CN103400372A - Three-dimensional topological information extraction method based on Reeb graph description - Google Patents
Three-dimensional topological information extraction method based on Reeb graph description Download PDFInfo
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Abstract
The invention provides a three-dimensional topological information extraction method based on Reeb graph description. The method comprises the steps of reading vertex and triangular facet information of an input grid file of a three-dimensional model, then respectively establishing point sequences and storing a corresponding triangular facet relationship; after the point sequences are obtained, marking a reference point according to certain rules, further establishing a virtual ground and calculating the geodesic distance of the vertex; establishing a Morse function according to the geodesic distance; and on the basis of the established Morse function, using a simplified triangle method to extract and obtain an initial Reeb graph and finally filtering redundant information in the initial Reeb graph to obtain a final Reeb graph to complete the extraction of the topological information of the three-dimensional model. The accompanying drawing in the abstract is a principle block diagram for the method. The method based on the topological description of the three-dimensional model has higher common applicability and the extraction result obtained by using the method is suitable for further application such as behavior analysis.
Description
Technical field
The present invention relates to computer graphics, graphical modeling, form fit field, particularly, the present invention relates to a kind of three-dimensional topology information extracting method of describing based on Reeb figure.
Background technology
Along with further developing of infotech, the object of information processing develops into the more abundant sufficient three-dimensional model of expression content from simple two dimensional model.Three-dimensional geometric information obtains by computer graphics and image processing techniques, it is a kind of mathematics reproduction to the raw data of the three-dimensional body of real world, and standard comparatively, but because its majority is only to the simple reproduction of master pattern, data volume is very huge, and redundant information is various, is unfavorable for further application, thereby to retrieval of identification, shape analysis and the application of three-dimensional model, computer animation, three-dimensional model etc., larger restriction is arranged.
The three-dimensional topology structural information can be accurately and the style characteristic of the description three-dimensional model of refining, and its distortion at model, simplification, curve reestablishing, shape analysis, Model Matching and retrieval, compression are transmitted and many fields such as three-dimensional animation are widely used and important effect.Along with the development of graphics, image processing techniques, describing method and the extraction algorithm thereof of topological structure more and more are subject to people's attention.
At present, axis (skeleton) method, Reeb figure method are to describe the main method of the topological structure of three-dimensional model.Axis (skeleton) method is expressed the topological structure feature of three-dimensional model from the skeleton angle of three-dimensional model.This type method can obtain extraction effect preferably under the higher condition of model resolution, responsive but its shortcoming is boundary noise, higher to the resolution requirement of model, the iterative computation complexity is high.
Reeb figure is another kind of very important three-dimensional topology information description method.The method is extracted the topological structure feature by some cluster functional value is identical and on same connected component.The computing method of Reeb figure mainly contain: the height function method, and according to surperficial contour lines creation Reeb figure, the method function definition is simple, convenience of calculation, but shortcoming is the link relation calculation of complex, the Reeb figure of gained is in outside model sometimes; Method of characteristic point, utilize mapping to obtain the Morse function, then finds key point, finally determines Reeb figure, and the method exists and connects dyscalculia, and the Reeb of gained figure also likely is in outside model.
Summary of the invention
Purpose of the present invention is intended to solve at least one of above-mentioned technological deficiency, particularly for topology information, extracts the accurate not problem of computation complexity topological structure high, that extract, has proposed a kind of three-dimensional topology information extracting method of describing based on Reeb figure.
For achieving the above object, the present invention proposes a kind of three-dimensional topology information extracting method of describing based on Reeb figure, comprise the steps:
Step (1), read the 3D grid information of target, set up the grid vertex sequence and store the triangular facet relation;
Step (2), demarcation source point, utilize the geodesic distance of dijkstra's algorithm computing grid summit to source point;
Step (3), utilize geodesic distance structure Morse function, with the Morse function normalization and calculate extreme point and saddle point;
Step (4), utilize the triangular facet relation of grid model, by the triangle short cut technique, extract and obtain Initial R eeb figure;
Step (5), Initial R eeb figure is carried out filtering, remove redundant information, obtain final Reeb figure, complete the topology information of objective is extracted.
Wherein, set up the grid vertex sequence and store the triangular facet relation, comprising the data structure of the summit of setting up grid, limit, triangular facet:
A), vertex data structure
Read the vertex information of grid file, the storage apex coordinate, and set up the vertex index sequence.
B), limit data structure
Read the triangular facet information of grid file, every limit of diabolo, the index of storage respective vertices, calculate the Euclidean distance on limit and store.
C), face data structure
Read the triangular facet information of grid file, the index on three summits of storage.
Wherein, demarcate source point, utilize the geodesic distance of dijkstra's algorithm computing grid summit to source point, specific as follows:
Comparability for unified geodesic distance, at first need to set up virtual standard geodetic source point, the selection of this geodetic source point has peak method, space length method farthest, choose suitable source point scaling method according to the difference of the aspect of model, the peak method is fit to as the upright vertical models such as human body, and space length solstics method is fit to the strip model of accumbency.Specific as follows:
A), peak method
Select the peak of three-dimensional model gridding as the benchmark source point, the peak system of selection is expressed as:
V
selected＝max{v
n(y)|n＝1,2,...,N}
V wherein
SelectedRepresent selecteed source point, max{} is maximizing, v
n(y) the y coordinate components on n summit of expression, N are the summit sum of triangular mesh.
B), space length solstics method
Select method as source point in farthest 2 of theorem in Euclid space distance, be expressed as:
V
selected＝max{||v
i-v
j||
2|i＝1,2,...,N;j＝1,2,...,N}
V wherein
SelectedRepresent selecteed source point, max{} is maximizing, || v
i-v
j|| the expression vertex v
iAnd v
jSpace length, i and will represent respectively summit numbering, N is the summit sum of triangular mesh.
After demarcating source point, the geodesic line of this source point is arrived on all summits of finding in triangular mesh, and then calculates geodesic distance.Utilize dijkstra algorithm to ask for the concrete grammar of geodesic distance as follows:
What dijkstra's algorithm solved is the shortest route problem of single source point, i.e. the non-directed graph G of a given cum rights and source point V, ask from V to G in other shortest path a little.In the processing procedure of triangular mesh, the weights between 2 are the Euclidean distance of point-to-point transmission.
Introduce an auxiliary vectorial E, each the component E[i in E] value be starting point v
0To terminal v
iThe length of current shortest path.E[i] original state formulate according to the following rules: if from v
0To v
iConnection is arranged, be defined as the weights of connection, otherwise be defined as infinite ∞.Suppose that S is the set of having tried to achieve the terminal of shortest path, next shortest path (terminal of establishing this path is z), be perhaps (v so
0, z), or middle point through S arrives the path of summit z.Concrete computation process is as follows:
1), set up an adjacency matrix arcs and be used for replacing weighted-graph G, matrix element arcs[i] [j] expression connection (v
i, v
j) weights,, if this connection does not exist, with infinite ∞, replace.Set up simultaneously a vertex set S who has found shortest path, its original state is empty set.Initially auxiliaryization is vectorial according to the formula following formula:
E[i]＝arcs[0][i]
2), select vertex v
iIf meet E[i]=arcs[0] [i] found a new shortest path, upgrade S.
3) if meet E[]+arcs[] [i]＜E[k], by formula E[k]=E[k]+arcs[] [k] revise from v
0V to the limit sets out
kShortest path.
4), repetitive operation 2), 3), until from v
0Start all to find to all shortest paths on all the other all summits.
Wherein, use geodesic distance structure Morse function, with the Morse function normalization and calculate extreme point and saddle point.Specific as follows:
The Morse function is a smooth function that is defined on flow pattern M, and this function does not have the key point of degenerating, and its non degenerate key point (extreme point and saddle point) is isolated denumerable.Morse can guarantee that the topological property of stream shape itself can not change in the leaching process of Reeb figure.Non degenerate key point basis as the calculating of giving a definition:
1), for popular M, define a scalar function f thereon, obtain figure R by this function, namely f:M → R, be 0 if summit p meets its gradient on function f, is referred to as a key point.
2) if summit p is a key point, and the second order local derviation right and wrong of the f functional value of this some correspondence are unusual, and this is nonsingular key point so.
Wherein, the described triangular facet relation of utilizing grid model obtains Initial R eeb figure by the extraction of triangle short cut technique specific as follows:
For each gore of the triangular mesh of three-dimensional model, the simplifying the operation of iteration.At first determine shrinkage direction by the Mores function size on summit, then according to the mutual relationship on Atria bar limit, shrinking calculation obtains the arc of Reeb figure, thereby completes leg-of-mutton simplifying the operation; The Reeb figure result that generates previously that affects of the follow-up leg-of-mutton meeting iteration that simplifies the operation, until all gores of grid were all carried out and were simplified the operation.Because leg-of-mutton limit certainty and other triangles in triangular mesh are shared, the triangle of new input processing may have the situation that some limits participated in simplifying the operation, and therefore need to carry out different simplifying the operation according to different situations.Specific as follows:
1) the unreduced triangle of input, judge that it has several limits processed;
2) number on the limit processed according to the input triangle, carry out different simplifying the operation;
3) repeat 1), 2) until all triangles be disposed.
After all triangles are all simplified, obtain initial Reeb figure.
Wherein,, there is redundant information in the described Initial R eeb figure that obtains that extracts by the triangle short cut technique, and the inadequate refining of its description to the target topological structure is accurate, this is carried out redundancy filtering, obtains the final expression of target three-dimensional topology information.
When there is not hole (perhaps ring) in the three-dimensional model of reality, and there is circulation time in Initial R eeb figure, should, with the circulation filtering, obtain the result of more refining.Concrete computation process is as follows:
(1) at first find the circulation arc.
(2) select the first point of the point of the geodesic distance minimum in the circulation arc as new arc, side ground is apart from the tail point of maximum point as new arc.
(3) former circulation arc weighted calculation is obtained new arc.
(4) redundancy first point and the tail point in the new arc of removal
When Morse functional value in three-dimensional grid model is identical and be in point on same connected component may correctly do not merged to same point the time, can form the redundancy arc, as follows to the detailed process of redundancy arc filtering:
(1) find the redundancy arc
(2) intersection point of two arcs of selecting to exist redundancy relationship is as first point or the tail point of new arc, and anti-to establish intersection point be n; In selection redundancy arc, the node of Morse functional value and n difference maximum is as tail point or the first point of new arc.
(3) former circulation arc weighted calculation is obtained new arc.
(4) redundancy first point and the tail point in the new arc of removal.
A), redundancy arc filtering
In the simplification process, the point that is in same connected component and is arranged in same level is in the process of simplifying, and the point that is in same connected component and is positioned at same level may not be mapped to same point, the redundancy arc at this moment just occurred, thereby need to carry out filtering to this Reeb figure, its computation process is as follows:
(1) select to have same endpoints and 2 nearer arcs of maximum space distance.
(2) select the first point of the first point of the less arc of geodesic distance as new arc.
(3) weighted calculation obtains new arc.
(4) some end points degree this moment in former arc become 2, need these node filterings.
B), circulation arc filtering
May there be the circulation arc in initial Reeb figure.It explains inadequate refining, need to carry out filtering to this arc.Concrete computation process is as follows:
(1) at first find the circulation arc.
(2) select the first point of the point of the side ground distance minimum in the circulation arc as new arc, the point of side ground distance maximum is as the tail point of new arc.
(3) former circulation arc weighted calculation is obtained new arc.
(4) filter out redundant node in new arc.
, by the filtering of two types, obtain final Reeb figure.
The present invention's advantage compared with prior art is: the such scheme that the present invention proposes, can guarantee that the Reeb figure of extraction is positioned at the grid model body, and the topology of target is described refining and accurate, and computation complexity is low.
Description of drawings
Fig. 1 is the FB(flow block) according to the three-dimensional topology information extraction based on Reeb figure description of the embodiment of the present invention;
Fig. 2 extracts according to the Reeb figure of the embodiment of the present invention schematic diagram that calculates;
Fig. 3 extracts the FB(flow block) of Reeb figure according to the triangle short cut technique of the embodiment of the present invention;
Fig. 4 is the redundancy filtering schematic diagram according to the embodiment of the present invention;
Fig. 5 extracts structure results according to the Reeb figure of the embodiment of the present invention.
Embodiment
Below describe embodiments of the invention in detail, the example of described embodiment is shown in the drawings, and wherein same or similar label represents same or similar element or the element with identical or similar functions from start to finish.Be exemplary below by the embodiment that is described with reference to the drawings, only be used for explaining the present invention, and can not be interpreted as limitation of the present invention.
As shown in Figure 1, the inventive method specific implementation step is as follows:
Step (1), read the 3D grid information of target, set up the grid vertex sequence and store the triangular facet relation;
Grid file is the important carrier of storage three-dimensional model gridding, the shape of description three-dimensional body that can be careful, but data volume is large, and redundant information is various, is unfavorable for further application.The OBJ grid file is a kind of standard format of storage three-dimensional model gridding, and the summit of memory model, face, normal, texture coordinate and material are used information.The present embodiment only uses summit and surface information.Vertex information is the volume coordinate on summit, and surface information is the index on three summits of gore.Read the 3D grid information of target, set up the grid vertex sequence and store the triangular facet relation, to the limit, limit, face data structure be as follows:
A), vertex data structure
Read the vertex information of grid file, the storage apex coordinate, and set up the vertex index sequence.
B), limit data structure
Read the triangular facet information of grid file, every limit of diabolo, the index of storage respective vertices, calculate the Euclidean distance on limit and store.
C), face data structure
Read the triangular facet information of grid file, the index on three summits of storage.
Step (2), demarcation source point, utilize the geodesic distance of dijkstra's algorithm computing grid summit to source point; Comparability for unified geodesic distance, at first need to set up virtual standard geodetic source point, the selection of this geodetic source point has peak method, space length method farthest, choose suitable source point scaling method according to the difference of the aspect of model, the peak method is fit to as the upright vertical models such as human body, and space length solstics method is fit to the strip model of accumbency.Specific as follows:
A), peak method
Select the peak of three-dimensional model gridding as the benchmark source point, the peak system of selection is expressed as:
V
selected＝max{v
n(y)|n＝1,2,...,N}
V wherein
SelectedRepresent selecteed source point, max{} is maximizing, v
n(y) the y coordinate components on n summit of expression, N are the summit sum of triangular mesh.
B), space length solstics method
Select method as source point in farthest 2 of theorem in Euclid space distance, be expressed as:
V
selected＝max{||v
i-v
j||
2|i＝1,2,...,N;j＝1,2,...,N}
V wherein
SelectedRepresent selecteed source point, max{} is maximizing, || v
i-v
j|| the expression vertex v
iAnd v
jSpace length, i and will represent respectively summit numbering, N is the summit sum of triangular mesh.
After demarcating source point, the geodesic line of this source point is arrived on all summits of finding in triangular mesh, and then calculates geodesic distance.Utilize dijkstra algorithm to ask for the concrete grammar of geodesic distance as follows:
What dijkstra's algorithm solved is the shortest route problem of single source point, i.e. the non-directed graph G of a given cum rights and source point V, ask from V to G in other shortest path a little.In the processing procedure of triangular mesh, the weights between 2 are the Euclidean distance of point-to-point transmission.
Introduce an auxiliary vectorial E, each the component E[i in E] value be starting point v
0Arrive the length of the current shortest path of terminal vi.E[i] original state formulate according to the following rules: if from v
0To v
iConnection is arranged, be defined as the weights of connection, otherwise be defined as infinite ∞.Suppose that S is the set of having tried to achieve the terminal of shortest path, next shortest path (terminal of establishing this path is z), be perhaps (v so
0, z), or middle point through S arrives the path of summit z.Concrete computation process is as follows:
1), set up an adjacency matrix arcs and be used for replacing weighted-graph G, matrix element arcs[i] [j] expression connection (v
i, v
j) weights,, if this connection does not exist, with infinite ∞, replace.Set up simultaneously a vertex set S who has found shortest path, its original state is empty set.Initially auxiliaryization is vectorial according to the formula following formula:
E[i]＝arcs[0][i]
2), select vertex v
iIf meet E[i]=arcs[0] [i] found a new shortest path, upgrade S.
3) if meet E[]+arcs[] [i]＜E[k], by formula E[k]=E[k]+arcs[] [k] revise from v
0V to the limit sets out
kShortest path.
4), repetitive operation 2), 3), until from v
0Start all to find to all shortest paths on all the other all summits.
Step (3), utilize geodesic distance structure Morse function, with the Morse function normalization and calculate extreme point and saddle point;
The Morse function is a smooth function that is defined on flow pattern M, and this function does not have the key point of degenerating, and its non degenerate key point (extreme point and saddle point) is isolated denumerable.Below provide a system definition of Morse function:
Suppose a smooth manifold M, have a smooth function, if it meets following condition:
(1) f is at the M Smooth;
(2) f is continuous;
(3) f does not have the critical point of degenerating, and have at the most can several degenerations critical point.
Claim that function f is the Morse function of smooth manifold M.
Morse can guarantee that the topological property of stream shape itself can not change in the leaching process of Reeb figure.
Non degenerate key point basis as the calculating of giving a definition:
1), for popular M, define a scalar function f thereon, obtain figure R by this function, namely f:M → R, be 0 if summit p meets its gradient on function f, is referred to as a key point.
2) if summit p is a key point, and the second order local derviation right and wrong of the f functional value of this some correspondence are unusual, and this is nonsingular key point so.
Step (4), utilize the triangular facet relation of grid model, by the triangle short cut technique, extract and obtain Initial R eeb figure.
The computation process of triangle short cut technique extraction Reeb figure as shown in Figure 2.Fig. 2 has described the concrete computation process that Reeb figure extracts, and the left side is grid data, and the right is the Reeb figure that generates.Grid data Mesh comprises summit, limit and surface information; The Reeb graph structure comprises node and arc, the volume coordinate information of the Reeb node of graph that the node storage calculates, and arc is comprised of a series of coordinate points, and the starting point of this series coordinate points and terminal are the nodes of Reeb figure.In (a) in Fig. 2, the n in Reeb figure
0, n
2, n
3By respective vertices v in M
0, v
2, v
3Generate.α in figure
0→ (e
1, e
4) expression arc α
0By limit e
1, e
4Calculate.In (b) in Fig. 2, newly input one in M by vertex v
1With two limit e
0, e
2The new triangle that forms, by v
1With α
0Weighted calculation obtains a new node n
1, its corresponding arc also changes, as shown in FIG., and arc α
0Can be subject to again limit e
0Impact, on the right of the Reeb of its generation figure as Fig. 2 (b) as shown in.
Fig. 3 has described the calculation process of triangle short cut technique extraction Reeb figure,, to all triangles of grid model, according to the processed state on input Atria bar limit, carries out different operations,, until simplify all triangles, generates initial Reeb figure:
1), the unreduced triangle of input, judge that it has several limits processed;
2), according to 0 limit, 1 limit, 2 limits and 3 different conditions that limit is processed, carry out different simplifying the operation;
3), repetition 1), 2) until all triangles simplification are complete.
Step (5), Initial R eeb figure is carried out filtering, remove redundant information, obtain final Reeb figure, complete the topology information of objective is extracted.Extract the Initial R eeb figure that obtains by the triangle short cut technique, may have redundant information, the inadequate refining of its description to the target topological structure is accurate, need to carry out redundancy filtering, obtains the final expression of target three-dimensional topology information.Specifically comprise the filtering of redundancy arc and the filtering of circulation arc.
A), redundancy arc filtering
In the simplification process, be in same connected component and be arranged in the process of the point of same level in simplification, the point that is in same connected component and is positioned at same level may not be mapped to same point, as shown in the left figure of Fig. 4 (a), at this moment the redundancy arc has just appearred, thereby need to carry out filtering to this Reeb figure, its computation process is as follows:
(1) select to have same endpoints and 2 nearer arcs of maximum space distance.
(2) select the first point of the first point of the less arc of geodesic distance as new arc.
(3) weighted calculation obtains new arc, as shown in Fig. 4 (a) middle graph.
(4) redundant node on the elimination arc, some end points degree this moment in former arc become 2, need these node filterings.Final structure is as shown in (a) the right figure in Fig. 4.
B), circulation arc filtering
May there be the circulation arc in initial Reeb figure, as shown in (b) the left figure in Fig. 4.It explains inadequate refining, need to carry out filtering to this arc.Concrete computation process is as follows:
(1) at first find the circulation arc.
(2) select the first point of the point of the side ground distance minimum in the circulation arc as new arc, the point of side ground distance maximum is as the tail point of new arc.
(3) weighted calculation obtains new arc, as shown in (b) middle graph in Fig. 4.
(4) redundant node on the elimination arc, some end points degree this moment in former arc become 2, need these node filterings.Final structure is as shown in (b) the right figure in Fig. 4.
The present invention only extracts topology information for the objective that obtains grid model, the Reeb figure that Fig. 5 has provided two models and used the present invention to extract.The Reeb figure that extraction obtains has kept the original topology information of model, shows that the present invention is a kind of effective topology information describing method; With respect to original grid data, the advantage such as it is little that Reeb figure has data volume, simple in structure, be convenient to the further application such as behavior identification, abnormal behaviour analysis.
Non-elaborated part of the present invention belongs to those skilled in the art's known technology.
Claims (6)
1. scheme the three-dimensional topology information extracting method of describing based on Reeb for one kind, it is characterized in that performing step is as follows:
Step 1, read the three-dimensional model gridding information of target, sets up top points, edges, faces data structure, and with the triangular facet relation of this top points, edges, faces data structure storage three-dimensional model gridding;
Step 2, demarcate source point, adopt the space length on limit as weight, utilize the triangular facet relation on the summit in the triangular facet relation of three-dimensional model gridding and use dijkstra's algorithm calculate the three-dimensional model gridding summit to the shortest path through other each points on model surface of source point as geodesic distance;
Step 3, utilize geodesic distance that step 2 obtains as the Morse functional value, carries out after normalization obtaining the Morse functional value on each summit;
Step 4, utilize Mores functional value and the triangular facet relation on each summit, by the triangle short cut technique, extracts and obtain Initial R eeb figure;
Step 5, carry out filtering to Initial R eeb figure, removes redundant information, obtains final Reeb figure, completes the topology information of objective is extracted.
2. a kind of three-dimensional topology information extracting method of describing based on Reeb figure as claimed in claim 1, it is characterized in that: described step 1 is implemented as follows:
A, vertex data structure
Read the vertex information of three-dimensional model gridding file, the storage apex coordinate, and set up the vertex index sequence;
B, limit data structure
Read the triangular facet information of three-dimensional model gridding file, every limit of diabolo, the index of storage respective vertices, calculate the Euclidean distance on limit and store;
C, face data structure
Read the triangular facet relation of three-dimensional model gridding file, the index on three summits of storage.
3. a kind of three-dimensional topology information extracting method of describing based on Reeb figure as claimed in claim 1, it is characterized in that: step 2 is demarcated source point, adopt the space length on limit as weight, utilize the triangular facet relation on the summit in the triangular facet relation of three-dimensional model gridding and use dijkstra's algorithm calculate the three-dimensional model gridding summit to the shortest path through other each points on model surface of source point as geodesic distance; Be implemented as follows:
(1) demarcate source point
The standard geodetic source point that model is virtual, the selection of this geodetic source point has peak method, space length method farthest, choose suitable source point scaling method according to the difference of the aspect of model, to vertical model such as the upright employing peak methods such as human body, strip model to accumbency adopts space length solstics method, and is specific as follows:
A, peak method
Select the peak of three-dimensional model gridding as the benchmark source point, the peak system of selection is expressed as:
V
selected＝max{v
n(y)|n＝1,2,...,N}
V wherein
SelectedRepresent selecteed source point, max{} is maximizing, v
n(y) the y coordinate components on n summit of expression, N are the summit sum of triangular mesh;
B, space length solstics method
Select method as source point in farthest 2 of theorem in Euclid space distance, be expressed as:
V
selected＝max{||v
i-v
j||
2|i＝1,2,...,N;j＝1,2,...,N}
V wherein
SelectedRepresent selecteed source point, max{} is maximizing, || v
i-v
j|| the expression vertex v
iAnd v
jSpace length, i and j will represent respectively that summit numbering, N are the summit sum of triangular mesh;
(2) after demarcating source point, adopt the space length on limit as weight, utilize the triangular facet relation on summit and use the geodesic distance of dijkstra's algorithm computing grid summit to source point, specific as follows:
After demarcating source point, find all summits in triangular mesh to the geodesic line of this source point, and then calculate geodesic distance, utilize dijkstra algorithm to ask for the concrete grammar of geodesic distance as follows:
For the shortest route problem of single source point, the non-directed graph G of a given cum rights and source point V, ask from V to G in other shortest path a little, in the processing procedure of triangular mesh, the weights between 2 are the Euclidean distance of point-to-point transmission;
Each component E[i in auxiliary vectorial E] value be starting point v
0To terminal v
iThe length of current shortest path, E[i] original state formulate according to the following rules: if from v
0To v
iConnection is arranged, be defined as the weights of connection, otherwise be defined as infinite ∞, suppose that S is the set of having tried to achieve the terminal of shortest path, next shortest path so, the terminal of establishing this path is z, is perhaps (v
0, z), or middle point through S arrives the path of summit z, concrete computation process is as follows:
A, set up an adjacency matrix arcs and be used for replacing weighted-graph G, matrix element arcs[i] [j] expression connects (v
i, v
j) weights,, if this connection does not exist, with infinite ∞, replace, set up simultaneously a vertex set S who has found shortest path, its original state is empty set, according to the initial auxiliaryization vector of formula following formula:
E[i]＝arcs[0][i]
B, selection vertex v
iIf meet E[i]=arcs[0] [i] found a new shortest path, upgrade S;
If C meets E[]+arcs[] [i]＜E[k], by formula E[k]=E[k]+arcs[] [k] revise from v
0V to the limit sets out
kShortest path;
D, repetitive operation B, C, until from v
0Start all to find to all shortest paths on all the other all summits.
4. a kind of three-dimensional topology information extracting method of describing based on Reeb figure as claimed in claim 1, is characterized in that: adopt the geodesic distance on summit as the morse functional value in step 3.
5. a kind of three-dimensional topology information extracting method of describing based on Reeb figure as claimed in claim 1, it is characterized in that: described step 4 is utilized Mores functional value and the triangular facet relation on each summit of model meshes, extract and obtain Initial R eeb figure by the triangle short cut technique, the specific implementation process is as follows:
(41) the unreduced triangle of input, judge that it has several limits processed;
(42) number on the limit processed according to the input triangle, carry out different simplifying the operation;
(43) repeating step (41), step (42), until all triangles are disposed, after all triangles are all simplified, namely obtain initial Reeb figure.
6. a kind of three-dimensional topology information extracting method of describing based on Reeb figure as claimed in claim 5, it is characterized in that: when described step 5 couple Initial R eeb figure carries out filtering, when there is not hole (perhaps ring) in the three-dimensional model gridding of reality, and there is circulation time in Initial R eeb figure, should be with the circulation filtering, obtain the result of more refining, concrete computation process is as follows:
(1) at first find the circulation arc.
(2) select the first point of the point of the geodesic distance minimum in the circulation arc as new arc, side ground is apart from the tail point of maximum point as new arc;
(3) former circulation arc weighted calculation is obtained new arc;
(4) redundancy first point and the tail point in the new arc of removal;
When Morse functional value in three-dimensional grid model is identical and be in point on same connected component may correctly do not merged to same point the time, can form the redundancy arc, as follows to the detailed process of redundancy arc filtering:
(1) find the redundancy arc;
(2) intersection point of two arcs of selecting to exist redundancy relationship is as first point or the tail point of new arc, and anti-to establish intersection point be n; In selection redundancy arc, the node of Morse functional value and n difference maximum is as tail point or the first point of new arc;
(3) former circulation arc weighted calculation is obtained new arc;
(4) redundancy first point and the tail point in the new arc of removal;
, by the filtering of two types, obtain final Reeb figure.
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