CN1975786A - Progressive lattice generating method based on inverse loop subdivision - Google Patents

Abstract

The invention discloses a gradual mesh generation method based on inversed Loop breakdown, which belongs to geometric modeling technology area, especially involves a triangle mesh based surface simplification method. For any triangle mesh with breakdown continuity Mj=(Pj,Kj), the method includes follow steps: 1) mesh splitting: split culminations of the triangle mesh Mj to odd points set ODDj and even points set EVENj; 2) ODD point speculation: for each odd point, speculate its position ODD' with Loop breakdown, get the error value ej for each odd point ODDj by subtracting the speculative position value; 3) mesh update: delete odd set ODDj, the left even set EVENj forms next level culminations Pj-1, build new culmination connective information Kj-1, and generate a new simplified mesh Mj-1; 4) repeat above steps until the mesh is split to elemental mesh.

Description

A kind of progressive grid generation method based on contrary Loop segmentation

Technical field

The invention belongs to the solid modeling technology area, particularly relate to a kind of curved surface short-cut method based on triangular mesh.

Background technology

The expression of three-dimensional picture normally diabolo grid is played up and is obtained.In geometric modeling, have the strong sense of reality and smoothness in order to make described three-dimensional picture, usually need the triangle grid model of high complexity and high degree of detailization.Surface subdivision is a kind of method of very ripe generation geometric modeling, the grid that is generated is the grid (Remesh) of gridding again, and it is connective to have a segmentation, and is easy to operations such as gridding edition and grid division.On the other hand, along with popularizing of 3-D scanning equipment, obtaining of high density arbitrary topology grid data becomes more and more easier.Yet these grid datas do not have the segmentation connectivity, need carry out gridding again to grid data.In addition, even the topology of grid has the segmentation connectivity, the data of its grid also can not just in time be the extremal surfaces of a certain segmentation pattern, and the difference of grid data and subdivision curved surface is preserved as the surface subdivision data, accepts or rejects processing as required.

Again gridding is an important ring of arbitrary topology grid multiresolution analysis.Matthias Eck introduces the divided method resampling the earliest arbitrary mess is carried out multiresolution analysis.The method selects a suitable initial mesh M0 as parameter field M to be carried out parametrization to original mesh M, then M0 is resampled with segmentation, obtains having the connective new grid of segmentation.People such as Aaron Lee have provided a kind of method of gridding again by the multiresolution parametric surface (MAPS) of setting up the arbitrary topology grid; People such as Kobbelt have proposed a kind of gridding method again that shrinks encirclement (Shrink wrapping) that is called, and Zhou Hai etc. have proposed to utilize subdivision curved surface to rebuild the method for grid; Li Gui waits the subdivision curved surface of having analyzed with sharp-pointed characteristic clearly, has provided surface fitting method.Said method all can generate preferably has the connective Remesh of segmentation.

Hoppe has at first proposed the notion of progressive grid (Progressive Mesh), and with progressive grid arbitrary mess be expressed as efficiently, harmless and coding with continuous resolution, provided the effective implementation method of progressive grid simultaneously.Luo Xiaonan etc. have proposed the progressive grid generating algorithm based on the contrary butterfly segmentation of interpolation type, and figure transmission and the graph rendering of progressive grid application under mobile environment, solve the three-dimensional picture on the mobile device and shown problem, but the summit of the relevant 2-neighborhood of affine combination on butterfly segmentation summit, and the summit number that is associated is more, has influenced progressive grid greatly and has generated and graph rendering speed.

Summary of the invention

The present invention is directed to above deficiency, proposed a kind of progressive grid generation method, at first the redundant information in the grid is deleted in batches based on contrary Loop segmentation; Form the progressive grid of forming by base net lattice and a series of error amount at last.The present invention is applicable to have the connective triangular net of segmentation, at first will do pre-service for arbitrary mess.This algorithm with approach type segment pattern in contrary segmentation process as the interpolation type subdivision mode treatment, algorithm is applicable to multiple segmentation patterns such as interpolation type, approach type, with the contrary example that is subdivided into of Loop algorithm is illustrated in the literary composition.In addition,, make that lattice simplified arithmetic speed with the mesh reconstruction process is relative very fast because the summit number that the affine combination in summit of Loop segmentation pattern is associated is few, more effective in actual applications.

In order to realize goal of the invention, the technical scheme of employing is:

In triangle gridding, the summit that links to each other with six limits is defined as regular point, and all summits all are that the mesh definition of regular point is a regular net, and most summits are that the grid of regular point is half regular net, all contains singular point usually in the triangle gridding of arbitrary surface.

Key step based on the progressive grid generation method of segmenting against Loop comprises:

1) grid division: the vertex split of existing triangle gridding is become singular point collection ODD ^jWith pair-point collection EVEN ^j

2) singular point prediction:, before the deletion singular point,, adopt Loop segmentation prediction its position ODD ', with existing each singular point ODD to each singular point for the grid reduction and the reconstruction of three-dimension curved surface moulding ^jSubtract each other corresponding with predicted value obtains a set of error values e ^j

3) grid upgrades: delete singular point collection ODD ^jAfter, remaining pair-point collection EVEN ^jForm the summit P of one deck down ^J-1, upgrade the link information on these summits and form new triangle collection K ^J-1, generated the new grid after the simplification;

4) circulation above-mentioned steps can not divide up to final grid, generates base net lattice and a series of error amount.

The division rule of described step 1) grid division is:

Any one singular point is that pair-point is classified as the pair-point collection on a, the network selection lattice;

B, all of its neighbor point that will be adjacent with singular point are classified as the singular point collection;

C, symmetric points peripheral to these singular points and this pair-point symmetric position are made as pair-point, are classified as the pair-point collection;

The pair-point that d, recursive call pair-point are concentrated, at first that it is adjacent all of its neighbor point is classified as the singular point collection, the more peripheral symmetric points with this pair-point symmetric position of these singular points is made as pair-point, is classified as the pair-point collection, and all vertex splits finish in grid.

Described step 2) the error amount e in the singular point forecasting process ^jComputing method be:

$e_i^j=\mathrm{OD}{D}_i^j-\mathrm{OD}{D}_I^{\′}$

Wherein, j represents the grid number of plies, and i represents the singular point number of j layer grid.

Description of drawings

Fig. 1 is the progressive grid generation method flow diagram based on contrary Loop segmentation;

Fig. 2 is half regular net rough schematic view;

Fig. 3 concerns synoptic diagram for the summit;

Fig. 4 is prediction and renewal signal;

Fig. 5 is the progressive grid of head portrait model (number of vertex/triangular facet number) synoptic diagram;

Fig. 6 is the progressive grid of e-Sphere model (number of vertex/triangular facet number) synoptic diagram.

Embodiment

Below in conjunction with accompanying drawing this method is further set forth.

The progressive grid that is illustrated in figure 1 as based on contrary Loop segmentation generates method flow diagram.

If (P, K), wherein P represents the set of triangle gridding apex coordinate, P to triangle gridding M= _i=(x _i, y _i, z _i) (1≤i≤n), K represents to contain all triangle set of network topology information.

The main target of this algorithm is exactly with original mesh M ⁿ(P ⁿ, K ⁿ) be generated as the M of isomorphism ^j(P ^j, K ^j) (1≤j≤n), wherein M ⁰=(P ⁰, K ⁰) be the base net lattice.

If the initial surface grid is M ⁿ, after once simplifying, obtain M ^N-1, be M for j layer grid ^j, each lattice simplified following three processes that comprise.

(1) grid division: the vertex split of existing triangle gridding is become singular point collection ODD ^jWith pair-point collection EVEN ^jBecause all there is singular point in the three-dimensional picture grid, and the sharp-pointed characteristic of singular point ordinary representation curved surface need all remain.So when implementing at first on the network selection lattice any one singular point be classified as the pair-point collection for pair-point v, all of its neighbor point va that then will be adjacent with singular point is classified as the singular point collection, peripheral symmetric points vs with this pair-point symmetric position is made as pair-point to these singular points, be classified as the pair-point collection, the relation of each vertex position is seen shown in Figure 3.It is to utilize recursive call that pair-point is set, and all vertex splits finish in grid, and algorithm is as follows:

Look for any singular point v;

If { v concentrates at pair-point, returns success;

If v concentrates at singular point, return failure;

V is set (v) to pair-point collection SetEvenVertex;

Each consecutive point va for v

If { va is that singular point or va concentrate at pair-point, returns failure;

Va is set to singular point collection SetOddVertex (va);

Find the symmetric points vs of va and v;

Vs is set to pair-point collection SetEvenVertex (vs);

}

Return success

}

Fig. 2 is the signal that half regular net is simplified through secondary.The shade vertex of a triangle is the singular point ODD of each layer grid, and all the other points are pair-point EVEN.All singular points are redundant information, can delete, and keep all pair-points, to reach the simplification of grid.Observe Fig. 2 (a) and can find that singular point, pair-point are distributed in the triangle gridding regularly.The triangle that the triangle of shade is made up of singular point among the figure can be deleted.

(2) singular point prediction:, before the deletion singular point,, adopt Loop segmentation prediction its position ODD ', as shown in Figure 4 to each singular point for the grid reduction and the reconstruction of three-dimension curved surface moulding.With existing each singular point ODD ⁱSubtract each other corresponding with predicted value obtains a set of error values e ^j

$e_i^j=\mathrm{OD}{D}_i^j-\mathrm{OD}{D}_i^{\′}$

Wherein, j represents the grid number of plies, and i represents the singular point number of j layer grid.The O point is a singular point among Fig. 4 (a), and the E point is a pair-point, and Fig. 4 (b) obtains an O ' with the segmentation model prediction before being deletion O point, and the difference of its corresponding future position O ' of each singular point O promptly obtains error amount e ^jCollection.

(3) grid upgrades: delete singular point collection ODD ^jAfter, remaining pair-point collection EVEN ^jForm the summit P of one deck down ^J-1, upgrade the link information on these summits and form new triangle collection K ^J-1, generated the new grid M after the simplification ^J-1=(P ^J-1, K ^J-1).The grid of rebuilding behind Fig. 4 (c) signal deletion singular point.

Repeat above-mentioned three steps, with the initial mesh data M of complexity ⁿBe simplified to grid M ⁰Each level lattice simplified, the coordinate of singular point do not need to change.Data after the simplification obtain base net lattice and a series of error collection e ^jData, constitute the data of many levels: M ⁰→ e ¹→ e ²→ ... → e ^N-2→ e ^-1, generated progressive grid, i.e. (M ⁰, e ⁰) generation M ¹, (M ¹, e ¹) formation M ²..., (M ^N-1, e ^N-1) reducible M ⁿ, progressive grid sees Table 1.

The progressive grid that table 1 is made up of base net lattice and error

Progressive grid	M n	M n-1	...	M 1	M 0
						Error amount		e n-1	...	e 1	e 0

As Fig. 5, Figure 6 shows that the progressive grid of head portrait model (number of vertex/triangular facet number) synoptic diagram and the progressive grid of e-Sphere model (number of vertex/triangular facet number) synoptic diagram, experiment shows, this efficiency of algorithm height is compared with algorithm in the past, speed is fast, is easier to use in actual applications.

Claims (3)

1, a kind of progressive grid generation method based on contrary Loop segmentation is for having the internuncial triangle gridding M of segmentation arbitrarily ^j=(P ^j, K ^j), its key step comprises:

1) grid division: the vertex split of existing triangle gridding is become singular point collection ODD ^jWith pair-point collection EVEN ^j

2) singular point prediction:, before the deletion singular point,, adopt Loop segmentation prediction its position ODD ', with existing each singular point ODD to each singular point for the grid reduction and the reconstruction of three-dimension curved surface moulding ^jSubtract each other corresponding with predicted value obtains a set of error values e ^j

3) grid upgrades: delete singular point collection ODD ^jAfter, remaining pair-point collection EVEN ^jForm the summit P of one deck down ^J-1, upgrade the link information on these summits and form new triangle link information K ^J-1, generated the new grid M after the simplification ^J-1

4) circulation above-mentioned steps is base net lattice and a series of error amount up to the grid of final division.

2, the progressive grid generation method based on contrary Loop segmentation according to claim 1 is characterized in that, the division rule of described step 1) grid division is:

Any one singular point is that pair-point is classified as the pair-point collection on a, the network selection lattice;

B, all of its neighbor point that will be adjacent with singular point are classified as the singular point collection;

C, symmetric points peripheral to these singular points and this pair-point symmetric position are made as pair-point, are classified as the pair-point collection;

The pair-point that d, recursive call pair-point are concentrated, at first that it is adjacent all of its neighbor point is classified as the singular point collection, the more peripheral symmetric points with this pair-point symmetric position of these singular points is made as pair-point, is classified as the pair-point collection, and all vertex splits finish in grid.

3, the progressive grid generation method based on contrary Loop segmentation according to claim 1 is characterized in that described step 2) error amount e in the singular point forecasting process ^jComputing method be:

$e_i^j={\mathrm{ODD}}_i^j-{\mathrm{ODD}}_i^{\′}$

Wherein, j represents the grid number of plies, and i represents the singular point number of j layer grid.

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