CN104361632B - A kind of triangle gridding filling-up hole method based on Hermite RBFs - Google Patents
A kind of triangle gridding filling-up hole method based on Hermite RBFs Download PDFInfo
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Abstract
The invention discloses a kind of triangle gridding filling-up hole method based on Hermite RBFs, the method is comprised the following steps：After extracting hole border, based on the summit around hole and normal information, go out implicit surface using Hermite Interpolation Property of Radial Basis Function；Border is projected to into plane, Delaunay trigonometric ratios is then defined to hole border, and process is finely divided to the grid after trigonometric ratio；Finally newly-increased triangle is adjusted on implicit surface, completes to repair.The method has higher robustness and manually need not participate in, the repair efficiency that the grid hole larger to Curvature varying has had.
Description
Technical field
The invention belongs to geometric manipulations and 3-D scanning model repair field, and in particular to based on Hermite radial direction base letters
Several triangle gridding filling-up holes.
Background technology
Triangle gridding is a kind of important method for expressing of geometric model, is widely used in virtual reality, reverse-engineering, calculating
In the fields such as machine graphics.With the fast development of the Airborne Laser Scan, obtain more next by the threedimensional model of scan rebuilding
More it is widely applied.But the restriction due to measuring principle (insensitive such as on black), the reflexive impact of body surface or quilt
Blocking for scanning object self structure, scans the model for obtaining and often there is hole.These holes greatly govern model
Subsequent applications, such as 3D printing requires totally-enclosed model, and the shape analysis algorithm in a large amount of graphics also requires that model is not deposited
In hole.Therefore, application of the repairing of hole to model is significant.
For grid, filling-up hole people have done numerous studies, can be divided mainly into two class methods：Side based on surface mesh
Method and the method based on volume data, both approaches are each advantageous.Method based on surface mesh preferably can keep not lacking
Partial details, while can also better profit from the property of former grid, is adapted in the higher scene of detail.Based on body number
According to method adopt Global treatment mode, first by the model conversation of grid representation for volume representation model, then to body number
According to carrying out filling-up hole operation.The method is used in the occasion having high demands to algorithmic stability.
Filling-up hole based on surface mesh mainly has two big class：Surface fitting and directly is carried out according to hole and its peripheral information
Absent region is predicted and is repaired.In approximating method, Branch uses RBF after hole is extracted
(Radial Basis Function, RBF) is fitted to the part that hole is lacked, and then again perforated is sampled
Obtain model after filling-up hole.Due to the property of RBF itself, the method can not be fitted in some cases and meet hole
The curved surface of surrounding grid.Wang after hole border is extracted, using a group componential analysis (Principal Component
Analysis, PCA) fit Plane of hole coboundary point is obtained, hole border is projected in fit Plane, these points are calculated
Distance to fit Plane is used as height field.Height field is brought in mobile square law (Moving Least Square, MLS)
Obtain fitting surface.Hole border in fit Plane is sampled, sampled point is brought in equation determined by MLS and is obtained
To last filling-up hole model.Filling-up hole algorithm based on MLS has certain filling-up hole effect to on-plane surface hole, but for height
The hole repair effect of bending is undesirable.
The above-mentioned approximating method perforated repair efficiency larger for Curvature varying is undesirable, and some methods are at certain
Complete failure in the case of a little.Recently, Macedo proposes Hermite RBFs (Hemite Radial basis
Fucntion, HRBF) and apply it in a cloud reconstruction, this also becomes the focus studied at this stage.HRBF is theoretically
Solve the caused mistake reconstruction curved surface due to the selection of improper obligatory point of RBF presence.Simultaneously normal information is considered
In reconstructing system so that rebuild curved surface and can more reflect obligatory point property.Can be verily for the hole grid of higher curvature change
Rebuild the change that grid can verily react curvature.
Directly prediction and method for repairing and mending in, Liepa using angle and area as constraint, using dynamic programming strategy device to hole
Hole carries out triangle division；Then the grid slightly repaired according to the density subdivision of grid around hole, the side used in segmentation process
Exchange and ensure that Delaunay properties are met；Finally grid is carried out using umbrella smoothing operator smooth.The method is to hole
The larger model repairing effect of surrounding Curvature varying is bad, but also may produce Self-crossover.Xie proposes that one kind is entered based on difference
Change the filling-up hole method of algorithm：By minimize point to the distance between, the sampled point on hole border is matched.Then basis
Pairing result generates crossing plane, with reference to the plane and foramen primum hole border and the tangent line of one ring neighborhood intersection point, in crossing plane
Upper employing differential evolution algorithm predicts possible sampled point, and sampled point is projected to plane finally carries out trigonometric ratio.
In the method based on volume data, Ju carries out space division to model using Octree, in the structure of Octree
The voxel intersected with boundary edge is found, and then using the thought of similar Bresenham algorithms, a connection is generated in three dimensions
The plane of these boundary edges, repairs to hole.Dual contouring reconstruction models are used finally.Nooruddin is by grid
The model conversation of expression is homogeneous space voxel, using check number (Parity Count) and light penetration (Ray Stabbing)
The different conditions that process is produced in conversion process.Then opening (open) and closing (close) operator in Morphology Algorithm is transported
Use the hole repair that three dimensions complete spatial voxel.Contour surface is extracted using Marching Cubes algorithms finally.Phase
For the algorithm based on mesh amending, volume data method has the advantages that robustness is high, ensure manifold.But employ voxel
Intermediate representation, the model after causing to repair lose the details of master mould in a large number.The model larger for Curvature varying is without fine
Repair efficiency.
In sum, the preferable effect on plane hole is processed of the method based on surface mesh, but for curvature becomes
Changing larger grid can not have preferably process, and some methods are also possible to collapse.Based on patting at the method energy of volume data
Face hole, but the hole grid larger for Curvature varying can not produce intuitively filling-up hole effect.And due to volume data
Method is using global processing mode, more for the mesh details loss of non-lack part.The present invention can be to Curvature varying
Big hole produces the model for meeting mesh curvature variation tendency around hole, at the same the model after ensureing to repair in density and
Master mould is consistent.
The content of the invention
The technical problem to be solved in the present invention is：The deficiency that prior art changes hole repair to higher curvature is overcome, is
Generation can reflect nets declinable complete model around hole, there is provided a kind of triangle gridding filling-up hole method.The method is mainly utilized
Hermite RBFs produce the fitting surface for meeting mesh curvature change around hole, and wake up with a start sampling in perforated,
Then sampled point is mapped on fitting surface.
The present invention solves the technical scheme of above-mentioned technical problem：Triangle gridding based on Hermite RBFs is mended
Hole method, comprises the steps：
1) generate fitting surface
Step (1), hole border is detected in grid model.The characteristics of half of data structure be by grid per bar
While be decomposed into direction two one side of something (half-edge), this two half of in opposite direction.Per bar, half of record is adjacent
Triangle and two end points, each triangle records the one side of something for constituting it, and it is top that each summit records one with it
One side of something of point (outgoing vertex).Half of data structure saves the topology information of grid, can using these topology informations
With the adjacency information of quick-searching to each element (point, line, surface).Definition is boundary edge with an adjacent side of triangle,
The side data of grid are traveled through in the structure shown here, are found a seed boundary edge, are looked for then along this seed boundary edge counterclockwise
To next other boundary edges being adjacent until traveling through go back to again seed border.The annular of these boundary edge compositions is hole
Hole border.
Step (2), according to hole border and its neighborhood, obtain implicit surface using Hermite RBFs.Obtain hole
Behind the border of hole, as the summit on hole does not have a complete ring field, so accurate method line computation can not be carried out to which.
The three ring neighborhoods on hole border are chosen, using the position on summit and normal information in three ring neighborhoods as Hermite RBFs
Input, reconstructs the implicit surface for meeting mesh curvature change around hole.
2) triangle division on hole border
Step (3), the fit Plane that summit on hole border is generated as using PCA methods, and it is projected into the plane
On.It is a highly difficult thing directly to carry out trigonometric ratio in three dimensions, but also may introduce some other defects.And flat
Carry out on face trigonometric ratio be one by the problem of in-depth study, so the first step is to obtain hole side using PCA methods
The fit Plane on summit in boundary, then projects to hole border in the plane.The plane that PCA methods are obtained is really hole side
The least square fitting on summit in boundary.
Step (4) if, there is the border of Self-crossover, also need to optimize the minimal eigenvalue of PCA methods, hole be divided into into aperture
Hole.For the model that hole is bent with height, the projection in step (3) may be produced from intersection border in fit Plane,
So also needing to segmentation.Hole border is divided into into two parts, the minimal eigenvalue λ per part PCA methods is calculated respectivelyi3And λj3,
Assume λi3≥λj3.Take and work as λi3For minimum when segmentation hole is decomposed into into small holes.Ensure that each small holes projects to fitting flat
Border on face will not produce Self-crossover.
Step (5), the restricted Delaunay trigonometric ratios for carrying out based on scan line in the plane, and result back projection is returned
Three dimensions.Obtain in fit Plane after the projection of hole, using the restricted Delaunay trigonometric ratios based on scan line
(Constrained Delaunay Triangulation, CDT) carries out triangulation, CDT methods and biography to projecting polygon
The Delaunay methods of system are compared obvious advantage in speed.Then master mould is returned in the result back projection of triangle division.
3) perforated is sampled
Step (6), newly-increased triangle is carried out meeting the sub-dividing operations of density attributes.In order to ensure the close of newly-increased triangle
Around degree and hole, mesh-density is consistent, and also to can newly-generated Triangular Maps to step (2) it is middle given birth to
Into curved surface on.A density attributes are defined for borderline each summit of hole：The adjacent all edge lengths in the summit it is flat
Average.Newly-increased triangle to having obtained in step (5) is finely divided operation.The criterion of subdivision is to increase triangle core newly
To increase point newly, interpolation obtains the density attributes of the newly-increased point, if the density attributes and newly-increased point arrive three of original triangle shape
Point distance meets certain proportionate relationship, then the triangle is finely divided.Ensured using edge flip in segmentation process
Delaunay properties are guaranteed.This completes the sampling to perforated.
4) newly-increased point is mapped on implicit surface
Step (7), using gradient descent method by segment newly-increased summit be mapped on implicit surface.By in step (6)
On the implicit surface that the sampled point that Jing is obtained is generated in being mapped to step (2).Gradient descent method is a kind of side for seeking optimum value
Method, the continuous iteration adjustment step-length of the method is reaching the optimal value of function.Bring the gradient of HRBF and each newly-increased point into gradient
In the iterative formula of decline, final filling-up hole grid is obtained.
Advantage is the present invention compared with prior art：The present invention hole high for mesh curvature change around has preferably
Repair efficiency, and with higher stability.The present invention mainly has 2 points of contributions：First, using Hermite radial direction base letters
It is several that hole is fitted, obtain meeting the fitting surface of mesh curvature change around.Second, give a kind of new hole area
The domain method of sampling, the method adopt plane trigonometry and the sub-dividing operations based on density attributes.
Description of the drawings
Fig. 1 is algorithm overall flow figure；
Fig. 2 is half of data structure schematic diagram；
Fig. 3 is hole neighborhood schematic diagram；(a) ring neighborhood, (b) bicyclo- neighborhood；
Fig. 4 is the schematic diagram that projection is produced from cross hole；
Fig. 5 is that CDT initializes schematic diagram；
Fig. 6 is CDT summits event schematic diagram；A () current vertex projects the side for obtaining on wavefront, (b) by the two of the side
Individual end points is connected composition triangle with current vertex, if (c) being unsatisfactory for Delaunay properties, carries out edge flip；
Fig. 7 is CDT sides event schematic diagram；A () becomes the triangle for intersecting with limiting, (b) delete these trianglees, and root
It is divided into upper and lower two parts according to change is limited, trigonometric ratio is carried out to this two parts respectively (c)；
Fig. 8 is intermediate result of the present invention and end product design sketch；The model of (a) with hole, (b) according to hole and neighborhood
With the Hemite RBFs curved surface that obtains of fitting, (c) on hole the fit Plane on summit and its plane projection,
D after the completion of () plane trigonometry, three dimensions return in back projection, (e) newly-increased grid is finely divided and obtains sampled point, (f) will sampling
Point is mapped on curved surface；
Fig. 9 is the contrast effect figure of the present invention and tradition RBF methods.From left to right：The rabbit model of (a) with hole, base
The model repaired after RBF methods, the model after this method repairing, (b) the machine components model with hole, RBF methods are repaired
Model afterwards, the model after this method repairing.
Specific embodiment
Below in conjunction with the accompanying drawings and the specific embodiment of the present invention further illustrates the present invention.
Step (1) detects hole border in grid model.First with the point in half of data structure hoc mesh,
The elements such as line, face.As shown in Fig. 2 being that each edge in grid is decomposed in opposite direction two is half of the characteristics of the structure
(half-edge).In half of data structure, the one side of something (a in figure) in this, as starting endpoint is deposited on each summit, often
Individual triangle storage constitutes its one side of something (b in figure), half of per bar to deposit following content：The half of terminating point is (in figure
C), the triangle (d in figure) that the one side of something belongs to, lower bar one side of something (e in figure) that the one side of something is traveled through counterclockwise, with the half of phase negative side
To one side of something (f in figure).Half of data structure saves the topology information of grid, can be with quick-searching using these topology informations
To the adjacency information of each element (point, line, surface).Definition is boundary edge with an adjacent side of triangle, in Half-edge Structure
The side data of middle traversal grid, find a seed boundary edge, find next counterclockwise then along this seed boundary edge
Other boundary edges being adjacent are until traveling through go back to again seed border.The annular of these boundary edge compositions is hole border.
Step (2) obtains implicit surface using Hermite RBFs according to hole border and its neighborhood.Obtaining
Behind hole border, as the summit on hole does not have a complete ring neighborhood, so accurate normal meter can not be carried out to which
Calculate.The neighborhood definition of hole is as follows：
Assume that S is the simplex set constituted by the boundary edge of hole, M is the combinatorial manifold of model meshes.N (S, M) is
By at least exist with S the adjacent triangle sets in summit into simplex set, claim the simplex neighborhood that N (S, M) is S.It is fixed
K ranks (k-order) the simplex neighborhood of adopted hole is N (N (... N (S, M) ...), M), M), expression formula has k-1 layers nested, abbreviation k
Rank neighborhood, is designated as NK(S,M).The collection of hole boundary point is made to be combined into vh, the vertex set in hole k rank neighborhoods is vk, then vk-vhFor
K rings (k-ring) summit of hole.As shown in figure 3, a is a ring neighborhood, b is bicyclo- neighborhood.Three rings for choosing hole border are adjacent
Domain, is input into using the position on summit in three ring neighborhoods and normal information as Hermite RBFs, is reconstructed and is met hole week
The implicit surface of purse seine lattice Curvature varying.
Hermite Interpolation Property of Radial Basis Function problem can be described as follows：For the scattered point set given in three dimensionsAn Implicitly function f is found out in a function space H:R3→ R so as to meet f (xi)=0,In approximation theory, the problem is referred to as single order Hermite interpolation problems.Hypothesis has a Hilbert space
Its dual spaces of H are H*.Give a data setWherein γiIt is continuous linear functional, ciReal number, i.e. γi∈
H*, ci∈R.Target is to find a function f ∈ H so that ri(f)=ci, the General Cardinal in such function referred to as H spaces.It is right
In H spaces, such General Cardinal has countless, but meets the only one of which of H Norm minimums.This function can by it is inner this
Represent viThe linear combination of ∈ H is uniquely determined：And for each u ∈ H, γi(u)=<vi,u>.Will
f*And γiSimultaneous, obtains linear system A α=c, and the wherein element of matrix A is (A)i,j=γi(vj)=<vi,vj>H.
In Hermite interpolation problemsWherein DλIt is a differential operator, λ ∈ Nn, λjJ-th variable in expression u
The number of times being differentiated.As building, the method in H spaces is as follows.
Provide the RBF φ of a positive definite:R+→ R, while definition ψ=φ (| | | |).Existence anduniquess
Hilbert spaces, in the space, this is expressed asInner product is
For single order Hermite interpolation, when from global support function, its representation is as follows.
Wherein ψ (x)=φ (| | x | |), | | | | Euclidean distance is represented, for three-dimensional reconstruction typically takes φ (x)=x3。P
X ()=a+bx+by+cz, (x, y, z) are the coordinates of point x.Interpolation condition is brought into and can obtain in above-mentioned equation factor alphaj∈R
And βj∈R3：
H is hessian operators, is defined asAbove-mentioned interpolation condition is reconfigured and obtains being adapted to meter
Calculation form, for each (xi,ni) have：
From above formula, for three-dimensional each (xi,ni) can once calculate gradient and hessian squares with regard to ψ
Battle array, is obtained 4 × 4 matrixes, is then added with Polynomial Terms.Matrix combination of the had point Jing after above formula calculating obtains complete
Linear system.
Hermite RBFs are the improvement of conventional radial basic function, and it theoretically solves conventional radial base letter
Number is choosing the subjectivity randomness on obligatory point (off-surface points), substantially increases the reconstruction based on the function
Robustness.In addition, due to rebuild linear system using normal as interpolation condition so that the model of reconstruction can be preferably anti-
Reflect the property of interpolation point.The intermediate result for obtaining is as shown in Figure 8 b.
Step (3) generates the fit Plane of hole border vertices using PCA methods.Because directly carrying out three in three dimensions
Keratinization is a highly difficult thing, but also may introduce some other defects, and carry out in the plane trigonometric ratio be one
Jing is by the problem of in-depth study, so the first step is the fit Plane that summit on hole border is obtained using PCA methods, then
Hole border is projected in the plane.The plane that PCA methods are obtained is the least square fitting on summit on hole border, mainly
Step is as follows：
A) meansigma methodss on hole coboundary summit are calculatedWherein piIt is the border vertices on hole, n is
The number of border vertices,It is a point in required plane.Using this as a point in fit Plane.
B) obtainMatrix M is set up after point：Mi=(xi-x0,yi-y0,zi-z0), wherein MiIt is i-th row of matrix M, (xi,
yi,zi) it is piCoordinate.M has following form：
C) M is calculated with SVDTThree eigenvalue λs of M1≥λ2≥λ3, with λ3Corresponding characteristic vectorAs the method for plane
Vector.According toWithDetermine plane, the boundary edge of hole is projected in the plane.
Step (4) is also needed to optimize the minimal eigenvalue of PCA methods, hole is divided into aperture if there is the border of Self-crossover
Hole.For the complicated hole that height is folded, such as Fig. 4, above-mentioned projecting method can cause hole border to produce Self-crossover.Need this
Class hole is divided into two parts, and projecting to two planes respectively carries out subsequent operation again, in this step how to obtain hole most
It is key issue that optimal sorting cuts.In the method that three-dimensional point set projection plane is obtained by PCA, the value of minimal eigenvalue determines this
Fitting degree of a little points to plane：λ3Relative to λ1Less, the degree of fitting of expression plane and point set is higher.Therefore, minimize segmentation
In the minimal eigenvalue that latter two point set determines, that larger obtains optimum segmentation, that is, solve following optimization problem：
Wherein, PS1={ pj,...pn,...,pi-1},PS2={ pi,...p1,...,pj-1},It is PS respectively1,
PS2The minimal eigenvalue obtained by PCA methods.
Hole is decomposed into after small holes, can guarantee that each small holes projects to the border in fit Plane and will not be produced from
Intersect.After hole border projects to plane, the intuitive of follow-up calculating for convenience, by the Plane Rotation in x-y plane
Parallel position, and record the corresponding relation of the point in space and Plane-point.The intermediate result for obtaining is as shown in Figure 8 c.
Projection of the step (5) to hole in the fit Plane of generation in step (3) carries out three using the CDT based on scan line
Angle subdivision, CDT methods are compared with traditional Delaunay methods obvious advantage in speed.The step of CDT, is as follows：
A) initialize.All points are sorted from small to large according to y values, for y identicals point, are sorted according to x values.For each point
Addition additional information, indicates that whether the point is the upper end vertex of binding side.In order to avoid the discussion of excessive complex situations, addition two
Individual virtual point P-1, P-2, the two points respectively in the lower left and lower right of all input vertexs, as shown in Figure 5.By P-1, P-2,
P0Initial delta is connected and composed, by P0P-1,P0P-2As preliminary sweep wavefront.
B) scan.According to y value sizes, motion scan line from the bottom up.Just stop whenever scan line runs into a summit,
Summit event is processed if the summit is not the upper end vertex of a binding side, side event is otherwise processed.Summit event：By PiHang down
Directly project to wavefront and obtain Pj, determine PjThe side P of place wavefrontLPR(Fig. 6 a), connects Pi, PL, PLComposition new triangle (figure
6b), if the triangle is unsatisfactory for empty circle property, opposite side is adjusted, and the step is referred to as edge flip (Fig. 6 c)；Side event：When
If during the upper end vertex of front summit a line, just forming side event.First determine first triangle intersected with the side, then
The triangle (Fig. 7 a) that will intersect with the side along this traversing triangle to other.After the completion of traversal, delete with it is all with should
The intersecting triangle in side, and their summit is ranked up the Π obtained below e according to the position with side eLWith positioned at e
Top ΠUThis two parts is finally carried out the conventional CDT (Fig. 7 c) based on delta algorithm by (Fig. 7 b) respectively.
C) post processing.By all and virtual point P-1, P-2The triangle that is connected is deleted, and is added edge triangles and completed
Trigonometric ratio.
After the completion of the polygonal trigonometric ratio of boundary edge composition, according to the corresponding relation in upper step by two dimensional surface
Three dimensions return in point back projection.The intermediate result for obtaining is as shown in figure 8d.
Step (6) in order to ensure that mesh-density is consistent around the density and hole of newly-increased triangle, and also to
On the curved surface generated in newly-generated Triangular Maps to step (2), will can need to be finely divided operation to the triangle for increasing newly.
Comprise the following steps that：
A) it is each boundary point v on holeiAll increase a density attributes θ (xi), which is defined as：With viAdjacent side
The meansigma methodss of length.
B) to each newly-increased triangle (vm,vn,vl), calculate its barycenter vcWith its density attributes θ (vc):=(θ (vn)+θ
(vm)+θ(vl))/3.To each i=m, n, l：If α | | vc-vi| | ＞ θ (vc),α||vc-vi| | ＞ θ (vi), then just will
Triangle (vm,vn,vl) it is subdivided into (vc,vn,vl),(vm,vc,vl),(vm,vn,vc), while checking (vm,vn),(vm,vl),(vl,
vn) whether need to carry out edge flip.
If c) not having new triangle to produce in b jumps to d, b is otherwise jumped to.
D) exchange it is all it is newly-increased in needs exchange while.
In the implementation, chooseThe intermediate result for obtaining is as figure 8 e shows.
Step (7) after sampling terminates needs sampled point is adjusted on the curved surface of HRBF fittings.The present invention adopts gradient
The step for descent method is completed.The gradient calculation method of HRBF is：
H is as defined above for Hessian matrixes.After obtaining gradient, for each newly-increased summit r in repairing grid0, adopt
Mapped that on curved surface with following iterative formula：
Meet | | rk+1-rk| | during≤ε conditions, iteration stopping, ε are the range of error specified.
The algorithm of the present invention realizes that with visual studio 2010 and OpenGL allocation of computer used is：Dominant frequency
2.53GH, Xeon E5630 processors and 8G internal memories.When linear system determined by HRBF is solved using the LU in Eigen storehouses point
Solution.Method final effect figure is as illustrated in fig. 8f.Fig. 9 is the comparison diagram of this method and tradition based on RBF methods, is from left to right distinguished
It is the master mould with hole, the model Jing after RBF method filling-up holes, the model Jing after HRFB method filling-up holes.
Claims (4)
1. a kind of triangle gridding filling-up hole method based on Hermite RBFs, the hole for being applied to 3-D scanning model are repaiied
Mend, it is characterised in that comprise the steps：
(1) hole border is extracted, obtains hole border and its neighborhood summit, generated using Hermite RBFs and met
The implicit surface of mesh curvature change around hole；
(2) fit Plane on summit on hole border is generated using PCA methods, the hole border of extraction is projected to into the plane
On；If there is Self-crossover border, optimize the minimal eigenvalue of PCA methods, hole is decomposed into into small holes；Using based on scanning
The CDT algorithms of line carry out triangle division to the hole border projected in plane, then go back to the result back projection of triangle division
Master mould；
(3) in order to ensure that mesh-density is consistent around the density and hole of newly-increased triangle, be hole it is borderline each
Summit defines a density attributes, newly-increased triangle is finely divided as guidance using the density attributes, completes the choosing of sampled point
Take；
(4) the newly-increased summit segmented is mapped on the implicit surface that step (1) is generated using gradient descent method.
2. the triangle gridding filling-up hole method based on Hermite RBFs according to claim 1, it is characterised in that：
Step (1) includes：Using half of data structure tissue three-dimensional grid data；Side data in traversal grid, detect only with one
The adjacent side of triangle, as boundary edge；The closed-loop that end to end boundary edge is constituted constitutes a hole；Extract hole side
Boundary and the summit in field, using position and the normal information on these summits, generate with reference to Hermite RBFs and meet hole
The implicit surface of surrounding mesh curvature change.
3. the triangle gridding filling-up hole method based on Hermite RBFs according to claim 1, it is characterised in that：
Step (3) includes：In order to around the filling-up hole mesh-density that ensures to finally give and hole, mesh-density is consistent, need to step
Suddenly the newly-increased triangle in (3) is finely divided；Define density attributes for borderline each summit of hole, the attribute definition be with
The meansigma methodss of the adjacent all length of sides of this point；Then with newly-increased barycenter oftriangle coordinate as newly-increased point subdivision triangle,
Delaunay properties will be kept in segmentation process；The sampled point of perforated has been obtained after the completion of sub-dividing operations.
4. the triangle gridding filling-up hole method based on Hermite RBFs according to claim 1, it is characterised in that：
Step (4) includes：With reference to the sampled point in the implicit surface and step (3) generated in step (1), will be adopted using gradient descent method
Sampling point is mapped on implicit surface, is obtained being met and net around hole declinable filling-up hole grid.
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