CN103903304B - The arbitrary quadrilateral curved surface axis processed for product three-dimensional data generates method - Google Patents

Abstract

The invention discloses the arbitrary quadrilateral curved surface axis processed for product three-dimensional data and generate method, adopt method of loci to combine mobile Frenet frame, it is proposed that a kind of simple and quick axis generating algorithm。Engineering problem is applied more for B-rep three-dimensional entity model, this model has clear and definite boundary definition, what the information of the top points, edges, faces of model was all clear and definite is stored in model file, utilize these clear and definite information just can simplify traditional method of loci axis and generate method, thus reducing axis to generate required data volume。The present invention utilizes boundary information clear and definite in B-rep model to generate the condition of method as axis, and utilizes the feature of bisector to eliminate the calculating to branch point, reduces the factor affecting axis degree of accuracy。In order to ensure the degree of accuracy of axis, it is possible to adopt the density of insertion point to be controlled。

Description

The arbitrary quadrilateral curved surface axis processed for product three-dimensional data generates method

Technical field

The present invention relates to a kind of arbitrary quadrilateral curved surface axis processed for product three-dimensional data and generate method, be particularly suited for the CAD/CAE technology such as model simplification, model reconstruction, finite element adaptive grid generation, solid modelling。Relate to Patent classificating number G06 to calculate；Calculate；The counting general image real time transfer of G06T or produce G06T17/00 and model for the 3D of computer graphics。

Background technology

Model skeleton or centrage are also in axis, generally it is described as follows: in two-dimensional closed region, there is the disk of a radius variable at this intra-zone, this disk and zone boundary is kept to have at least two point of contacts, then this disk mobile, after the walked path of disk covers all regions, the line that the track that the center of circle of disk stays is constituted is called axis, is referred to as middle axial plane in the three-dimensional model。Axis is in each key link extensive application of CAD/CAE system, for instance model reconstruction, model analysis, computer vision, solid modelling and the feature extraction etc. in geometry designs。But, axis is also restricted in some applications, because not having a kind of algorithm quickly and accurately calculating axis at present, particularly generates axis under curved boundary conditions。

Blum proposes the concept of axis first time in 1967, and axis has the advantageous characteristic such as unique, reversible, symmetrical, homeomorphic。Axis is affected very big by the seriality on border, and also is difficult at that time extract curved boundary accurately。Before 10 years, the main introducing being the discovery that bisector, it is a special case of axis, but the method needs cut operator, adds the complexity of processing procedure。In recent years, Teixeira and Zucker have studied the relation between curl and axis curvature of a curve, tangent line and normal line vector three, gives the differential equation of the curve axis motion described by average curvature。Despite a lot of algorithms generated about axis, but generating stable is not also a pipe course with accurate axis。

The axis generating algorithm commonly used in CAD/CAE system at present is roughly divided into two classes: method of loci and Voronoi diagram method。Method of loci is the definition according to axis, allows the circle of a radius variable remain tangent with border, at least two, this region, then this track left by round heart is exactly axis。But this algorithm needs to judge that each point arrives whether the distance on each border is branch point with this point, namely has the position at two or more point of contact。This adds data volume virtually, will necessarily affect the efficiency of calculating。Voronoi diagram method be first by the border point set of given area by its discretization, generate Voronoi diagram according to this discrete point set, then what the summit of Voronoi diagram formed is exactly axis。But this algorithm is more suitable for two dimensional model, it is necessary to increase extra alternative condition and just can be extended to threedimensional model。

Summary of the invention

The present invention is directed to the proposition of problem above, and a kind of arbitrary quadrilateral curved surface axis processed for product three-dimensional data developed generate method, has following steps:

Model decomposition step: be four limits to quadrilateral surface model decomposition；Non-conterminous both sides in four described limits are divided into one group, and the two groups of limits obtained are respectively as playing initial line and terminating limit and two binding sides；

Interpolation procedure: obtain the merging vector of two binding sides by calculating the vector of two described binding sides, using the direction of this merging vector as interpolation direction, insert multiple insertion points by step-length δ；

Step is moved in insertion point: when described multiple insertion points are respectively positioned on model inside, calculate the distance of each insertion point and described two binding sides；Use the mode of iteration, mobile described insertion point, make the distance approximately equal of this insertion point and described two binding sides；

Step is determined in axis: repeat the above steps；When the equal approximately equal of the distance of described insertion point Yu two binding sides, utilizing described each insertion point structure B-spline curve, this curve approximation is the axis of quadrilateral surface model。

Step-length δ of the present invention is the distance between two insertion points, utilizes step-length δ can control the quantity of insertion point。Step-length δ is more little, and insertion point is more many, and the axis precision generated is more high；Insertion point is more few, and the amount of calculation generating axis is more little。

Further, it is contemplated that owing to having chosen initial line and having terminated the difference on limit, it is possible to can cause that the space coordinates of insertion point is positioned at outside tetragon model。Therefore insertion point of the present invention is moved and is at least also had insertion point in step and judge and mobile step:

Calculate the distance d of insertion point P and two binding sides₁And d₂, and and d₁And d₂Intersection point q with two binding sides₁And q₂, q₁And q₂Between distance be d, d=| | q₁q₂| |；The direction vector of insertion point P is obtained according to Frenet frame formula ${\stackrel{\→}{e}}_1=q_1{q}_2/\left|\right|q_1{q}_2{\left|\right|}_2;$

Relatively d₁、d₂Relation with d: if d₁> d or d₂> d, then insertion point P is outside model area；

If d₁>d₂, then some P alongDirection displacement Δ=| (d₁-d₂) |/2；If d₁<d₂, then some P alongRightabout displacement Δ=| (d₁-d₂) |/2；After insertion point P is moved to model inside, update this point coordinates；

If d₁< d and d₂< d, it was shown that some P, inside model, is not temporarily adjusted。

By above-mentioned decision process, it is ensured that each insertion point is all located at the inside of tetragon model, it is ensured that the carrying out of algorithm。

Preferably, described " using alternative manner, mobile described insertion point, make the distance approximately equal of this insertion point and described two binding sides " specifically comprises the steps of:

Calculate the distance d of insertion point P and two binding sides₁And d₂, determining that insertion point is when tetragon model is internal: obtain, according to Frenet frame formula, the direction vector that P position adjusts

If d₁>d₂, some P alongDirection displacement Δ₁；

If d₁<d₂, some P alongRightabout displacement Δ₁；

Repeat the above steps, until d₁/d₂=ε, stops computing；Wherein 0.99 < ε < 1.01；Displacement Δ₁Value be | (d₁-d₂)|/2ⁿ, wherein n value is the number of times that twice continuous moving direction is inconsistent。

In described interpolation procedure, described " obtaining the merging vector of two binding sides by calculating the vector of two described binding sides " particularly as follows:

Set A₁And A₂For two described binding sides；Press initial line to the direction terminating limit, obtain two binding side A₁And A₂VectorUtilize vector to merge formula (1) and calculate the interpolation direction vector obtaining insertion point

$\stackrel{\&RightArrow;}{e}={\stackrel{\&RightArrow;}{e}}_{a1}+{\stackrel{\&RightArrow;}{e}}_{a2}---\left(1\right)$

Described " inserting multiple insertion points by step-length δ " particularly as follows:

Rising, initial line takes midpoint P₁As starting point, the direction vector according to interpolationWith step-length δ, utilize formula (2) to calculate the coordinate P of next insertion point₂(x,y)

$\left\{\begin{array}{c}{P}_2.x=P_1.x+\stackrel{\&RightArrow;}{e}.x*\mathrm{\&delta;}\\ P_2.y=P_1.y+\stackrel{\&RightArrow;}{e}.y*\mathrm{\&delta;}\end{array}\right.---\left(2\right)$

If P₂Arrive the distance d terminating limit less than step-length δ, represent that newly inserted point is already close to terminating limit, it is no longer necessary to new insertion point, so P₂It it is exactly last terminating point；Otherwise, continue into new insertion point P*。

Owing to have employed technique scheme, the arbitrary quadrilateral curved surface axis processed for product three-dimensional data provided by the invention generates method, adopts method of loci to combine mobile Frenet frame, it is proposed that a kind of simple and quick axis generating algorithm。Engineering problem is applied more for B-rep three-dimensional entity model, this model has clear and definite boundary definition, what the information of the top points, edges, faces of model was all clear and definite is stored in model file, utilize these clear and definite information just can simplify traditional method of loci axis and generate method, thus reducing axis to generate required data volume。The present invention utilizes boundary information clear and definite in B-rep model to generate the condition of method as axis, and utilizes the feature of bisector to eliminate the calculating to branch point, reduces the factor affecting axis degree of accuracy。In order to ensure the degree of accuracy of axis, it is possible to adopt the density of insertion point to be controlled。

Accompanying drawing explanation

Technical scheme for clearer explanation embodiments of the invention or prior art, introduce the accompanying drawing used required in embodiment or description of the prior art is done one simply below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the premise not paying creative work, it is also possible to obtain other accompanying drawing according to these accompanying drawings。

Fig. 1 is axis generating algorithm flow chart；

Fig. 2 is tetragon each limit packet schematic diagram；

Fig. 3 is insertion point algorithm schematic diagram；

Fig. 4 is adjustment insertion point to model schematic internal view；

Fig. 5 is for adjusting position, insertion point schematic diagram on axis；

The axis that Fig. 6 is the four irregular curved tetragons in limit generates design sketch, and Fig. 6 a is original tetragon model；Fig. 6 b is the axis schematic diagram obtained by inventive algorithm；

Fig. 7 is Fillet Feature face decomposing schematic representation；

Fig. 8 is model after machine components model fillet simplification design sketch a archetype b circular bead characteristic simplification；

It is crossing for the axis that constraints generation d limit, axis bc, da are constraints generation axis e both direction that Fig. 9 utilizes axis parted pattern to generate c limit, grid a initial model b model four limit ab, cd, forms grid。

Detailed description of the invention

For making the purpose of embodiments of the invention, technical scheme and advantage clearly, below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear complete description:

As Figure 1-Figure 5: a kind of arbitrary quadrilateral curved surface axis processed for product three-dimensional data generates method, mainly comprises the following steps that

In model decomposition step shown in tetragon each limit packet schematic diagram 2。Tetragon each edge is divided into two groups by " limit is non-conterminous with limit " principle, A₁And A₂Be one group as binding side, limit B₁And B₂For another group, respectively as playing initial line and terminating limit。The trend of the axis selected is wanted in the main consideration having selected initial line peace treaty bundle limit。

The described interpolation procedure of present invention is as shown in Figure 3: insertion point algorithm schematic diagram。Set B₁For playing initial line, B₂For terminating limit, A₁And A₂For binding side。When specifically chosen initial line and termination limit, the main trend considering to want the target axis of acquisition, with two limits of target axis less parallel (moving towards consistent) as binding side, remaining two limits can be used as initial line and termination limit。

Press initial line to the direction terminating limit, obtain the vector of two binding sidesUtilize vector to merge formula (1) calculating to obtainIt is the interpolation direction vector of insertion point。

$\stackrel{\&RightArrow;}{e}={\stackrel{\&RightArrow;}{e}}_{a1}+{\stackrel{\&RightArrow;}{e}}_{a2}---\left(1\right)$

Rising, initial line takes midpoint P₁As starting point, the direction vector according to interpolationWith step-length δ, utilize formula (2) to calculate the coordinate P of next insertion point₂(x, y)。

$\left\{\begin{array}{c}{P}_2.x=P_1.x+\stackrel{\&RightArrow;}{e}.x*\mathrm{\&delta;}\\ P_2.y=P_1.y+\stackrel{\&RightArrow;}{e}.y*\mathrm{\&delta;}\end{array}\right.---\left(2\right)$

If P₂Arrive the distance d terminating limit less than step-length δ, represent that newly inserted point is already close to terminating limit, it is no longer necessary to new insertion point, so P₂It it is exactly last terminating point。Otherwise, continue into new insertion point P^*。

Step-length δ is in tetragon model 1/5th of most minor face in the present embodiment。

Further, it is contemplated that owing to having chosen initial line and having terminated the difference on limit, it is possible to can cause that the space coordinates of insertion point is positioned at outside tetragon model。Therefore insertion point of the present invention move step at least also has insertion point judge and mobile step as shown in Figure 4。Adjust insertion point to model schematic internal view。To acquired insertion point P, calculate this point and arrive the beeline d of two binding sides₁And d₂, and the some q corresponding with beeline₁And q₂(it is positioned at binding side A₁And A₂On point), according to Frenet frame formula calculate obtain direction vector。

${\stackrel{\&RightArrow;}{e}}_1=q_1{q}_2/\left|\right|q_1{q}_2{\left|\right|}_2;$

Judge that the position of insertion point P is whether inside model area, if not inside model, inside adjustment to model, it is judged that and method of adjustment is as follows:

According to a P to binding side A₁And A₂The corresponding point q of beeline₁And q₂, obtain distance d=| | q₁q₂| |。Comparison point P to the beeline d of binding side₁、d₂And the relation between d。

If d₁> d or d₂> d, then some P is outside model area。If d₁>d₂, then some P alongDirection move a certain distance Δ=| (d₁-d₂) |/2；If d₁<d₂, then some P alongRightabout move a certain distance Δ=| (d₁-d₂) |/2。After insertion point P is moved to model inside, update this point coordinates；

If d₁< d and d₂< d, it was shown that some P, inside model, is temporarily made without adjusting。

Such as Fig. 5: adjust position, each insertion point and make it drop on schematic diagram on axis。To each insertion point, it is adjusted by following rule:

If (a) d₁>d₂, some P alongDirection moves a certain distance Δ₁；

If (b) d₁<d₂, some P alongRightabout moves a certain distance Δ₁；

If (c) d₁=d₂(approximately equal), updates some P coordinate figure。

Displacement Δ in the present invention₁Initial value is set to | (d₁-d₂) |/2。When twice continuous print moving direction is inconsistent, secondary displacement Δ₁It is reduced into | (d₁-d₂) |/4, adopt iterative algorithm repeatedly to adjust position a little until two constraint back gauges of some P arrival are equal。Displacement Δ₁Value be | (d₁-d₂)|/2ⁿ, wherein n value is the number of times that twice continuous moving direction is inconsistent。Alternative manner is adopted repeatedly to adjust position a little, if making the point of insertion arrive binding side have certain difficulty apart from essentially equal, so approximately equal, i.e. d₁/d₂=ε, ε are close to 1。For high-precision axis, ε is more good closer to 1, but operation efficiency can reduce。

In the present invention, each model instance ε value is 0.99 < ε < 1.01。

Axis such as Fig. 6: the four irregular curved tetragons in limit generates design sketch。In commercial production cad model, relatively multi-model is regular, but also has some irregular models。Axis generating algorithm is tested by the irregular obstacle body model adopting complexity high。As shown in Figure 6 a, the tetragon of the four irregular bendings in limit is adopted。After importing this model, application axis generating algorithm, effect is as shown in Figure 6 b。Although bilateral bending makes the direction of insertion point and is not exactly equal to the direction vector of binding side, but through the adjustment to insertion point so that insertion point can be dropped on axis。Recycling has obtained the some structure B-spline curve on axis, and this curve is the axis of bending tetragon curved surface, meets the symmetry of axis。

Axis is utilized to realize circular bead characteristic simplification。Patent " the circular bead characteristic simplification method based on fillet axis " (201310578463.1) discloses and utilizes axis segmentation Fillet Feature curved surface, reconstructs divided curved surface and corresponding seating surface, thus the method realizing circular bead characteristic simplification。Most of Fillet Feature are made up of four edges, two smooth limits and two common limits。With smooth limit as constraints, common limit, as playing initial line and terminating limit, just meets the axis generating algorithm that this patent proposes, therefore can generate axis on this Fillet Feature curved surface。As it is shown in fig. 7, with smooth limit e₄And e₇For binding side, common limit e₅And e₆For playing initial line and terminating limit, generate axis e₈Fillet Feature curved surface is divided into two face F3 and F4；Two end points of axis are by limit e simultaneously₅It is divided into two sections of a₁And a₂, limit e₆It is divided into b₁And b₂Two sections。Fig. 8 is machine components, is made up of 20 faces, wherein comprises multiple Fillet Feature, utilizes axis segmentation reconstruct fillet surface, simplifies Fillet Feature, and the face number of model reduces to 11, and the model after simplification is as shown in Figure 8 b。

Axis parted pattern is utilized to realize mess generation。In axis generation method, the constraints border generated as axis。Utilizing axis parted pattern, the border of each subregion is also affected by the constraint on border so that all subregion border is similar。The axis generated in given area divides the area into two parts of equity, if continuing to divide by these two regions, will obtain some approximately equalised subregions。Exchanging binding side with playing initial line, terminating the relation on limit, again carry out same division, so obtained a series of sequential cells are the grid of generation。

Given closed area as illustrated in fig. 9, is divided into tetragon: limit ab, bc, cd, da form。Limit ab, cd are generated axis ef as constraints, by this Region Decomposition, forms two regions, as shown in figure 9b。Then judge, it is determined that condition: in each region, most minor face is less than or equal to initial mesh border setting value。Dissatisfied decision condition divides again, and as is shown in fig. 9 c respectively using limit ae, fd and limit eb, cf as two axis of constraints regeneration, former region is divided into four sub regions, now meets decision condition and terminates dividing。Exchange master mould binding side with playing initial line, terminating the relation on limit, again carry out same division using limit bc, da as constraints, generate such as three axis of Fig. 9 d。Twice different directions divides six axis generated and intersects, and crossed node is grid node, grid node a series of continuous print tetragons being formed by connecting are grid cell, as shown in figure 9e。

The above; it is only the present invention preferably detailed description of the invention; but protection scope of the present invention is not limited thereto; any those familiar with the art is in the technical scope that the invention discloses; it is equal to replacement according to technical scheme and inventive concept thereof or is changed, all should be encompassed within protection scope of the present invention。

Claims (1)

1. the arbitrary quadrilateral curved surface axis processed for product three-dimensional data generates a method, has following steps:

Model decomposition step: be four limits by quadrilateral surface model decomposition；Non-conterminous both sides in four described limits are divided into one group, and the two groups of limits obtained are respectively as playing initial line and terminating limit and two binding sides；

Interpolation procedure: obtain the merging vector of two binding sides by calculating the vector of two described binding sides, using the direction of this merging vector as interpolation direction, insert multiple insertion points by step-length δ；

Step is moved in insertion point: when described multiple insertion points are respectively positioned on model inside, calculate the distance of each insertion point and described two binding sides；Use the mode of iteration, mobile described insertion point, make the distance approximately equal of this insertion point and described two binding sides；

Step is determined in axis: repeat the above steps；When the equal approximately equal of the distance of described insertion point Yu two binding sides, utilizing each insertion point structure B-spline curve, this curve approximation is the axis of quadrilateral surface model；

Described insertion point is moved at least also has insertion point judgement and mobile step in step:

Calculate the distance d of insertion point P and two binding sides₁And d₂, and and d₁And d₂Intersection point q with two binding sides₁And q₂, q₁And q₂Between distance be d, d=| | q₁q₂| |；The direction vector that P position adjusts is obtained according to Frenet frame formula

Relatively d₁、d₂Relation with d: if d₁> d or d₂> d, then insertion point P is outside model area；

If d₁>d₂, then some P alongDirection displacement Δ=| (d₁-d₂) |/2；If d₁<d₂, then some P alongRightabout displacement Δ=| (d₁-d₂) |/2；After insertion point P is moved to model inside, update the coordinate of some P；

If d₁< d and d₂< d, it was shown that some P, inside model, is not temporarily adjusted；

Wherein, use alternative manner, mobile described insertion point, make the distance approximately equal of this insertion point and described two binding sides specifically comprise the steps of:

Calculate the distance d of insertion point P and two binding sides₁And d₂, determining that insertion point is when tetragon model is internal: obtain, according to Frenet frame formula, the direction vector that P position adjusts

If d₁>d₂, some P alongDirection displacement Δ 1；

If d1 < d2, some P alongRightabout displacement Δ 1；

Repeat the above steps, until d₁/d₂=ε, stops computing；Wherein 0.99 < ε < 1.01；Displacement Δ₁Value be | (d₁-d₂)|/2ⁿ, wherein n value is the number of times that twice continuous moving direction is inconsistent；

In described interpolation procedure, by calculate the vector of two described binding sides obtain two binding sides merging vector particularly as follows:

Set A₁And A₂For two described binding sides；Press initial line to the direction terminating limit, obtain two binding side A₁And A₂VectorWithUtilize vector to merge formula (1) and calculate the interpolation direction vector obtaining insertion point

$\stackrel{\&RightArrow;}{e}={\stackrel{\&RightArrow;}{e}}_{a1}+{\stackrel{\&RightArrow;}{e}}_{a2}---\left(1\right)$

Wherein, by step-length δ insert multiple insertion points particularly as follows:

Rising, initial line takes midpoint P₁As starting point, the direction vector according to interpolationWith step-length δ, utilize formula (2) to calculate the coordinate P of next insertion point₂(x, y)；

$\left\{\begin{array}{c}{P}_2.x=P_1.x+\stackrel{\&RightArrow;}{e}.x*\mathrm{\&delta;}\\ P_2.y=P_1.y+\stackrel{\&RightArrow;}{e}.y*\mathrm{\&delta;}\end{array}\right.---\left(2\right)$

If P₂Arrive the distance d terminating limit less than step-length δ, represent that newly inserted point is already close to terminating limit, it is no longer necessary to new insertion point, so P₂It it is exactly last terminating point；Otherwise, continue into new insertion point P*。