CN109683552A - A kind of Machining Path generation method on the complicated point cloud model of basal plane curve orientation - Google Patents
A kind of Machining Path generation method on the complicated point cloud model of basal plane curve orientation Download PDFInfo
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Abstract
A kind of Machining Path generation method the invention belongs to Computerized Numerical Control processing technology field, on the complicated point cloud model of basal plane curve orientation.Firstly, extracting the boundary point of point cloud and sequence, orderly boundary point sequence curve is formed, then be divided into four edges circle point sequence curve；According to four point sequence curve building Kong Siji curved surfaces and lead curve is constructed on the basal plane；Then, a cloud is biased using rose cutter radius as offset or dish；The least square projection model for establishing guiding point-to-point cloud, provides the Weighting and projecting direction calculative strategy of the model operating point；By lead curve along on the projecting direction iterative projection to bias point cloud of calculating, to generate Non intrusive method.The method of the present invention has crossed point cloud data to the complicated structure process of CAD parameter model, is directly based upon measurement pointcloud and carries out tool-path planning, effectively shortens the manufacturing cycle that part manufacturing is measured from part prototype, reduces the cost of processing and manufacturing.
Description
Technical field
The invention belongs to and Computerized Numerical Control processing technology field, in particular to a kind of complicated point cloud model of basal plane curve orientation
On Machining Path generation method.
Background technique
It is dense and accurately point cloud can more meticulously indicate zero currently, with the fast development of 3D scanning device
The geometry of part physical prototype, is applied to all trades and professions, such as reverse-engineering (RE), rapid prototyping moulding (RP) etc..
In order to realize the quick manufacture of these part physical prototypes, traditional treatment process is set first with contact or non-cpntact measurement
The standby measurement pointcloud for obtaining part prototype, then from Surface Reconstruction from Data Cloud parameter CAD model, numerical control processing is planned on CAD model
Cutter path.But the reconstruct from measurement data to parameter CAD model is the process an of complexity and time-consuming, accounts for and entirely sets
Meter, the manufacturing cycle 60% or more.Although current business CAD software such as CATIA, Imageware etc. be provided from
Point cloud data to parametric surface reverse engineer function, but dependent on the point cloud complex region of designer's experience, region
Splicing cutting, approximation accuracy and continuity between dough sheet control and thus caused inevitably model is modified repeatedly,
Realization of the numerical-control processing method based on parametric surface when towards point cloud data is seriously limited to run and in manufacturing enterprise
Practical application.Discrete data is crossed to the cumbersome construction process of parametric surface, point cloud data is directly based upon and realizes complex-curved zero
The Efficient CNC machining of part is undoubtedly the effective way for breaking through the above problem.The Chinese invention patent " one of Zhang Yingjie et al. application
Kind of the cutter path based on measurement data directly generates method " knife of numerical control processing is generated by using the method for oriented projection
Have track (patent No.: CN 102608954A), but this method can more reflect curve form and spy with of the present invention
This basal plane of the hole of sign and iterative least square projecting method are significantly different.Document " Zhang YJ, Ge LL.Adaptive tool
path generation on point-sample surfaces.Precis Eng 2011；35 (4): it is mentioned in 591-601. "
A kind of point shadow casting technique based on level set is gone out, to directly generate cutter path on cloud.Document " Liu Y, Xia
S,Qian X.Direct numerical control(NC)path generation:from discrete points to
continuous spline paths.ASME Trans,J Comput Inf Sci Eng2012；12(3): 031002-1-
A kind of method based on moving least squares surfaces projection is proposed in 12 ".Currently, both at home and abroad for based on point cloud model
Point cloud data at random is mainly first converted to simple Z-map or triangle gridding mould by Machining Path generation method
Type recycles method of section to generate cutter path.The side based on level set projection and Moving Least Squares plane projection having proposed
Method also has with the method for present invention point cloud Direct Least Square iterative projection significantly different.This invention address that finding one kind
The method that cutter path can be directly generated on the point cloud of contact or the measurement of non-contact scanning device, is not related to non-linear excellent
Change and mathematical calculation process simple, intuitive, have crossed the construction process of point cloud data CAD parameter model, have avoided model conversion
During some problems for occurring, can effectively shorten new product development cycle and measure part from part prototype
The manufacturing cycle of manufacture reduces the cost of processing and manufacturing.
Summary of the invention
To overcome the shortcomings of processing path generation method on existing point cloud model, it is bent that the present invention provides a kind of basal planes
Machining Path generation method on the complicated point cloud model of line guiding, realization are directly based upon point cloud data and generate processing road
Routing method.
Technical solution of the present invention:
A kind of Machining Path generation method on the complicated point cloud model of basal plane curve orientation, comprising the following steps:
Step a extracts the boundary point of point cloud and sorts to boundary point, forms orderly boundary point sequence curve, then
It is divided into four edges circle point sequence curve；
Specific steps include:
A1. any point p on selected point cloud, and local coordinate system is established using p as origin, in coordinate systemBe p point and
Its K neighborhood point set CK(p) unit vector in any point line direction in,It is p point and its K neighborhood point set CK(p) it is fitted
The unit normal vector of plane,It isWithVector product；
A2. by K neighborhood point set CK(p) it projects toProjection point set C is obtained in the plane at placeK pro(p), for
Any point Indicate point p and pointLine and axisAngle；
A3. all angles are calculatedAnd the difference of two continuous anglesIf maximum angular differenceMore than specified
Angle thresholdThen point p is exactly boundary point；
A4. it sorts to boundary point: boundary point being looked for concentrate any point as start boundary pointIt is found on side
The closest approach that boundary's point is concentratedThen by vectorSearch direction as next boundary point
A5. it enablesThen along search directionIt is concentrated in boundary point and finds distanceNearest boundary point
Then enableIt updates and searches directionUntil search to start boundary pointWhen terminate；
Step b according to four point sequence curve building Kong Siji curved surfaces and constructs lead curve on the basal plane；
The building equation of lead curve point is as follows:
In formula, ri,jIndicate j-th of guiding point on i-th of lead curve, ni,jIndicate list of the guiding point on basal plane
Position normal vector；
Step c is biased a cloud using rose cutter radius as offset or dish；
Step d establishes the least square projection model of guiding point-to-point cloud, determines projecting direction and participates in subpoint meter
The weight of the operating point of calculation is generated by lead curve along on the projecting direction iterative projection to bias point cloud of calculating without interference
Cutter path；
Specific steps include:
D1. the plane least square projection model of the point-to-point cloud model on lead curve are as follows:
In formula, pgFor lead curve point,It is point cloud data, wiIt is and data pointRelevant weight because
Son is determined by formula (5)；
D2. E (d in formula (2)pro) condition of minimum value is obtained as dE (dpro)/ddpro=0, thus obtain dproAre as follows:
D3. projecting direction are as follows:
In formula:Indicate the direction vector of projection, ni,jIndicate unit normal vector of the guiding point on basal plane,Table
Show on a cloud nearPointUnit normal vector；
D4. weight wjIt determines as the following formula:
In formula,For lead curve point pgWith operating pointBetween distance,ForAnd throwing
Hachure LpDistance；
D5. by lead curve along on the projecting direction iterative projection to bias point cloud of calculating, when the difference of iteration twice
Meet given error precision or terminates iteration when reaching maximum number of iterations.
Compared with prior art, beneficial effects of the present invention: the present invention is directly based upon measurement pointcloud and carries out cutter path
Construction, crossed the process of point cloud data surface fitting, can effectively shorten the life for measuring part manufacturing from part prototype
The manufacturing cycle is produced, design and manufacture cost is reduced.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention.
Fig. 2 is the extraction schematic diagram of point cloud boundary data point.
Fig. 3 (a) is the sequence schematic diagram of scattered data points.
Fig. 3 (b) is the segmentation schematic diagram of four edges circle point sequence curve.
Fig. 4 (a)-(c) is a schematic diagram for cloud biasing.
Fig. 5 is the schematic diagram that projecting direction calculates.
Fig. 6 is the example of obtained machining path.
Specific embodiment
The process of Machining Path generation method on a kind of complicated point cloud model of basal plane curve orientation of the invention
Figure is as shown in Figure 1.Specific implementation process of the invention is described in detail with implementation steps with reference to the accompanying drawing:
Step 1. extracts the number of boundary strong point of point cloud.
Any point p on step 1.1. selected point cloud first, and local coordinate system ξ is established by origin of p(L), in coordinate
In system,It is p point and its K neighborhood point set CK(p) unit vector in any point line direction in,It is that p point and its K are adjacent
The unit normal vector of domain point set institute fit Plane,It isWithVector product.
Step 1.2. is by K neighborhood point set CK(p) it projects toIn plane, projection point set C is obtainedK pro(p), for
Any point Indicate point p and pointLine and axisAngle, indicated with following formula:
Step 1.3. calculates neighborhood point set CK(p) the corresponding angle of every bitAnd calculate the difference of two continuous anglesIf maximum angular differenceMore than specified angle threshold
Then point p is exactly boundary point.Fig. 2 is the schematic diagram for extracting number of boundary strong point.
Step 1.4. point all on step search point cloud like this, obtains then boundary point set
The sequence at step 2. number of boundary strong point.Selection any point is concentrated in boundary pointAs start boundary pointThen boundary point at random is ranked up according to the following steps:
Step 2.1. is in boundary point setMiddle searching range pointsNearest pointThen by vectorSearch direction as next boundary pointAs shown in Fig. 3 (a).
Step 2.2. is enabledThen along search directionFind distanceNearest boundary pointSame time pointFollowing formula should be met:
Wherein θthIt is specified angle threshold.
If step 2.3. (3) formula is set up, enableIt updates and searches direction
Step 2.4. is until search to start boundary pointWhen terminate, otherwise going to step 2.2 continues searching.
Step 3. constructs Coons base curved surface and lead curve
Step 3.1. specifies four angle points by interactive operation, is sorted using the process that four angle points obtain step 2
Boundary curve is divided into 4 sections of point sequence curves (PSC), and as shown in Fig. 3 (b), each segmentation is intended with B-spline Curve
It closes:
Wherein 0≤u, v≤1, r0(u)、r1(u)、r0(v) and r1(v) meet the compatibility condition of knot vector.
Four angle points meet the following conditions:
Step 3.2. constructs Coons basal plane by the bilinear interpolation of four edges circle curve.Simplest bilinearity
The Coons representation of a surface is as follows:
R (u, v)=s1(u,v)+s2(u,v)-s3(u,v) (6)
Wherein s1(u, v) and s2(u, v) is to be located at r0(u) and r1(u) and r0(v) and r1(v) linearly putting between
Sample curved surface, s3(u, v) is a tensor product curved surface, which is the bilinearity song defined by four angle points in formula (5)
Face.
Step 3.3. constructs lead curve point.The building equation of lead curve point is as follows:
Wherein ri,jIndicate j-th of guiding point on i-th of lead curve, ni,jIndicate list of the guiding point on basal plane
Position normal vector.I-th PSC lead curve is denoted as
The biasing of step 4. cloud
In order to avoid the machining interference between cutter and point cloud model, carried out by offset or dish of rose cutter tool radius
Biasing, the biased direction of each data point are the normal direction of the point.
Step 4.1. can first calculate the association of point K neighborhood point set to estimate the normal direction of each data point in a cloud
Variance matrix.Enable CK(p) the K neighborhood point set of point p is indicated, then its 3 × 3 covariance matrix HpIt is calculated by following formula:
Wherein qj∈CK(p), j=1, L, k.To HpSingular value decomposition is carried out, then HpThe corresponding feature of minimal eigenvalue to
Amount is exactly the normal vector n of p pointp, i.e. np=emin.Fig. 4 (a) is calculated cloud normal vector in aforementioned manners.
Step 4.2. unifies the direction of normal, and makes the process side of all normals direction point clouds, as shown in Fig. 4 (b).It is first
Each of the normal direction for first making a normal direction for cloud angle point p point correspond to angle point on basal plane with it is consistent, then adjust p point
The normal direction of neighborhood point, so thatpThe angle of the normal direction of each neighborhood point of the normal direction and p point of point, which is no more than, to be referred to
Determine angle threshold:
Wherein np, nneigIt is the normal direction of p point He its neighborhood point respectively,It is angle threshold, size is usually less than
π/2。
The biasing P of step 4.3. point cloudoffsetIt can be calculated by following formula:
Poffset:po=p+npRc (10)
It is wherein RcBall head knife radius.What Fig. 4 (c) was indicated is a cloud biasing schematic diagram
Step 5. calculates projecting direction, as shown in figure 5, projecting direction is determined by following formula:
In formulaIndicate the direction vector of projection, ni,jIndicate unit normal vector of the guiding point on basal plane,Table
Show on a cloud nearPointUnit normal vector.
Step 6. establishes the least square projection model of guiding point-to-point cloud, determines the weight of operating point.
Step 6.1. lead curve point is as follows along projective representation of the projecting direction on bias point cloud:
qpro=pg+dpronpro (12)
In formula, qproFor subpoint to be asked, dproIndicate projector distance, nproIndicate projecting direction.
The least square projection model of step 6.2. lead curve point-to-point cloud are as follows:
In formula, whereinIt is point cloud data, wiIt is and data pointWeight, it is true by formula (16)
It is fixed.
Objective function E (d in step 6.3. formula (13)pro) obtain minimum value condition are as follows:
It is hereby achieved that:
Step 6.4. weight wiIt determines as the following formula
In formula,For point to be projectedWith lead curve point pgThe distance between,ForWith
Projection line LpDistance.Drop shadow curve's equation is as follows:
Lp=pg+tnpro (17)
Step 7. iterates to calculate the subpoint on lead curve point-to-point cloud, and sequential connection subpoint forms cutter road
Diameter.
Step 7.1. selects bias point cloud as initialization point set P0, subpoint is calculated using formula (12) (15)
qpro；
Step 7.2. calculates weight { w in the l times iteration by publicity (18)iThreshold value wlimit；
In formula, wmeanAnd wmaxRespectively all weight { wiAverage value and maximum value.
If the point P that the operating point step 7.3. is concentratedlWeight wjGreater than threshold value wlimit, then it is retained in operating point
It concentrates；Otherwise it is concentrated from operating point and is deleted, to update work point set；
Step 7.4. calculates the subpoint in the l+1 times iteration according to new work point setAnd calculate following iteration
Terminate criterion:
In formula, εprFor given computational accuracy, KmaxFor maximum number of iterations.If meeting above-mentioned Stopping criteria,
Iteration ends；Otherwise, point to be projected is updated toContinue above-mentioned iterative process until Stopping criteria is satisfied.
In conclusion the present invention is directly based upon the construction that measurement pointcloud carries out cutter path, point cloud data is crossed and has arrived
The construction process of CAD parameter model can effectively shorten and measure the production cycle that part fabricates, drop from part prototype
Low design and manufacture cost.Due to can more easily plan efficient cutter motor pattern on simple basal plane, to enable cutter
Enough path topologies most suitable on cloud carry out highly-efficient processing.
Claims (1)
1. the Machining Path generation method on a kind of complicated point cloud model of basal plane curve orientation, which is characterized in that including
Following steps:
Step a, the boundary point for extracting point cloud simultaneously sort to boundary point, form orderly boundary point sequence curve, then by its
It is divided into four edges circle point sequence curve；
Specific steps include:
A1. any point p on selected point cloud, and local coordinate system is established using p as origin, in coordinate systemIt is p point and its K neighborhood
Point set CK(p) unit vector in any point line direction in,It is p point and its K neighborhood point set CK(p) list of institute's fit Plane
Position normal line vector,It isWithVector product；
A2. by K neighborhood point set CK(p) it projects toProjection point set C is obtained in the plane at placeK pro(p), for any
A bitJ=1, L, k,Indicate point p and pointLine and axisAngle；
A3. all angles are calculatedAnd the difference of two continuous anglesIf maximum angular differenceMore than specified angle threshold
ValueThen point p is exactly boundary point；
A4. it sorts to boundary point: boundary point being looked for concentrate any point as start boundary pointIt is found in boundary point
The closest approach of concentrationThen by vectorSearch direction as next boundary point
A5. it enablesThen along search directionIt is concentrated in boundary point and finds distanceNearest boundary pointThen enableIt updates and searches directionUntil search to start boundary pointWhen terminate；
Step b according to four point sequence curve building Kong Siji curved surfaces and constructs lead curve on the basal plane；
The building equation of lead curve point is as follows:
In formula, ri,jIndicate j-th of guiding point on i-th of lead curve, ni,jIndicate per unit system of the guiding point on basal plane
Vector；
Step c is biased a cloud using rose cutter radius as offset or dish；
Step d establishes the least square projection model of guiding point-to-point cloud, determines projecting direction and participates in the work that subpoint calculates
The weight for making point, by lead curve along on the projecting direction iterative projection to bias point cloud of calculating, generation is without interference cutter road
Diameter；
Specific steps include:
D1. the plane least square projection model of the point-to-point cloud model on lead curve are as follows:
In formula, pgFor lead curve point,I=0, L, n are point cloud data, wiIt is and data pointRelevant weight, by
Formula (5) determines；
D2. E (d in formula (2)pro) condition of minimum value is obtained as dE (dpro)/ddpro=0, thus obtain dproAre as follows:
D3. projecting direction are as follows:
In formula:Indicate the direction vector of projection, ni,jIndicate unit normal vector of the guiding point on basal plane,Indicate point
On cloud nearPointUnit normal vector；
D4. weight wjIt determines as the following formula:
In formula,For lead curve point pgWith operating pointBetween distance,ForWith projection line Lp
Distance；
D5. by lead curve along on the projecting direction iterative projection to bias point cloud of calculating, when the difference of iteration twice meets
Given error precision or while reaching maximum number of iterations, terminate iteration.
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