CN101510316A - Deformation design method for product STL model - Google Patents

Abstract

The invention provides a deformation design method of a product STL model, which is characterized in that the approaching plane of an editing area of the product STL model is solved by adopting the least square method, the vertex of the product STL model is projected to the approaching plane to set up a local plane coordinate system of a projection point set and obtain an axial bounding rectangle with minimum area of the projection point set, the vertex of the product STL model is parameterized, the reference curved surface of the editing area is solved, the mapping relation between the vertex of the product STL model and the projection point on the reference curved surface is set up, the control vertex of the reference curved surface is adjusted, the displacement of the projection point is calculated, the vertex coordinate of the product STL model is adjusted according to the displacement of the projection point to finish the deformation of the editing area of the product STL model, a first-order geometric continuous triangular B * zier curved surface is constructed for the deformed model to realize smoothing treatment of the model, and a smoothed product STL model is obtained by dispersing the triangular B * zier curved surface to finish the deformation innovative design of the product STL model. The method can accurately control the model shape and effectively improve the smoothness and deformation design efficiency of the product STL model.

Description

The deformation design method of STL model of products

Technical field

The invention provides a kind of deformation design method of STL model of products, belong to product reverse Engineering Technology field.

Background technology

In the product reverse-engineering, equipment such as common employing laser scanner obtain the scattered point cloud data of product entity model surface, and these data are carried out triangulation generate the STL model, approach former solid model, but realize often need making amendment in the design innovative process based on STL model of products to reconstruction model follow-up.For this problem, mainly by reconstruction model being converted into the nurbs surface model, implementation model is revised in main flow CAD system (UGNX, CATIA, PRO/E etc.) at present.Owing in the surface model transfer process, need a large amount of man-machine interactively surface modeling operations and be prone to the model accuracy loss, in addition for the nurbs surface built-up pattern of complexity, in the main flow CAD system, also be difficult to make amendment, therefore study direct deformation design method based on STL model of products, the various negative effects of avoiding the surface model conversion to be caused, reverse innovative design efficient of product and quality are significant for improving.

The prior art literature search is found, mainly is at present to realize the STL model of products shape adjustments by the method that the controlling models of being set up is out of shape.Wang Jianzhe etc. are at academic journal " computer engineering and application " 2002,17 (3), in the scientific paper of delivering on the P95-97 " based on the 3 D human body Free Transform method of NURBS ", by constructing three enough big parameter N URBS free bodies, to treat that modified product STL model is embedded in the free body, adjust the free body control vertex and realize the STL model of products distortion, this method can realize the STL model of products bulk deformation, but is difficult to realize local deformation control.Section moral congruence is at academic journal " computer engineering and application " 2006,33 (3), in the scientific paper of delivering on the P88-90 " based on the 3D grid Local Edit of skeleton ", earlier determine editing area by the user, draw be out of shape after the corresponding editor's curve of skeleton, again according to the corresponding relation between STL model vertices and skeleton curve and the editor's curve, editing operations such as the translation of realization STL model node and rotation, this method is by the extraction model skeleton, but adjust skeleton end points implementation model local deformation, but can't implementation model surface details feature editor.Zhou Tingfang etc. are at academic journal " computer-aided design (CAD) and graphics journal " 2006,18 (3), in the scientific paper of delivering on the P443-450 " based on the grid model deformation technology of hierarchical B-splines ", by to the parametrization of editing area and uniform resampling and adopt hierarchical B-splines match sampled point to obtain the basic curved surface of STL model of products, by editing hierarchical B-splines base curved surface or directly editing STL model of products, but implementation model surface details feature editor, but owing to the STL model of products behind the editor is not optimized processing, the model fairness is relatively poor.Qin Xujia etc. are at academic journal " computer-aided design (CAD) and graphics journal " 2004,16 (4), in the scientific paper of delivering on the P444-448 " the Local Edit algorithm of grid model ", the employing mode of approaching is obtained the editing area control mesh, editing area after the segmentation is carried out deformation design, the local light that can realize STL model of products is along distortion, but deformation process needs repeated calculation segmentation grid vertex coordinate, and the distortion operand is big, efficient is low.

In sum, existing deformation design method at STL model of products exists and is difficult to problems such as implementation model local surfaces minutia editor, editor back model fairness is poor, distortion efficient is low.

Summary of the invention

The object of the present invention is to provide a kind of deformation design method of STL model of products, adjust and fairness, and improve STL model of products distortion efficient with effective control STL model of products local shape.Its technical scheme is:

A kind of deformation design method of STL model of products, it is characterized in that steps in sequence is: 1) adopt least square method to find the solution the plane of approaching of STL model of products editing area, method is specifically: choose the STL model of products editing area alternately by mouse, establishing institute favored area summit is p ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂) ..., p _k(x _k, y _k, z _k), institute asks and approaches plane equation is ax+by+cz+d=0, order

$A=\left[\begin{array}{cccc}{x}_1& y_1& z_1& 1\\ x_2& y_2& z_2& 1\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ x_k& y_k& z_k& 1\end{array}\right],$

Then the plane fitting equation is

$A\left[\begin{array}{c}a\\ b\\ c\\ d\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ \·\\ \·\\ \·\\ 0\end{array}\right],$

Adopt the proper vector estimation technique to find the solution this equation, to matrix A ^TA carries out svd and gets

$A^{T}A=U\left[\begin{array}{cccc}{\mathrm{\ω}}_1& 0& 0& 0\\ 0& {\mathrm{\ω}}_2& 0& 0\\ 0& 0& {\mathrm{\ω}}_3& 0\\ 0& 0& 0& {\mathrm{\ω}}_4\end{array}\right]V^T,$

Wherein U and V are orthogonal matrix, ω ₁, ω ₂, ω ₃, ω ₄Be A ^TThe eigenwert of A, wherein minimal eigenvalue characteristic of correspondence vector is the least square solution of plane fitting equation, and its substitution is approached plane equation, thereby obtains the plane of approaching of STL model of products editing area; 2) with the STL model of products summit to approaching plane projection, set up projection point set part plan coordinate system, and obtain the area minimum axial direction area-encasing rectangle of projection point set; 3) to the STL model of products vertex parameterization and find the solution the reference curved surface of editing area, set up the STL model of products summit and with reference to the mapping relations between subpoint on the curved surface, method is specifically: the parameter coordinate is limited to scope [0,1] standard parameterization that realization approaches plane inner projection point in, the subpoint that the parameter value on STL model of products summit is corresponding with it has identical parameter value, so can get the parameter value on STL model of products summit, the preset reference curved surface is the tensor product B é zier curved surface of n * m time, obtains with reference to curved surface control vertex P by uniform sampling in local coordinate system _0,0, P _0,1..., P _{0, n}, P _1,0..., P _{1, n}..., P _{M, 0}, P _{M, 1}..., P _{M, n}, based on the reference surface equation of Bernstein polynomial computation editing area; 4) adjust with reference to the curved surface control vertex and calculate the subpoint displacement, adjust the STL model of products apex coordinate, finish the distortion of STL model of products editing area according to the subpoint displacement; 5) distorted pattern is made up how much continuous triangle Bezier curved surfaces of single order, the implementation model fairing processing is obtained the STL model of products of fairing by discrete triangle Bezier curved surface, realizes the distortion innovative design of STL model of products.

For realizing goal of the invention, the deformation design method of described STL model of products, in step 2) in, calculate the projection point set area minimum axial direction area-encasing rectangle method specifically: is true origin with each summit of STL model of products at the center of gravity q that approaches projection point set on the plane, with center of gravity q at a distance of farthest subpoint q _jThe vector that constitutes with center of gravity q is the u axle, cross center of gravity q and set up local coordinate system perpendicular to u axle and the vector that approaches the planar process vector n for the v axle, finds the solution the coordinate (u of subpoint under local coordinate system _i, v _i), and the axial area-encasing rectangle area of calculating subpoint, find the solution the axial area-encasing rectangle area of subpoint under new coordinate system by rotating coordinate system, allow local coordinate system rotate a circle by specified angle around its true origin, with axial area-encasing rectangle area a hour corresponding local coordinate be the parameter coordinate system of subpoint, because coordinate system rotation angle θ and anglec of rotation θ+pi/2, axial area-encasing rectangle area when θ+π or θ+3 pi/2s equates, so only (0, pi/2) rotation local coordinate system in the scope, the axial area-encasing rectangle that the rotation back is obtained is the approximate minimum area-encasing rectangle of projection point set, set a trap portion's coordinate system in approaching the plane when its true origin anglec of rotation ρ axial area-encasing rectangle area minimum, adopt formula:

$\left[\begin{array}{c}{u}_i^{\′}\\ v_i^{\′}\\ r\end{array}\right]=\left[\begin{array}{ccc}\cos \mathrm{\ρ}& \sin \mathrm{\ρ}& 0\\ -\sin \mathrm{\ρ}& \cos \mathrm{\ρ}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]$

Find the solution the coordinate of subpoint under new coordinate system

For realizing goal of the invention, the deformation design method of described STL model of products, in step 4), adjustment is with reference to the curved surface control vertex and calculate the subpoint displacement, the method of adjusting the STL model of products apex coordinate according to the subpoint displacement is specifically: in can the accurate recording adjustment process with reference to the subpoint displacement on STL model of products summit on the curved surface, and set up STL model of products summit and subpoint mapping relations, introduce the identification information of a structure record product STL model vertices, the subpoint coordinate on the parameter value on STL model of products summit and STL model of products summit, in adjusting with reference to curved surface control vertex deformation process, subpoint coordinate in this structure upgrades in time, and calculate its displacement, identification information according to this structure projection summit is revised the grid vertex coordinate by same displacement, by adjusting the adjustment that realizes STL model of products with reference to the control vertex of curved surface, upgrade control vertex, with reference to the new coordinate employing formula on projection summit on the curved surface $S(u,v)=\underset{r=0}{\overset{n}{\mathrm{\Σ}}}\underset{s=0}{\overset{m}{\mathrm{\Σ}}}{B}_{r,n}\left(u\right)B_{s,m}\left(v\right)P_{r,s}$ Find the solution, travel through all projection summits and adjust corresponding STL model vertices coordinate and realize that STL model of products dynamically adjusts.

The present invention compared with prior art has the following advantages:

1) STL model of products is carried out the local deformation design, on the basis of the original feature of reserving model, realized the model detail characteristic design;

2) with the deformation design region limits in more among a small circle, effectively reduce the calculated amount of deformation design, improved distortion efficient;

3) realize the optimization process of STL model of products based on the triangle Bezier curved surface theory, effectively improved the fairness of STL model of products.

Description of drawings

Fig. 1 is program realization flow figure of the present invention;

Fig. 2 is the embodiment of the invention one an apple products STL illustraton of model;

Fig. 3 is the floor map of approaching of the embodiment of the invention one apple editing area;

Fig. 4 is that the minimum area-encasing rectangle of the embodiment of the invention one projection point set area is found the solution synoptic diagram;

Fig. 5 is the deformation effect figure of embodiment one;

Fig. 6 is the embodiment of the invention two planar products STL illustratons of model;

Fig. 7 is the deformation effect figure of embodiment two;

Fig. 8 is the embodiment of the invention three dairy products STL illustratons of model;

Fig. 9 is the deformation effect figure of embodiment three.

Embodiment

The invention will be further described below in conjunction with drawings and Examples:

Fig. 1 is the deformation design method program realization flow figure of STL model of products of the present invention.At first select the STL model of products editing area alternately by mouse, calculate the plane of approaching of editing area based on the local triangle dough sheet The data least square method of obtaining, plane projection is approached to it in each tri patch summit of editing area, set up local coordinate system based on the projection vertex set, calculate the area minimum axial direction area-encasing rectangle of projection point set by the rotation local coordinate system, by the STL model of products vertex parameterization of editing area being set up the reference curved surface of editing area, set up the STL model of products summit and with reference to the mapping relations between subpoint on the curved surface, adjustment is with reference to the curved surface control vertex and calculate the subpoint displacement, adjust the STL model of products apex coordinate according to the subpoint displacement, finish the distortion of STL model of products editing area, at last distorted pattern is made up how much continuous triangle Bezier curved surfaces of single order, the implementation model fairing processing, and obtain the STL model of products of fairing by discrete triangle Bezier curved surface, realize the distortion innovative design of STL model of products.

Embodiment one: edit apple products STL model bottom section shown in Figure 2, with its stretched chassis.

As shown in Figure 3, select apple bottom section tri patch alternately, each tri patch summit p in the storage institute favored area by mouse ₁(30.0787,159.2667,16.0342), p ₂(29.32109,159.2667,16.0475) ..., p _k(35.6642,87.9783,18.6326) are in each point coordinate substitution matrix A, wherein

$A=\left[\begin{array}{cccc}{x}_1& y_1& z_1& 1\\ x_2& y_2& z_2& 1\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ x_k& y_k& z_k& 1\end{array}\right]$

To matrix A ^TA carries out svd and gets

$A^{T}A=U\left[\begin{array}{cccc}{\mathrm{\ω}}_1& 0& 0& 0\\ 0& {\mathrm{\ω}}_2& 0& 0\\ 0& 0& {\mathrm{\ω}}_3& 0\\ 0& 0& 0& {\mathrm{\ω}}_4\end{array}\right]V^T$

Wherein U and V are orthogonal matrix, ω ₁, ω ₂, ω ₃, ω ₄Be A ^TThe eigenwert of A, wherein minimal eigenvalue characteristic of correspondence vector is the plane fitting equation

$A\left[\begin{array}{c}a\\ b\\ c\\ d\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ \·\\ \·\\ \·\\ 0\end{array}\right]$

Least square solution, its substitution is approached plane equation ax+by+cz+d=0, thereby obtains the plane of approaching of STL model of products editing area, plane, control mesh place is the plane of approaching of editing area as shown in Figure 3.

As shown in Figure 4, plane projection being approached to it in each summit of apple editing area tri patch, obtain the homolographic projection point, calculate the coordinate of projection point set center of gravity q, is true origin with q, with q at a distance of farthest subpoint q _jThe vector that constitutes with q is the u axle, crosses q and set up local coordinate system perpendicular to the vector of u axle and n for the v axle, finds the solution the coordinate (u of subpoint under local coordinate system _i, v _i), and the axial area-encasing rectangle area of calculating subpoint.Find the solution the axial area-encasing rectangle area of subpoint under new coordinate system by rotating coordinate system.Specified coordinate is that each anglec of rotation is π/36, and local coordinate ties up to and approaches in the plane axial area-encasing rectangle area minimum when its true origin anglec of rotation is 23.6135 ° in the example, adopts formula:

$\left[\begin{array}{c}{u}_i^{\′}\\ v_i^{\′}\\ r\end{array}\right]=\left[\begin{array}{ccc}\cos \mathrm{\ρ}& \sin \mathrm{\ρ}& 0\\ -\sin \mathrm{\ρ}& \cos \mathrm{\ρ}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}u\\ v\\ 1\end{array}\right],$

Find the solution the coordinate of subpoint under new coordinate system

The parameter coordinate is limited to scope [0,1] standard parameterization that realization approaches plane inner projection point in, the subpoint that the parameter value on STL model of products summit is corresponding with it has identical parameter value, so can get the parameter value on STL model of products summit, the preset reference curved surface is 4 * 4 times a tensor product B é zier curved surface, obtains with reference to curved surface control vertex P by uniform sampling in local coordinate system _0,0, P _0,1..., P _{0, n}, P _1,0..., P _{1, n}..., P _{M, 0}, P _{M, 1}..., P _{M, n}, then be with reference to surface equation $S(u,v)=\underset{r=0}{\overset{n}{\mathrm{\Σ}}}\underset{s=0}{\overset{m}{\mathrm{\Σ}}}{B}_{r,n}\left(u\right)B_{s,m}\left(v\right)P_{r,s}$ 0≤u≤1,0≤v≤1 wherein, basis function B _{R, n}(u) and B _{S, m}(u) be the Bernstein polynomial expression.

Set up the STL model of products summit and with reference to the mapping relations between subpoint on the curved surface, adjustment is with reference to the curved surface control vertex and calculate the subpoint displacement, for can accurate recording in the adjustment process with reference to the subpoint displacement on STL model of products summit on the curved surface, and set up STL model of products summit and subpoint mapping relations, introduce data structure AdjustPt, it is defined as follows:

typedef?struct?ADJUST_PT{

Int id; The sign id information of // corresponding product STL model vertices

Double u, v; The parameter value on // STL model of products summit

Double x, y, z; The subpoint coordinate on // STL model of products summit

}AdjustPt；

In the distortion of the mesh process, AdjustPt object coordinate upgrades in time, and the displacement of calculating the AdjustPt object, revise the grid vertex coordinate according to AdjustPt object id information by same displacement, by adjusting the distortion that realizes triangle grid model with reference to the control vertex of curved surface, upgrade control vertex, travel through all AdjustPt objects, the employing formula $S(u,v)=\underset{r=0}{\overset{n}{\mathrm{\Σ}}}\underset{s=0}{\overset{m}{\mathrm{\Σ}}}{B}_{r,n}\left(u\right)B_{s,m}\left(v\right)P_{r,s}$ Find the solution new coordinate, adjust corresponding grid apex coordinate, finish the distortion of STL model of products editing area according to the displacement of AdjustPt object with reference to AdjustPt object corresponding point on the curved surface.

Distorted pattern is made up how much continuous triangle Bezier curved surfaces of single order, and the implementation model fairing processing is obtained the STL model of products of fairing by discrete triangle Bezier curved surface, finishes the distortion innovative design of STL model of products, and effect as shown in Figure 5.

Embodiment two: setting local deformation is 4 * 4 times tensor product B é zier curved surface with reference to curved surface, and planar S TL model Local Edit shown in Figure 6 is formed the convex domain of " TEST " printed words, and method is the same, and effect as shown in Figure 7.

Embodiment three: setting local deformation is 4 * 4 times tensor product B é zier curved surface with reference to curved surface, and the STL model of ox shown in Figure 8 is edited, and edits out two peaks at ox STL model back, and method is the same, and effect as shown in Figure 9.

Claims (3)

1, a kind of deformation design method of STL model of products, it is characterized in that steps in sequence is: 1) adopt least square method to find the solution the plane of approaching of STL model of products editing area, method is specifically: choose the STL model of products editing area alternately by mouse, establishing institute favored area summit is p ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂) ..., p _k(x _k, y _k, z _k), institute asks and approaches plane equation is ax+by+cz+d=0, order

$A=\left[\begin{array}{cccc}{x}_1& y_1& z_1& 1\\ x_2& y_2& z_2& 1\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ x_k& y_k& z_k& 1\end{array}\right],$

Then the plane fitting equation is

$A\left[\begin{array}{c}a\\ b\\ c\\ d\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ \·\\ \·\\ \·\\ 0\end{array}\right],$

Adopt the proper vector estimation technique to find the solution this equation, to matrix A ^TA carries out svd and gets

$A^{T}A=U\left[\begin{array}{cccc}{\mathrm{\ω}}_1& 0& 0& 0\\ 0& {\mathrm{\ω}}_2& 0& 0\\ 0& 0& {\mathrm{\ω}}_3& 0\\ 0& 0& 0& {\mathrm{\ω}}_4\end{array}\right]V^T,$

Wherein U and V are orthogonal matrix, ω ₁, ω ₂, ω ₃, ω ₄Be A ^TThe eigenwert of A, wherein minimal eigenvalue characteristic of correspondence vector is the least square solution of plane fitting equation, and its substitution is approached plane equation, thereby obtains the plane of approaching of STL model of products editing area; 2) with the STL model of products summit to approaching plane projection, set up projection point set part plan coordinate system, and obtain the area minimum axial direction area-encasing rectangle of projection point set; 3) to the STL model of products vertex parameterization and find the solution the reference curved surface of editing area, set up the STL model of products summit and with reference to the mapping relations between subpoint on the curved surface, method is specifically: the parameter coordinate is limited to scope [0,1] standard parameterization that realization approaches plane inner projection point in, the subpoint that the parameter value on STL model of products summit is corresponding with it has identical parameter value, so can get the parameter value on STL model of products summit, the preset reference curved surface is the tensor product B é zier curved surface of n * m time, obtains with reference to curved surface control vertex P by uniform sampling in local coordinate system _0,0, P _0,1..., P _{0, n}, P _1,0..., P _{1, n}..., P _{M, 0}, P _{M, 1}..., P _{M, n}, based on the reference surface equation of Bernstein polynomial computation editing area; 4) adjust with reference to the curved surface control vertex and calculate the subpoint displacement, adjust the STL model of products apex coordinate, finish the distortion of STL model of products editing area according to the subpoint displacement; 5) distorted pattern is made up how much continuous triangle Bezier curved surfaces of single order, the implementation model fairing processing is obtained the STL model of products of fairing by discrete triangle Bezier curved surface, realizes the distortion innovative design of STL model of products.

2, the deformation design method of STL model of products as claimed in claim 1, it is characterized in that: in step 2) in, the method of calculating projection point set area minimum axial direction area-encasing rectangle is specifically: is true origin with the STL model of products summit at the center of gravity q that approaches projection point set on the plane, with q at a distance of farthest subpoint q _jThe vector that constitutes with q is the u axle, crosses q and set up local coordinate system perpendicular to the vector of u axle and n for the v axle, finds the solution the coordinate (u of subpoint under local coordinate system _i, v _i), and the axial area-encasing rectangle area of calculating subpoint, find the solution the axial area-encasing rectangle area of subpoint under new coordinate system by rotating coordinate system, allow local coordinate system rotate a circle by specified angle around its true origin, with axial area-encasing rectangle area a hour corresponding local coordinate be the parameter coordinate system of subpoint, because coordinate system rotation angle θ and anglec of rotation θ+pi/2, axial area-encasing rectangle area when θ+π or θ+3 pi/2s equates, so only (0, pi/2) rotation local coordinate system in the scope, the axial area-encasing rectangle that the rotation back is obtained is the approximate minimum area-encasing rectangle of projection point set, set a trap portion's coordinate system in approaching the plane when its true origin anglec of rotation ρ axial area-encasing rectangle area minimum, adopt formula:

$\left[\begin{array}{c}{u}_i^{\′}\\ v_i^{\′}\\ r\end{array}\right]=\left[\begin{array}{ccc}\cos \mathrm{\ρ}& \sin \mathrm{\ρ}& 0\\ -\sin \mathrm{\ρ}& \cos \mathrm{\ρ}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}u\\ v\\ 1\end{array}\right],$

Find the solution the coordinate of subpoint under new coordinate system

3, the deformation design method of STL model of products as claimed in claim 1, it is characterized in that: in step 4), introduce the identification information of a structure record product STL model vertices, the subpoint coordinate on the parameter value on STL model of products summit and STL model of products summit, in adjusting with reference to curved surface control vertex deformation process, subpoint coordinate in this structure upgrades in time, and calculate its displacement, identification information according to this structure projection summit is revised the grid vertex coordinate by same displacement, by adjusting the adjustment that realizes STL model of products with reference to the control vertex of curved surface, upgrade control vertex, with reference to the new coordinate employing formula on projection summit on the curved surface $S(u,v)=\underset{r=0}{\overset{n}{\mathrm{\Σ}}}\underset{s=0}{\overset{m}{\mathrm{\Σ}}}{B}_{r,n}\left(u\right)B_{s,m}\left(v\right)P_{r,s}$ Find the solution, travel through all projection summits and adjust corresponding STL model vertices coordinate and realize that STL model of products dynamically adjusts.

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