CN103679814A - Processing method and device for triangle mesh model - Google Patents

Processing method and device for triangle mesh model Download PDF

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CN103679814A
CN103679814A CN201210320745.7A CN201210320745A CN103679814A CN 103679814 A CN103679814 A CN 103679814A CN 201210320745 A CN201210320745 A CN 201210320745A CN 103679814 A CN103679814 A CN 103679814A
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cost
representative points
candidate vertices
summit
ratio
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李建福
邓翔
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Siemens AG
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Abstract

The embodiment of the invention discloses a processing method and device for a triangle mesh model. The method comprises the following steps: computing the mean curvature of each vertex, and determining a vertex pair of two vertexes of which the mean curvatures are smaller than the preset mean curvature threshold as a candidate vertex pair; for each candidate vertex pair, determining the positions of target vertexes corresponding to the candidate vertex pair, wherein the target vertexes are used for replacing the candidate vertex pair during removing the candidate vertex pair; according to the distance from the target vertexes to all triangle patches having any one vertex in the candidate vertex pair, determining first consideration for removing the candidate vertex pair; according to the shape features of all triangle patches having the target vertexes, determining second consideration for removing the candidate vertex pair; according to the first consideration and the second consideration, determining the consideration for removing the candidate vertex pair; removing one candidate vertex pair with the minimum consideration, and using the target vertexes corresponding to the removed candidate vertex pair to replace the candidate vertex pair. The method and the device can try to avoid processing corresponding vertex pair to avoid generating an abnormal triangle.

Description

A kind of disposal route of triangular mesh model and device
Technical field
The present invention relates to digital image processing techniques, particularly a kind of disposal route of triangular mesh model and device.
Background technology
In the application of computer graphics, the geometric model of object adopts triangle surface to represent conventionally.But, along with the increase of object model complicacy, represent that the quantity of the needed triangle surface of object increases greatly.For example, in the application such as three-dimensional laser scanning in kind, medical image three-dimensional reconstruct, remote sensing images terrain reconstruction, the quantity of triangle surface usually reaches 1,000,000 even necessarily, well beyond the processing power of graphic hardware and network transmission.
Therefore, in computer graphics, an important step is exactly to process by grid the model that replaces high complexity with the model of low complex degree, maintains the key character of object simultaneously, approaches preferably the original-shape of object.
In order to reduce the complexity of triangular mesh model, can on visual effect, affect little part patch grids information by removing or revise in model, such as summit, limit or triangle surface etc., reduces the quantity of grid model intermediate cam shape dough sheet.The simplification of triangular mesh model is that the aspect of model changes minimum in the situation that as far as possible before and after guaranteeing to simplify, and finds the reduced representation method of minimum number triangle surface.The simplification process of triangular mesh model is generally: to given original triangle grid model, according to certain shortcut calculation, under certain constraint, it is carried out to a series of simplification basic operation, until the grid model after the simplification that obtains requiring.
At present, edge contraction method is a kind of relatively more conventional lattice simplified method.The basic thought of edge contraction method is: for calculating an error matrix in each summit in triangular mesh model, according to the cost of edge contraction in error matrix computing grid and the position of representative points, then according to collapse cost, carry out from small to large folding operation.Specifically comprise: select the limit of Least-cost in grid model and two summits relevant to this limit, these two summits " are folded " to representative points, then revise topological relation, the limit relevant to these two summits is mapped to representative points; Upgrade the error matrix on each summit, then recalculate the cost of edge contraction and the position of representative points in grid model, again select the limit of Least-cost and two summits relevant to this limit to simplify the operation; Repeat said process, until be met the grid model of requirement.Fig. 1 is the schematic diagram of edge contraction method in prior art.As shown in Figure 1, suppose in the triangular mesh model shown in figure (a) vertex v 1and v 2between the limit that is Least-cost, limit.Therefore, vertex v 1and v 2be " folded " to representative points v ' 12.Accordingly, the limit relevant to these two summits is mapped to representative points v ' 12, obtain the triangular mesh model as shown in figure (b).
The edge contraction method based on Quadric Error Metrics that Garland proposes is a kind of edge contraction method of classics, the method is used the quadratic sum of distance of the plane that representative points is associated to two summits with folded limit as error, calculate fairly simple, speed is fast.But the edge contraction method of Garland based on Quadric Error Metrics, in simplification process, because representative points may be positioned at optional position, when the position of representative points and relevant summit are very near, can produce some abnormal triangle surfaces around.These abnormal triangle surfaces have a very large drift angle and two very little drift angles conventionally, and this is very disadvantageous for follow-up processing.That is to say, in the method for Garland, owing to not taking into full account the shape facility of the triangle surface generating in simplification process, cause simplifying the triangle that shape anomaly easily appears in result, this may have a strong impact on the reconstruction quality of the follow-up subdivision curved surface based on simplified model.Specifically ask for an interview M.Garland, et.al., " Surface Simplification Using QuadricError Metrics, " Computer Graphics (SIGGRAPH ' 97Proceedings), 1997, pp.209-216.
Summary of the invention
The embodiment of the present invention provides a kind of disposal route and device of triangular mesh model, to avoid producing abnormal triangle surface in processing procedure.
The technical scheme that the embodiment of the present invention proposes comprises:
A kind of disposal route of triangular mesh model, wherein, described triangular mesh model is comprised of summit and triangle surface, two summits on the same limit of triangle surface form a summit pair, the mean curvature on a summit reflects the curvature statistical nature of the actual object that described triangular net model is corresponding, the treating method comprises: calculate the mean curvature on summit described in each, the summit that the mean curvature on two summits is all less than to default mean curvature threshold value is to being defined as candidate vertices pair; For candidate vertices pair described in each, determine the position of the representative points corresponding with it, described representative points be used for removing described candidate vertices to time replace described candidate vertices pair; According to described representative points, to all distances that have with the triangle surface on any summit of described candidate vertices centering, determine and remove the first cost that described candidate vertices is right; According to the shape facility with all triangle surfaces of described representative points, determine and remove the second cost that described candidate vertices is right; According to described the first cost and described the second cost, determine and remove the cost that described candidate vertices is right; Remove a candidate vertices pair of Least-cost, with the candidate vertices with being removed, corresponding representative points is replaced.
A kind for the treatment of apparatus of triangular mesh model, wherein, described triangular mesh model is comprised of summit and triangle surface, two summits on the same limit of triangle surface form a summit pair, the mean curvature on summit reflects the curvature statistical nature of the actual object that described triangular net model is corresponding, this device comprises: representative points determination module, for calculating the mean curvature on summit described in each, the summit that the mean curvature on two summits is all less than to default mean curvature threshold value is to being defined as candidate vertices pair; For candidate vertices pair described in each, determine the position of the representative points corresponding with it, described representative points be used for removing described candidate vertices to time replace described candidate vertices pair; Cost computing module, for according to described representative points to all distances that have with the triangle surface on any summit of described candidate vertices centering, determine and remove the first cost that described candidate vertices is right; According to the shape facility with all triangle surfaces of described representative points, to determine and remove the second cost that described candidate vertices is right, described the second cost is to remove the second error that operation brings; According to described the first cost and described the second cost, determine and remove the cost that described candidate vertices is right; Remove module, remove a candidate vertices pair of Least-cost, with the candidate vertices with being removed, corresponding representative points is replaced
A kind for the treatment of apparatus of triangular mesh model, described triangular mesh model is comprised of summit and triangle surface, two summits that belong to the same limit of same triangle surface form a summit pair, described device comprises: processor and the storer being connected with described processor communication, in wherein said storer, store machine readable instructions, described processor is for the instruction of execute store, to carry out the step described in said method.
Compared with prior art, in the disposal route of the triangular mesh model proposing in the present invention and device, when determining and removing the right cost in each summit, except consider representative points to all with the distance of summit corresponding to this representative points to the triangle surface being associated, also further considered the shape facility of all triangle surfaces that are associated with representative points.Like this, for issuable abnormal triangle surface, remove the right cost in its corresponding summit larger.Therefore, can avoid processing corresponding summit to avoid generating abnormal triangle as far as possible.
Accompanying drawing explanation
Fig. 1 is the schematic diagram of edge contraction method in prior art.
The process flow figure of a kind of triangular mesh model that Fig. 2 provides for the embodiment of the present invention.
The structural representation of the treating apparatus of a kind of triangular mesh model that Fig. 3 provides for one embodiment of the invention.
The structural representation of the treating apparatus of a kind of triangular mesh model that Fig. 4 provides for another embodiment of the present invention.
The disposal route sub-process figure of a kind of triangular mesh model that Fig. 5 further provides for the embodiment of the present invention.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with the accompanying drawing embodiment that develops simultaneously, technical scheme of the present invention is elaborated.The embodiment of the present invention further provides a kind of short-cut method of triangular mesh model, and the method can avoid producing abnormal triangle surface in simplification process.
The technical scheme that the present invention proposes comprises:
A disposal route for triangular mesh model, wherein, triangular mesh model is comprised of summit and triangle surface, and two summits that belong to the same limit of same triangle surface form a summit pair, and the method comprises:
The mean curvature of calculating summit described in each, the summit that the mean curvature on two summits is all less than to default mean curvature threshold value is to being defined as candidate vertices pair;
For candidate vertices pair described in each, determine the position of the representative points corresponding with it, described representative points be used for removing described candidate vertices to time replace described candidate vertices pair;
According to described representative points, to all distances that have with the triangle surface on any summit of described candidate vertices centering, determine and remove the first cost that described candidate vertices is right;
According to the shape facility with all triangle surfaces of described representative points, to determine and remove the second cost that described candidate vertices is right, described the second cost is to remove the second error that operation brings;
According to described the first cost and described the second cost, determine and remove the cost that described candidate vertices is right;
Remove a candidate vertices pair of Least-cost, with the candidate vertices with being removed, corresponding representative points is replaced.
From technique scheme, can find out, in the grid processing method proposing in the present invention, when determining and removing the right cost in each summit, except consider representative points to all with the distance of summit corresponding to this representative points to the triangle surface being associated, also further considered the shape facility of all triangle surfaces that are associated with described representative points.Like this, for issuable abnormal triangle surface, remove the right cost in its corresponding summit larger.Therefore, can avoid processing corresponding summit to avoid generating abnormal triangle as far as possible.
Below by specific embodiment, also come by reference to the accompanying drawings the above-mentioned technical characterictic of the present invention, advantage and implementation thereof to be further described.
The process flow diagram of the disposal route of a kind of triangular mesh model that Fig. 2 provides for the embodiment of the present invention.As shown in Figure 2, the method comprises the following steps.
Step 201, for each summit in triangular mesh model to (v 1, v 2), be identified for replacing summit to (v 1, v 2) representative points v ' 12position.
In triangular mesh model, there are two vertex v on every limit of each triangle surface 1and v 2, summit is to (v 1, v 2).In this step, need to determine that each summit is to (v 1, v 2) corresponding representative points v ' 12.In processing procedure, this representative points v ' 12be used for replacing summit to (v 1, v 2), like this, just reduced a limit in triangular mesh model.That is to say, for limit, shrink (v 1, v 2) → v ' 12, need to determine representative points v ' according to certain principle 12position, make the grid model after processing approach as much as possible original grid model.
The method of Garland Quadric Error Metrics of take is below example, to determining representative points v ' 12the method of position be described.According to the method, Quadric Error Metrics reaches minimizing point just as representative points v ' 12.
Concrete, in triangular mesh model, each summit can be regarded the intersection point of a series of planes as, comprises the intersection point of all triangle surfaces on this summit.Therefore, each summit and a series of triangle surface can be connected.If with vertex v 1the set of the triangle surface being associated is S 1, with vertex v 2the set of the triangle surface being associated is S 2, objective definition vertex v ' 12the error at place is representative points v ' 12to S 1and S 2in the quadratic sum of distance of each triangle surface being associated,
Figure BDA00002087514700041
p=[A wherein, B, C, D] t, represent S set 1and S 2in a plane, A, B, C, D are the coefficients of plane equation Ax+By+Cz+D=0, and A 2+ B 2+ C 2=1; V represents representative points v ' 12three-dimensional coordinate vector.
For summit to (v 1, v 2), its representative points v ' 12position can by minimize Δ (v ' 12) solve, by solving equation group
Figure BDA00002087514700042
obtain representative points v ' 12position.If this system of equations, without solution, is chosen vertex v 1or vertex v 2or vertex v 1and v 2mid point as representative points v ' 12.Concrete computation process is prior art, does not repeat them here.Take the method for Quadric Error Metrics above as example is to representative points v ' 12definite being described, in actual applications, those skilled in the art also can adopt additive method to determine representative points v ' 12position.Such as the minimum method (Hoppe of the energy function using in the Progressive Mesh algorithm that adopts Hoppe to propose, H.Progressive meshes.In:Proceedings ofthe SIGGRAPH ' 96.1996, pp.99-108.), the grid that minimizes that Lindstrom and Turk propose is processed the geometric properties changing method (Lindstrom such as front and back volume and area, P., Turk, G. Fast and memoryefficient polygonal simplification.In:Proceedings ofthe IEEE Visualization ' 98.1998.279 ~ 284), and the people such as Cohen proposes the plane projection Continuous Mappings method based on linear programming etc. and determines representative points position (Cohen, J., Manocha, D., Olano, M.Simplifying polygonal models using successive mappings.In:Proceedings of the IEEE Visualization ' 97.1997.395 ~ 402).Which kind of method is the embodiment of the present invention to adopting determine representative points v ' 12position do not limit.
Step 202, for each summit in triangular mesh model to (v 1, v 2), according to representative points v ' 12to all and summit to (v 1, v 2) distance of the triangle surface that is associated, determine and remove this summit to (v 1, v 2) the first cost.
In this step, remove summit to (v 1, v 2) the first cost this removes the error brought of operation.This error can be according to representative points v ' 12to all and summit to (v 1, v 2) distance of the triangle surface that is associated determines.With summit to (v 1, v 2) triangle surface that is associated is for having vertex v 1the set of triangle surface is S 1with there is vertex v 2the set of the triangle surface being associated is S 2union.
In the present embodiment, the method for Garland Quadric Error Metrics of still take is example, to determining, removes summit to (v 1, v 2) the calculating of the first cost describe.Concrete, can calculate the first cost according to following formula (1):
cost 1(v 1,v 2)=v TQv (1)
Wherein, cost 1(v 1, v 2) representing the first cost, Q represents Quadric Error Metrics matrix, v represents representative points v ' 12three-dimensional coordinate vector.Concrete computation process is the state of the art, does not repeat them here.
The method of Garland Quadric Error Metrics of take is above example, and the calculating of the first cost is illustrated.In the Quadric Error Metrics method of Garland, mainly considered the geometric distance of representative points to all triangle surfaces that are associated.In actual applications, considering, outside geometric distance, can also further according to the color on summit, Texture eigenvalue, to determine the first cost.The embodiment of the present invention does not limit the computing method of the first cost.Also can adopt in addition other than the minimum method of the energy function using in the Progressive Mesh algorithm that Hoppe proposes as the above-mentioned, Lindstrom and Turk propose minimize grid process before and after the geometric properties changing method such as volume and area, and the people such as Cohen proposes the plane projection Continuous Mappings method based on linear programming etc. and determines the first cost.The embodiment of the present invention does not limit the computing method of the first cost.
Step 203, for each summit in triangular mesh model to (v 1, v 2), according to representative points v ' 12the shape facility of all triangle surfaces that are associated is determined and is removed this summit to (v 1, v 2) the second cost.
Consider that abnormal triangle surface has a very large drift angle and two very little drift angles conventionally, therefore the such circumcircle of triangle surface and ratio of inscribe radius of a circle is conventionally larger, and its longest edge and the ratio of the length of side of minor face and the ratio of the number of degrees of maximum drift angle and minimum drift angle are conventionally also larger.
In the present embodiment, and the shape facility of all triangle surfaces of being associated of representative points can comprise: and the circumcircle of all triangle surfaces that is associated of representative points and the ratio of inscribe radius of a circle and/or and the ratio of the length of side of the longest edge of all triangle surfaces of being associated of described representative points and minor face and/or and the maximum drift angle of all triangle surfaces that is associated of described representative points and the ratio of the number of degrees of minimum drift angle.
In addition, those skilled in the art also can adopt other modes (such as the number of degrees of maximum drift angle, the number of degrees of minimum drift angle etc.) to describe the shape facility of triangle surface.
In this step, the ratio of the length of side of the circumcircle of triangle surface and the ratio of inscribe radius of a circle and longest edge and minor face of take is example, and the computation process of the second cost is described.It should be noted that in actual applications, can utilize any one of triangle surface or the combination of a plurality of shape facilities to calculate the second cost.
For convenience, below by the ratio of the circumcircle of triangle surface and inscribe radius of a circle the ratio referred to as radius, the ratio by the ratio of the length of side of the longest edge of triangle surface and minor face referred to as the length of side.
In this step, and representative points v ' 12the all triangle surfaces that are associated refer to: all representative points v ' that comprise 12triangle surface.Due to representative points v ' 12for replacing summit to (v 1, v 2), so in triangular mesh model, comprise summit to (v 1, v 2) in the limit on any one summit need to be mapped to representative points v ' 12.Like this, will form new triangle surface.These new triangle surfaces comprise representative points v 12.
Due to representative points v ' 12the triangle surface being associated has a plurality of, so need to calculate each and representative points v ' 12the shape facility of the triangle surface being associated, the i.e. ratio of the radius of each triangle surface and the ratio of the length of side.Then calculate respectively the mean value of ratio of radius and the mean value of the ratio of the length of side of all triangle surfaces.Because the mean value of ratio of radius and the mean value of the ratio of the length of side of triangle surface may have the different orders of magnitude, therefore in order to calculate accurately, further the mean value of the mean value of the ratio of the radius of diabolo dough sheet and the ratio of the length of side is normalized respectively, obtains the mean value of ratio of normalized radius and the mean value of the ratio of the normalized length of side.Certainly, also can be before calculating the mean value of ratio of radius and the mean value of the ratio of the length of side of all triangle surfaces, first the ratio of the ratio of the pair radius of all triangle surfaces and the length of side is normalized, and then according to the ratio of the ratio of the normalized radius of all triangle surfaces and the normalized length of side, calculate respectively the mean value of ratio of normalized radius and the mean value of the ratio of the normalized length of side.
After obtaining the mean value of ratio of normalized radius and the mean value of the ratio of the normalized length of side, can calculate according to formula (2) below, obtain removing summit to (v 1, v 2) the second cost:
cost 2(v 1,v 2)=αβ(v′ 12)+βτ(v′ 12)(2)
Wherein, cost 2(v 1, v 2) representative remove summit to (v 1, v 2) the second cost; ρ (v ' 12) mean value of ratio of radius of normalized all triangle surfaces that are associated with representative points that is; τ (v ' 12) be the mean value of the ratio of the length of side of normalized all triangle surfaces that are associated with representative points; α and β are weight factor, in the present embodiment, can make alpha+beta=1.
The ratio of radius and the ratio of the length of side of all triangle surfaces of being associated with representative points of take is above example, and the computation process of the second cost is illustrated.When calculating the second cost according to other shape facilities of triangle surface, it is similar that computing method are caught up with the description of face, do not repeat them here.
It should be noted that in actual applications, step 202 and 203 does not have the requirement of sequencing, can first perform step 202, calculates the first cost, can first perform step 203 yet, calculates the second cost.Or step 202 and 203 is carried out simultaneously.Step 202 in the embodiment of the present invention and 203 is only for convenience, does not limit the execution sequence of these two steps.
Step 204, according to the first cost and the second cost, calculates and removes summit to (v 1, v 2) cost.
After calculating the first cost and the second cost, in the present embodiment, can calculate and remove summit to (v according to formula (3) below 1, v 2) cost:
cost(v 1,v 2)=w 1cost 1(v 1,v 2)+w 2cost 2(v 1,v 2)(3)
Wherein, cost (v 1, v 2) representative removes the right cost in this summit, cost 1(v 1, v 2) represent the first cost, cost 2(v 1, v 2) represent the second cost, w 1and w 2for weight factor, in the present embodiment, can make w 1+ w 2=1.For example, can make w 1=0.6, w 2=0.4.These are only the exemplary value of the embodiment of the present invention, in actual applications, those skilled in the art can get other values according to actual conditions.The embodiment of the present invention is to w 1and w 2concrete value do not limit.
According to the first cost and the calculating of the second cost, removing summit to (v 1, v 2) cost time, because the order of magnitude of the first cost and the second cost may be different, so can remove summit to (v in calculating 1, v 2) cost before, to the advanced row normalized of the first cost and the second cost.After being normalized, then according to normalized the first cost and normalized the second cost, according to (4), calculating and remove summit to (v 1, v 2) cost.
cost(v 1,v 2)=w 1cost′ 1(v 1,v 2)+w 2cost′ 2(v 1,v 2)(4)
Wherein, cost ' 1(v 1, v 2) represent normalized the first cost, cost ' 2(v 1, v 2) represent normalized the second cost.
Except above-mentioned formula (3) and formula (4), also can calculate and remove summit to (v according to additive method 1, v 2) cost.For example, can calculate and remove summit to (v according to formula (5) below 1, v 2) cost:
cost(v 1,v 2)=cost′ 2(v 1,v 2)×cost 1(v 1,v 2)(5)
In formula (5), cost ' 2(v 1, v 2) be normalized the second cost, it is multiplied by the first cost as a form factor, to obtain removing summit to (v 1, v 2) cost.According to formula (5), calculating and removing summit to (v 1, v 2) cost time, can only to the second cost, be normalized, the first cost can not be normalized.
In this step, also can obtain removing summit to (v by other computing method 1, v 2) cost, as long as the first cost and the second cost have been considered in the calculating of this cost.
In embodiments of the present invention, when calculating the second cost, owing to having considered and representative points v ' 12the mean value ρ of the ratio of the radius of all triangle surfaces that are associated (v ' 12) and the mean value τ of the ratio of the length of side (v ' 12), for after removing, may generate abnormal vertex of a triangle pair, its ρ (v ' 12) and τ (v ' 12) larger, so its cost is also larger, thereby can avoid removing corresponding summit to avoid generating abnormal triangle as far as possible.
Step 205, all summits of triangular mesh model centering, selects a summit pair of Least-cost, and removes this summit pair.
The summit of in this step, establishing Least-cost is to being (v 1, v 2), remove summit to (v 1, v 2) and and vertex v 1and v 2relevant limit, with representative points v ' 12replace summit to (v 1, v 2), will with vertex v 1and v 2relevant limit is mapped to representative points v ' 12.Wherein, with vertex v 1relevant limit is that triangular mesh model comprises vertex v 1all limits; With vertex v 2relevant limit is that triangular mesh model comprises vertex v 2all limits.
By above step 201, to 205, completed one of diabolo grid model and taken turns processing procedure.Because triangular mesh model may need many wheels, process, can obtain the final processing triangular mesh model meeting the demands, therefore, after step 205, the embodiment of the present invention may further include following steps.
Step 206, for the summit being removed to (v 1, v 2) relevant summit pair, recalculate the position of its representative points and remove the right cost in this summit.
The structure of triangular mesh model that removed operation change due to step 205, thus all with the summit being removed to (v 1, v 2) the right representative points in relevant summit position and remove the right cost in this summit and need to recalculate.
Concrete, for the summit being removed to (v 1, v 2), relative summit is to being all vertex v that comprise 1or v 2summit pair.That is to say, for all vertex v that comprise 1or v 2summit pair, the position of its representative points and remove the right cost in this summit and need to recalculate.Concrete computation process is similar with previous description, at this, no longer repeats.
Step 207, judges whether current grid model meets predefined processing requirements, if met, and process ends; Otherwise, return to step 205.
In this step, can be by judging whether current grid model meets predefined processing requirements and judge whether process ends.If current grid model meets predefined processing requirements, processing procedure finishes, process ends; Otherwise, return to step 205.Predefined processing requirements can comprise simplifies required iterations, and the number of vertex after simplification accounts for the number percent of the number of vertex of original model, the number of vertex after simplification or total cost and the error upper limit setting in advance etc.
In addition, between the grid model of processing and original grid model, produce excessive error, can also set in advance an error upper limit.Now, the right cost in summit that needs record to be removed, has added up the right cost in the summit being at every turn removed to be used as total cost.
Concrete, can first judge whether current grid model meets predefined processing requirements, if met, process ends.If do not met, more total cost and the error upper limit setting in advance, if total cost has reached the error upper limit, process ends; Otherwise, return to step 205.
In actual applications, also can first judge whether total cost reaches the set error upper limit, and then judge whether current grid model meets predefined processing requirements.That is, if judge total cost, reached the error upper limit, end process process.If total cost does not reach the error upper limit, judge that whether current grid model meets the processing requirements setting in advance, if met, end process process; Otherwise, return to step 205.
Except above-mentioned judgment mode, those skilled in the art also can arrange other Rule of judgment, judge whether by other means end process process.The embodiment of the present invention does not limit how judging whether end process process.
From said method embodiment, can find out, in the method providing in the embodiment of the present invention, when determining and removing the right cost in each summit, except consider representative points to all with the distance of summit corresponding to this representative points to the triangle surface being associated, also further considered the shape facility of all triangle surfaces that are associated with described representative points.Like this, for issuable abnormal triangle surface, remove the right cost in its corresponding summit larger.Therefore, can avoid processing corresponding summit to avoid generating abnormal triangle as far as possible.
In addition, in the disposal route of above-mentioned triangular mesh model, because the tolerance of distance has only been considered in the calculating of error matrix, the grid model after processing distributes comparatively even, and the grid model after therefore processing can not well keep the important geometric properties of model surface.
In order farthest to keep the key character of triangular mesh model, the embodiment of the present invention can further utilize curvature to determine candidate vertices before step 201, and the follow-up processing operation all candidate vertices based on determined is carried out.
Because triangular mesh model is to the approaching of curved surface, so for more smooth region, part triangle surface can remove, to reduce the quantity of triangle surface.But, for seamed edge, corner angle and border etc., can fully reflect the characteristic information of triangle model and the region of size, the big rise and fall of curved surface, wish to retain more details, the place that namely triangle surface should dense distribution.The triangle surface in this region should be postponed and be removed or do not remove.That is to say, can delete triangle surface according to the fluctuating situation of the regional of curved surface.Because curvature has reflected the degree of crook of curve, so, in embodiments of the present invention, can judge by curvature the key character of triangular mesh model.
Concrete, before step 201, the method for the embodiment of the present invention may further include following steps.Refer to Fig. 5, the disposal route sub-process figure of a kind of triangular mesh model that Fig. 5 further provides for the embodiment of the present invention.
Step S1, calculates the mean curvature k on each summit in triangular mesh model m.
In the present embodiment, for convenient, calculate, by comparing the mean curvature on summit, judge delete which summit.The mean curvature k on summit mbe defined as the principal curvatures k on this summit 1and k 2mean value, i.e. k m=(k 1+ k 2)/2.
The principal curvatures k on summit 1and k 2computation process be prior art, do not repeat them here.Specifically can participate in Publication about Document: (1) N.Dyn, K.Hormann, S.Kim, D.Levin, Optimizing 3d triangulations using discrete curvature analysis, in:T.Lyche, L.L.Schumaker (Eds.), Mathematical Methods in CAGD:Oslo 2000, Vanderbilt University Press, Nashville, TN, 2001, pp.135 – 146.(2) B.Hamann, Curvature approximation for triangulated surfaces, Computing Supplements 8 (1993) 139 – 153.(3) D.S.Meek, D.J.Walton, On surface normal and Gaussian curvature approximations givendata sampled from a smooth surface, Computer Aided Geometric Design 17 (6) (2000) 521 – 543.
Calculating the principal curvatures k on summit 1and k 2after, can be according to k m=(k 1+ k 2)/2 calculate the mean curvature on this summit.
Step S2, the summit that all mean curvatures is less than to described mean curvature threshold value is defined as candidate vertices.
Because the larger summit of mean curvature value has represented the key character in grid model conventionally, therefore, in embodiments of the present invention, only have summit that mean curvature is less than mean curvature threshold value just as candidate vertices, follow-up processing procedure is all carried out based on determined candidate vertices.
In this step, mean curvature threshold value can be the constant setting in advance, for example 10.Now, if the curvature value on all summits that calculate between 5 to 15, determines that the summit of mean curvature value in 5 to 10 scopes is candidate vertices.
In addition, in different triangular mesh models, the span of the mean curvature on summit may be different, for example, the mean curvature on the summit of some triangular mesh models is between 5 to 15, and the mean curvature on the summit of some triangular mesh models is between 20 to 30.At this moment, adopt unified mean curvature threshold value cannot accurately determine candidate vertices.Therefore, in this step, can dynamically determine mean curvature threshold value, for example, according to the curvature fractile threshold parameter of user's input, determine.Such as, if user wish that protection at least 20% the summit that has remarkable visual signature is not processed and fall, can input parameter 80%.Now, if the set of the value of the mean curvature on all summits that calculate is A, the principle of mean curvature threshold value setting is: make in set A 80% mean curvature be less than described mean curvature threshold value.According to this principle, can calculate mean curvature threshold value.Because this mean curvature threshold value is to determine according to the dynamic state of parameters of user's input, so go for various triangular mesh models.
According to above scheme, can find out to only have summit that mean curvature is less than mean curvature threshold value just as candidate vertices, follow-up processing procedure is all carried out based on determined candidate vertices.Like this, the method that the embodiment of the present invention provides can produce the abnormal leg-of-mutton while avoiding, and further at utmost keeps the key character of original mesh model.
Corresponding above-mentioned method, the embodiment of the present invention has further proposed a kind for the treatment of apparatus of triangular mesh model, as shown in Figure 3.This device comprises:
Representative points determination module 31, for calculating the mean curvature on summit described in each, the summit that the mean curvature on two summits is all less than to default mean curvature threshold value is to being defined as candidate vertices pair; For candidate vertices pair described in each, determine the position of the representative points corresponding with it, described representative points be used for removing described candidate vertices to time replace described candidate vertices pair;
Cost computing module 32, for according to described representative points to all distances that have with the triangle surface on any summit of described candidate vertices centering, determine and remove the first cost that described candidate vertices is right; According to the shape facility with all triangle surfaces of described representative points, to determine and remove the second cost that described candidate vertices is right, described the second cost is to remove the second error that operation brings; According to described the first cost and described the second cost, determine and remove the cost that described candidate vertices is right;
Remove module 33, remove a candidate vertices pair of Least-cost, with the candidate vertices with being removed, corresponding representative points is replaced.
In addition, this device can further include: normalized module 34, and for each ratio of shape facility described in normalization, or, the mean value of each ratio of shape facility described in normalization.
The concrete function of above modules can, referring to embodiment of the method part, not repeat them here.
Another embodiment of the present invention further provides a kind for the treatment of apparatus of triangular mesh model, as shown in Figure 4.This device comprises: processor 41, storer 42, wherein, processor 41 and storer 42 communication connections, in storer 42, store machine readable instructions, described instruction is for making processor 41 carry out the step of the disposal route of above-mentioned triangular mesh model, wherein, the performed concrete operation steps of processor 41 is identical with the description of previous methods embodiment part with process, does not repeat them here.
Storer 42 can be floppy disk, hard disk, magneto-optic disk, CD (as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), tape, Nonvolatile memory card and ROM.
The foregoing is only preferred embodiment of the present invention, in order to limit the present invention, within the spirit and principles in the present invention not all, any modification of making, be equal to replacement, improvement etc., within all should being included in the scope of protection of the invention.

Claims (13)

1. the disposal route of a triangular mesh model, wherein, described triangular mesh model is comprised of summit and triangle surface, two summits on the same limit of triangle surface form a summit pair, the mean curvature on a summit reflects the curvature statistical nature of the actual object that described triangular net model is corresponding, the treating method comprises:
The mean curvature of calculating summit described in each, the summit that the mean curvature on two summits is all less than to default mean curvature threshold value is to being defined as candidate vertices pair;
For candidate vertices pair described in each, determine the position of the representative points corresponding with it, described representative points be used for removing described candidate vertices to time replace described candidate vertices pair;
According to described representative points, to all distances that have with the triangle surface on any summit of described candidate vertices centering, determine and remove the first cost that described candidate vertices is right;
According to the shape facility with all triangle surfaces of described representative points, determine and remove the second cost that described candidate vertices is right;
According to described the first cost and described the second cost, determine and remove the cost that described candidate vertices is right;
Remove a candidate vertices pair of Least-cost, with the candidate vertices with being removed, corresponding representative points is replaced.
2. method according to claim 1, is characterized in that, the shape facility of all triangle surfaces that described basis and representative points are associated is determined to remove this candidate vertices the second right cost comprises:
Determine that each has the shape facility of the triangle surface of described representative points; Wherein, described shape facility comprises following any one ratio:
The circumcircle of each triangle surface and the ratio of inscribe radius of a circle with described representative points;
There is the longest edge of each triangle surface of described representative points and the ratio of the length of side of minor face; Or
There is the maximum drift angle of each triangle surface of described representative points and the ratio of the angle of minimum drift angle.
Determine the mean value of the described shape facility of all triangle surfaces with described representative points;
According to the mean value of described shape facility, determine described the second cost.
3. method according to claim 1, is characterized in that, the shape facility of all triangle surfaces that described basis and representative points are associated is determined to remove this candidate vertices the second right cost comprises:
Determine that each has the shape facility of the triangle surface of described representative points; Wherein, described shape facility comprises following at least two ratios:
The circumcircle of each triangle surface and the ratio of inscribe radius of a circle with described representative points;
There is the longest edge of each triangle surface of described representative points and the ratio of the length of side of minor face; And
There is the maximum drift angle of each triangle surface of described representative points and the ratio of the angle of minimum drift angle.
Determine the mean value of each ratio of the described shape facility of all triangle surfaces with described representative points;
The mean value of described each ratio is weighted on average;
According to described result of weighted average, determine described the second cost.
4. method according to claim 3, is characterized in that, further comprises: each ratio of shape facility described in normalization, or, the mean value of each ratio of shape facility described in normalization.
5. method according to claim 1, is characterized in that, described according to described the first cost and described the second cost, determines to remove this candidate vertices right cost comprises:
Respectively described the first cost and the second cost are normalized;
According to described normalized the first cost and normalized the second cost, according to following formula, determine and remove the cost that this candidate vertices is right:
cost(v 1,v 2)=w 1cost′ 1(v 1,v 2)+w 2cost′ 2(v 1,v 2)
Wherein, (v 1, v 2) be candidate vertices pair, cost (v 1, v 2) representative remove candidate vertices to (v 1, v 2) cost, cost ' 1(v 1, v 2) represent normalized the first cost, cost ' 2(v 1, v 2) represent normalized the second cost, w 1and w 2for weight factor.
6. method according to claim 1, is characterized in that, described according to described the first cost and described the second cost, determines to remove this candidate vertices right cost comprises:
Described the second cost is normalized;
According to described the first cost and normalized the second cost, according to following formula, determine and remove the cost that this candidate vertices is right:
cost(v 1,v 2)=cost′ 2(v 1,v 2)×cost 1(v 1,v 2)
Wherein, (v 1, v 2) be candidate vertices pair, cost (v 1, v 2) representative removes the cost that this candidate vertices is right, cost 1(v 1, v 2) generation
Table the first cost, cost ' 2(v 1, v 2) represent normalized the second cost.
7. the treating apparatus of a triangular mesh model, wherein, described triangular mesh model is comprised of summit and triangle surface, two summits on the same limit of triangle surface form a summit pair, the mean curvature on summit reflects the curvature statistical nature of the actual object that described triangular net model is corresponding, it is characterized in that, this device comprises:
Representative points determination module, for calculating the mean curvature on summit described in each, the summit that the mean curvature on two summits is all less than to default mean curvature threshold value is to being defined as candidate vertices pair; For candidate vertices pair described in each, determine the position of the representative points corresponding with it, described representative points be used for removing described candidate vertices to time replace described candidate vertices pair;
Cost computing module, for according to described representative points to all distances that have with the triangle surface on any summit of described candidate vertices centering, determine and remove the first cost that described candidate vertices is right; According to the shape facility with all triangle surfaces of described representative points, determine and remove the second cost that described candidate vertices is right; According to described the first cost and described the second cost, determine and remove the cost that described candidate vertices is right;
Remove module, remove a candidate vertices pair of Least-cost, with the candidate vertices with being removed, corresponding representative points is replaced.
8. device according to claim 7, is characterized in that, described cost computing module is further used for,
Determine that each has the shape facility of the triangle surface of described representative points; Wherein, described shape facility comprises following any one ratio:
The circumcircle of each triangle surface and the ratio of inscribe radius of a circle with described representative points;
There is the longest edge of each triangle surface of described representative points and the ratio of the length of side of minor face; Or
There is the maximum drift angle of each triangle surface of described representative points and the ratio of the angle of minimum drift angle.
Determine the mean value of the described shape facility of all triangle surfaces with described representative points;
According to the mean value of described shape facility, determine described the second cost.
9. device according to claim 7, is characterized in that, described cost computing module is further used for,
Determine that each has the shape facility of the triangle surface of described representative points; Wherein, described shape facility comprises following at least two ratios:
The circumcircle of each triangle surface and the ratio of inscribe radius of a circle with described representative points;
There is the longest edge of each triangle surface of described representative points and the ratio of the length of side of minor face; And
There is the maximum drift angle of each triangle surface of described representative points and the ratio of the angle of minimum drift angle.
Determine the mean value of each ratio of the described shape facility of all triangle surfaces with described representative points;
The mean value of described each ratio is weighted on average;
According to described result of weighted average, determine described the second cost.
10. device according to claim 9, is characterized in that, further comprises:
Normalized module, for each ratio of shape facility described in normalization, or, the mean value of each ratio of shape facility described in normalization.
11. devices according to claim 7, is characterized in that, described cost computing module is further used for,
Respectively described the first cost and the second cost are normalized;
According to described normalized the first cost and normalized the second cost, according to following formula, determine and remove the cost that this candidate vertices is right:
cost(v 1,v 2)=w 1cost′ 1(v 1,v 2)+w 2cost′ 2(v 1,v 2)
Wherein, (v 1, v 2) be candidate vertices pair, cost (v 1, v 2) representative remove candidate vertices to (v 1, v 2) cost, cost ' 1(v 1, v 2) represent normalized the first cost, cost ' 2(v 1, v 2) represent normalized the second cost, w 1and w 2for weight factor.
12. devices according to claim 7, is characterized in that, described cost computing module is further used for,
Described the second cost is normalized;
According to described the first cost and normalized the second cost, according to following formula, determine and remove the cost that this candidate vertices is right:
cost(v 1,v 2)=cost′ 2(v 1,v 2)×cost 1(v 1,v 2)
Wherein, (v 1, v 2) be candidate vertices pair, cost (v 1, v 2) representative removes the cost that this candidate vertices is right, cost 1(v 1, v 2) represent the first cost, cost ' 2(v 1, v 2) represent normalized the second cost.
The treating apparatus of 13. 1 kinds of triangular mesh models, described triangular mesh model is comprised of summit and triangle surface, two summits that belong to the same limit of same triangle surface form a summit pair, it is characterized in that, described device comprises: processor and the storer being connected with described processor communication, in wherein said storer, store machine readable instructions, described processor is for the instruction of execute store, to execute claims the step of 1-6.
CN201210320745.7A 2012-08-31 2012-08-31 Processing method and device for triangle mesh model Pending CN103679814A (en)

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