CN102881044A - Simplification method of three-dimensional grid model based on triangle folding - Google Patents

Abstract

The invention provides a simplification method of a three-dimensional grid model based on triangle folding. According to the simplification method, folding points of each triangle in the model are calculated by vertex projection, geometrical elements in grid patterns are folded to achieve the aim of simplification, and error control is performed on simplification by combination with volume errors caused in simplification, the maximum area value and normal vector errors. The simplification method solves the problems that the data transmission quantity and the storage quantity of three-dimensional images are over large, geometrical characteristics of an original model are effectively maintained while errors of a simplified model are reduced, and the simplification method has important application values in the fields of computer aided design and medical image systems and the like.

Description

A kind of short-cut method of the three-dimensional grid model based on triangle collapse

Technical field

The invention belongs to image processing field, relate to a kind of method of the simplification three-dimensional grid model based on triangle collapse.

Background technology

To obtain technology constantly perfect along with three-dimensional data, and people can obtain the more and more three-dimensional model of elaborate.In computer graphics, because triangle is the basic display unit that many graphic hardwares are directly supported, so triangle grid model remains the main expression mode of present three-dimensional model.Complicated model has all proposed very high requirement to the memory capacity of computing machine, processing speed, render speed, transfer efficiency etc., yet under many circumstances, high-resolution model is always unnecessary, we can replace master pattern with relatively simple model, and this need to simplify three-dimensional grid model.The three-dimensional grid model simplification refers to keeping under the constant prerequisite of master mould geometric configuration, with the approximate model of the least possible triangle number, limit number and number of vertex structure master pattern.

The geometric element elimination method is a kind of important Graphic Simplification Method in the existing three-dimensional grid model short-cut method, the method is according to the geometry topology information of master mould, and deletion is to how much " pel " (points, edges, faces) of model geometric feature affects less under the prerequisite of the certain geometric error of maintenance.Mainly be divided into vertex deletion method, edge contraction method, triangle collapse method etc.

The vertex deletion method is a kind of unit that is take the summit, one by one the summit is removed from model by certain criterion, to reduce the lattice simplified method of data volume.Formed cavity uses again the method for trigonometric ratio to fill up after removing the summit.Schroeder adopts the plane criterion to realize this algorithm the earliest, and it has calculates comparatively fast, need not to take the advantage of too many internal memory, but this algorithm is only applicable to flow shape, and it is keeping there is certain difficulty aspect the smoothness of the surface.Have again subsequently more accurate error Measure Algorithm that the algorithm of Schroeder is improved, these algorithms can generate the model of better quality, but need more time of cost and space.

The edge contraction method be with a certain limit in the grid by certain criterion new summit that permeates, and two the leg-of-mutton areas adjacent with this limit deteriorate to zero method.Hoppe at first adopts energy-optimised method to realize Edge collapse algorithm, and the effect of simplified model is best in all short-cut method, but this algorithm time complexity is high, is not suitable for the occasion higher to time requirement.Garland has proposed the Quadric Error Metrics Edge collapse algorithm of (Quadric Error Metric is called for short QEM) subsequently.This algorithm speed is fast, the quality of simplified model is only second to the energy optimizing method of Hoope, but only considered the tolerance of distance in QEM, the grid after the simplification distributes comparatively even, therefore can not well keep the important geometric properties of model surface behind extensive the simplification.The lot of domestic and international scholar improved the QEM algorithm afterwards, improved the quality of simplified model.Except above-mentioned two kinds of algorithms that are applied to edge contraction, Cohen simplifies grid model with edge contraction in conjunction with Continuous Mappings; The importance degree on Andre Gusziec definition limit comes legal limit folded according to importance degree order from small to large etc.

The triangle collapse method is by merging into leg-of-mutton three summits a bit, and the deletion area deteriorates to zero adjacent triangle, thereby realizes algorithm that triangle grid model is simplified.It is the continuity of Edge collapse algorithm, have than Edge collapse algorithm speed advantage faster, its problem of mainly considering be how to calculate folding after position and the folding order of how to confirm on new summit.This algorithm is at first proposed by Hamann, and with leg-of-mutton curvature and equal angular product as the error after simplifying, triangle elongated like this and low curvature is at first deleted, this algorithm can keep profile preferably, but its complexity is higher.Gieng has also proposed similar Triangle Collapse Algorithm, the cost of triangle collapse is defined as the product of leg-of-mutton area and curvature, but the computation complexity of this algorithm is still higher, and area and curvature belong to two different geometric senses, simply multiply each other and can not effectively reflect area and these two criterions of curvature.Pan Zhigeng combines the QEM algorithm that triangle collapse and Garland propose, and has provided a kind of method of transmitting simplification error.The fast effect of the method speed is better, but that triangle is simplified stylish vertex position is uncertain, and has ignored the factors such as triangle individual shapes, area, directly causes regional area over-simplification and long and narrow leg-of-mutton generation.Zhou Yuanfeng makes amendment to the method for Pan Zhigeng, has proposed the short-cut method under the volume square tolerance, and the method has been optimized triangle gridding, and the quality of gained triangle gridding is better.Liu Xiangyun has proposed a kind ofly to carry out the folding shortcut calculation of continuous triangle shape according to probable value, accelerated simplification speed, but piecewise interval is not unique in the folding probability function of segmentation, can produce long and narrow triangle in the triangle grid model.

In the research of lattice simplified this class problem, not only to consider simplification speed, also to improve as much as possible the precision after the simplification.In above-mentioned three kinds of shortcut calculations, triangle collapse is the fastest algorithm of geometric element deletion algorithm medium velocity, but this algorithm is difficult to obtain balance at computation complexity and the aspect of model aspect keeping two.The present invention is directed to this defective that present algorithm exists, proposed a kind of new 3D grid shortcut calculation based on triangle collapse.

Summary of the invention

The purpose of this invention is to provide a kind of efficient triangle collapse short-cut method, its essence is when the point that reduces model and face, effectively kept the feature of model, and the error control that produces during with model simplification within the specific limits.

For realizing that the technical scheme that the object of the invention adopts is such, a kind of short-cut method of the three-dimensional grid model based on triangle collapse may further comprise the steps:

1) obtains the triangle grid model of testee;

2) determine each leg-of-mutton folding point in the described triangle grid model;

3) calculate respectively when folding according to each folding point the volumetric errors that produces, the model after namely folding and the volumetric errors value V between the initial model _i(i=1,2,3 ..., n represents leg-of-mutton numbering);

4) by sorting from small to large volumetric errors value and deposit chained list in;

5) obtain the corresponding minimum volume error amount of first element of chained list;

6) when described minimum volume error amount less than the defined volume threshold Y of user _vThe time, according to the corresponding leg-of-mutton folding point of described minimum volume error amount model is folded simplification, and by 2), 3) in computing method recomputate involved area each leg-of-mutton folding point and volumetric errors, upgrade 4) in chained list, turn afterwards step 5);

When described minimum volume error amount during greater than the defined volume threshold of user, end operation.

The present invention also provides a kind of preferred method, i.e. a kind of short-cut method of the three-dimensional grid model based on triangle collapse is characterized in that:

1) obtains the triangle grid model of testee;

2) determine each leg-of-mutton folding point in the described triangle grid model;

3) calculate respectively when folding according to each folding point the error that produces, the model after namely folding and the volumetric errors value V between the initial model _i(i=1,2,3 ..., n represents leg-of-mutton numbering), folding after affected leg-of-mutton maximum area value S _i, folding after the maximum angle error amount α that produces before and after folding of affected leg-of-mutton normal vector _i

4) with all V _iValue sorts from small to large and deposits chained list, while and V in _iCorresponding leg-of-mutton numbering, S _i, α _iAlso deposit the corresponding node in the chained list in;

5) the volumetric errors value that first element is deposited in described chained list is greater than the defined threshold value Y of user _vThe time, end simplifies the operation;

The volumetric errors value that first element is deposited in described chained list is less than the defined volume threshold Y of user _v, and the S that first element is deposited in the described chained list _iValue is less than the defined maximum area threshold value of user Y _s, and the α that first element is deposited in the described chained list _iValue is less than the defined angle threshold Y of user _αThe time, according to the corresponding leg-of-mutton folding point of first element in the described chained list model is folded simplification, and by 2), 3) in computing method recomputate each leg-of-mutton folding point and error of involved area when simplifying, upgrade 4) in chained list, turn afterwards step 5);

First element is less than the defined volume threshold Y of user in described chained list _v, and the S that first element is deposited in the described chained list _iOr α _iValue is greater than the defined threshold value of user, then corresponding triangle does not fold simplification, select afterwards second element in the described chained list, adopt the method for judging first element in the described chained list in this step to judge, by that analogy, when the volumetric errors of the table tail that arrives chained list or current judgement element greater than the defined volume threshold of user, end simplifies the operation.

In above-mentioned method for optimizing, except setting model after folding and the volumetric errors value V between the initial model _iThreshold value outside, also to set respectively folding after affected leg-of-mutton maximum area value S _i, the maximum angle error amount α that produces before and after folding of affected leg-of-mutton normal vector _iThreshold value, and need V _i, S _iAnd α _iJust select V during all less than separately threshold value _iThe minimum folding point of value folds and simplifies the operation.

Description of drawings

Device of the present invention can further specify by the indefiniteness embodiment that accompanying drawing provides.

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is part triangle gridding synoptic diagram in the handled triangle grid model of the present invention;

Fig. 3 is the folding synoptic diagram that simplifies the operation of intermediate cam shape of the present invention;

Fig. 4 is that intermediate cam shape folding error of the present invention is analyzed synoptic diagram;

Fig. 5 is the contrast synoptic diagram of QEM algorithm and algorithm of the present invention among the embodiment.

Embodiment

The invention will be further described below in conjunction with drawings and Examples, only limits to following embodiment but should not be construed the above-mentioned subject area of the present invention.In the situation that does not break away from the above-mentioned technological thought of the present invention, according to ordinary skill knowledge and customary means, make various replacements and change, all should be included in the scope of the present invention.

A kind of short-cut method of the three-dimensional grid model based on triangle collapse may further comprise the steps:

1) obtains the triangle grid model of testee;

Among the embodiment, formed triangle grid model adopts MC (Marching Cubes) algorithm to rebuild by Industrial CT Slicing Image and obtains, the present invention is not limited only to the triangle grid model that said method obtains, it is applicable to simplify the stream shape triangle grid model that the whole bag of tricks obtains, and stream shape triangle grid model is that mostly to be two triangles most common on any limit in the model.Referring to Fig. 2 or Fig. 3, the triangle T of described triangle grid model _iV is used in (i is leg-of-mutton numbering) expression _jEach summit in (j is the numbering on summit) expression triangle grid model is known quantity.Described vertex v _iThe leg-of-mutton definition of single order neighborhood of j is mentioned in the prior art, is: with vertex v _iAll triangles of direct neighbor are used

Expression; Equally, described triangle T _iSingle order neighborhood triangle be defined as: triangle T _iThe single order neighborhood triangle on each summit and do not comprise T _iAll the leg-of-mutton set of itself are used Expression.

Referring to A part among Fig. 3, triangle T _i, i.e. Δ v _I1v _I2v _I3Single order neighborhood triangle be: Δ v _I2v _I5v _I6, Δ v _I1v _I3v _I9, Δ v _I1v _I5V _I2Δ v _I3v _I8v _I9, Δ v _I1v _I9v _I4, Δ v _I2v _I7v _I3, Δ v _I3v _I7v _I8, Δ v _I1v _I4v _I5With Δ v _I2v _I6v _I7

In addition, the triangle in the model is folded the implication of simplifying and belong in the art known.Take Fig. 3 as example, triangle T _i, i.e. Δ v _I1v _I2v _I3And the leg-of-mutton original state of single order neighborhood is shown in A part among Fig. 3, to Δ v _I1v _I2v _I3When folding, with Δ v _I1v _I2v _I3Three summits be merged into a new some v _I0, i.e. the folding point v that the present invention will determine _I0, simultaneously, those and Δ v _I1v _I2v _I3Three continuous line segments in summit are also all linked v accordingly _I0On, thereby cause Δ v _I1v _I2v _I3Single order neighborhood triangle change, wherein a part of triangle is degenerated to line segment, another part then just deforms, the leg-of-mutton variation of single order neighborhood causes producing certain error between simplified model and the initial model, the size of error amount is determining each leg-of-mutton fold sequence in the triangle grid model, and definite scheme of fold sequence also is another aspect of the present invention.A shown in Fig. 3 partly is initial model, and B partly is the simplified model of A part gained after once folding simplification.

This step can be set up topological structure when actual treatment.The purpose of setting up topological structure just is that it can carry out the inquiry of syntople between the points, edges, faces easily, is beneficial to the calculating of folding point, simultaneously so that behind the triangle collapse between the points, edges, faces renewal of syntople also quite simple.

In the table of summit, coordinate figure, normal vector and the single order neighborhood triangle on summit recorded on each summit.The following expression of summit structure:

2) determine each leg-of-mutton folding point in the described triangle grid model.This step is not to be that will to carry out reality to each triangle folding, and when just hypothesis will fold certain triangle, calculates this leg-of-mutton folding point, can be described as to pre-determine each leg-of-mutton folding point before folding triangle yet.With Fig. 3 intermediate cam shape T _iBe example, because this triangle comprises v _I1, v _I2, v _I3Three summits, this step namely are if folding triangle T _i, how to confirm folding point v _I0, circular is as follows:

v _i0=γ ₁·v′ _i1+γ ₂·v′ _i2+γ ₃·v′ _i3

Wherein $v_{i1}^{\′}={\mathrm{\λ}}_1\·\frac{\underset{T_{i1}\∈\{\mathrm{FOT}{\}}_{T_i}}{\mathrm{\Σ}}{P}_{T_{i1}}\·S_{T_{i1}}}{\underset{T_{i1}\∈\{\mathrm{FOT}{\}}_{T_i}}{\mathrm{\Σ}}{S}_{T_{i1}}}+{\mathrm{\λ}}_2\·v_{i1},$ It has represented vertex v _I1At folding point v _I0In component value, v ' _I2, v ' _I3Computing method and v ' _I1Similar, represented respectively vertex v _I2, v _I3At folding point v _I0In component value, in the formula

The expression vertex v _I1In triangle T _I1In subpoint, triangle T _I1The expression triangle T _iSingle order neighborhood triangle set in each triangle,

The expression triangle T _I1Area, λ ₁, λ ₂Expression represents respectively subpoint And vertex v _I1To v ' _I1Influence coefficient, λ ₁, λ ₂Value be 0～1.0, in an embodiment of the present invention, λ ₁Get 0.6, λ ₂Get 0.4.Folding point v _I0Calculating in, γ ₁, γ ₂, γ ₃Represent each component value v ' _I1, v ' _I2, v ' _I3Factor of influence, its value all is 0～1.0, and γ ₁+ γ ₂+ γ ₃=1, calculate γ for simplifying ₁, γ ₂, γ ₃All get in an embodiment of the present invention

Said method can keep the geometric properties of master pattern preferably by the position of each triangle collapse point of control.As shown in Figure 3, determine triangle T _iFolding point v _I0The time, select triangle T _i, i.e. Δ v _I1v _I2v _I3Single order neighborhood triangle be three vertex v _I1, v _I2, v _I3The projecting plane.The selection on projecting plane has taken into full account affected relevant topology triangle when folding, and related triangle number is also few, can locate fast, and the processing time shortens greatly, and in addition, selected projecting plane can well strengthen local feature.

The model of A part among Fig. 3 is calculated according to above-mentioned steps, in the A part each triangle collapse point coordinate referring to table 1, special concern Δ v _I1v _I2v _I3Folding point coordinate (119.54537,44.78644,1.59037).

Each triangle collapse point coordinate of A part among table 1 Fig. 3

3) calculate respectively when folding according to each folding point the error that produces, the model after namely folding and the volumetric errors value V between the initial model _i(i=1,2,3 ..., n represents leg-of-mutton numbering), folding after affected leg-of-mutton maximum area value S _i, folding after the maximum angle error amount α that produces before and after folding of affected leg-of-mutton normal vector _i

This step is with step 2), be not to be will carry out reality to each triangle to fold, and just calculate the error that produces when hypothesis will fold certain triangle, the cost the when size of these error amounts has reflected triangle collapse.According to the size of error amount, can determine the fold sequence when triangle grid model is simplified, the error of simplified model is controlled within the as far as possible little scope.

One embodiment of the present invention are only considered V _iValue is namely selected the minimum V less than threshold value _iCorresponding triangle fold to simplify and generates new model, and then the regional corresponding parameter that new model changes with respect to initial model is recomputated error when further folding, judges whether to continue folding simplification.

Preferred implementation of the present invention then will be considered above-mentioned V _i, S _iAnd α _iThree kinds of error amounts, V _i, S _iAnd α _iJust can fold during all less than separately threshold value.

Fig. 4 is the error analysis synoptic diagram of A part among Fig. 3, folded triangle T _i, i.e. Δ v _I1v _I2v _I3Single order neighborhood triangle be Δ v _I1v _I4v _I5, Δ v _I2v _I5v _I6, Δ v _I2v _I6v _I7, Δ v _I3v _I7v _I8, Δ v _I3v _I8v _I9, Δ v _I1v _I9v _I4, Δ v _I2v _I7v _I3, Δ v _I1v _I5v _I2, Δ v _I1v _I3v _I9, Δ v _I1v _I2v _I3Be folded into a v _I0The time, the model after folding and the volumetric errors value V between the initial model _iBe expressed as: with v _I0For the summit, with Δ v _I1v _I2v _I3And single order neighborhood triangle totally 10 tetrahedron volume sums that triangle is the bottom surface, its calculation expression is as follows:

$V_i=\underset{T_j\∈\{\mathrm{FOT}{\}}_{T_i}\∪T_i}{\mathrm{\Σ}}\frac{1}{3}(v_{i0}\·P_{T_j}^T)\·S_{T_j}$

V in the formula _I0The expression triangle T _iFolding point, folding point v _I0Coordinate be designated as (x _i, y _i, z _i, 1); Triangle T _jRepresent triangle T _iAnd each triangle in the set of single order neighborhood triangle, establish triangle T _jThe plane equation at place is a _jX+b _jY+c _jZ+d _j=0, wherein Order

The expression triangle T _jArea.Can effectively control the phenomenon of master pattern volume-diminished by volumetric errors, so that simplified model approaches master pattern as far as possible from geometric aspects.In computation process, because the volume that calculates of above-mentioned volume computing formula a part of volume may occur for just, a part of volume is for negative, even is zero situation, so can't measure accurately volume change.Caused total square volumetric errors when this patent adopts the measure of volume square to calculate a triangle collapse, it is expressed as follows:

$V_i^2=\underset{T_j\∈{\left\{\mathrm{FOT}\right\}}_{T_i}\∪T_i}{\mathrm{\Σ}}\frac{1}{9}(v_{i0}\·P_{T_j}^T{P}_{T_j}\·v_{i0}^T)\·S_{T_j}^2$

In the formula $P_{T_j}^T{P}_{T_j}=\left[\begin{array}{cccc}{a}_j^2& a_j{b}_j& a_j{c}_j& a_j{d}_j\\ a_j{b}_j& b_j^2& b_j{c}_j& b_j{d}_j\\ a_j{c}_j& b_j{c}_j& c_j^2& c_j{d}_j\\ a_j{d}_j& b_j{d}_j& c_j{d}_j& d_j^2\end{array}\right].$

Δ v _I1v _I2v _I3Folding point be v _I0The time, Δ v _I1v _I2v _I3And single order neighborhood triangle Δ v _I1v _I4v _I5, Δ v _I2v _I5v _I6Δ v _I2v _I6v _I7, Δ v _I3v _I7v _I8, Δ v _I3v _I8v _I9, Δ v _I1v _I9v _I4, Δ v _I2v _I7v _I3, Δ v _I1v _I5v _I2, Δ vi1v _I3v _I9The folding Δ v that is reduced to _I0v _I4v _I5, Δ v _I0v _I5v _I6, Δ v _I0v _I6v _I7, Δ v _I0v _I7v _I8, Δ v _I0v _I8v _I9, Δ v _I0v _I9v _I4, folding Δ v _I1v _I2v _I3The leg-of-mutton maximum area of rear affected single order neighborhood is above-mentioned 6 leg-of-mutton maximum areas, and calculation expression is as follows:

S _i=max{S _i1,S _i2,S _i3,…S _in}

S in the formula _I1, S _I2, S _I3S _InRepresent respectively triangle T _iThe leg-of-mutton area of single order neighborhood of distortion after folding.The reason of considering the maximum area value is: if there is local mild zone in the model, the error that produces after these zones are folding is very little, even is zero, thereby is easy to occur the phenomenon of over-simplification, causes this zone to produce excessive triangle

Δ v _I1v _I2v _I3Be folded into folding point v _I0The time, Δ v _I1v _I2v _I3Single order neighborhood triangle Δ v _I1v _I4v _I5, Δ v _I2v _I5v _I6, Δ v _I2v _I6v _I7, Δ v _I3v _I7v _I8, Δ v _I3v _I8v _I9, Δ v _I1v _I9v _I4, Δ v _I2v _I7v _I3, Δ v _I1v _I5v _I2, Δ v _I1v _I3v _I9Be updated to Δ v _I0v _I4v _I5, Δ v _I0v _I5v _I6, Δ v _I0v _I6v _I7, Δ v _I0v _I7v _I8, Δ v _I0v _I8v _I9, Δ v _I0v _I9v _I4, variation has occured with respect to the normal vector of initial delta in newly-generated leg-of-mutton normal vector, and we are with Δ v _I1v _I2v _I3Angular error after folding is defined as Δ v _I1v _I2v _I3The maximal value that the leg-of-mutton normal vector of its single order neighborhood changes with respect to the angle that occurs before folding after folding, it is expressed as follows:

$a_i=\max \{\arccos ({\stackrel{\→}{n}}_{i0}\·{\stackrel{\→}{n}}_{i0}^{\′}),\arccos ({\stackrel{\→}{n}}_{i1}\·{\stackrel{\→}{n}}_{i1}^{\′}),\·\·\·\arccos ({\stackrel{\→}{n}}_{\mathrm{in}}\·{\stackrel{\→}{n}}_{\mathrm{in}}^{\′})\}$

In the formula

The expression triangle T _iThe leg-of-mutton unit normal vector of its single order neighborhood before folding, The expression triangle T _iThe leg-of-mutton unit normal vector of single order neighborhood of distortion after folding.During simplification, the control angle error can avoid the triangle rotating angle excessive, even the phenomenon of upset occurs.

Continuation is calculated the result of the model in Fig. 3 A part according to above-mentioned steps and associative list 1 take Fig. 3 as example, and various error amounts see Table 2:

Three kinds of folding error values of A part among table 2 Fig. 3

4) with all V _iValue sorts from small to large and deposits chained list, while and V in _iCorresponding leg-of-mutton numbering, S _i, α _iAlso deposit the corresponding node in the chained list in;

5) this step divides following three kinds of situations to process:

The volumetric errors value that first element is deposited in described chained list is greater than the defined threshold value Y of user _vThe time, end simplifies the operation.

The volumetric errors value that first element is deposited in described chained list is less than the defined volume threshold Y of user _v, and the S that first element is deposited in the described chained list _iValue is less than the defined maximum area threshold value of user Y _s, and the α that first element is deposited in the described chained list _iValue is less than the defined angle threshold Y of user _αThe time, according to the corresponding leg-of-mutton folding point of first element in the described chained list model is folded simplification, and by 2), 3) in computing method recomputate each leg-of-mutton folding point and error of involved area when simplifying, upgrade 4) in chained list, turn afterwards step 5).

The volumetric errors value that first element is deposited in described chained list is less than the defined volume threshold Y of user _v, and the S that first element is deposited in the described chained list _iOr α _iValue is greater than the defined threshold value of user, then corresponding triangle does not fold simplification, select afterwards second element in the described chained list, adopt the method for judging first element in the described chained list in this step to judge, by that analogy, when the volumetric errors of the table tail that arrives chained list or current judgement element greater than the defined volume threshold of user, end simplifies the operation.

Above-mentioned steps divides three kinds of situations to process, and namely guarantees V _i, S _iAnd α _iValue is all just simplified folding less than the triangle of threshold value, and is from V _iThe minimum triangle of value begins to judge.

Continuation A in Fig. 3 sets volumetric errors threshold value Y partly as example _v=4mm ³Maximum area threshold value Y _s=20mm ₂Angular error threshold value Y _α=2 °.Because Δ v _I1v _I2v _I3Corresponding volumetric errors value is 2.9897mm ₃, and be the minimum volume error amount, it is worth less than Y _v=4mm ₃, continue to judge, because Δ v _I1v _I2v _I3Corresponding S _i=16.0242mm ₂Less than Y _s, α _i=0.08773 ° less than Y _α, should be with Δ v _I1v _I2v _I3Inner point (119.54537,44.78644,1.59037) partly carries out folding operation for folding point to A among Fig. 3, and it is described to be among Fig. 3 the B part after folding.

B among Fig. 3 is partly continued folding operation.

Comprise 6 triangles in the B part among Fig. 3, i.e. Δ v _I0v _I8v _I9, Δ v _I0v _I9v _I4, Δ v _I0v _I5v _I6, Δ v _I0v _I7v _I8, Δ v _I0v _I4v _I5With Δ v _I0v _I6v _I7, folding point coordinate and three kinds of error amounts are as shown in table 3:

Each triangle collapse point coordinate and three kinds of folding error values in table 3 Fig. 3 B part

As shown in Table 3, the minimum volume error amount is 4.16496mm ³, i.e. Δ v _I0v _I8v _I9Corresponding error amount is greater than threshold value Y _v=4mm ³, end operation.

The present invention realizes with Visual C++6.0 programming at the PC of 2.53GHz Intel (R) Core (TM) i3CPU, 1.92GB internal memory.At last, table 4 has provided the QEM algorithm of Garland and the contrast of our algorithm travelling speed.Wheel hub model in Fig. 5 can be found out by data in the table as example, and when difference was simplified degree, the speed of our algorithm was slightly faster than the QEM algorithm of Garland.

Show table 4QEM algorithm and operation time of the present invention (unit: second)

Claims (2)

1. the short-cut method based on the three-dimensional grid model of triangle collapse is characterized in that, may further comprise the steps:

1) obtains the triangle grid model of testee;

2) determine each leg-of-mutton folding point in the described triangle grid model;

3) calculate respectively when folding according to each folding point the volumetric errors that produces, the model after namely folding and the volumetric errors value V between the initial model _i(i=1,2,3 ..., n represents leg-of-mutton numbering);

4) by sorting from small to large volumetric errors value and deposit chained list in;

5) obtain the stored minimum volume error amount of first element of chained list;

6) when described minimum volume error amount less than the defined volume threshold Y of user _vThe time, according to the corresponding leg-of-mutton folding point of described minimum volume error amount model is folded simplification, and by 2), 3) in computing method recomputate involved area each leg-of-mutton folding point and volumetric errors, upgrade 4) in chained list, turn afterwards step 5);

When described minimum volume error amount during greater than the defined volume threshold of user, end operation.

2. short-cut method based on the three-dimensional grid model of triangle collapse is characterized in that:

1) obtains the triangle grid model of testee;

2) determine each leg-of-mutton folding point in the described triangle grid model;

3) calculate respectively when folding according to each folding point the error that produces, the model after namely folding and the volumetric errors value V between the initial model _i(i=1,2,3 ..., n represents leg-of-mutton numbering), folding after affected leg-of-mutton maximum area value S _i, folding after the maximum angle error amount α that produces before and after folding of affected leg-of-mutton normal vector _i

4) with all V _iValue sorts from small to large and deposits chained list, while and V in _iCorresponding leg-of-mutton numbering, S _i, α _iAlso deposit the corresponding node in the chained list in;

5) the volumetric errors value that first element is deposited in described chained list is greater than the defined threshold value Y of user _vThe time, end simplifies the operation;

The volumetric errors value that first element is deposited in described chained list is less than the defined volume threshold Y of user _v, and the S that first element is deposited in the described chained list _iValue is less than the defined maximum area threshold value of user Y _s, and the α that first element is deposited in the described chained list _iValue is less than the defined angle threshold Y of user _αThe time, according to the corresponding leg-of-mutton folding point of first element in the described chained list model is folded simplification, and by 2), 3) in computing method recomputate each leg-of-mutton folding point and error of involved area when simplifying, upgrade 4) in chained list, turn afterwards step 5);

First element is less than the defined volume threshold Y of user in described chained list _v, and the S that first element is deposited in the described chained list _iOr α _iValue is greater than the defined threshold value of user, then corresponding triangle does not fold simplification, select afterwards second element in the described chained list, adopt the method for judging first element in the described chained list in this step to judge, by that analogy, when the volumetric errors of the table tail that arrives chained list or current judgement element greater than the defined volume threshold of user, end simplifies the operation.

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