this summit is written as P ₁=(z), if z＞0, this summit is with respect to the deflection angle φ of plane AOB for x, y ₁=2 π-φ ' ₁, otherwise, φ ₁=φ ' ₁, wherein

(9) for each grid vertex that belongs to bone OB in the three-dimensional model, the local coordinate on this summit is written as P ₂=(z), if z＞0, this summit is with respect to the deflection angle φ of plane AOB for x, y ₂=2 π-φ ₂', otherwise, φ ₂=φ ₂', wherein And P ₂'=(x, y, 0), P ₂"=(P ₂α) α;

(10) parameter N is set, the grid vertex of three-dimensional model is divided into N zone according to the deflection angle with respect to plane AOB, deflection angle is being numbered of zone of the grid vertex correspondence of φ

, φ=φ when the summit belongs to bone OA ₁, and φ=φ when belonging to bone OB ₂

(11) according to vector the projection value on corresponding bone of following each grid vertex of method calculating three-dimensional model with articulation point O formation,

1. for each grid vertex that belongs to bone OA in the three-dimensional model, the projection value of vector on bone OA that this grid vertex and articulation point O constitute equals y, and y is from the local coordinate P of this grid vertex ₁=(x, y, z);

2. for each grid vertex that belongs to bone OB in the three-dimensional model, the projection value of vector on bone OB that this grid vertex and articulation point O constitute is P ₂μ _{B '}/ | μ _{B '}|, P wherein ₂Be this grid vertex local coordinate;

(12) in the obtaining step (10) in each regional distorted area and the zone of transition and belong to the vector that the grid vertex of bone OA and articulation point O constitute, the minimum value l of the projection value on bone OA ₁And the minimum value l that belongs to the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂

(13) make deformed region and the summit in the transitional region local coordinate after torsional deflection of calculating three-dimensional model with the following method, wherein torsional deflection angle is w ₁,

1. for each grid vertex that belongs to bone OA in the distorted area of three-dimensional model and the zone of transition, its local coordinate is written as P ₁, from the result of calculation of step (11), obtain the projection value l of vector on bone OA that this grid vertex and articulation point O constitute _P1, from the result of calculation of step (12), obtain in the distorted area in zone of this grid vertex correspondence and the zone of transition and belong to the grid vertex of bone OA and the vector that articulation point O constitutes, the minimum value l of the projection value on bone OA ₁And belong to minimum value l in the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂, wherein the zone of this grid vertex correspondence obtains from the division result of step (10);

2. put P ₁Rotation angle θ around bone OA _P1=w ₁* (L ₁-l _P1)/(L ₁-l ₁+ L ₂-l ₂)-w ₁, summit P ₁The local coordinate P of corresponding point after the torsional deflection ₁'=P ₁R _P1 ^T, rotation matrix R wherein _P1For:

$R_{P1}=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_{P1}\right)& 0& \sin \left({\mathrm{\θ}}_{P1}\right)\\ 0& 1& 0\\ -\sin \left({\mathrm{\θ}}_{P1}\right)& 0& \cos \left({\mathrm{\θ}}_{P1}\right)\end{array}\right]$

3. for each grid vertex that belongs to bone OB in the distorted area of three-dimensional model and the zone of transition, its local coordinate is written as P ₂, from the result of calculation of step (11), obtain the projection value l of vector on bone OB that this grid vertex and articulation point O constitute _P2, from the result of calculation of step (12), obtain in the distorted area in zone of this grid vertex correspondence and the zone of transition and belong to the grid vertex of bone OA and the vector that articulation point O constitutes, the minimum value l of the projection value on bone OA ₁' and belong to minimum value l in the projection value of vector on bone OB that the grid vertex of bone OB and articulation point O constitute ₂', wherein the zone of this grid vertex correspondence obtains from the division result of step (10);

4. put P ₂Rotation angle θ around bone OA _P2=w ₁* (L ₁-l ₁'+l _P2-l ₂')/(L ₁-l ₁'+L ₂-l ₂')-w ₁, summit P ₂The local coordinate P of corresponding point after the torsional deflection ₂'=P ₂R _P2 ^T, rotation matrix R wherein _P2For:

$R_{P2}=\left[\begin{array}{ccc}\cos \left({\mathrm{\θ}}_{P2}\right)& 0& \sin \left({\mathrm{\θ}}_{P2}\right)\\ 0& 1& 0\\ -\sin \left({\mathrm{\θ}}_{P2}\right)& 0& \cos \left({\mathrm{\θ}}_{P2}\right)\end{array}\right]$

(14) make the local coordinate of summit after torsional deflection in the non-deformation zone territory of calculating three-dimensional model with the following method, wherein torsional deflection angle is w ₁,

For each grid vertex that belongs to bone OA in the three-dimensional model non-deformation zone territory, local coordinate is P before its distortion, the local coordinate P ' after this vertex deformation=PR ₁ ^T, rotation matrix R wherein ₁For:

$R_1=\left[\begin{array}{ccc}\cos (-w_1)& 0& \sin (-w_1)\\ 0& 1& 0\\ -\sin (-w_1)& 0& \cos (-w_1)\end{array}\right]$

For each grid vertex that belongs to bone OB in the three-dimensional model non-deformation zone territory, its local coordinate is constant before and after distortion;

(15) make the local coordinate of calculating distortion back three-dimensional model correspondence with the following method be tied to the transformation matrix F of world coordinate system ₁':

F ₁' be 4 * 4 matrixes, ${F_1}^{\′}=\left[\begin{array}{cccc}{\mathrm{\α}}^{\′T}& {\mathrm{\β}}^{\′T}& {\mathrm{\γ}}^{\′T}& {{\mathrm{\μ}}_o}^{\′T}\\ 0& 0& 0& 1\end{array}\right],$

Subscript T representing matrix matrix transpose operation wherein,

And, vector

Vector γ '=γ "/| γ " |,

Vector α '=β ' * γ ', μ _o' be that articulation point O is out of shape the vector representation of the coordinate in world coordinate system afterwards, A ₂, O ₂, B ₂Be articulation point A, O, the coordinate of B distortion back in world coordinate system;

Be tied to the transformation matrix of world coordinate system according to local coordinate behind the local coordinate of each grid vertex of three-dimensional model that obtains and the three-dimensional model deformation, draw the three-dimensional model after the distortion, finish the torsional deformation of three-dimensional model.

2. according to the described a kind of three-dimensional model torsional deformation method of claim 1, it is characterized in that, near three-dimensional model surface mesh shangguan node O, select two summit P in the step (1) based on rotation angle interpolation ₁, P ₂The time, as preferably, should make plane OP ₁P ₂With bone OA and bone OB angle separately about equally.

3. according to the described a kind of three-dimensional model torsional deformation method of claim 1, it is characterized in that, judge in the step (3) that summit and articulation point A are at plane OP based on rotation angle interpolation ₁P ₂The same side method be:

To a summit in the grid, the vector representation of the coordinate in world coordinate system is P, and the vector representation of the coordinate of articulation point A in world coordinate system is μ _A,

Calculate f _P=nP+s, f _A=n μ _AIf+s is f _PWith f _AJack per line judges that then summit P and summit A are at plane OP ₁P ₂The same side, otherwise judge that summit P and summit A be not at plane OP ₁P ₂The same side.

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