CN101799936A - Feature-sensitive curve reestablishing method based on subdivisions - Google Patents
Feature-sensitive curve reestablishing method based on subdivisions Download PDFInfo
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Abstract
The invention relates to a feature-sensitive curve reestablishing method based on subdivisions, comprising the following steps of: firstly, rapidly reestablishing a smooth zone under the control of a smooth threshold value to form a plurality of smooth subdivisions, carrying out smooth processing, feature detection and feature expansion on boundaries by a topology element classification technology, and then sewing the smooth subdivisions or gaps on the subdivisions in sharp feature positions through a subdivision sewing process. The invention not only avoids difficulties in a reestablishing algorithm, which are caused by undersampling and sharp features, but also effectively avoids a complex mathematics test for ensuring topology integrity in a boundary advancing algorithm, such as triangular intersecting detection, and simultaneously effectively detects and restores the sharp features lost in sampling.
Description
Technical field
The present invention relates to field of Computer Graphics, be specifically related to curve reestablishing method based on undirected scattered data being point set.
Background technology
Rebuilding curved surface from scattered data points all has a wide range of applications in various fields such as reverse-engineering, computer graphics, computer visions.Although the GRIDDING WITH WEIGHTED AVERAGE of a few features sensitivity that exists can be recovered the feature on the curved surface preferably, it is oriented that these algorithms all require data point set, and promptly each data point comprises method Vector Message accurately.Other algorithm supposes that all potential curved surface is smooth everywhere, causes as a result grid surface to lose useful sharp features, even can not generate correct stream shape surface mesh.Thereby some pre-service or post-processing technology are used to recover sharp features, make to develop fast and accurately at polygon model or point cloud model that feature detection techniques becomes one of current research focus.But for polygon model and point cloud model, the detection of sharp features is still a difficult problem.
In the curve reestablishing algorithm, have simply by constantly generating the new leg-of-mutton reconstruction technique that advances based on the border on the border of grid, efficiently, be easy to handle the advantage of boundary surface.Yet, be difficult to handle and have the data point set of owing to sample or containing sharp features also as most of algorithms.Application number is that 200710041295.7 patent " unordered some cloud being converted to the system and method for triangle gridding based on adaptive flatness " is although disclosed algorithm can improve the reconstructed mesh quality that comprises sharp features to a certain extent, but can not produce the grid and the data point set of better quality to containing sharp features or owing to sample, stream shape surface mesh causes bad surface mesh thereby be difficult to produce effectively, so algorithm is healthy and strong inadequately.People such as JENKE [JENKE P., WAND M., STRASSER W.:Patch-graph reconstruction for piecewisesmooth surfaces [C] .In Proc.Vision, Modeling and Visualization, 2008:3-12.] adopt the border based on sheet figure to advance algorithm can generate high-quality surface mesh effectively, this algorithm is based on MLS (Moving least surface, mobile least square) projection operation, on the border with owe sampling place and can not produce correct projection, therefore also healthy and strong inadequately.Simultaneously belong to curved surface and approach,, more can produce high-quality curved surface based on the curve reestablishing of interpolation for high-precision applications occasions such as CAD based on the reconstruction of MLS.
The content of invention
Above-mentioned shortcoming at existing curve reestablishing algorithm, the applicant improves through research, provide another kind can overcome above-mentioned shortcoming effectively based on the curve reestablishing algorithm of the feature-sensitive of burst, not only avoided owing to sample and the difficulty brought to reconstruction algorithm of sharp features, also avoided the border to advance in the algorithm effectively in order to guarantee that the complete complex mathematical test of topology detects as triangle intersect, detects and recover simultaneously the sharp features of losing in the sampling effectively.
Technical scheme of the present invention is as follows:
A kind of curve reestablishing method of the feature-sensitive based on burst may further comprise the steps:
1) burst is rebuild: by a plurality of burst process of reconstruction the smooth domain of potential curved surface is carried out gridding, each burst process of reconstruction is divided into following three steps:
A. the smooth expansion of burst: determine the seed trigonometric ratio zone of each burst,, according to the preferential order of subtended angle boundary edge is carried out the triangle expansion and surpass smooth threshold values up to the smooth value of all boundary edge from the boundary edge in seed trigonometric ratio zone;
B. burst element classification and feature detection: the topological element of the burst that smooth expansion obtains to burst carries out the classification of smooth element and non-smooth element, delete non-smooth boundary element, follow the tracks of detected characteristics and accurate location feature point position or insert the new feature point by sharp features;
C. tile features expansion:, under the prerequisite of smooth threshold values control and the local slickness maintenance of curved surface, smooth expansion is further carried out on the burst border by the new feature point of unique point of reorientating or insertion;
2) sew up reconstruction: in the border of all bursts, select suitable boundary edge based on priority rule, carry out border extension and find more unique point, finally sew up different bursts or the slit in the burst at the sharp features place based on local surface intersection.
Smooth threshold values scope described in the steps A is 0.08～0.2.
Seed trigonometric ratio zone described in the steps A is meant the zone that all triangles constituted around a point.
Topological element described in the step B comprises summit, triangle and limit.
Smooth expansion described in the step C is divided into simple extension and feature expansion; Simple extension is extended triangular shape and be labeled as smooth triangle only; Feature expansion is also carried out feature and is asked exact position or the insertion new feature point of friendship to determine unique point except that extended triangular shape, and writes down the candidate information of the active edges around this unique point and the renewal.
The concrete steps that described stitching is rebuild are: the boundary edge of all bursts is assigned in first formation and second formation according to the subtended angle prioritizing, in first formation boundary edge of smoothness less than smooth threshold values, and end points or optimum are the boundary edge of unique point, it in second formation remaining boundary edge, according to the boundary edge in first formation earlier, the order of the boundary edge in second formation of back carries out the iteration expansion.
Useful technique effect of the present invention is:
Algorithm of the present invention is controlled based on smooth threshold values, advances the curve reestablishing process to be decomposed into that burst is rebuild on the border and sews up and rebuild two processes, can handle the data point set of owing to sample or containing sharp features effectively, produces the surface mesh of high-quality characteristic sensitivity.Not only avoided owing to sample and the difficulty brought to reconstruction algorithm of sharp features, also avoided the border to advance in the algorithm effectively in order to guarantee that the complete complex mathematical test of topology detects as triangle intersect, detects and recover simultaneously the sharp features of losing in the sampling effectively.
Description of drawings
Fig. 1 is the half of data structure synoptic diagram of revising.
Fig. 2 is the synoptic diagram in seed trigonometric ratio zone.
Fig. 3 is the synoptic diagram that candidate region and optimum are selected.
Fig. 4 is the inventive method is carried out curve reestablishing to the Mechpart model a procedure chart.
To be the inventive method carry out the comparison diagram of the result of curve reestablishing and Hoppe, Cocone, IPD arithmetic result to the Mechpart model to Fig. 5.
Fig. 6 is the inventive method is carried out curve reestablishing to the Bunny model a procedure chart.
To be the inventive method carry out the comparison diagram of the result of curve reestablishing and Hoppe, Cocone, IPD arithmetic result to the Bunny model to Fig. 7.
Fig. 8 is the inventive method is carried out curve reestablishing to the Fandisk model a procedure chart.
To be the inventive method carry out the comparison diagram of the result of curve reestablishing and Hoppe, Cocone, IPD arithmetic result to the Fandisk model to Fig. 9.
Figure 10 is the reconstructed results figure of the inventive method to the smooth-feature model.
Figure 11 is the reconstructed results figure of the inventive method to the mannequin model.
Figure 12 is the reconstructed results figure of the inventive method to the dino model.
Embodiment
Below in conjunction with accompanying drawing, the present invention is specifically described by embodiment.
For ease of understanding, at first data structure related among the present invention and term are described:
Data structure: search for making things convenient for the k neighborhood, with kd-tree (kd_tree) the storage input point set P of static state, with the point of coordinate modification in the Hash table storage algorithm and the new feature point of insertion.Half of data structure is one of key data structure of expression stream shape surface mesh, because the grid of the present invention in rebuilding is not stream shape grid usually, represents the grid rebuild with the half of data structure of modification for this reason.The principal feature of the half of data structure of described modification is, each summit at the most may be related two sector regions independently, as shown in Figure 1, summit V association wherein two independently fan-shaped trigonometric ratio zones.
For the grid in making up, each does not have corresponding oppositely half of one side of something to be called boundary edge or active edges, otherwise is called inner edge.Related one side of something all is that the summit of inner edge is called interior point, and related one side of something is that the summit of boundary edge is called frontier point, and the point that can not be considered grid vertex is called point of rejection, be not point of rejection and do not have in abutting connection with half of point and be called isolated point.
The smooth value of inner edge: establish N
1, N
2Be respectively two associated leg-of-mutton per unit system vectors of inner edge AB, the smooth value defined of this inner edge AB is: θ
AB=1-(N
1* N
2)
2
For an active edges, the border advances algorithm to select an optimum to constitute a new triangle in a plurality of possible candidate points, thereby the border is expanded.Therefore, for active edges, adopt the result of calculation of following formula to define the smooth value of this active edges with related leg-of-mutton per unit system vector with potential new triangle.
The positive back side: establishing from the related leg-of-mutton per unit system vector of active edges of A sensing B is N
ABC, AB is the per unit system vector that A points to B, establishes AB and N
ABCCross product AB * N
ABCThe per unit system vector be No, then (A No) has defined an oriented plane, and the space is divided into two, and claims that a side of No indication is the front of active edges AB, and opposite side is the back side.
Maximum angular criterion and preferred value: the present invention is that active edges selects the optimal candidate point to carry out the triangle expansion with the maximum angular criterion, i.e. the maximum of the subtended angle ∠ ACB of active edges AB and its candidate point C formation is generally optimum.This subtended angle also is used to comform and selects the preferred value of best active edges in the multi-activity limit, and the active edges preferred value of no optimum is minimum, and active edges is stored in the active edges Priority Queues according to this preferred value.
Below each step of the present invention is elaborated:
Burst is rebuild
Each burst carries out gridding since a seed delta-shaped region through smooth expansion, element classification and feature detection, three steps of feature expansion smooth domain to potential curved surface under smooth threshold values control, and promptly trigonometric ratio is rebuild.
The smooth expansion of burst
The overall process of the smooth expansion of burst is: the seed trigonometric ratio zone of determining each burst, from the boundary edge in seed trigonometric ratio zone, according to the preferential order of subtended angle boundary edge is carried out the triangle expansion and surpass smooth threshold values up to the smooth value of all boundary edge.
At first determine the seed delta-shaped region of each burst, each active edges of seed delta-shaped region is determined selection information such as its candidate point, optimum, smooth value and preferred value, and smooth value is added the active edges Priority Queues less than all active edges of smooth threshold values according to the preferred value with the portrayal of active edges subtended angle.Each active edges of not expanding in the active edges Priority Queues is carried out the triangle expansion, newly-generated active edges is determined selection information and smooth value is inserted Priority Queues less than the active edges of smooth threshold values, continue this process up to the smooth value of all active edges greater than smooth threshold values position.This process comprises that mainly the best extension point of seed trigonometric ratio, active edges is selected, three basic operations of triangle expansion of active edges.
The seed trigonometric ratio:
As shown in Figure 2, if isolated point is O, the average sample length of point set is L, at first looks for an abutment points A in length is not less than the abutment points of certain distance (as L/3), look for the abutment points B of a subtended angle ∠ OBA maximum again in remaining point, △ OAB constitutes an initial seed triangle.Adopt similar process to the half of OB of activity, seek an abutment points C, constitute triangle △ OBC, continue such process up to forming a circular trigonometric ratio zone around the O sealing.In this seed delta-shaped region formation process,, then think to form seed trigonometric ratio zone around this point if certain inner edge does not satisfy smooth value condition.
When burst was rebuild beginning, whether algorithm is always paid the utmost attention to those points with maximum x coordinate, y coordinate or z coordinate can constitute seed trigonometric ratio zone.Like this, can guarantee to have definite direction outwardly from the burst in these seed trigonometric ratio zones.
The best extension point of active edges is selected:
Be that an active edges selects an optimum to carry out the key issue that the triangle expansion is a border propelling algorithm.The present invention controls the expansion of active edges with light guiding valve value, adopt accurate survey of range of influence and maximum subtended angle to carry out the quick expansion of smooth domain effectively, needn't carry out complicated triangle intersect test to guarantee topological integrality, and the expansion of characteristic area can obtain the grid of feature-sensitive by newly-generated unique point and in conjunction with different priority rules and local surface intersection.
As shown in Figure 3, to active edges AB, its another summit of related triangle is C, and the active edges of establishing its adjacency is DA and BE, if D is positioned at the back side of AB or angle ∠ BAD greater than 135 °, structure and AB angle are 135 ° of vector of unit length V in the ABC plane
1Point to A, and be positioned at the positive side of AB, otherwise V
1Just get the vector of unit length of DA direction.In like manner, vector of unit length V of structure from the B point
2If the method vector of triangle ABC is N
ABC, definable vector of unit length N=AB * N
ABC, N
1=V
1* N
ABC, N
2=V
2* N
ABC
Three planes (N, A), (N
1, A), (N
2, positive top-cross collection B) constitutes the candidate region that the optimum of selecting AB is carried out the triangle expansion, and algorithm is at first sought candidate point in the common factor of the k of A, B neighboring region, as does not find also to concentrate at it again and look for candidate point.Each candidate point S should satisfy following condition: be not point of rejection or interior point, do not have half of AS or SB, be positioned at the candidate region, subtended angle ∠ ASB not too small (as less than 18 degree).
After the optimum S of an active edges AB determines, its subtended angle ∠ ASB is as the preferred value on this limit, its smooth value and other candidate point information are preserved along with this active edges together, and according to its smooth value whether less than smooth threshold values, AB is put into active edges Priority Queues or alternative formation.When the candidate information of active edges when particularly optimum changes in abutting connection with leg-of-mutton establishment owing to it, this active edges is also inserted Priority Queues or alternative formation again according to its smooth value.
The triangle expansion of active edges:
Expansion is similar to common border and advances algorithm to the triangle of active edges, promptly generates a triangle isolated or that sew up with the adjacent side.Because at most only related 2 sector regions independently in summit when isolated leg-of-mutton generation may destroy this restriction, are not then temporarily expanded this active edges in the half of data structure of revising.
In addition, the process that also has the orientation of a burst.In a burst, new leg-of-mutton generation has opposite direction by two one side of something sharing same geometrical edge and guarantees that this triangle has consistent direction with other triangles in the burst.Because initial seed trigonometric ratio zone not necessarily has consistent extroversion, the burst of two contacts not necessarily has consistent direction, for this reason, and in the progradation of border, when the optimum of an active edges contacts the another one burst, need to check whether these 2 bursts have consistent direction.If the active edges from A to B has optimum S, the potential triangle △ BAS of expansion active edges AB will produce an one side of something that points to A from B, therefore the direction of △ BAS depends on active edges AB, the algorithm employing is similar to the virtual trigonometric ratio process filling triangle △ BAS of seed trigonometric ratio and the space between the existing triangle of S, two one side of something of the inner edge association in this virtual trigonometric ratio zone should have opposite direction to guarantee topological integrality, in view of the above, whether will the reverse direction of certain burst of decision.When two bursts all were unoriented burst, wherein any one burst can reverse; Otherwise that not directed burst and be labeled as directed burst can reverse.
Burst element classification and feature detection
The topological element of the burst that smooth expansion obtains to burst carries out the classification of smooth element and non-smooth element, deletes non-smooth boundary element, follows the tracks of detected characteristics and accurate location feature point position or inserts the new feature point by sharp features.
The smooth expansion of burst is to finish the border propelling by smooth value is carried out the triangle expansion less than the active edges of smooth threshold values, newly-generated triangle is except that closing with this smooth side seam, also may sew up with the adjacency active edges, the inner edge of sewing up with the adjacency triangle is not necessarily less than smooth threshold values, therefore, the branch slice graticule that generates is not necessarily smooth everywhere, may there be rough sharp limit, on the other hand, although adopt smooth threshold values control border extension process, can not guarantee that borderline point just in time is positioned on the local smooth surface of this burst, contact point particularly, possible some frontier point is positioned on the local smooth surface of other bursts.For further avoiding in sharpened areas or owing the difficulty of the border extension of sample area, the present invention adopts the method for topological element (point, limit, triangle) classification and feature detection, smooth treatment is carried out on the burst border, based on the method for characteristic curve detection and local surface intersection, reorientation unique point or insertion new feature point.Grid elements is carried out slickness classification and characteristic curve detects, simultaneously method reorientation unique point or the insertion new feature point by local surface intersection.Concrete steps are as follows:
With two smooth threshold values θ
FeatureAnd θ
Sharp(θ
Feature＞θ
Sharp) detection of control characteristic.θ at first
FeatureBe used to discern initial sharp-pointed inner edge, adopting existing characteristic curve tracking to carry out characteristic curve from the sharp-pointed inner edge that is adjacent to the border then follows the tracks of, because the grid during the present invention rebuilds is incomplete grid, may comprise some holes, when certain characteristic edge is followed the tracks of next characteristic edge, adopt average sharpness but not the sharpness sum as the sharpness of following the tracks of string, end at certain frontier point or reach the maximum length of following the tracks of and follow the tracks of string.When signature tracking runs into the sharpness of the characteristic edge that boundary edge or current tracking obtain less than θ
SharpThe time, then this characteristic curve tracing process finishes.
The characteristic curve that obtains for tracking, if a limit is only arranged, and an end is interior point, and then this limit is not a characteristic edge, and this inner marker is designated as slick spot, and its related frontier point is labeled as non-slick spot.All of its neighbor is labeled in the limit of characteristic curve in order to avoid be repeated to follow the tracks of, and the point on the characteristic curve is marked as unique point.For the contact point that connects two sector regions, enough (its smooth value is greater than θ greatly if there is dihedral angle from the plane at two fan-shaped triangle places of difference
Feature), then this also is a unique point.All of its neighbor is marked as non-smooth triangle in the triangle of unique point.The average smooth value that does not belong to any non-smooth leg-of-mutton inner edge is defined as the smooth value θ of this burst
Seg, for each non-sharp-pointed inner edge, if its smooth value is greater than α θ
Seg, (α gets 2 in the present invention), this limit is labeled as non-smooth limit, otherwise is smooth limit.A frontier point is marked as non-slick spot, if it satisfies in abutting connection with inner edge: have only an inner edge, smooth inner edge number to be less than non-smooth inner edge number, more than 1 non-smooth inner edge.The triangle that is adjacent to unique point and non-smooth boundary point is marked as non-smooth triangle.
For non-smooth boundary point, the slick spot of getting near its some carries out the quadratic polynomial surface fitting: promptly at first use from its nearest a small amount of point and carry out plane fitting, carry out the match of local secondary polynomial surface based on this plane with the local coordinate of these slick spots then.Local fit residual error based on these slick spots determines whether this frontier point is smooth, if this frontier point is still rough, then delete this frontier point and related triangle thereof, otherwise, whether this point of mark and related triangle thereof all are smooth, and further have more non-smooth triangle can transfer smooth triangle near the inspection with this local fit curved surface.
For the inner edge that an end points is not a unique point, if its related triangle is smooth, then this limit also is smooth.
For unique point, two quadratic polynomial curved surfaces of our same matches, the enough close discrete point of sampling and be converted into world coordinates respectively on two local curved surfaces is determined accurate characteristic point position with the surface intersection method of iteration MLS projection again.For the unique point reposition of trying to achieve,, and revise grid and connect if, then insert the new feature point at reposition apart from its original position distance excessive (as greater than half of average sample length, i.e. L/2).Therefore, the unique point after each is accurately located has the local smooth surface of two associations at least.
The tile features expansion
By the new feature point of unique point of reorientating or insertion, under the prerequisite of smooth threshold values control and the local slickness maintenance of curved surface, smooth expansion is further carried out on the burst border.
Through top border smooth treatment, unique point reorientation and insertion new feature point, remaining border triangle all is smooth triangle, can continue burst is expanded.The end points of active edges or optimum may be unique points, because smooth threshold values is the value of user's appointment, if fully with light guiding valve value control expansion process, may make some potential smooth triangle can not get expansion, for this reason, adopt finer step decision active edges whether can expand and how to expand in the tile features extension phase, the expansion of this moment can be divided into simple extension and feature expansion, simple extension is extended triangular shape and be labeled as smooth triangle only, and feature expansion is except that extended triangular shape, also carry out feature and ask exact position or the insertion new feature point of friendship, and write down the candidate information of the active edges around this unique point and the renewal to determine unique point.If unique point is positioned at more than three on the local curved surface, be called multi-characteristic points.
To an active edges AB, its optimal candidate point is S, and concrete steps are as follows:
1) if A, B are positioned on the same characteristic curve, do not expand;
2) if S is a multi-characteristic points, simple extension then;
3) if S is the unique point that isolates, check from AB whether can arrive on certain local curved surface of S by smooth inner edge, in this way, simple extension then;
4) if S is not an isolated point, check from AB whether can arrive S by smooth inner edge, in this way, simple extension then;
5) if S is a unique point, the smooth value of AB is less than smooth threshold values, and has one to be to be positioned at same the unique point on the characteristic curve, then simple extension with S among A, the B;
6) if having 2 to be unique point among A, B, the S, if can obtain a multi-characteristic points F by how local surface intersection, and F can be used as suitable candidate point, and then AB and F constitute new triangle, be feature expansion, need the candidate information of recording feature point F and renewal active edges on every side;
7) if S is a contact point, the smooth value that two related fan-shaped intermediate cam shape constitutes surpasses smooth threshold values, carries out feature with the local smooth surface of two sector region correspondences and asks friendship, and as success, then feature expansion arrives the new feature point;
8) if S is isolated point but is not unique point that AB has one to have same isolated point in abutting connection with active edges CD, and the smooth value of AB and CD is less than the average smooth value of burst or the AB average smooth value in abutting connection with inner edge, then simple extension AB and CD;
9) if S is isolated point but is not unique point that and AB has one to be unique point, checks whether S is positioned on certain local smooth surface of AB.
Through above-mentioned a series of step each active edges is expanded, made burst be further expanded, more unique point is found or reorientates.Till can not find the one side of something that to expand, finished the expansion of whole burst.
Sew up and rebuild
Under the situation of unglazed guiding valve value control, in the border of all bursts, select suitable boundary edge based on priority rule, carry out border extension and find more unique point, finally sew up different bursts or the slit in the burst at the sharp features place based on local surface intersection.
In the time can not finding any burst that can expand again, the burst process of reconstruction finishes, and this moment may be between burst or some slits that need sew up of burst existence itself.The present invention adopts the stitching process of reconstruction that is similar to the tile features expansion that these slits are sewed up.All remaining active edges are collected into two Priority Queues Q
1And Q
2, Q
1By the storage of the preferential order of subtended angle to smooth value less than smooth threshold values or contain the active edges of feature end points, and Q
2Then be to the Priority Queues of all the other active edges by local surface fitting residual error ordering.Algorithm is sewed up reconstruction iteratively by following two steps:
1) employing is similar to the process of tile features expansion to Q
1In active edges expand, new active edges is inserted Q
1And Q
2, and the active edges that can not expand is inserted Q
2, up to Q
1For sky just changes step 2 over to;
2) employing is similar to the process of tile features expansion to Q
2In active edges expand, new active edges is inserted Q
1And Q
2
Below adopt the inventive method that some typical point set models are tested, and with test result with
(1) Cocone[AMENTA N., CHOI S., DEY T., LEEKHA N, A simplealgorithm for homeomorphic surface reconstruction[C] .16th ACM Symposium onComputational Geometry, 2000:213-222.], (2) Hoppe[HOPPE H., DEROSET., DUCHAMP T., MCDONALD J., STUET-ZLE W.:, Surface reconstruction fromunorganized points[C] .ACM SIGGRAPH 1992 Conference Proceedings:71-78.], (3) IPD[Lin H.W., Tai C.L., Wang G.J.:, A Mesh Reconstruction AlgorithmDriven by Intrinsic Property of Point Cloud[J] .Computer-Aided Design (2004), 36 (1): 1-9.] etc. the gridding result of famous curve reestablishing algorithm compare.
Embodiment 1:
Fig. 4 is the inventive method is carried out curve reestablishing to the Mechpart model a procedure chart.Wherein, a) be initial point set model; B) be that burst is rebuild but do not carried out the result that border smooth treatment and feature are asked friendship; C) be to comprise the complete burst reconstructed results that border smooth treatment and feature are asked friendship; D), e) be final curve reestablishing result.As can be seen from Figure 4, the inventive method has been recovered the characteristic information that the Mechpart model is lost effectively in sampling.
The comparison diagram of Fig. 5 result that to be the inventive method rebuild the Mechpart model and Hoppe, Cocone, IPD arithmetic result.Wherein, a) be the result of Hoppe algorithm; B) be the result of Cocone algorithm; C) be the result of IPD algorithm; D) be reconstructed results of the present invention.As can be seen from Figure 5, though the Hoppe algorithm can be rebuild correct stream shape curved surface, lost characteristic information; The grid that the cocone algorithm produces has the seamed edge that loses shape and contains some cavities; The IPD algorithm has produced incorrect grid; And the reconstructed results of the inventive method obviously is better than the result of above-mentioned three kinds of existing algorithms.
Embodiment 2:
Fig. 6 is the inventive method is carried out curve reestablishing to the Bunny model a procedure chart.Wherein, a) be initial point set model; B) be that burst is rebuild but do not carried out the result that the genial feature of boundary light is asked friendship; C) be to comprise the complete burst reconstructed results that the genial feature of boundary light is asked friendship; Figure d) be the different angles view of final reconstructed results.As can be seen from Figure 6, the inventive method has been recovered the characteristic information that the Bunny model is lost effectively in sampling.
The comparison diagram of Fig. 7 result that to be the inventive method rebuild the Bunny model and Hoppe, Cocone, IPD arithmetic result.Wherein, a) be the result of Hoppe algorithm; B) be the result of Cocone algorithm; C) be the result of IPD algorithm; D) be reconstructed results of the present invention.Present embodiment uses the data point of Stanford " Bunny " model of simplifying as the input point set, this model only has 4138 points and owes sampling degree height at the ear place because of simplification degree height, cause the local tangential plane of Hoppe algorithm to calculate failure, incorrect directed distance function makes the Hoppe algorithm failure based on Marching Cube iso-surface extracting; Same Cocone and IPD algorithm can not produce correct gridding at the ear place; And algorithm of the present invention can produce the surface mesh of feature-sensitive effective, healthy and strongly.
Embodiment 3:
Fig. 8 is the inventive method is carried out curve reestablishing to the Fandisk model a procedure chart.Wherein, a) be initial point set model; B) be that burst is rebuild but do not carried out the result that the genial feature of boundary light is asked friendship; C) be to comprise the complete burst reconstructed results that the genial feature of boundary light is asked friendship; D) be last reconstructed results.As can be seen from Figure 8, the inventive method has been recovered the characteristic information that the Fandisk model is lost effectively in sampling.
The comparison diagram of Fig. 9 result that to be the inventive method rebuild the Fandisk model and Hoppe, Cocone, IPD arithmetic result.Wherein, a) be the result of Hoppe algorithm; B) be the result of Cocone algorithm; C) be the result of IPD algorithm; D) be result of the present invention.As can be seen from Figure 9, for the Fandisk model that has irregular sampling and sharp features in the present embodiment, the gridding result of Hoppe, Cocone, three algorithms of IPD exists significantly anti-aliasing, and the IPD algorithm has also generated incorrect grid.
Embodiment 4,5,6:
Figure 11, Figure 12, Figure 13 are respectively the reconstructed results of the inventive method to smooth-feature, mannequin, dino model.For these uniform samplings and FREEFORM SURFACE MODEL, the inventive method can be carried out curve reestablishing effectively as other algorithms as can be seen.For the FREEFORM SURFACE MODEL as the dino model, if smooth threshold values is made as 1, then just be equal to general border and advance reconstruction algorithm, distinguish with general border propelling algorithm and be that the present invention does not need to carry out any triangle intersect inspection and still produces correct stream shape grid.And to the mannequin model, we are made as 0.2 with smooth threshold values, and the ear place has produced sharp features as can be seen.For the model among smooth-feature model and the embodiment 1～3, smooth threshold values all is made as 0.1.The appointment of in fact smooth threshold values is loose relatively, but too small threshold values is easy to generate too much burst, and excessive threshold values makes the result be equal to general border propelling algorithm.Smooth threshold values is at 0.08 to 0.2 grid that can both produce than good quality.
Table 1 shows on IBM T60 notebook computer, and the present invention is to the ruuning situation of above-mentioned test model:
Table 1 the present invention is to the operation result of test model
| The Model model | The Points point | The segments burst | The vertices summit | Feature vertices feature summit | Triangles triangle section | Smooth reconstruction burst is rebuild (unit: second) | Stitching reconstruction sews up and rebuilds (unit: second) |
| ??Mechpart | ??4102 | ??13 | ??4300 | ??573 | ??8619 | ??0.176608 | ??0.324223 |
| ??Fandisk | ??10000 | ??12 | ??10230 | ??834 | ??20445 | ??0.4678 | ??0.483614 |
| ??Bunny | ??2503 | ??6 | ??2527 | ??280 | ??5050 | ??0.0993043 | ??0.124142 |
| ??smooth-feature | ??1433 | ??6 | ??1608 | ??204 | ??3212 | ??0.0532318 | ??0.103343 |
| ??mannequin | ??11703 | ??2 | ??11695 | ??264 | ??23371 | ??0.429751 | ??0.14142 |
| ??dino | ??56307 | ??1 | ??56302 | ??0 | ??112599 | ??2.59522 | ??0.0872099 |
As known from Table 1, the present invention in the burst process of reconstruction owing to do not need complex mathematical test to guarantee topological integrality, the existing border of its efficiency ratio advances algorithm fast, but feature ask hand over and the border more time-consuming owing to surface fitting and MLS projection when sewing up, make its efficient reduce some again, all things considered, efficient of the present invention and existing border advance algorithm equally matched.
Above-described only is preferred implementation of the present invention, the invention is not restricted to above embodiment.Be appreciated that those skilled in the art under the prerequisite that does not break away from spirit of the present invention and design, can make other improvement and variation.
Claims (6)
1. curve reestablishing method based on the feature-sensitive of burst is characterized in that may further comprise the steps:
1) burst is rebuild: by a plurality of burst process of reconstruction the smooth domain of potential curved surface is carried out gridding, each burst process of reconstruction is divided into following three steps:
A. the smooth expansion of burst: determine the seed trigonometric ratio zone of each burst,, according to the preferential order of subtended angle boundary edge is carried out the triangle expansion and surpass smooth threshold values up to the smooth value of all boundary edge from the boundary edge in seed trigonometric ratio zone;
B. burst element classification and feature detection: the topological element of the burst that smooth expansion obtains to burst carries out the classification of smooth element and non-smooth element, delete non-smooth boundary element, follow the tracks of detected characteristics and accurate location feature point position or insert the new feature point by sharp features;
C. tile features expansion:, under the prerequisite of smooth threshold values control and the local slickness maintenance of curved surface, smooth expansion is further carried out on the burst border by the new feature point of unique point of reorientating or insertion;
2) sew up reconstruction: in the border of all bursts, select suitable boundary edge based on priority rule, carry out border extension and find more unique point, finally sew up different bursts or the slit in the burst at the sharp features place based on local surface intersection.
2. according to the curve reestablishing method of the described feature-sensitive based on burst of claim 1, it is characterized in that: the smooth threshold values scope described in the steps A is 0.08～0.2.
3. according to the curve reestablishing method of the described feature-sensitive based on burst of claim 1, it is characterized in that: the seed trigonometric ratio zone described in the steps A is meant the zone that all triangles constituted around a point.
4. according to the curve reestablishing method of the described feature-sensitive based on burst of claim 1, it is characterized in that: the topological element described in the step B comprises summit, triangle and limit.
5. according to the curve reestablishing method of the described feature-sensitive based on burst of claim 1, it is characterized in that: the smooth expansion described in the step C is divided into simple extension and feature expansion; Simple extension is extended triangular shape and be labeled as smooth triangle only; Feature expansion is also carried out feature and is asked exact position or the insertion new feature point of friendship to determine unique point except that extended triangular shape, and writes down the candidate information of the active edges around this unique point and the renewal.
6. according to the curve reestablishing method of the described feature-sensitive based on burst of claim 1, it is characterized in that the concrete steps that described stitching is rebuild are:
The boundary edge of all bursts is assigned in first formation and second formation according to the subtended angle prioritizing, in first formation boundary edge of smoothness less than smooth threshold values, and end points or optimum are the boundary edge of unique point, it in second formation remaining boundary edge, according to the boundary edge in first formation earlier, the order of the boundary edge in second formation of back carries out the iteration expansion.
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