CN108682043A - A kind of complex-curved measure planning method based on parameter mapping - Google Patents
A kind of complex-curved measure planning method based on parameter mapping Download PDFInfo
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Abstract
A kind of complex-curved measure planning method based on parameter mapping of the present invention belongs to field of precision measurement, is related to a kind of complex-curved measure planning method mapped based on parameter.In this method, triangle mesh curved surface is mapped to by plane parameter domain using mesh parameterization method, forms the Plane Gridding Model on triangle mesh curved surface vertex and plane parameter domain vertex correspondence.The boundary profile of Plane Gridding Model is extracted, and using boundary contour as guiding line segment, requires to bias each line segment along normal orientation according to measurement accuracy, generate the measuring route for covering entire Plane Gridding Model.Again by each measuring route inverse mapping to triangle mesh curved surface, measurement of curved surface path is obtained；Finally the strings high differentiation such as use is layouted on measurement of curved surface path, completes complex-curved measure planning.The method increase measurement efficiencies, reduce complex-curved measure planning difficulty, versatile, can meet the requirement that is uniformly processed of each class model measurement of curved surface path planning under same frame.
Description
Technical field
The invention belongs to field of precision measurement, more particularly to a kind of complex-curved measure planning side based on parameter mapping
Method.
Background technology
Complex-curved to be widely used in the fields such as aerospace, automobile, mold, accurate measure is to ensure that part is final
Process the important link of geometric accuracy.When practical measurement, series of discrete sampled point is arranged often through in piece surface, to obtain
Obtain complex-curved geometry.For this purpose, it is to meet measurement accuracy and efficiency to measuring route and measuring point distribution make rational planning for
It is required that important leverage.The mode measured for the more complex part of face shape, generally use subregion.However, subregion is excessive, then without
Method Precise Representation curved surface various pieces, influence curve reestablishing precision；Subregion is too small, it will cause tested " fragment " is on the high side, measures
Efficiency is low, and increases curved surface precision splicing difficulty.In measurement path planning, section check is actually used, by equidistant
Parallel plane and surface intersection obtain and measure track.However, in three dimensions, carrying out point, line, surface intersection operation, time-consuming,
And easily omit important tested feature.Triangular gridding curve model is the linear approximation to initial three-dimensional surface model, because of its number
According to simple in structure, moulding fast and flexible, topological adaptable and computational efficiency is high the features such as, be widely used in numerical control and add
The fields such as work, texture mapping, reverse-engineering.Spatial complex curved surface can be established and put down by carrying out parameterized treatment to triangle mesh curved surface
Face maps the correspondence between domain.Therefore, it may be implemented on 3 D complex curved surface using the parameter mapping method of triangle gridding
Measure planning provides feasible scheme choosing to the dimension-reduction treatment of two dimensional surface measure planning for complex-curved precise high-efficiency measurement
It selects.
2004, Yu Gang etc. invented a kind of curved face measurement method in patent of invention CN1719194A, by curved surface to be measured
Multiple Delta Regions are divided into, the centers of gravity of all Delta Regions is made to be less than predetermined threshold at a distance from subpoint on curved surface with it,
The vertex of each Delta Region is chosen as measurement point.2006, Sun Yuwen etc. was invented in patent of invention CN100418027C
A kind of curved surface numerical control processing method of helix guidance, using based on spline interpolation plane systematic or non-equidistant helix as parameter
Line generates the machining locus of three physical dimensions by mapping.
However, the above method does not refer to the complex-curved measure planning method mapped based on parameter.
Invention content
Present invention mainly solves technical barrier be to overcome existing method insufficient, towards complex-curved high-precision, high efficiency
Measurement request has invented a kind of complex-curved measure planning method mapped based on parameter.In this method, using parameter mapping side
Method, realize 3 D complex curved surface on measure planning to two dimensional surface measure planning dimension-reduction treatment, by the curved surface in space measurement
Geometry calculating is converted into plane geometry calculating, reduces and directly carries out in three dimensions spent by point, line, surface intersection operation
Time improves measurement efficiency, reduces the difficulty of complex curved surface parts measure planning；It is retouched since complex curved surface parts are different
Grid model can be reconstructed by stating model, can meet each class model measurement of curved surface path planning at the unification under same frame
The requirement of reason.
The technical solution adopted by the present invention is a kind of complex-curved measure planning method mapped based on parameter, feature
It is in measure planning method, to use mesh parameterization method that triangle mesh curved surface is mapped to plane parameter domain first, form three
Angle grid surface vertex and the one-to-one Plane Gridding Model in plane parameter domain vertex；Secondly the side of Plane Gridding Model is extracted
Boundary's profile, and using boundary contour as guiding line segment, require to bias each line segment along normal orientation according to measurement accuracy, it is raw
At the measuring route for covering entire Plane Gridding Model；Again by each measuring route inverse mapping to triangle mesh curved surface, obtain
Measurement of curved surface path；Finally the strings high differentiation such as use is layouted on measurement of curved surface path, completes complex-curved measure planning.Method
It is as follows：
The technical solution adopted by the present invention is a kind of complex-curved measure planning method mapped based on parameter, feature
It is：It in measure planning method, uses mesh parameterization method that triangle mesh curved surface is mapped to plane parameter domain first, forms three
Angle grid surface vertex and the one-to-one Plane Gridding Model in plane parameter domain vertex；Secondly the side of Plane Gridding Model is extracted
Boundary's profile, and using boundary contour as guiding line segment, require to bias each line segment along normal orientation according to measurement accuracy, it is raw
At the measuring route for covering entire Plane Gridding Model；Again by each measuring route inverse mapping to triangle mesh curved surface, obtain
Measurement of curved surface path；Finally the strings high differentiation such as use is layouted on measurement of curved surface path, completes complex-curved measure planning.Method
It is as follows：
Triangle mesh curved surface Γ is carried out plane parameter by the first step
Using the grid surface parametric method based on least square conformal projection, plane is carried out to triangle mesh curved surface Γ
Parameterized treatment.First, in triangular surface piece TsUpper structure orthogonal frameWhereinWithFor orthogonal frame ξ(s)Three reference axis,For triangular surface piece TsMethod arrow, osFor triangular surface piece TsOn it is any one
Point, and ensure that the orthogonal frame for sharing two adjacent triangular surface pieces of a line has consistent direction.In orthogonal frame ξ(s)
Lower structure maps r：(x, y) → (u, v),
A upper point r (x, the y)=u+iv of triangle mesh curved surface Γ are plural form.Under least square meaning, triangle is defined
Mapping condition δ (Γ) on grid surface Γ is,
Wherein, AsFor triangular surface piece TsArea.
The object function δ (C) under triangle mesh curved surface Γ least squares meaning is as a result,
Wherein, i1, i2 and i3 are respectively triangular surface piece TsIn three vertex index；Ci1、Ci2、Ci3Respectively triangle is bent
Dough sheet TsCorresponding vertex on the P of plane parameter domain；(xi1, yi1)、(xi2, yi2) and (xi3, yi3) it is respectively triangular surface piece TsTop
Point coordinates；wi1=(xi3-xi2)+i(yi3-yi2)、wi2=(xi1-xi3)+i(yi1-yi3) and wi3=(xi2-xi1)+i(yi2-yi1) be
Coordinate Relation Parameters.The correspondence of triangle mesh curved surface Γ and plane parameter domain P are established as a result, and it is bent to form triangle gridding
Vertex of surface and the one-to-one Plane Gridding Model Ω in Planar Mapping domain vertex.
Second step, the boundary of extraction Plane Gridding Model Ω
First in Plane Gridding Model Ω build vertex, side, planar delta piece topological relation, then pass through create top
Point, side, planar delta piece syntople, extract adjacent planar delta piece quantity be 1 side as boundary.IfIt is the set on vertex in Plane Gridding Model Ω,It is
The set on side, { T in Plane Gridding Model Ωpk| j=1,2 ..., n } be Plane Gridding Model Ω intermediate cam planar chips set,
J indicates that the vertex serial number of planar delta piece, k indicate the quantity of planar delta piece.If vertexIt is a certain planar delta piece Tpk's
Vertex, then planar delta piece TpkIt is vertexAn adjacent planar delta piece；If sideIt is a certain planar delta piece Tpk's
Side, then planar delta piece TpkIt is sideAn adjacent planar delta piece；If sideThere are two adjacent planar delta piece TpkWith
Tpk+1, then sideIt is internal edges, if sideOnly there are one adjacent planar delta piece Tpk, then sideIt is boundary edge.Plane grid
Topological relation formed after, from setMiddle search only 1 adjacent planar delta piece
Side constitutes the set { L of boundary edgel| l=1,2 ... m }.Due to set { Ll| l=1,2 ... m } in line segment be random alignment
, the line segment in set is connected by head and the tail sequence, obtains the closed boundary profile of Plane Gridding Model Ω
Third walks, the planning survey path in the P of plane parameter domain
Closed boundary profile is calculated firstPer unit system arrowThe closed boundary profile that will be extractedAs initial
Track obtains first measuring route by bias ΔClosed boundary profileIt is to be joined end to end by multiple discrete line segments
Composition.In closed boundary profileBiasing during be related to the biasing and their mutual intersection operations of line segment.If
Boundary edge LlStarting point S (xs, ys), terminal E (xe, ye), per unit system arrowCalculation formula be,
Line segment S ' E ' after biasing are,
To eliminate the intersection interference path caused by biasing, two straightway intersection points need to be calculated.If given straightway first and last
The plane coordinates of two endpoints is (x respectivelys, ys), (xe, ye), then the parametric equation of the straight line is,
If two straightway L1With L2, two endpoint is respectively (xs1, ys1), (xe1, ye1)；(xs2, ys2), (xe2, ye2)。
First determine whether the direction vector of two straight lines is equal；If differing, illustrate two straight line intersections, by four extreme coordinates generations
Entering parametric equation can obtain,
In α generations, are returned formula (4), are found intersection.After line segment biasing, the interference generated by intersection between biasing line segment is eliminated.Then
Successive ignition is carried out, it is final to obtain the measuring route collection for covering entire Plane Gridding Model ΩWherein N
For number of paths.
4th step generates triangle mesh curved surface Γ measuring routes
All planar delta pieces of Plane Gridding Model Ω are searched for first, determine three belonging to the point in each circular path
Angle plane piece calculates the point corresponding empty then according to the mapping relations between plane parameter domain P to triangle mesh curved surface Γ
Between three-dimensional coordinate on triangle mesh curved surface Γ.For any point on the P of plane parameter domainIts pair on grid surface
Ying DianFor：
Mapping calculation one by one is carried out to the measuring route in plane, obtains triangle mesh curved surfaceMeasuring route collection
5th step, using etc. actions difference regulation draw measuring point distribution
When measure scan when, constantly calculate movement locus current sampling point and recorded a little be wired to this section of movement rail
The height h at mark center, by judging whether current sampled point is included in record with given franchise value.The calculating of action h is public
Formula is：
Wherein, A=xi-xi-1, B=yi-yi-1, wherein (xi, yi) it is current calculating point diCoordinate, (xi-1, yi-1) be away from
Point d is calculated from currentiNearest point di-1Coordinate；(xc, yc) it is di-1With diMidpoint dcCoordinate.
The beneficial effects of the invention are as follows using parameter mapping method, realize that measure planning is flat to two dimension on 3 D complex curved surface
The dimension-reduction treatment of planar survey planning converts the surface geometry calculating in space measurement to plane geometry and calculates, reduces directly
The time spent by point, line, surface intersection operation is carried out in three dimensions, is improved measurement efficiency, is reduced complex-curved zero
The difficulty of part measure planning.Solve the problems, such as that Boolean calculation efficiency is low in existing method three dimensions, method is versatile, can expire
The requirement that is uniformly processed of each class model measurement of curved surface path planning of foot under same frame, to improving complex-curved detection essence
Degree, efficiency are of great significance.
Description of the drawings
The complex-curved measure planning flow charts of attached drawing 1-；Attached drawing 2- typical deltas grid surface and measuring point distribution map；Attached drawing
The Plane Gridding Model of 3- typical delta grid surfaces and plane survey path planning figure.Wherein, Γ-triangle mesh curved surface, Ω-
Plane Gridding Model,The measuring route of-the 0 triangle mesh curved surface Γ,The measurement of-the 0 Plane Gridding Model Ω
Path, plThe sampled point of triangle mesh curved surface Γ.
Specific implementation mode
In conjunction with attached drawing and the technical solution specific embodiment that the present invention will be described in detail.
The triangle mesh curved surface Γ that the present embodiment uses shares 1821 nodes, 3512 for Mexico's straw hat surface model
The size of a triangular unit, grid model minimum bounding box is 160mm × 160mm × 80mm, and offset or dish Δ takes 5mm, action
Franchise is 2mm.Mesh parameterization method is used to set up the correspondence of triangle mesh curved surface and plane parameter domain first, in turn
Trajectory planning and measuring point distribution, basic flow chart such as attached drawing 1 are measured in plane parameter domain.The specific steps of method are such as
Under：
Triangle mesh curved surface Γ is carried out plane parameter by the first step
Using based on least square conformal projection grid surface parametric method, triangle mesh curved surface Γ is parameterized
Processing.First in each triangular surface piece TsUpper structure orthogonal frameWhereinFor triangle song
Dough sheet TsLaw vector, osFor triangular surface piece TsOn any point, and ensure share a line two adjacent triangular surfaces
The orthogonal frame of piece has consistent direction, thus obtains triangular surface piece TsThree vertex are in orthogonal frame ξ(s)Under part
Coordinate (x1, y1)、(x2, y2)、(x3, y3), in orthogonal frame ξ(s)Lower structure maps r：(x, y) → (u, v) is shown in formula (1)：
A upper point r (x, the y)=u+iv of triangle mesh curved surface Γ are plural form.Under least square meaning, triangle is defined
Mapping condition on grid surface Γ is formula (2)：
Each triangular surface piece TsVertex vt (s)Specify a plural number Ct=at+ibt, whole triangle mesh curved surface Γ is most
Small two object functions multiplied under meaning are formula (3),
Thus the correspondence of triangle mesh curved surface and plane parameter domain is set up, triangle mesh curved surface vertex is formed and puts down
Face maps the one-to-one Plane Gridding Model Ω in domain vertex.
Second step, the boundary of extraction Plane Gridding Model Ω
First in Plane Gridding Model Ω build vertex, side, planar delta piece topological relation, then pass through create top
Point, side, planar delta piece syntople, extract adjacent planar delta piece quantity be 1 side as boundary.IfIt is the set on vertex in Plane Gridding Model Ω,It is
The set on side, { T in Plane Gridding Model Ωpj| j=1,2 ..., n } be Plane Gridding Model Ω intermediate cam planar chips set,
If vertexIt is a certain planar delta piece TpjVertex, then planar delta piece TpjIt is vertexAn adjacent planar delta
Piece；If sideIt is a certain planar delta piece TpjSide, then planar delta piece TpjIt is sideAn adjacent planar delta piece；If
SideThere are two adjacent planar delta piece TpjAnd Tpj+1, then sideIt is internal edges, if sideOnly there are one adjacent planar deltas
Piece Tpi, then sideIt is boundary edge.After the topological relation of plane grid is formed, from setIn
Search only has the side of 1 adjacent planar delta piece, constitutes the set { L of boundary edgek| k=1,2 ... m }.{ L will be gatheredk| k=1,
2 ... m in line segment by head and the tail sequence be connected, obtain the closed boundary profile of Plane Gridding Model Ω
Third walks, the planning survey path in the P of plane parameter domain
Closed boundary profile is calculated firstPer unit system arrowThe closed boundary profile that will be extractedAs initial
Track obtains first measuring route by bias Δ lClosed boundary profileIt is to be joined end to end by multiple discrete line segments
Composition.In closed boundary profileBiasing during be related to the biasing and their mutual intersection operations of line segment.If
Boundary edge LkStarting point S (xs, ys), terminal E (xe, ye), per unit system arrowCalculation formula be formula (4),
Line segment S ' E ' after biasing are formula (5),
To eliminate the intersection interference path caused by biasing, two straightway intersection points need to be calculated.If given straightway first and last
The plane coordinates of two endpoints is (x respectivelys, ys), (xe, ye), then the parametric equation of the straight line is formula (6),
If two straightway L1With L2, two endpoint is respectively (xs1, ys1), (xe1, ye1)；(xs2, ys2), (xe2, ye2)。
It first determines whether the direction vector of two straight lines is equal, if differing, illustrates two straight line intersections, then enable L1Parameter be α,
Four extreme coordinates, which are substituted into parametric equation, to be obtained：
In α generations, are returned formula (4), are found intersection.After line segment biasing, the interference generated by intersection between biasing line segment is eliminated.Then
Successive ignition is carried out, it is final to obtain the measuring route collection for covering entire Plane Gridding Model ΩWherein N
For number of paths.As shown in Figure 3.
4th step：, generate triangle mesh curved surface Γ measuring routes
All planar delta pieces of Plane Gridding Model Ω are searched for first, determine three belonging to the point in each circular path
Angle plane piece calculates the point corresponding empty then according to the mapping relations between plane parameter domain P to triangle mesh curved surface Γ
Between three-dimensional coordinate on triangle mesh curved surface Γ.For any point on the P of plane parameter domainIts pair on grid surface
Ying DianFor formula (8)：
Mapping calculation one by one is carried out to the measuring route in plane, obtains triangle mesh curved surfaceMeasuring route collection
5th step：Using etc. actions regulation draw measuring point distribution
When measuring scanning, the line (string) for constantly calculating movement locus current sampling point and having recorded a little arrives the Duan Yun
The height h of dynamic track centers, by judging whether current sampled point is included in record with given franchise value.The meter of action h
Calculating formula (9) is：
Wherein, A=xi-xi-1, B=yi-yi-1, wherein (xi, yi) it is current calculating point diCoordinate, (xi-1, yi-1) be away from
Point d is calculated from currentiNearest point di-1Coordinate；(xc, yc) it is di-1With diMidpoint dcCoordinate.
Thus 8393 sampled points are obtained, see attached drawing 2,3.
The present invention realizes the dimension-reduction treatment of measure planning on 3 D complex curved surface to two dimensional surface measure planning, by space
Geometry calculating in measurement, which is transformed into plane domain, to be carried out, and is reduced and is directly carried out point, line, surface intersection operation in three dimensions
The spent time, measurement efficiency is improved, reduces the difficulty of complex curved surface parts measure planning.Due to complex curved surface parts
Different descriptive models can be reconstructed into grid model, therefore can meet each class model measurement of curved surface path planning in same frame
The requirement being uniformly processed under frame.
Claims (1)
1. a kind of complex-curved measure planning method based on parameter mapping, characterized in that in measure planning method, use first
Triangle mesh curved surface is mapped to plane parameter domain by mesh parameterization method, forms triangle mesh curved surface vertex and plane parameter domain
The one-to-one Plane Gridding Model in vertex；Secondly extract Plane Gridding Model boundary profile, and using boundary contour as
Line segment is guided, requires to bias each line segment along normal orientation according to measurement accuracy, generates and cover entire Plane Gridding Model
Measuring route；Again by each measuring route inverse mapping to triangle mesh curved surface, measurement of curved surface path is obtained；Finally use etc. strings
High differentiation is layouted on measurement of curved surface path, completes complex-curved measure planning；Method is as follows：
Triangle mesh curved surface г is carried out plane parameter by the first step
Using based on least square conformal projection grid surface parametric method, plane parameter is carried out to triangle mesh curved surface г
Processing constructs the mapping of triangle mesh curved surface г to plane parameter domain P；First, in triangular surface piece TsUpper structure orthogonal frameWhereinWithFor orthogonal frame ξ(s)Three reference axis,For triangular surface piece Ts
Method arrow, osFor triangular surface piece TsOn any point, and ensure share a line two adjacent triangular surface pieces it is orthogonal
Frame has consistent direction；In orthogonal frame ξ(s)Lower structure maps r:(x, y) → (u, v),
A upper point r (x, the y)=u+iv of triangle mesh curved surface г are plural form；Under least square meaning, triangle gridding is defined
Mapping condition δ (Γ) on curved surface г is,
Wherein, AsFor triangular surface piece TsArea；
The object function δ (C) under triangle mesh curved surface г least squares meaning is as a result,
Wherein, i1, i2 and i3 are respectively triangular surface piece TsIn three vertex index；Ci1、Ci2、Ci3Respectively triangular surface piece Ts
Corresponding vertex on the P of plane parameter domain；(xi1,yi1)、(xi2,yi2) and (xi3,yi3) it is respectively triangular surface piece TsVertex is sat
Mark；wi1=(xi3-xi2)+i(yi3-yi2)、wi2=(xi1-xi3)+i(yi1-yi3) and wi3=(xi2-xi1)+i(yi2-yi1) it is coordinate
Relation Parameters；The correspondence of triangle mesh curved surface г and plane parameter domain P are established as a result, form triangle mesh curved surface vertex
With the one-to-one Plane Gridding Model Ω in Planar Mapping domain vertex；
Second step, the boundary of extraction Plane Gridding Model Ω
First in Plane Gridding Model Ω build vertex, side, planar delta piece topological relation, then by create vertex,
Side, planar delta piece syntople, extract adjacent planar delta piece quantity be 1 side as boundary；IfIt is the set on vertex in Plane Gridding Model Ω,
It is the set on side in Plane Gridding Model Ω, { Tpk| j=1,2 ..., n be Plane Gridding Model Ω intermediate cam planar chips collection
It closes, j indicates that the vertex serial number of planar delta piece, k indicate the quantity of planar delta piece；If vertexIt is a certain planar delta piece
TpkVertex, then planar delta piece TpkIt is vertexAn adjacent planar delta piece；If sideIt is a certain planar delta piece
TpkSide, then planar delta piece TpkIt is sideAn adjacent planar delta piece；If sideThere are two adjacent planar delta pieces
TpkAnd Tpk+1, then sideIt is internal edges, if sideOnly there are one adjacent planar delta piece Tpk, then sideIt is boundary edge；Plane
After the topological relation of grid is formed, from setMiddle search only has 1 adjacent planar delta piece
Side, constitute the set { L of boundary edgel| l=1,2 ... m }；Due to set { Ll| l=1,2 ... m in line segment be to arrange at random
Row, the line segment in set is connected by head and the tail sequence, obtains the closed boundary profile of Plane Gridding Model Ω
Third walks, the planning survey path in the P of plane parameter domain
Closed boundary profile is calculated firstPer unit system arrowThe closed boundary profile that will be extractedAs track primary
Mark obtains first measuring route by bias ΔClosed boundary profileIt is to be joined end to end group by multiple discrete line segments
At；In closed boundary profileBiasing during be related to the biasing and their mutual intersection operations of line segment；If side
Boundary side LlStarting point S (xs,ys), terminal E (xe,ye), per unit system arrowCalculation formula be,
Line segment S'E' after biasing is,
To eliminate the intersection interference path caused by biasing, two straightway intersection points need to be calculated；If given straightway first and last two
The plane coordinates of endpoint is (x respectivelys,ys), (xe,ye), then the parametric equation of the straight line is,
If two straightway L1With L2, two endpoint is respectively (xs1,ys1), (xe1,ye1)；(xs2,ys2), (xe2,ye2)；First
Judge whether the direction vector of two straight lines is equal；If differing, illustrate two straight line intersections, four extreme coordinates are substituted into ginseng
Number equation can obtain,
In α generations, are returned formula (4), are found intersection；After line segment biasing, the interference generated by intersection between biasing line segment is eliminated；Then it carries out
Successive ignition, it is final to obtain the measuring route collection for covering entire Plane Gridding Model ΩWherein N is road
Diameter quantity；
4th step generates triangle mesh curved surface г measuring routes
All planar delta pieces of Plane Gridding Model Ω are searched for first, determine that the triangle belonging to the point in each circular path is flat
Dough sheet calculates the point in corresponding space three then according to the mapping relations between plane parameter domain P to triangle mesh curved surface г
Three-dimensional coordinate on the grid surface г of angle.For any point on the P of plane parameter domainIts corresponding points on grid surfaceFor：
Mapping calculation one by one is carried out to the measuring route in plane, obtains the measuring route collection of triangle mesh curved surface г
5th step, using etc. actions difference regulation draw measuring point distribution
When measure scan when, constantly calculate movement locus current sampling point and recorded being wired in this section of movement locus a little
The height h of the heart, by judging whether current sampled point is included in record with given franchise value.The calculation formula of action h is：
Wherein, A=xi-xi-1, B=yi-yi-1, wherein (xi,yi) it is current calculating point diCoordinate, (xi-1,yi-1) work as distance
Preceding calculating point diNearest point di-1Coordinate；(xc,yc) it is di-1With diMidpoint dcCoordinate.
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