CN101872490A - Improved three-dimensional model deformation method under abrupt change in coordinate axis direction - Google Patents

Abstract

The invention discloses an improved three-dimensional model deformation method under abrupt change in coordinate axis direction, in which a three-dimensional model is divided into a deformation area, a transition area and a non-deformation area. In the deformation area of the three-dimensional model, the local coordinate of the deformed grid peak is obtained by utilizing an interpolation method to compute an arc curve corresponding to the grid peak after bending deformation so as to realize smooth transition of the surface of the three-dimensional model at the nearby area of a joint point and the stretching and compression in the corresponding area of the three-dimensional area after bending deformation; the local coordinate of the grid peak after deformation in the non-deformation area is obtained by carrying out European style conversion on a part of peaks in the non-deformation area; the smooth transition between the non-deformation area and the deformation area on the surface of the three-dimensional model is realized via interpolation on the distance from the grid peak in the transition area to skeleton; and the bending deformation of the three-dimensional model when the included angle of the skeleton is larger than 180 degrees is realized by revising the computation process of the local coordinates of the grid peaks of the deformation area, the transition area and the non-deformation area under abrupt change in coordinate axis direction of a local coordinate system.

Description

Three-dimensional model deformation method under a kind of improved abrupt change in coordinate axis direction

Technical field

The present invention relates to the three-dimensional model deformation method under a kind of improved abrupt change in coordinate axis direction, belong to computer graphics, virtual reality technology field.

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.

In " a kind of method for bending deformation of three-dimensional model " based on circular curve, three-dimensional model is divided into distorted area, zone of transition and non-deformation zone, in flexural deformation, by the coordinate after the circular curve acquisition distorted area grid vertex distortion of calculating distorted area grid vertex correspondence, according to the flexural deformation parameter non-deformation zone grid vertex is carried out corresponding euclidean transformation, by the zone of transition grid vertex is carried out the seamless link that interpolation realizes distorted area and non-deformation zone apart from the distance of bone.

But in flexural deformation, when angle of bend less than 0, the angle that is the bone of articulation point both sides increases, the angle of the bone of articulation point both sides may be greater than 180 ° at this moment, then after after the distortion local coordinate system being upgraded to the transformation matrix of world coordinate system, the x axle of local coordinate system and z direction of principal axis are opposite with original direction, are called abrupt change in coordinate axis direction.In this case, use said method will obtain wrong deformation result.

At the deficiency of said method, the inventive method proposes the three-dimensional model deformation method under a kind of improved abrupt change in coordinate axis direction.

Summary of the invention

The objective of the invention is to overcome the defective of prior art,, propose the three-dimensional model deformation method under a kind of improved abrupt change in coordinate axis direction 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 the three-dimensional model vertex deformation:

(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 _BThe vector representation of the coordinate of expression articulation point B in world coordinate system.

(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, to belonging 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) 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, y from the local coordinate P=of this grid vertex (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;

(9) center of circle local coordinate O ' of the circular curve of each grid vertex correspondence of three-dimensional model=(d/cos (υ)) γ, central angle θ=π-υ * 2, the point O ' to bone OA apart from r=dtan (υ), wherein γ=γ '/| γ ' |, γ '=(α+b)/2, υ=arccos (α b)/2, and α=μ _{B '}/ | μ _{B '}|, b=(0,1,0).

(10) for each grid vertex in three-dimensional model deformation district, the t value of this summit correspondence

The location parameter ratio value of this summit on corresponding circular curve

Wherein P ' is the local coordinate of the subpoint of this summit on the AOB of plane, the local coordinate on this summit be written as P=(x, y, z), P '=(x, y, 0) then, vectorial χ=(1,0,0).Obtain the maximal value t in all t values _MAXWith minimum value t _MIN

(11) calculate the t value of each grid vertex correspondence in the three-dimensional model zone of transition according to following method,

1. for each grid vertex that belongs to bone OA in the three-dimensional model zone of transition, the t value of this summit correspondence is-x that wherein the local coordinate of this grid vertex is P ₁=(x, y, z);

2. for each grid vertex that belongs to bone OB in the three-dimensional model zone of transition, the t value of this summit correspondence is P wherein ₂' be the local coordinate of the subpoint of this summit on the AOB of plane, the local coordinate of this grid vertex is P ₂=(x, y, z), P then ₂'=(x, y, 0), some C coordinate is d α.

(12) make the local coordinate of summit after flexural deformation of the deformed region that calculates three-dimensional model with the following method, wherein flexural deformation angle is w ₂,

1. if θ+w ₂＜0, at this moment, abrupt change in coordinate axis direction can take place after tying up to distortion in the local coordinate of partial model correspondence, if θ+w ₂＜0, the central angle θ ' after then being out of shape=-(θ+w ₂), otherwise θ '=θ+w ₂, if θ+w ₂＜0 and | θ ' |=| θ |, the corresponding t value of circular arc that then length remains unchanged in deformation process in three-dimensional model t _C=-(t _MAX+ t _MIN)/2, otherwise, t _C=d[θ cot (θ/2)-θ ' cot (θ '/2)]/(θ '-θ);

2. the minimum value t ' in the t value of all grid vertexes in the distorted area of three-dimensional model after being out of shape _MIN=t _C-t _m, t wherein _m=(t _MAX-t _MIN)/2;

3. if t _C+ t _m＜[d/sin (θ '/2)] [1-cos (θ '/2)], then the maximal value t ' in the t value of all grid vertexes in the distorted area of distortion back three-dimensional model _MAX=[d/sin (θ '/2)] [1-cos (θ '/2)], otherwise t ' _MAX=t _C+ t _m

4. the center of circle local coordinate O "=(x of the circular curve of each grid vertex correspondence of three-dimensional model after being out of shape ₀, y ₀, 0), x wherein ₀=dcot (θ '/2), y ₀=d, the radius r of circular curve '=x;

5. for each grid vertex in three-dimensional model deformation district, the preceding local coordinate of this grid vertex distortion is written as P=, and (x, y z), obtain the t value t on this summit from the result of calculation of step (10) ₁, if θ+w ₂＜0, the t value t after this vertex deformation ₂=t ' _MAX-(t ' _MAX-t ' _MIN) (t ₁-t _MIN)/(t _MAX-t _MIN), otherwise, t ₂=t ' _MIN+ (t ' _MAX-t ' _MIN) (t ₁-t _MIN)/(t _MAX-t _MIN), from the result of calculation of step (10), obtain the ratio value τ on this summit, the local coordinate P ' after this vertex deformation=(x ', y ', z '), wherein x '=x ₀+ (r '+t ₂) cos (π+θ ' τ), y '=y ₀+ (r '+t ₂) sin (π+θ ' τ), if θ+w ₂＜0, z '=-z, otherwise, z '=z.

(13) make the local coordinate of summit after flexural deformation of the transitional region of calculating three-dimensional model with the following method, wherein flexural deformation angle is w ₂,

1. for each the grid vertex P that belongs to bone OA in the three-dimensional model transitional region ₁, from step (8), obtain the projection value l of vector on bone OA that this summit and articulation point O constitute in the step result of calculation 1. _P1, from step (11), obtain the t value t on this summit in the step result of calculation 1. _P1

2. if θ+w ₂＜0, then the preceding t value of distortion is t in the deformed region of three-dimensional model _P1The increment σ=t ' of grid vertex t value after distortion _MAX-(t ' _MAX-t ' _MIN) (t _P1-t _MIN)/(t _MAX-t _MIN)+t _P1, otherwise, σ=t ' _MIN+ (t ' _MAX-t ' _MIN) (t _P1-t _MIN)/(t _MAX-t _MIN)-t _P1, if θ+w ₂＜0, summit P then ₁T value t ' after the distortion _P1=σ * (L ₁-l _P1)/(L ₁-d)-t _P1, otherwise, t ' _P1=t _P1+ σ * (L ₁-l _P1)/(L ₁-d);

3. summit P ₁Local coordinate is written as (x before the distortion ₁, y ₁, z ₁), if θ+w ₂＜0, summit P then ₁Local coordinate P after the distortion ₁'=(-t ' _P1, y ₁,-z ₁), otherwise, P ₁'=(-t ' _P1, y ₁, z ₁);

4. for each the grid vertex P that belongs to bone OB in the three-dimensional model transitional region ₂, from step (8), obtain the projection value t of vector on bone OB that this summit and articulation point O constitute in the step result of calculation 2. _P2, from step (11), obtain the t value t on this summit in the step result of calculation 2. _P2

5. if θ+w ₂＜0, then the preceding t value of distortion is t in the deformed region of three-dimensional model _P2The increment σ '=t ' of grid vertex t value after distortion _MAX-(t ' _MAX-t ' _MIN) (t _P2-t _MIN)/(t _MAX-t _MIN)+t _P2, otherwise, σ '=t ' _MIN+ (t ' _MAX-t ' _MIN) (t _P2-t _MIN)/(t _MAX-t _MIN)-t _P2, if θ+w ₂＜0, summit P then ₂T value t ' after the distortion _P2=σ ' * (L ₂-l _P2)/(L ₂-d)-t _P2, otherwise, t ' _P2=t _P2+ σ ' * (L ₂-l _P2)/(L ₂-d);

6. if θ+w ₂＜0, summit P then ₂Local coordinate P after the distortion ₂'=(x ₂', y ₂' ,-z ₂), otherwise, P ₂'=(x ₂', y ₂', z ₂), z wherein ₂Be summit P ₂Z coordinate in the local coordinate before the distortion, x ₂' and y ₂' from summit P ₂The local coordinate P of the subpoint of distortion back on the AOB of plane ₂"=(x ₂', y ₂', 0), P wherein ₂"=l _P2α '+t ' _P2γ ', α '=(cos (θ '-pi/2), sin (θ '-pi/2), 0),

C '=d α '.

(14) make the local coordinate of summit after flexural deformation in the non-deformation zone territory of calculating three-dimensional model with the following method, wherein flexural deformation angle is w ₂,

For each grid vertex that belongs to bone OA in the three-dimensional model non-deformation zone territory, if θ+w ₂＜0, then x coordinate and the negate of z graticule ticks in its local coordinate of distortion back, otherwise its local coordinate is constant before and after distortion;

For each grid vertex that belongs to bone OB 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, the turning axle direction vector is written as ρ ₁=(x, y, z), rotation matrix R then ₁For:

$R_1=\left[\begin{array}{ccc}(1-\cos \left(w\right))x^2+\cos \left(w\right)& (1-\cos \left(w\right))\mathrm{xy}-\sin \left(w\right)z& (1-\cos \left(w\right))\mathrm{xz}+\sin \left(w\right)y\\ (1-\cos \left(w\right))\mathrm{xy}+\sin \left(w\right)z& (1-\cos \left(w\right))y^2+\cos \left(w\right)& (1-\cos \left(w\right))\mathrm{yz}-\sin \left(w\right)x\\ (1-\cos \left(w\right))\mathrm{xz}-\sin \left(w\right)y& (1-\cos \left(w\right))\mathrm{yz}+\sin \left(w\right)x& (1-\cos \left(w\right))z^2+\cos \left(w\right)\end{array}\right]$

Rotation angle w=w wherein ₂, ρ ₁=(0,0,1),

If θ+w ₂＜0, then with the x coordinate and the negate of z graticule ticks of the local coordinate of the grid vertex that calculates.

(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 flexural 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.Distorted area at three-dimensional model, by the local coordinate after obtaining the grid vertex distortion at the circular curve that uses interpolation method computing grid summit correspondence after the flexural deformation, thereby the three-dimensional model surface is in the smooth transition of articulation point near zone after the realization flexural deformation, and the stretching of three-dimensional model respective regions and compression; In flexural deformation,, the part summit in the non-deformation zone of three-dimensional model obtains the local coordinate of non-deformation zone grid vertex after distortion by being carried out corresponding European conversion; In flexural deformation,, can realize the smooth transition between three-dimensional model surface non-deformation zone and the distorted area by the grid vertex in the three-dimensional model zone of transition is carried out interpolation to the distance of bone; By the correction to distorted area, zone of transition and non-deformation zone grid vertex local coordinate computation process under the abrupt change in coordinate axis direction of local coordinate system in the deformation process, the flexural deformation of the three-dimensional model in the time of can realizing the bone angle greater than 180 °.

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 three-dimensional model to be carried out diastrophic method.

Next carrying out flexural deformation with the three-dimensional model that the shank and the pin of human body are formed is example, and 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, it is as follows that this three-dimensional model is carried out diastrophic method:

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

(7) calculate three-dimensional model deformation zone corresponding center of circle local coordinate O ', central angle θ and O ' to bone OA apart from r, result of calculation O '=(0.6346,0.125,0), θ=0.3890, r=0.6346.

(8), calculate t value and this summit location parameter ratio value on corresponding circular curve of this summit correspondence for each grid vertex in three-dimensional model deformation district.Obtain the maximal value t in the t value of all grid vertexes in the deformed region of three-dimensional model _MAXWith minimum value t _MINCalculate the t value of each grid vertex correspondence in the three-dimensional model transitional region.

(9) make the local coordinate of each grid vertex after flexural deformation in the distorted area that calculates three-dimensional model with the following method, wherein flexural deformation angle w ₂=-0.523599:

From the result of calculation of step (7), obtain the θ value of three-dimensional model, from the result of calculation of step (8), obtain the t of three-dimensional model correspondence _MAXAnd t _MINValue; θ+w ₂=-0.1346＜0, sudden change has taken place in change in coordinate axis direction, the central angle θ ' after the distortion=-(θ+w ₂)=0.1346, because | θ ' | ≠ | θ |, so use formula t _C=d[θ cot (θ/2)-θ ' cot (θ '/2)]/(θ '-θ) calculate the t value t of the circular arc correspondence that length remains unchanged in the deformation process _C, t _C=0.0109; Maximal value t ' in the deformed region of calculating distortion back three-dimensional model in the t value of all grid vertexes _MAXWith minimum value t ' _MINCenter of circle local coordinate O behind the calculating three-dimensional model deformation " and radius r ', O "=(1.8546,0.125,0), r '=1.8546; For each grid vertex in the three-dimensional model deformation district, from the result of calculation of step (8), obtain the t value t of this grid vertex ₁And the ratio value on this summit, calculate the t value t after this vertex deformation ₂, calculate the local coordinate after this vertex deformation then.

(10) make the local coordinate of each grid vertex after flexural deformation in the zone of transition of calculating three-dimensional model with the following method, wherein flexural deformation angle w ₂=-0.523599:

For each the grid vertex P that belongs to bone OA in the three-dimensional model transitional region ₁, from the result of calculation of step (8), obtain the t value t on this summit ₁', from the result of calculation of step (6), obtain the projection value l of vector on bone OA that this summit and articulation point O constitute; θ+w ₂=-0.1346＜0, sudden change has taken place in change in coordinate axis direction, therefore uses formula σ=t ' _MAX-(t ' _MAX-t ' _MIN) (t ₁'-t _MIN)/(t _MAX-t _MIN)+t ₁The t value is t in the ' calculating three-dimensional model deformation zone ₁' the increment σ of grid vertex t value after distortion; Summit P ₁T value t after the distortion ₂'=σ * (L ₁-l)/(L ₁-d)-t ₁'; Summit P ₁Local coordinate P after the distortion ₁'=(-t ₂', y ₁,-z ₁), y wherein ₁And z ₁Be summit P ₁Y coordinate and z coordinate before the distortion; For each the grid vertex P that belongs to bone OB in the three-dimensional model transitional region ₂, from the result of calculation of step (8), obtain the t value t on this summit ₁", from the result of calculation of step (6), obtain the projection value l ' of vector on bone OB that this summit and articulation point O constitute; θ+w ₂=-0.1346＜0, sudden change has taken place in change in coordinate axis direction, therefore uses formula σ '=t ' _MAX-(t ' _MAX-t ' _MIN) (t ₁" t _MIN)/(t _MAX-t _MIN)+t ₁" the t value is t in the calculating three-dimensional model deformation zone ₁" the increment σ ' of grid vertex t value after distortion; Summit P ₂T value t after the distortion ₂"=σ ' * (L ₂-l ')/(L ₂-d)-t ₁"; Calculate summit P ₂Local coordinate P after the distortion ₂'.

(11) calculate rotation matrix R, wherein rotation angle w=w ₂, turning axle direction vector ρ ₁=(0,0,1); For each grid vertex that belongs to bone OB in the three-dimensional model non-deformation zone territory, its local coordinate is P, the local coordinate P '=PR after this summit flexural deformation ^T, θ+w ₂Therefore=-0.1346＜0, sudden change has taken place in change in coordinate axis direction, with the x coordinate and the negate of z graticule ticks of the local coordinate of the grid vertex that calculates; θ+w ₂Therefore=-0.1346＜0, sudden change has taken place in change in coordinate axis direction, with the x coordinate and the negate of z graticule ticks that belong in the three-dimensional model non-deformation zone territory in the local coordinate of grid vertex of bone OA.

(12) the corresponding coordinate of articulation point in world coordinate system is A behind the three-dimensional model deformation ₂=(0.1957,0.3889,0.0695), O ₂=(0.054,0.0399 ,-0.3295), B ₂=(0.1076 ,-0.0343 ,-0.3245) 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 flexural 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. the three-dimensional model deformation method under the improved abrupt change in coordinate axis direction, 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:

(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;

(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 _BThe vector representation of the coordinate of expression articulation point B in world coordinate system;

(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, to belonging 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) 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, y from the local coordinate P=of this grid vertex (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;

(9) center of circle local coordinate O ' of the circular curve of each grid vertex correspondence of three-dimensional model=(d/cos (υ)) γ, central angle θ=π-υ * 2, the point O ' to bone OA apart from r=dtan (υ), wherein γ=γ '/| γ ' |, γ '=(α+b)/2, υ=arccos (α b)/2, and α=μ _{B '}/ | μ _{B '}|, b=(0,1,0);

(10) for each grid vertex in three-dimensional model deformation district, the t value of this summit correspondence The location parameter ratio value of this summit on corresponding circular curve

Wherein P ' is the local coordinate of the subpoint of this summit on the AOB of plane, the local coordinate on this summit be written as P=(x, y, z), P '=(x, y, 0) then, vectorial χ=(1,0,0); Obtain the maximal value t in all t values _{MAX and}Minimum value t _MIN

(11) calculate the t value of each grid vertex correspondence in the three-dimensional model zone of transition according to following method,

1. for each grid vertex that belongs to bone OA in the three-dimensional model zone of transition, the t value of this summit correspondence is-x that wherein the local coordinate of this grid vertex is P ₁=(x, y, z);

2. for each grid vertex that belongs to bone OB in the three-dimensional model zone of transition, the t value of this summit correspondence is

P wherein ₂' be the local coordinate of the subpoint of this summit on the AOB of plane, the local coordinate of this grid vertex is P ₂=(x, y, z), P then ₂'=(x, y, 0), some C coordinate is d α;

(12) make the local coordinate of summit after flexural deformation of the deformed region that calculates three-dimensional model with the following method, wherein flexural deformation angle is w ₂,

1. if θ+w ₂＜0, at this moment, abrupt change in coordinate axis direction can take place after tying up to distortion in the local coordinate of partial model correspondence, if θ+w ₂＜0, the central angle θ ' after then being out of shape=-(θ+w ₂), otherwise θ '=θ+w ₂, if θ+w ₂＜0 and | θ ' |=| θ |, the corresponding t value of circular arc that then length remains unchanged in deformation process in three-dimensional model t _C=-(t _MAX+ t _MIN)/2, otherwise, t _C=d[θ cot (θ/2)-θ ' cot (θ '/2)]/(θ '-θ);

2. the minimum value t ' in the t value of all grid vertexes in the distorted area of three-dimensional model after being out of shape _MIN=t _C-t _m, t wherein _m=(t _MAX-t _MIN)/2;

3. if t _C+ t _m＜[d/sin (θ '/2)] [1-cos (θ '/2)], then the maximal value t ' in the t value of all grid vertexes in the distorted area of distortion back three-dimensional model _MAX=[d/sin (θ '/2)] [1-cos (θ '/2)], otherwise t ' _MAX=t _C+ t _m

4. the center of circle local coordinate O "=(x of the circular curve of each grid vertex correspondence of three-dimensional model after being out of shape ₀, y ₀, 0), x wherein ₀=dcot (θ '/2), y ₀=d, the radius r of circular curve '=x;

5. for each grid vertex in three-dimensional model deformation district, the preceding local coordinate of this grid vertex distortion is written as P=, and (x, y z), obtain the t value t on this summit from the result of calculation of step (10) ₁, if θ+w ₂＜0, the t value t after this vertex deformation ₂=t ' _MAX-(t ' _MAX-t ' _MIN) (t ₁-t _MIN)/(t _MAX-t _MIN), otherwise, t ₂=t ' _MIN+ (t ' _MAX-t ' _MIN) (t ₁-t _MIN)/(t _MAX-t _MIN), from the result of calculation of step (10), obtain the ratio value τ on this summit, the local coordinate P ' after this vertex deformation=(x ', y ', z '), wherein x '=x ₀+ (r '+t ₂) cos (π+θ ' τ), y '=y ₀+ (r '+t ₂) sin (π+θ ' τ), if θ+w ₂＜0, z '=-z, otherwise, z '=z;

(13) make the local coordinate of summit after flexural deformation of the transitional region of calculating three-dimensional model with the following method, wherein flexural deformation angle is w ₂,

1. for each the grid vertex P that belongs to bone OA in the three-dimensional model transitional region ₁, from step (8), obtain the projection value l of vector on bone OA that this summit and articulation point O constitute in the step result of calculation 1. _P1, from step (11), obtain the t value t on this summit in the step result of calculation 1. _P1

2. if θ+w ₂＜0, then the preceding t value of distortion is t in the deformed region of three-dimensional model _P1The increment σ=t ' of grid vertex t value after distortion _MAX-(t ' _MAX-t ' _MIN) (t _P1-t _MIN)/(t _MAX-t _MIN)+t _P1, otherwise, σ=t ' _MIN+ (t ' _MAX-t ' _MIN) (t _P1-t _MIN)/(t _MAX-t _MIN)-t _P1, if θ+w ₂＜0, summit P then ₁T value t ' after the distortion _P1=σ * (L ₁-l _P1)/(L ₁-d)-t _P1, otherwise, t ' _P1=t _P1+ σ * (L ₁-l _P1)/(L ₁-d);

3. summit P ₁Local coordinate is written as (x before the distortion ₁, y ₁, z ₁), if θ+w ₂＜0, summit P then ₁Local coordinate P after the distortion ₁'=(-t ' _P1, y ₁,-z ₁), otherwise, P ₁'=(-t ' _P1, y ₁, z ₁);

4. for each the grid vertex P that belongs to bone OB in the three-dimensional model transitional region ₂, from step (8), obtain the projection value t of vector on bone OB that this summit and articulation point O constitute in the step result of calculation 2. _P2, from step (11), obtain the t value t on this summit in the step result of calculation 2. _P2

5. if θ+w ₂＜0, then the preceding t value of distortion is t in the deformed region of three-dimensional model _P2The increment σ '=t ' of grid vertex t value after distortion _MAX-(t ' _MAX-t ' _MIN) (t _P2-t _MIN)/(t _MAX-t _MIN)+t _P2, otherwise, σ '=t ' _MIN+ (t ' _MAX-t ' _MIN) (t _P2-t _MIN)/(t _MAX-t _MIN)-t _P2, if θ+w ₂＜0, summit P then ₂T value t ' after the distortion _P2=σ ' * (L ₂-l _P2)/(L ₂-d)-t _P2, otherwise, t ' _P2=t _P2+ σ ' * (L ₂-l _P2)/(L ₂-d);

6. if θ+w ₂＜0, summit P then ₂Local coordinate P after the distortion ₂'=(x ₂', y ₂' ,-z ₂), otherwise, P ₂'=(x ₂', y ₂', z ₂), z wherein ₂Be summit P ₂Z coordinate in the local coordinate before the distortion, x ₂' and y ₂' from summit P ₂The local coordinate P of the subpoint of distortion back on the AOB of plane ₂"=(x ₂', y ₂', 0), P wherein ₂"=l _P2α '+t ' _P2γ ', α '=(cos (θ '-pi/2), sin (θ '-pi/2), 0),

C '=d α ';

(14) make the local coordinate of summit after flexural deformation in the non-deformation zone territory of calculating three-dimensional model with the following method, wherein flexural deformation angle is w ₂,

For each grid vertex that belongs to bone OA in the three-dimensional model non-deformation zone territory, if θ+w ₂＜0, then x coordinate and the negate of z graticule ticks in its local coordinate of distortion back, otherwise its local coordinate is constant before and after distortion;

For each grid vertex that belongs to bone OB 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, the turning axle direction vector is written as ρ ₁=(x, y, z), rotation matrix R then ₁For:

$R_1=\left[\begin{array}{ccc}(1-\cos \left(w\right))x^2+\cos \left(w\right)& (1-\cos \left(w\right))\mathrm{xy}-\sin \left(w\right)z& (1-\cos \left(w\right))\mathrm{xz}+\sin \left(w\right)y\\ (1-\cos \left(w\right))\mathrm{xy}+\sin \left(w\right)z& (1-\cos \left(w\right))y^2+\cos \left(w\right)& (1-\cos \left(w\right))\mathrm{yz}-\sin \left(w\right)x\\ (1-\cos \left(w\right))\mathrm{xz}-\sin \left(w\right)y& (1-\cos \left(w\right))\mathrm{yz}+\sin \left(w\right)x& (1-\cos \left(w\right))z^2+\cos \left(w\right)\end{array}\right]$

Rotation angle w=w wherein ₂, ρ ₁=(0,0,1),

If θ+w ₂＜0, then with the x coordinate and the negate of z graticule ticks of the local coordinate of the grid vertex that calculates;

(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 flexural deformation of three-dimensional model.

2. according to the three-dimensional model deformation method under the described a kind of improved abrupt change in coordinate axis direction 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) 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 three-dimensional model deformation method under the described a kind of improved abrupt change in coordinate axis direction of claim 1, it is characterized in that, judge in the step (3) 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.

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