CN108647399A - A kind of biasing means of composite surface - Google Patents
A kind of biasing means of composite surface Download PDFInfo
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- CN108647399A CN108647399A CN201810344589.5A CN201810344589A CN108647399A CN 108647399 A CN108647399 A CN 108647399A CN 201810344589 A CN201810344589 A CN 201810344589A CN 108647399 A CN108647399 A CN 108647399A
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Abstract
The invention belongs to computer aided design and manufacture fields, and disclose a kind of biasing means of composite surface, include the following steps：(1) by the discrete original triangle grid model of generation of original surface model, and its normal vector information is built；(2) judge that original mesh point is in continuous or discrete regions；(3) the original mesh point progress grid for being directed to gap regions in (2) is filled up；(4) whole self intersection is carried out to original mesh point and original triangle grid model to detect；(5) on original triangle grid model, the self intersection region of judgement in removal (2) and (4)；(6) to including that the original triangle grid model of normal vector information is biased in (1)；(7) cavity generated on biasing triangle grid model is filled up.The present invention advantageously accounts for basic problem present in commercial Application, not only increases applicability and efficiency, and easy to implement, flexibility is higher, is conducive to promote and apply.
Description
Technical field
The invention belongs to computer aided design and manufacture fields, more particularly, to a kind of biasing side of composite surface
Method.
Background technology
In computer aided design and manufacture field, the biasing of surface model is widely used in rapid shaping technique, number
Control processing, the multiple fields such as robot path planning.In rapid shaping field, surface model biasing can to geometrical model into
Row pretreatment, improves the case where model quality is reduced with precision caused by by the manufacture of layer and layer on model,
Repair on curved surface due to curved surface is discontinuous and caused by fold the defects of.The biasing means of a set of perfect composite surface model are not
The quality of product can be only improved, rejection rate is reduced.Meanwhile processing efficiency can be promoted, in industrial circle important role.
Through being retrieved to existing literature, the method for the biasing in relation to surface model is as follows.
First method is by all curved surfaces of bias model, for the curved surface after biasing by being cut to curved surface
Or the mode extended, by the curve reestablishing after biasing at a closed threedimensional model, the surface model after as biasing.First
It is biased for the point on model, generates sphere, be biased for the side on model, cylinder is generated, on model
Face face is biased, generate parallel plane, then the intersecting area after biasing is cut and is extended.This one kind side
Method calculating is extremely complex, and situations such as numerical value is unstable is susceptible in the tangential contact area of curved surface.
Second method is by Surface tessellation into triangle grid model (QU X, STUCKER B.A 3D surface
Offset method for STL-format models [J] .Rapid Prototyping Journal), by triangle
The mesh point of grid model is biased the biasing realized to surface model.Wherein, the normal vector of mesh point by calculate with
What the mean vector for the triangular plate normal vector that the mesh point is connected obtained, this method be suitable only for mesh point be located at compared with
To be continuous, the situation on gentle curve is likely to result in the mistakes such as topology conflict for sharp side or cusp region and occurs.Together
When, this method largely relies on the discrete way of triangle gridding, and different discrete way is likely to result in mesh point correspondence
Normal vector differ.
Invention content
For the disadvantages described above or Improvement requirement of the prior art, the present invention provides a kind of biasing means of composite surface,
It ensure that the accuracy of model biasing.
To achieve the above object, it is proposed, according to the invention, provide a kind of biasing means of composite surface, which is characterized in that its
Include the following steps：
(1) by the discrete original triangle grid model of generation of the original surface model of composite surface, and the original triangulation network is built
The normal vector information of lattice model；
(2) judge that the original mesh point in original triangle grid model is in continuum or discrete regions, to non-
Each original mesh point of continuum is biased calculating, and identifies whether the original mesh point after biasing calculating will produce notch
Or it is in self intersection region；
(3) it is directed to the original mesh point that notch is generated in step (2), carrying out grid in original triangle grid model fills out
It mends；
(4) whole self intersection is carried out to original mesh point and original triangle grid model to detect；
(5) on original triangle grid model, the self intersection region in removal step (2) and step (4)；
(6) to including that the original triangle grid model of normal vector information is biased in step (1), biasing triangle is obtained
Grid model；
(7) cavity generated on biasing triangle grid model is filled up.
Preferably, it is that the mesh point and Grid Edge on original triangle grid model establish normal vector letter in step (1)
Breath.
Preferably, step (2) includes following sub-step：
(2.1) all mesh points on triangle grid model are found out；
(2.2) all Grid Edges where arbitrary mess point are obtained；
(2.3) for the Grid Edge E where the mesh pointiWith Grid Edge E adjacent theretoi+1, obtain EiAnd Ei+1Institute respectively
Triangular plate SiAnd Si+1, also obtain EiThe mesh point p at both ends1And p2；
According to the normal vector information of establishment, p is obtained1Respectively in SiAnd Si+1On normal vector information and obtain p2Respectively
In SiAnd Si+1On normal vector, calculate p1In SiAnd Si+1On normal vector angle angle1And p2In SiAnd Si+1On
Normal vector angle angle2；
(2.4) if angle1Or angle2More than assigned error at, then to EiAnd Ei+1The triangular plate S at placeiAnd Si+1's
Mesh point is biased, and judges the triangular plate S that the mesh point after biasing is constitutedi' and Si+1' whether intersect；If triangular plate Si′
With triangular plate Si+1' intersection and angle1 be more than assigned error at, judge p1It is located at self intersection region after biasing, if Si' and
Si+1' intersection and angle2 be more than assigned error at, then judge p2It is located at self intersection region after biasing；If Si' and Si+1' not phase
It hands over and angle1 is more than assigned error at, then judge p1Notch is will produce after biasing, if angle2 is more than assigned error at, then
Judge p2It will produce notch after biasing；Here, the mesh point that will produce notch after biasing is named as gap regions point.
Preferably, step (3) includes following sub-step：
(3.1) virtual boundary set VE is created, wherein virtual boundary is the boundary inside mesh point, length 0；
(3.2) it is directed to determining gap regions point, virtual boundary is added inside such mesh point, and is virtual boundary structure
Normal vector information is built, newly added virtual boundary is added in set VE；Virtual boundary will be for the notch after biasing
Region creates patch grids；
(3.3) return to step (3.2), to complete to add virtual boundary inside all gap regions points；
(3.4) the arbitrary virtual boundary e being directed in virtual boundary set VE1, obtain e1Two endpoint p1And p2And p1
And p2Corresponding normal vector f1And f2, wherein p1, p2Coordinate it is equal；
(3.5) normal direction vector f is calculated1And f2Between angle theta, action is calculated according to θ and offset or dish r
chordHeight：
It is less than or equal to given action error c in chordHeighttUnder conditions of, on circular arc between consecutive points it is corresponding most
Big central angle θmaxIt indicates as follows：
For the maximum angle θ for meeting under conditions of being less than action errormax, according to normal vector f1And f2Between angle theta
Calculate e1It inside needs to be inserted into N number of mesh point：
N=θ/θmax-1
(3.6) in e1It is interior, from p1To p2It is inserted into N number of mesh point：It is inserted into j-th of mesh point pjIt needs to calculate and biases the grid
Point pjNormal vector fj：
By e1Disconnect interpenetration network point pj, wherein the mesh point p of insertionjCoordinate and p1It is equal, setting mesh point pjMethod
It is f to vectorj, j=0,1,2 ... N；
(3.7) to e1It is interior that the N number of mesh point being inserted into is needed to repeat step (3.6), to complete for virtual boundary e1Slotting point
Operation；
(3.8) step (3.6)~step (3.7) is repeated to all fictitious lines in set VE, to complete to all virtual
The slotting point on side operates；
(3.9) the corresponding virtual dough sheet progress grid of fictitious line after the slotting point of extraction is filled up, in virtual dough sheet region
Add new triangle gridding.
Preferably, step (4) includes following sub-step：
(4.1) set selfPoints is created, for storing the point of intersection generated；
(4.2) all triangular plates in triangle grid model are saved as into kdTree structures；
(4.3) the arbitrary mess point point being directed on triangle grid model, if mesh point point is to know in step (2)
It is located at the point in self intersection region after other biasing, then the point is added in set selfPoints, and update mesh point
Point, subsequently into step (4.3), conversely, then entering step (4.4)；
(4.4) mesh point point is biased according to the offset or dish of setting, the mesh point after being biased
Opoint；Using offset or dish as radius, Opoint is that the centre of sphere makees a ball, utilizes ball and the kdTree phases for storing all triangular plates
It hands over, obtains the triangular plate that self intersection occurs；
(4.5) triangular plate being connected with mesh point point is searched in the triangular plate that self intersection occurs, and is being occurred certainly
This kind of triangular plate is deleted in the triangular plate of intersection, and collection then is added in the corresponding mesh point of the remaining triangular plate that self intersection occurs
It closes in selfPoints；
(4.6) step (4.3)~step (4.5) is repeated, to complete to position after all biasings in original triangle grid model
In the screening of the mesh point in self intersection region.
Preferably, in step (6), for all mesh points on original triangle grid model, along original triangle gridding
Original triangle grid model is biased, obtains according to given offset or dish by the normal vector that the mesh point on model is established
To biasing triangle grid model.
Preferably, step (7) includes following sub-step：
(7.1) it creates and waits for filling cavity set repairHoles；
(7.2) it for a cavity finalhole in the empty set finalHoles behind removal self intersection region, obtains
To the corresponding net boundaries of finalhole, and sort；
(7.3) it according to the normal vector information of the corresponding mesh points of finalhole and the mesh point, establishes
The corresponding projection planes of finalhole project to the corresponding mesh points of finalhole and Grid Edge on the projection plane；
(7.4) the point of intersection that the finalhole after projection is generated on a projection plane is found, according to the point of intersection position
Ratio on place side is projected back in on original cavity finalhole, and it is corresponding in original cavity finalhole to obtain the point of intersection
Two points, the two point between build Grid Edge, finalhole is split from the Grid Edge of composition, formed two skies
Hole carries out sequence again to two new cavities of formation to boundary；
(7.5) steps (7.2) to step (7.4) are repeated for two new cavities, until to project to projection flat in any cavity
There is no the point of intersection behind face, then finalhole is added in set repairHoles, updates finalhole, return to step
(7.2), it to complete the division for all cavities in set finalHoles, avoids that topological structure occurs on a projection plane
Conflict；
(7.6) it for the newer set repairHoles during step (7.1) to step (7.5), obtains
Empty repairhole in repairHoles；
(7.7) hole region is filled up：It is new by adding to cavity repairhole for arbitrary cavity repairhole
The mode of triangular plate filled up；After completion is filled up, repairhole is updated；
(7.8) step (7.6)~step (7.7) is repeated, cavity all in repairHoles is filled out in completion
It mends.
Preferably, step (7.7) includes following sub-step：
(7.7.1) obtains the corresponding mesh point of each Grid Edge in repairhole, calculates the corresponding throwings of repairhole
Shadow plane, repairhole is projected on projection plane, obtains the subpoint of mesh point on a projection plane；
Coordinate system is converted into the projection plane coordinates system using the center of projection plane as coordinate origin by (7.7.2), is calculated
The subpoint P " under current coordinate system1, P "2…..P″n；By P "1, P "2…..P″nThe region that line is constituted is named as polygon,
The angle on the corresponding adjacent both sides of polygon Arbitrary Boundaries point is calculated, n is the quantity of subpoint；
(7.7.3) takes the boundary point P " of adjacent both sides angle value minimumk, obtain and boundary point P "kConnected other two
Boundary point is P "k-1And P "k+1, connect P "k-1With P "k+1, k=1,2 ... n；
(7.7.4) judges junction curve P "k-1P″k+1Whether intersect with the side of polygon, wherein intersection point P "k-1With P "k+1It removes
Outside, if intersection, abandons P "k, the boundary point of next angle minimum is selected to be entered step if non-intersecting
(7.6.5)；
(7.7.5) removes the P in Polygonal Boundary point set "kPoint and surface boundary P "kP″k-1With P "kP″k+1, to complete
With P " in pairs of polygonk+1, P "k-1With P "k+1For the filling in the region of boundary point, the corresponding side of next minimum angle is found
Boundary's point, enters step (7.6.3).
Preferably, step (7.7.2) includes following sub-step：
A) boundary point of polygon is obtained, these boundary points are P "1, P "2..., P "n；
B) compare P "1, P "2... P "nIn the directions x component, find out the point with maximum x-component, be denoted asWherein, the component in the directions x refers to boundary point P "1, P "2... P "nIn three Cartesian coordinates
Under along x-axis coordinate components；
C) and then again compareIn the directions y component, find out one with maximum y-component
A point P "k, previous vertex is P "k-1, the latter vertex is P "k+1, vector
Wherein, the component in the directions y refers to coordinate P "1, P "2... P "nAlong the coordinate components of y-axis under three Cartesian coordinates；
D) it is P " to calculate vertexiAngle, θi, wherein θiRefer on polygon with P "iTwo connected boundary point P "i-1
With P "i+1Respectively with P "iThe angle on the boundary of composition enables Wherein, i=1,
2,…n；
If (Va×Vb)×Vtemp>=0, then
Conversely, then
In general, through the invention it is contemplated above technical scheme is compared with the prior art, can obtain down and show
Beneficial effect：
1) present invention advantageously accounts for basic problem present in commercial Application, not only increases applicability and efficiency, easily
In implementation, flexibility is higher, is conducive to promote and apply.
2) biasing for effectively realizing composite surface model entirety, ensure that the accuracy of model biasing, is widely used in
Robot path planning, the multiple fields such as curved surface reparation.
Description of the drawings
Fig. 1 is a kind of flow diagram of the biasing means for composite surface model that better embodiment of the present invention provides；
Fig. 2 is the topological relation for being related to the adjacent triangular plate in position using a kind of biasing means of composite surface model in Fig. 1
Schematic diagram；
Fig. 3 is to be related to calculating in arbitrary gap regions using a kind of biasing means of composite surface model in Fig. 1 being inserted into
The schematic diagram of mesh point number；
Fig. 4 a~Fig. 4 c are to be related to being inserted into net in gap regions using a kind of biasing means of composite surface model in Fig. 1
The schematic diagram of lattice point；Wherein, Fig. 4 a are a Grid Edge the lacking after prebias on arbitrary mess point there are two normal vector
Schematic diagram is filled up in mouth region domain, and Fig. 4 b are each there are two a Grid Edges of normal vector lacking after prebias on two mesh points
Schematic diagram is filled up in mouth region domain, and 4c is that there are three gap regions of the arbitrary mess point of normal vector after prebias to fill up signal
Figure；
Fig. 5 is related to original mesh point and original triangle using a kind of biasing means of composite surface model in Fig. 1
Grid model carries out the schematic diagram of whole self intersection detection；
Fig. 6 is the original being related to using a kind of biasing means of composite surface model in Fig. 1 to including normal vector information
The schematic diagram that beginning triangle grid model is biased；
Fig. 7 is related to being produced on biasing triangle grid model using a kind of biasing means of composite surface model in Fig. 1
The schematic diagram that the boundary in raw cavity is projected；
Fig. 8 is to relate to the use of sky to biasing the empty boundary generated on triangle grid model and project using in Fig. 7
Hole projected boundary carries out the schematic diagram of hole-filling.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
It does not constitute a conflict with each other and can be combined with each other.
Referring to Fig. 1, a kind of biasing means for composite surface model that better embodiment of the present invention provides, the combination
The use of the biasing means of surface model, solves in commercial Application, more provides the efficiency of processing operation.
A kind of biasing means of composite surface model mainly include the following steps that：
Composite surface is separated into triangle grid model, and establishes normal vector for mesh point and Grid Edge by step 1,
Middle Grid Edge is the side where mesh point.In the topological relation of triangle grid model, a side is shared by two triangular plates, because
This line is made of two one side of something, and one side of something is Grid Edge, triangular plate corresponding with other Grid Edges composition.According to Grid Edge
The triangular plate normal vector direction at place can obtain direction of the Grid Edge on triangular plate using the right-hand rule.Therefore, one
The corresponding two grid edge directions in side shared by two triangular plates are opposite.
Referring to Fig. 2, in present embodiment, composite surface is separated into triangle grid model, triangle grid model is by having
Limit triangular plate is constituted according to certain topological relation, and triangle grid model approaches surface model.Wherein, topological relation characterizes
Connection relation between triangular plate.In fig. 2, any two is connected triangular plate shares same side, two mesh points it
Between a line be made of two one side of something, half of direction is opposite.The vertical triangular plate of normal vector of figure intermediate cam piece outwardly, root
According to topological relation, half edge direction on the triangular plate need to meet right-hand screw rule with normal vector.Its middle finger direction is three
The normal vector of cornual plate, therefore the corresponding Half-edge Structure of the triangular plate surrounds the triangular plate according to direction of rotation counterclockwise.
Step 2 specifically includes following steps：
(2.1) all mesh points on triangle grid model are traversed；
(2.2) all Grid Edges where arbitrary mess point are obtained, the corresponding Grid Edge of the mesh point is traversed；
(2.3) it is directed to arbitrary mess side EiWith Grid Edge E adjacent theretoi+1, obtain EiAnd Ei+1Dough sheet where respectively.
If EiAnd Ei+1The dough sheet at place is triangular plate SiAnd Si+1, obtain EiThe mesh point p at both ends1And p2, created according to claims 2
The method arrow information built, obtains p1Respectively in SiAnd Si+1On normal vector, obtain p2Respectively in SiAnd Si+1On normal vector,
Calculate p1In SiAnd Si+1On normal vector angle angle1 and p2In SiAnd Si+1On normal vector angle angle2.
(2.4) if angle1 or angle2 is more than assigned error at, then to EiAnd Ei+1The triangular plate S at placeiAnd Si+1's
Mesh point is biased, and judges the triangular plate S that the mesh point after biasing is constitutedi' and Si+1' whether intersect.If Si' and Si+1' phase
It hands over, judges p1And p2Self intersection region is likely located at after biasing.If angle1 is more than assigned error at, then judge p1After biasing
Positioned at self intersection region, if angle2 is more than assigned error at, then judge p2It is located at self intersection region after biasing.If Si' and
Si+1' non-intersecting, then judge p1And p2Notch may be will produce after biasing, if angle1More than assigned error at, then judge p1Partially
Notch may be will produce by postponing, if angle2More than assigned error at, then judge p2Notch may be will produce after biasing.
Step 3 specifically includes following steps：
(3.1) virtual boundary set VE is created, wherein virtual boundary is the boundary inside mesh point, length 0；
(3.2) for the mesh point that will produce notch after determining biasing, wherein the grid of notch will be will produce after biasing
Point is named as gap regions point, virtual boundary is added inside such mesh point, and build normal vector information for virtual boundary,
Newly added virtual boundary is added in set VE.Virtual boundary will create grid surface for the gap regions after biasing
Piece.It repeats the above steps, to complete to add virtual boundary inside all gap regions points；
(3.2) the arbitrary virtual boundary e being directed in virtual boundary set VE1, obtain e1Two endpoint p1, p2And p1,
p2Corresponding normal vector f1And f2, wherein since the length of virtual boundary is 0, p1, p2Coordinate be equal；
(3.3) normal direction vector f is calculated1And f2Between angle theta, action is calculated according to θ and offset or dish r
chordHeight：
Fig. 3 left hand views are please referred to, in present embodiment, according to f1, f2With r by e1Biasing, obtains the end after corresponding biasing
Point p1', p2', obtain circular arcCorresponding string p1′p2', string p is calculated by formula1′p2' arrive circular arcIt is maximum away from
From as action chordHeight.
It is less than or equal to given action error c in chordHeighttUnder conditions of, it is corresponding between consecutive points on circular arc
Maximum central angle θmax：
For the maximum angle θ for meeting under conditions of being less than action errormax, according to normal vector f1And f2Between angle theta
Calculate e1It inside needs to be inserted into N number of mesh point：
N=θ/θmax-1
(3.4) in e1It is interior, from p1To p2It is inserted into N number of mesh point：Being inserted into j-th of mesh point needs calculating to bias the mesh point
Normal vector fjAnd the mesh point p being inserted intoj' coordinate.
pj'=fj·r+pj
To e1It is interior that the N number of mesh point being inserted into is needed to repeat the above steps, to complete for virtual boundary e1Slotting point operation, j
=0,1,2 ... N.
Fig. 3 right part of flg is please referred to, in present embodiment, according to f1, f2With r by e1Biasing obtains e1Corresponding two after biasing
A endpoint p1', p2', met by step (3.2)Corresponding action error ctUnderUpper adjacent point circular arc
Corresponding maximum central angle θmax.By θmaxFormula is substituted into, is obtained after being inserted into N number of mesh point, consecutive pointsUpper consecutive points
The corresponding action of circular arc meets action error ct.In fig. 2 from p1To p2When being inserted into j-th of mesh point, p is obtained1', p2' corresponding
Normal vector f1, f2, the corresponding normal vector f of j-th of mesh point is calculated according to formulaj, due to pjCoordinate and p1And p2It is equal,
Therefore pj' corresponding coordinate is p1Along normal vector fjDirection offset or dish be r mesh point.
(3.5) step (3.2) to step (3.4) is executed to all fictitious lines in set VE, to complete to all virtual
The slotting point on side operates.
(3.6) the corresponding virtual dough sheet of fictitious line after point, the hole-filling method of invocation step (7), in void are inserted in extraction
Add new triangle gridding in quasi- dough sheet region.
Fig. 4 a~Fig. 4 c are please referred to, in present embodiment, for the gap regions point identified in step 2, in the inside of point
Fictitious line is created, the length of fictitious line is 0.The normal vector of corresponding two endpoints of virtual boundary is obtained, calculates and needs in void
The several points of insertion in region after quasi- edge offset, and new triangular plate is inserted into gap regions according to insertion point, Fig. 4 a~
The filling situation of three kinds of gap regions shown in Fig. 4 c includes slotting point and adds new triangular plate.
Step 4 specifically includes following steps：
(4.1) set selfPoints is created, for storing the point of intersection generated；
(4.2) all triangular plates in triangle grid model are saved as into kdTree structures；
(4.3) the arbitrary mess point point being directed on triangle grid model, if the point is the biasing identified in step (2)
It is located at the point in self intersection region afterwards, then the point is added in set selfPoints, updates mesh point point, enter step
(4.3).Conversely, entering step (4.4).
(4.4) point is biased according to certain offset or dish, the mesh point Opoint after being biased.With inclined
It is radius to set distance, and Opoint is that the centre of sphere makees a ball.Intersected with the kdTree for storing all triangular plates using ball, obtaining may
The triangular plate of self intersection occurs.
(4.5) triangular plate being connected with point may be being searched in the triangular plate of self intersection, and in possible self intersection
This kind of triangular plate is deleted in triangular plate.Set selfPoints is added in the corresponding mesh point of triangular plate of remaining possible self intersection
In.
(4.6) step (4.3) to step (4.5) is repeated, to complete to being located at certainly after all biasings in triangle grid model
The screening of the mesh point of intersecting area.
Referring to Fig. 5, in present embodiment, for arbitrary mess point p, if p is biasing for what is identified in step (2)
It is located at the point in self intersection region afterwards, which is directly added into set selfPoints.If it is not, as shown in figure 5, by point p
Biasing, offset or dish r obtain bias point p ', are the centre of sphere with bias point p ', offset or dish r is that radius creates a ball, with the ball
Intersect with kdTree.Intersect if ball exists with kdTree, the triangular plate of intersection need to be screened, if intersected with kdTree
Triangular plate be the triangular plate being connected with p, wherein the triangular plate being connected with p in Figure 5 be F1, F2…F6, exclude this kind of three
Cornual plate sequentially adds remaining triangle piece corresponding mesh point in set selfPoints.
Step 5, for all the points on triangle grid model, along the normal vector that mesh point is established, by triangle gridding
Model is biased, the triangle grid model after being biased.
Referring to Fig. 6, in present embodiment, according to the normal vector size of mesh point in diagram, by entire triangle gridding
Model is biased according to the size of normal vector, the triangle grid model after being biased, wherein grid model feature is approached
Curved surface features.
The specific sub-step of step six is as follows：
(6.1) it creates and waits for filling cavity set repairHoles；
(6.2) for a cavity finalhole in obtained empty set finalHoles, finalhole is obtained
Corresponding net boundary, and sort.
(6.3) the normal vector information according to the corresponding mesh points of finalhole and mesh point on curved surface is established
The corresponding projection planes of finalhole.The corresponding mesh points of finalhole and Grid Edge are projected on projection plane.
(6.4) due to the conflict of topological structure, the finalhole after projection will produce the point of intersection on a projection plane.
The point of intersection is found, is projected back in on original cavity finalhole in the ratio on place side according to the point of intersection position, obtained from phase
Intersection point corresponding two points in finalhole.Grid Edge is built between the two points, by finalhole from the net of composition
Lattice split at side, form two cavities.Sequence again is carried out to boundary to two new cavities of formation.
(6.5) step (7.2) is repeated to (7.4) are repeated, until any cavity projection in space for two new cavities
There is no the point of intersection after to projection plane.Finalhole is added in set repairHoles, finalhole is updated, is entered
Step (7.2) to complete the division for all cavities in set finalHoles avoids that topological knot occurs on a projection plane
The conflict of structure.
Referring to Fig. 7, in present embodiment, according to the corresponding mesh point P of empty hole1, P2…..nAnd P1, P2…..n
Normal vector information on curved surface builds the corresponding projection planes of cavity hole, hole is projected on projection plane, due to
Hole after the conflict projection of topological structure generates the point of intersection P on a projection planeinter, as shown in fig. 7, according to the point of intersection
PinterPosition, by PinterIt is projected back in on original cavity hole, obtains the mesh point P corresponding to original cavityinter1With
Pinter2, in Pinter1And pinter2Between build Grid Edge, by hole from Pinter1And Pinter2Between split, formed two cavities.
The two new cavities formed carry out classification and sequence again to boundary.Step (7.2) is repeated extremely for two new cavities
(7.4), until any cavity in space does not have intersection point after projecting to projection plane.
(6.6) it for the newer set repairHoles during (7.1) to (7.5), obtains in repairHoles
One of cavity repairhole.
(6.7) hole region is filled up：For arbitrary cavity repairhole, to the region by adding new triangular plate
Mode is filled up.After completion is filled up, repairhole is updated, is entered step (7.6).
(6.8) by (7.6) to (7.7) to complete to fill up cavity all in repairHoles.
It includes following sub-step that hole region, which fills up algorithm,：
(6.7.1) obtains the corresponding mesh point of each Grid Edge in repairhole, calculates the corresponding throwings of repairhole
Shadow plane, repairhole is projected on projection plane, obtains the subpoint of mesh point on a projection plane.
Coordinate system is converted into the projection plane coordinates system using the center of projection plane as coordinate origin by (6.7.2).It calculates
The corresponding coordinate P " of subpoint under current coordinate system1, P "2…..P″n.By P "1, P "2…..P″nThe region name that line is constituted
For polygon, the angle on the corresponding adjacent both sides of polygon Arbitrary Boundaries point is calculated.
(6.7.3) takes the boundary point P " of adjacent both sides angle value minimumk, obtain and boundary point P "kConnected other two
Boundary point is P "k-1And P "k+1, connect P "k-1With P "k+1
(6.7.4) judges junction curve P "k-1P″k+1Whether intersect with the side of polygon, wherein intersection point P "k-1With P "k+1It removes
Outside, if intersection, abandons P "k, select the boundary point of next angle minimum.If non-intersecting, enter step
(7.7.5)；
(6.7.5) removes the P in Polygonal Boundary point set "kPoint and surface boundary P "kP″k-1With P "kP″k+1, to complete
With P " in pairs of polygonk+1, P "k-1With P "k+1For the filling in the region of boundary point, the corresponding side of next minimum angle is found
Boundary's point, enters step (7.7.3).
The angle for calculating the corresponding adjacent both sides of polygon Arbitrary Boundaries point includes following sub-step：
A) boundary point for obtaining polygon is defined as P "1, P "2..., P "n；
B) compare P "1, P "2... P "nIn the directions x component, find out the point with maximum x-component, be denoted asWherein, the component in the directions x refers to three-dimensional coordinate P "1, P "2... P "nIn three-dimensional cartesian coordinate
Along the coordinate components of x-axis under system.
C) and then again compareIn y-component, find out a point with maximum y-component
P″k, previous vertex is P "k-1, next vertex is P "k+1, vector Its
In, the component in the directions y refers to three-dimensional coordinate P "1, P "2... P "nAlong the coordinate components of y-axis under three Cartesian coordinates.
D) it is P " to calculate vertexiAngle, θi, wherein θiRefer on polygon with P "iTwo connected boundary point P "i-1
With P "i+1Respectively with P "iThe angle on the boundary of composition, if Wherein,
If (Va×Vb)×Vtemp>=0, then
Conversely, then
Referring to Fig. 8, in present embodiment, the boundary point of polygon is P respectively1、2、P3…..11.Firstly the need of finding side
There is the point of maximum x-component, i.e. P in boundary's point3、P4、P5, from P3、P4、P5Find out the point P with maximum y-component3, P3Previous top
Point is P2, the latter vertex is P4, therefore vectorBoundary point is traversed, boundary is calculated
The angle on corresponding two boundaries of point.First against the P in Fig. 61Point,It can using formula
To obtain P1The angle of corresponding adjacent boundary.In this way, it is possible to calculate the angle of the corresponding adjacent edge of each boundary point.
The present invention provides a kind of biasing means of composite surface model, this method effective solution is in commercial Application
The efficiency of mould processing, improves product quality, has popularity.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, all within the spirits and principles of the present invention made by all any modification, equivalent and improvement etc., should all include
Within protection scope of the present invention.
Claims (9)
1. a kind of biasing means of composite surface, which is characterized in that it includes the following steps：
(1) by the discrete original triangle grid model of generation of the original surface model of composite surface, and original triangle gridding mould is built
The normal vector information of type；
(2) judge that the original mesh point in original triangle grid model is in continuum or discrete regions, to discontinuous
Each original mesh point in region is biased calculating, and identifies whether the original mesh point after biasing calculating will produce notch or place
In self intersection region；
(3) it is directed to the original mesh point that notch is generated in step (2), carrying out grid in original triangle grid model fills up；
(4) whole self intersection is carried out to original mesh point and original triangle grid model to detect；
(5) on original triangle grid model, the self intersection region in removal step (2) and step (4)；
(6) to including that the original triangle grid model of normal vector information is biased in step (1), biasing triangle gridding is obtained
Model；
(7) cavity generated on biasing triangle grid model is filled up.
2. a kind of biasing means of composite surface as described in claim 1, it is characterised in that：
It is that the mesh point and Grid Edge on original triangle grid model establish normal vector information in step (1).
3. a kind of biasing means of composite surface as claimed in claim 1, it is characterised in that：Step (2) includes following son
Step：
(2.1) all mesh points on triangle grid model are found out；
(2.2) all Grid Edges where arbitrary mess point are obtained；
(2.3) for the Grid Edge E where the mesh pointiWith Grid Edge E adjacent theretoi+1, obtain EiAnd Ei+1Where respectively
Triangular plate SiAnd Si+1, also obtain EiThe mesh point p at both ends1And p2；
According to the normal vector information of establishment, p is obtained1Respectively in SiAnd Si+1On normal vector information and obtain p2Respectively in Si
And Si+1On normal vector, calculate p1In SiAnd Si+1On normal vector angle angle1And p2In SiAnd Si+1On normal direction
Vector angle angle2；
(2.4) if angle1Or angle2More than assigned error at, then to EiAnd Ei+1The triangular plate S at placeiAnd Si+1Grid
Point is biased, and judges the triangular plate S that the mesh point after biasing is constitutedi' and Si+1' whether intersect；If triangular plate Si' and three
Cornual plate Si+1' intersection and angle1 be more than assigned error at, judge p1It is located at self intersection region after biasing, if Si' and Si+1' phase
It hands over and angle2 is more than assigned error at, then judge p2It is located at self intersection region after biasing；If Si' and Si+1' it is non-intersecting and
Angle1 is more than assigned error at, then judge p1Notch is will produce after biasing, if angle2 is more than assigned error at, then judge
p2It will produce notch after biasing；Here, the mesh point that will produce notch after biasing is named as gap regions point.
4. a kind of biasing means of composite surface as claimed in claim 3, it is characterised in that：Step (3) includes following son
Step：
(3.1) virtual boundary set VE is created, wherein virtual boundary is the boundary inside mesh point, length 0；
(3.2) it is directed to determining gap regions point, virtual boundary is added inside such mesh point, and method is built for virtual boundary
To vector information, newly added virtual boundary is added in set VE；Virtual boundary will be for the gap regions after biasing
Create patch grids；
(3.3) return to step (3.2), to complete to add virtual boundary inside all gap regions points；
(3.4) the arbitrary virtual boundary e being directed in virtual boundary set VE1, obtain e1Two endpoint p1And p2And p1And p2
Corresponding normal vector f1And f2, wherein p1, p2Coordinate it is equal；
(3.5) normal direction vector f is calculated1And f2Between angle theta, action chordHeight is calculated according to θ and offset or dish r：
It is less than or equal to given action error c in chordHeighttUnder conditions of, the corresponding maximum center of circle between consecutive points on circular arc
Angle θmaxIt indicates as follows：
For the maximum angle θ for meeting under conditions of being less than action errormax, according to normal vector f1And f2Between angle theta calculate
e1It inside needs to be inserted into N number of mesh point：
N=θ/θmax-1
(3.6) in e1It is interior, from p1To p2It is inserted into N number of mesh point：It is inserted into j-th of mesh point pjIt needs to calculate and biases mesh point pj's
Normal vector fj：
By e1Disconnect interpenetration network point pj, wherein the mesh point p of insertionjCoordinate and p1It is equal, setting mesh point pjNormal direction to
Amount is fj, j=0,1,2 ... N；
(3.7) to e1It is interior that the N number of mesh point being inserted into is needed to repeat step (3.6), to complete for virtual boundary e1Slotting point behaviour
Make；
(3.8) step (3.6)~step (3.7) is repeated to all fictitious lines in set VE, to complete to all fictitious lines
Insert point operation；
(3.9) the corresponding virtual dough sheet progress grid of fictitious line after the slotting point of extraction is filled up, in the addition in virtual dough sheet region
New triangle gridding.
5. a kind of biasing means of composite surface as claimed in claim 4, it is characterised in that：Step (4) includes following son
Step：
(4.1) set selfPoints is created, for storing the point of intersection generated；
(4.2) all triangular plates in triangle grid model are saved as into kdTree structures；
(4.3) the arbitrary mess point point being directed on triangle grid model, if mesh point point is to be identified in step (2)
It is located at the point in self intersection region after biasing, then the point is added in set selfPoints, and update mesh point point, so
After enter step (4.3), conversely, then entering step (4.4)；
(4.4) mesh point point is biased according to the offset or dish of setting, the mesh point Opoint after being biased；With
Offset or dish is radius, and Opoint is that the centre of sphere makees a ball, is intersected with the kdTree for storing all triangular plates using ball, is sent out
It is born from the triangular plate of intersection；
(4.5) triangular plate being connected with mesh point point is searched in the triangular plate that self intersection occurs, and self intersection is occurring
Triangular plate in delete this kind of triangular plate, set then is added in the remaining corresponding mesh point of triangular plate that self intersection occurs
In selfPoints；
(4.6) step (4.3)~step (4.5) is repeated, to complete to being located at certainly after all biasings in original triangle grid model
The screening of the mesh point of intersecting area.
6. a kind of biasing means of composite surface as claimed in claim 1, it is characterised in that：
In step (6), for all mesh points on original triangle grid model, along the grid on original triangle grid model
Original triangle grid model is biased by the normal vector that point is established according to given offset or dish, obtains the biasing triangulation network
Lattice model.
7. a kind of biasing means of composite surface as claimed in claim 1, it is characterised in that：Step (7) includes following son
Step：
(7.1) it creates and waits for filling cavity set repairHoles；
(7.2) it for a cavity finalhole in the empty set finalHoles behind removal self intersection region, obtains
The corresponding net boundaries of finalhole, and sort；
(7.3) according to the normal vector information of the corresponding mesh points of finalhole and the mesh point, finalhole pairs is established
The projection plane answered projects to the corresponding mesh points of finalhole and Grid Edge on the projection plane；
(7.4) the point of intersection that the finalhole after projection is generated on a projection plane is found, according to the point of intersection position in institute
Ratio on side is projected back in on original cavity finalhole, obtains the point of intersection corresponding two in original cavity finalhole
It is a, Grid Edge is built between the two points, finalhole is split from the Grid Edge of composition, forms two cavities, it is right
The two new cavities formed carry out sequence again to boundary；
(7.5) step (7.2) to step (7.4) is repeated for two new cavities, until after any cavity projects to projection plane
There is no the point of intersection, then finalhole is added in set repairHoles, updates finalhole, return to step
(7.2), it to complete the division for all cavities in set finalHoles, avoids that topological structure occurs on a projection plane
Conflict；
(7.6) it for the newer set repairHoles during step (7.1) to step (7.5), obtains
Empty repairhole in repairHoles；
(7.7) hole region is filled up：For arbitrary cavity repairhole, to cavity repairhole by adding new three
The mode of cornual plate is filled up；After completion is filled up, repairhole is updated；
(7.8) step (7.6)~step (7.7) is repeated, cavity all in repairHoles is filled up in completion.
8. a kind of biasing means of composite surface as claimed in claim 7, it is characterised in that：Step (7.7) includes following
Sub-step：
(7.7.1) obtains the corresponding mesh point of each Grid Edge in repairhole, and it is flat to calculate the corresponding projections of repairhole
Face projects to repairhole on projection plane, obtains the subpoint of mesh point on a projection plane；
Coordinate system is converted into the projection plane coordinates system using the center of projection plane as coordinate origin by (7.7.2), and calculating is being worked as
Subpoint P " under preceding coordinate system1, P "2.....P″n；By P "1, P "2.....P″nThe region that line is constituted is named as polygon, counts
The angle on the corresponding adjacent both sides of polygon Arbitrary Boundaries point is calculated, n is the quantity of subpoint；
(7.7.3) takes the boundary point P " of adjacent both sides angle value minimumk, obtain and boundary point P "kOther two connected boundary
Point is P "k-1And P "k+1, connect P "k-1With P "k+1, k=1,2 ... n；
(7.7.4) judges junction curve P "k-1P″k+1Whether intersect with the side of polygon, wherein intersection point P "k-1With P "k+1Except, such as
Fruit is intersected, then abandons P "k, the boundary point of next angle minimum is selected to be entered step (7.6.5) if non-intersecting；
(7.7.5) removes the P in Polygonal Boundary point set "kPoint and surface boundary P "kP″k-1With P "kP″k+1, to completion pair
With P " in polygonk+1, P "k-1With P "k+1For the filling in the region of boundary point, the corresponding boundary point of next minimum angle is found,
It enters step (7.6.3).
9. calculating the angle on the corresponding adjacent both sides of polygon Arbitrary Boundaries point as claimed in claim 8, it is characterised in that：
Step (7.7.2) includes following sub-step：
A) boundary point of polygon is obtained, these boundary points are P "1, P "2..., P "n；
B) compare P "1, P "2... P "nIn the directions x component, find out the point with maximum x-component, be denoted asWherein, the component in the directions x refers to boundary point P "1, P "2... P "nIn three Cartesian coordinates
Under along x-axis coordinate components；
C) and then again compareIn the directions y component, find out a point with maximum y-component
P″k, previous vertex is P "k-1, the latter vertex is P "k+1, vectorIts
In, the component in the directions y refers to coordinate P "1, P "2... P "nAlong the coordinate components of y-axis under three Cartesian coordinates；
D) it is P " to calculate vertexiAngle, θi, wherein θiRefer on polygon with P "iTwo connected boundary point P "i-1With
P″i+1Respectively with P "iThe angle on the boundary of composition enables Wherein, i=1,
2,…n；
If (Va×Vb)×Vtemp>=0, then
Conversely, then
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| CN112755523A (en) * | 2021-01-12 | 2021-05-07 | 网易（杭州）网络有限公司 | Target virtual model construction method and device, electronic equipment and storage medium |
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