CN103400372B - A kind of three-dimensional topology information extracting method described based on Reeb figure - Google Patents
A kind of three-dimensional topology information extracting method described based on Reeb figure Download PDFInfo
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Abstract
The present invention proposes a kind of three-dimensional topology information extracting method described based on Reeb figure, the grid file to the threedimensional model of input, reads its summit and triangular facet information, sets up point sequence the most respectively and store corresponding triangular facet relation.After obtaining point sequence, according to certain regular reference-calibrating point, and then set up virtually and calculate the geodesic distance on summit；Morse function is set up according to geodesic distance.Using triangle short cut technique to extract on this basis and obtain initial Reeb figure, finally the figure filtering of Initial R eeb is removed redundancy and obtain final Reeb figure, thus complete the topology information to threedimensional model and extract, Figure of abstract is the theory diagram of the present invention.According to the present invention, the Turbo codes method of threedimensional model being had the most universal suitability, it extracts result and is suitable to the application further such as behavior analysis.
Description
Technical field
The present invention relates to computer graphics, graphical modeling, form fit field, specifically, the present invention relates to one
The three-dimensional topology information extracting method described based on Reeb figure.
Background technology
Along with the further development of information technology, the object of information processing is in simple two dimensional model develops into express
Hold more abundant sufficient threedimensional model.Three-dimensional geometric information is to be obtained by computer graphics and image processing techniques
, it is that a kind of mathematics of initial data of the three-dimensional body to real world reproduces, and more specification, but due to
Its majority is only to reproduce the simple of archetype, and data volume is very huge, and redundancy is various, further should be unfavorable for
With, thus to identification, shape analysis and the application of threedimensional model, computer animation, the retrieval etc. of threedimensional model, have
Bigger restriction.
Three dimensional topology information can the accurate style characteristic describing threedimensional model of refine, it is in the deformation of model, letter
Change, curve reestablishing, shape analysis, Model Matching have widely with retrieval, many fields such as transmission and three-dimensional animation of compressing
Application and important effect.Along with graphics, the development of image processing techniques, the description method of topological structure and extraction thereof
Algorithm is increasingly subject to people's attention.
At present, axis (skeleton) method, Reeb figure method are the main method of the topological structure describing threedimensional model.Axis (bone
Frame) method expresses the topological features of threedimensional model from the skeleton angle of threedimensional model.This type method is at model resolution relatively
Preferable extraction effect can be obtained under conditions of height, but its shortcoming is boundary noise sensitivity, the resolution requirement to model
Higher, iterative computation complexity is high.
Reeb figure is another kind of particularly important three-dimensional topology information description method.The method by by identical for functional value and
Point cluster on same connected component extracts topological features.The computational methods of Reeb figure mainly have: height function method, root
Scheming according to surface contour lines creation Reeb, the definition of the method function is simple, convenience of calculation, but a disadvantage is that link relation calculates multiple
It is miscellaneous, outside the Reeb figure of gained is sometimes in model body；Method of characteristic point, utilizes mapping to obtain Morse function, then looks for key
Point, finally determines that Reeb schemes, and the method exists and connects dyscalculia, and the Reeb figure of gained is also possible to be in outside model body.
Summary of the invention
The purpose of the present invention is intended at least solve one of above-mentioned technological deficiency, extracts especially for topology information and calculates complexity
The accurate not problem of the topological structure that degree is high, extract, it is proposed that a kind of three-dimensional topology information described based on Reeb figure carries
Access method.
For achieving the above object, the present invention proposes a kind of three-dimensional topology information extracting method described based on Reeb figure, bag
Include following steps:
Step (1), the three-dimensional grid information of reading target, set up grid vertex sequence and store triangular facet relation；
Step (2), demarcation source point, utilize dijkstra's algorithm to calculate the grid vertex geodesic distance to source point；
Step (3), geodesic distance is utilized to construct Morse function, by Morse function normalization and calculate extreme point and saddle point；
Step (4), utilize the triangular facet relation of grid model, extracted by triangle short cut technique and obtain Initial R eeb and scheme；
Step (5), Initial R eeb figure is filtered, removes redundancy, obtain final Reeb figure, complete three-dimensional
The topology information of target is extracted.
Wherein, set up grid vertex sequence and store triangular facet relation, including the data setting up the summit of grid, limit, triangular facet
Structure:
A), vertex data structure
Read the vertex information of grid file, store apex coordinate, and set up vertex index sequence.
B), limit data structure
Read the triangular facet information of grid file, each edge of diabolo, the index of storage respective vertices, calculate the European of limit
Distance also stores.
C), face data structure
Read the triangular facet information of grid file, the index on three summits of storage.
Wherein, demarcate source point, utilize dijkstra's algorithm to calculate the grid vertex geodesic distance to source point, specific as follows:
In order to unify the comparability of geodesic distance, it is necessary first to setting up virtual standard geodetic source point, the selection of this geodetic source point has
The farthest method of peak method, space length, chooses suitable source point scaling method according to the difference of the aspect of model, and peak method is suitable for
Such as vertical models such as upright human bodies, space length solstics method is suitable for the strip model of accumbency.Specific as follows:
A), peak method
The peak selecting three-dimensional model gridding is expressed as benchmark source point, peak system of selection:
Vselected=max{vn(y) | n=1,2 ..., N}
Wherein VselectedRepresenting selected source point, max{} is maximizing, vnY () represents the y-coordinate component on the n-th summit,
N is the summit sum of triangular mesh.
B), space length solstics method
Select theorem in Euclid space in farthest 2 one as the method for source point, be expressed as:
Vselected=max{ | | vi-vj||2| i=1,2 ..., N;J=1,2 ..., N}
Wherein VselectedRepresenting selected source point, max{} is maximizing, | | vi-vj| | represent vertex viAnd vjSpace away from
From, i with summit numbering will be represented respectively, N is the summit sum of triangular mesh.
After demarcating source point, find the geodesic curve to this source point of all summits in triangular mesh, and then calculate geodesic distance.Profit
The concrete grammar asking for geodesic distance with dijkstra algorithm is as follows:
What dijkstra's algorithm solved is the shortest route problem of single source point, i.e. gives the non-directed graph G and source point V of a cum rights,
In asking from V to G other shortest path a little.In the processing procedure of triangular mesh, the weights between 2 are two
Euclidean distance between point.
Introducing the vectorial E of an auxiliary, the value of each component E [i] in E is starting point v0To terminal viCurrent shortest path
Length.The original state of E [i] is formulated according to the following rules: if from v0To viThere is connection, be then defined as the weights connected, no
Then it is defined as infinite ∞.Assume that S is the set of the terminal having tried to achieve shortest path, then next shortest path (sets this road
The terminal in footpath is z), or is (v0, z), or centre through S point arrive summit z path.Specifically calculated
Journey is as follows:
1), setting up an adjacency matrix arcs for replacing weighted-graph G, matrix element arcs [i] [j] represents and connects (vi,vj)
Weights, if this connection does not exists, then replace with infinite ∞.Set up a vertex set having found shortest path simultaneously
Closing S, its original state is empty set.According to formula following formula initially auxiliary vector:
E [i]=arcs [0] [i]
2), vertex v is selectediIf meeting E [i]=arcs [0] [i], have found a new shortest path, updating S.
3) if meeting E []+arcs [] [i] ＜ E [k], then revise from v by formula E [k]=E [k]+arcs [] [k]0Set out vertex vk
Shortest path.
4), repetitive operation 2), 3), until from v0Start to all shortest paths on remaining all summit all to find.
Wherein, geodesic distance structure Morse function is used, by Morse function normalization and calculate extreme point and saddle point.Specifically
As follows:
The smooth function that Morse function is defined in flow pattern M, the key point that this function is not degenerated, and its non degenerate
Key point (extreme point and saddle point) is isolated denumerable.Morse can guarantee that the topological property extraction at Reeb figure of manifold itself
During will not change.Non degenerate key point is according to being defined below calculating:
1), for popular M, one scalar function f of definition, obtains figure R, i.e. f:M → R by this function thereon,
If it is 0 that summit p meets its gradient on function f, referred to as one key point.
2) if summit p is a key point, and the second order local derviation of f function value corresponding to this point is non-unusual, then should
Point is nonsingular key point.
Wherein, the described triangular facet relation utilizing grid model, extracted by triangle short cut technique and obtain Initial R eeb figure tool
Body is as follows:
For each gore of the triangular mesh of threedimensional model, the carrying out of iteration simplifies operation.First by the Mores on summit
Function size determines shrinkage direction, and then according to the mutual relation on Atria bar limit, shrinking calculation obtains the arc of Reeb figure,
Thus complete the simplification operation of a triangle；The Reeb figure that the impact simplifying operation meeting iteration of follow-up triangle above generates
As a result, until all gores of grid had performed to simplify operation.Limit certainty and triangular mesh due to triangle
In other trianglees share, the triangle of newly inputted process there may be some limits participated in simplify operation situation, because of
This needs to carry out different simplification operations according to different situations.Specific as follows:
1) unreduced triangle is inputted, it is judged that it has several limits processed；
2) according to the number on the processed limit of input triangle, different simplification operations is carried out；
3) repeat 1), 2) until all trianglees be disposed.
After all trianglees all simplify, obtain initial Reeb figure.
Wherein, described Initial R eeb obtained of being extracted by triangle short cut technique is schemed, and there is redundancy, and it is to target topology
The inadequate refine of description of structure is accurate, and this carries out redundancy filtering, obtains the final expression of target three-dimensional topology information.
When actual threedimensional model does not exist hole (or ring), and when Initial R eeb figure exists circulation, it should circulation is filtered
Remove, obtain the result of more refine.Concrete calculating process is as follows:
(1) circulation arc is first found.
(2) selecting the point circulating the geodesic distance minimum in arc as the first point of new arc, the point of ground, side distance maximum is as new arc
Tail point.
(3) former circulation arc weighted calculation is obtained new arc.
(4) the redundancy first point in new arc and tail point are removed
When in three-dimensional grid model, Morse functional value point that is identical and that be on same connected component may be correctly merged into
During same point, redundancy arc can be formed, as follows to the detailed process of redundancy arc filtering:
(1) redundancy arc is found
(2) select the intersection point that there are two arcs of redundancy relationship as the first point of new arc or tail point, anti-set intersection point as n；Select
The node that in redundancy arc, Morse functional value and n difference are maximum is as the tail point of new arc or first point.
(3) former circulation arc weighted calculation is obtained new arc.
(4) the redundancy first point in new arc and tail point are removed.
A), redundancy arc filtering
During simplification, it is in same connected component and is positioned at the point of same level during simplifying, being in same connection
Component and be positioned at the point of same level and may be not mapped to same point, has at this moment occurred as soon as redundancy arc, to this Reeb
Figure is filtered, and it is as follows that it calculates process:
(1) select that there are same endpoints and 2 nearer arcs of maximum space distance.
(2) first point of the arc that selection geodesic distance is less is as the first point of new arc.
(3) weighted calculation obtains new arc.
(4) some end points in former arc are now spent and are become 2, need to be filtered by these nodes.
B), circulation arc filtering
Initial Reeb figure there may be circulation arc.It states inadequate refine, needs to be filtered this arc.Specifically calculated
Journey is as follows:
(1) circulation arc is first found.
(2) ground, side in selection circulation arc is apart from the minimum first point as new arc of putting, and the point of ground, side distance maximum is as new arc
Tail point.
(3) former circulation arc weighted calculation is obtained new arc.
(4) redundant node in new arc is filtered out.
By two kinds of filtering, obtain final Reeb figure.
Present invention advantage compared with prior art is: the such scheme that the present invention proposes, and can guarantee that the Reeb figure position of extraction
In grid model body, accurate to the Turbo codes refine of target, and computation complexity is low.
Accompanying drawing explanation
Fig. 1 is the FB(flow block) of the three-dimensional topology information retrieval described based on Reeb figure according to the embodiment of the present invention；
Fig. 2 is that the Reeb figure according to the embodiment of the present invention extracts the schematic diagram calculated；
Fig. 3 is the FB(flow block) that the triangle short cut technique according to the embodiment of the present invention extracts Reeb figure；
Fig. 4 is the redundancy filtering schematic diagram according to the embodiment of the present invention；
Fig. 5 is that the Reeb figure according to the embodiment of the present invention extracts structure results.
Detailed description of the invention
Embodiments of the invention are described below in detail, and the example of described embodiment is shown in the drawings, the most from start to finish phase
Same or similar label represents same or similar element or has the element of same or like function.Below with reference to attached
The embodiment that figure describes is exemplary, is only used for explaining the present invention, and is not construed as limiting the claims.
As it is shown in figure 1, the inventive method to implement step as follows:
Step (1), the three-dimensional grid information of reading target, set up grid vertex sequence and store triangular facet relation；
Grid file is the important carrier of storage three-dimensional model gridding, it is possible to the careful shape describing three-dimensional body, but data
Amount is big, and redundancy is various, is unfavorable for applying further.OBJ grid file is a kind of reticle of storage three-dimensional model gridding
Formula, the storage summit of model, face, normal, texture coordinate and material use information.The present embodiment only uses summit and surface information.
Vertex information is the space coordinates on summit, and surface information is the index on three summits of gore.Read the three-dimensional grid information of target,
Set up grid vertex sequence and store triangular facet relation, obtaining pushing up points, edges, faces data structure as follows:
A), vertex data structure
Read the vertex information of grid file, store apex coordinate, and set up vertex index sequence.
B), limit data structure
Read the triangular facet information of grid file, each edge of diabolo, the index of storage respective vertices, calculate the European of limit
Distance also stores.
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 dijkstra's algorithm to calculate the grid vertex geodesic distance to source point；For unification
The comparability of geodesic distance, it is necessary first to setting up virtual standard geodetic source point, the selection of this geodetic source point has peak method, sky
The farthest method of spacing, chooses suitable source point scaling method according to the difference of the aspect of model, and peak method is suitable for such as upright human body
Etc. vertical model, space length solstics method is suitable for the strip model of accumbency.Specific as follows:
A), peak method
The peak selecting three-dimensional model gridding is expressed as benchmark source point, peak system of selection:
Vselected=max{vn(y) | n=1,2 ..., N}
Wherein VselectedRepresenting selected source point, max{} is maximizing, vnY () represents the y-coordinate component on the n-th summit,
N is the summit sum of triangular mesh.
B), space length solstics method
Select theorem in Euclid space in farthest 2 one as the method for source point, be expressed as:
Vselected=max{ | | vi-vj||2| i=1,2 ..., N;J=1,2 ..., N}
Wherein VselectedRepresenting selected source point, max{} is maximizing, | | vi-vj| | represent vertex viAnd vjSpace away from
From, i with summit numbering will be represented respectively, N is the summit sum of triangular mesh.
After demarcating source point, find the geodesic curve to this source point of all summits in triangular mesh, and then calculate geodesic distance.Profit
The concrete grammar asking for geodesic distance with dijkstra algorithm is as follows:
What dijkstra's algorithm solved is the shortest route problem of single source point, i.e. gives the non-directed graph G and source point V of a cum rights,
In asking from V to G other shortest path a little.In the processing procedure of triangular mesh, the weights between 2 are two
Euclidean distance between point.
Introducing the vectorial E of an auxiliary, the value of each component E [i] in E is starting point v0Current shortest path to terminal vi
The length in footpath.The original state of E [i] is formulated according to the following rules: if from v0To viThere is connection, be then defined as the weights connected,
Otherwise it is defined as infinite ∞.Assume that S is the set of the terminal having tried to achieve shortest path, then next shortest path (sets this
The terminal in path is z), or is (v0, z), or centre is through the path of the some arrival summit z of S.Specifically calculated
Journey is as follows:
1), setting up an adjacency matrix arcs for replacing weighted-graph G, matrix element arcs [i] [j] represents and connects (vi,vj)
Weights, if this connection does not exists, then replace with infinite ∞.Set up a vertex set having found shortest path simultaneously
Closing S, its original state is empty set.According to formula following formula initially auxiliary vector:
E [i]=arcs [0] [i]
2), vertex v is selectediIf meeting E [i]=arcs [0] [i], have found a new shortest path, updating S.
3) if meeting E []+arcs [] [i] ＜ E [k], then revise from v by formula E [k]=E [k]+arcs [] [k]0Set out vertex vk
Shortest path.
4), repetitive operation 2), 3), until from v0Start to all shortest paths on remaining all summit all to find.
Step (3), geodesic distance is utilized to construct Morse function, by Morse function normalization and calculate extreme point and saddle point；
The smooth function that Morse function is defined in flow pattern M, the key point that this function is not degenerated, and its non degenerate
Key point (extreme point and saddle point) is isolated denumerable.The system that Morse function is given below defines:
Assume smooth manifold M, there is a smooth function, if it meets following condition:
(1) f is at M Smooth；
(2) f is continuous print；
(3) critical point that f does not degenerate, and at most have can the critical point of several degenerations.
Then title function f is a Morse function of smooth manifold M.
Morse can guarantee that the topological property of manifold itself will not change during the extraction of Reeb figure.
Non degenerate key point is according to being defined below calculating:
1), for popular M, one scalar function f of definition, obtains figure R, i.e. f:M → R by this function thereon,
If it is 0 that summit p meets its gradient on function f, referred to as one key point.
2) if summit p is a key point, and the second order local derviation of f function value corresponding to this point is non-unusual, then should
Point is nonsingular key point.
Step (4), utilize the triangular facet relation of grid model, extracted by triangle short cut technique and obtain Initial R eeb and scheme.
Triangle short cut technique extracts the calculating process of Reeb figure as shown in Figure 2.Fig. 2 describes the concrete calculating that Reeb figure extracts
Process, the left side is grid data, and the right is the Reeb figure generated.Grid data Mesh comprises summit, limit and surface information；
Reeb graph structure comprises node and arc, and node stores the spatial coordinated information of calculated Reeb node of graph, and arc is to be by one
Row coordinate points forms, and the starting point of this series coordinate points and terminal are the nodes of Reeb figure.In (a) in Fig. 2, Reeb schemes
In n0、n2、n3It is by respective vertices v in M0、v2、v3Generate.α in figure0→(e1,e4) represent arc α0It is by limit
e1、e4It is calculated.In (b) in Fig. 2, in M newly inputted one by vertex v1With two limit e0、e2The new triangle of composition,
Then by v1With α0Weighted calculation obtains a new node n1, its corresponding arc also changes, as shown in FIG., and arc α0Meeting
Again by limit e0Impact, Reeb figure that it generates is as shown on the right of Fig. 2 (b).
Fig. 3 describes triangle short cut technique and extracts the calculation process of Reeb figure, and all trianglees to grid model, according to defeated
The processed state entering Atria bar limit carries out different operations, until simplifying all trianglees, generating initial Reeb and scheming:
1), unreduced triangle is inputted, it is judged that it has several limits processed；
2), according to the processed different conditions in 0 limit, 1 limit, 2 limits and 3 limits, different simplification operations is carried out；
3), repeat 1), 2) until all trianglees simplify complete.
Step (5), Initial R eeb figure is filtered, removes redundancy, obtain final Reeb figure, complete three-dimensional
The topology information of target is extracted.Extracted Initial R eeb obtained to scheme by triangle short cut technique, it is understood that there may be redundancy, its
The inadequate refine of description to target topology is accurate, needs to carry out redundancy filtering, obtains the final table of target three-dimensional topology information
Show.Specifically include the filtering of redundancy arc and circulation arc filtering.
A), redundancy arc filtering
During simplification, it is in same connected component and is positioned at the point of same level during simplifying, being in same connection
Component and be positioned at the point of same level and may be not mapped to same point, shown in figure as left in Fig. 4 (a), has at this moment occurred as soon as redundancy arc,
So that be filtered this Reeb figure, it is as follows that it calculates process:
(1) select that there are same endpoints and 2 nearer arcs of maximum space distance.
(2) first point of the arc that selection geodesic distance is less is as the first point of new arc.
(3) weighted calculation obtains new arc, as shown in Fig. 4 (a) middle graph.
(4) eliminating the redundant node on arc, some end points in former arc are now spent and are become 2, need to be filtered by these nodes.?
Shown in whole structure figure as right in (a) in Fig. 4.
B), circulation arc filtering
Initial Reeb figure there may be circulation arc, shown in figure as left in (b) in Fig. 4.It states inadequate refine, needs this
Arc is filtered.Concrete calculating process is as follows:
(1) circulation arc is first found.
(2) ground, side in selection circulation arc is apart from the minimum first point as new arc of putting, and the point of ground, side distance maximum is as new arc
Tail point.
(3) weighted calculation obtains new arc, as shown in (b) middle graph in Fig. 4.
(4) eliminating the redundant node on arc, some end points in former arc are now spent and are become 2, need to be filtered by these nodes.Finally
Structure figure as right in (b) in Fig. 4 shown in.
The present invention extracts topology information only for the objective obtaining grid model, and Fig. 5 gives two models and use
The Reeb figure that the present invention extracts.Extract the Reeb figure obtained and maintain the original topology information of model, show that the present invention is a kind of
Effective topology information describes method；Relative to original grid data, it is little that Reeb figure has data volume, and simple in construction etc. is excellent
Gesture, it is simple to the application further such as Activity recognition, Deviant Behavior analysis.
Non-elaborated part of the present invention belongs to the known technology of those skilled in the art.
Claims (4)
1. the three-dimensional topology information extracting method described based on Reeb figure, it is characterised in that realize step as follows:
Step 1, read target three-dimensional model gridding information, set up top points, edges, faces data structure, and with this summit, limit,
The triangular facet relation of face data structure storage three-dimensional model gridding；
Step 2, demarcates source point, uses the space length on limit as weight, utilizes in the triangular facet relation of three-dimensional model gridding
The triangular facet relation on summit and use dijkstra's algorithm calculate three-dimensional model gridding summit to source point on model surface its
The shortest path of his each point is as geodesic distance；
Step 3, utilizes the geodesic distance that step 2 obtains as Morse functional value, obtains each summit after being normalized
Morse functional value；
Step 4, is utilized Morse functional value and the triangular facet relation on each summit, is extracted by triangle short cut technique and obtain Initial R eeb
Figure；
Step 5, is filtered Initial R eeb figure, removes redundancy, obtains final Reeb figure, completes three-dimensional mesh
Target topology information is extracted；
Described step 4 utilizes Morse functional value and the triangular facet relation on each summit of model meshes, is extracted by triangle short cut technique
Obtain Initial R eeb figure, implement process as follows:
(41) unreduced triangle is inputted, it is judged that it has several limits processed；
(42) according to the number on the processed limit of input triangle, different simplification operations is carried out；
(43) repeat step (41), step (42) is disposed until all trianglees, after all trianglees all simplify,
I.e. obtain initial Reeb figure；
When Initial R eeb figure is filtered by described step 5, when actual three-dimensional model gridding does not exist hole or ring, and
When there is circulation in Initial R eeb figure, it should circulation filtered, obtain the result of more refine, concrete calculating process is as follows:
(1) circulation arc is first found；
(2) selecting the first point as new arc of putting of the geodesic distance minimum in circulation arc, the point of geodesic distance maximum is as new arc
Tail point；
(3) former circulation arc weighted calculation is obtained new arc；
(4) the redundancy first point in new arc and tail point are removed；
When in three-dimensional model gridding, Morse functional value point that is identical and that be on same connected component may be correctly merged into
During same point, redundancy arc can be formed, as follows to the detailed process of redundancy arc filtering:
(1) redundancy arc is found；
(2) select the intersection point that there are two arcs of redundancy relationship as the first point of new arc or tail point, anti-set intersection point as n；Select
The node that in redundancy arc, Morse functional value and n difference are maximum is as the tail point of new arc or first point；
(3) former circulation arc weighted calculation is obtained new arc；
(4) the redundancy first point in new arc and tail point are removed；
By two kinds of filtering, obtain final Reeb figure.
A kind of three-dimensional topology information extracting method described based on Reeb figure, it is characterised in that:
Described step 1 is implemented as follows:
A, vertex data structure
Read the vertex information of three-dimensional model gridding file, store apex coordinate, and set up vertex index sequence；
B, limit data structure
Read the triangular facet information of three-dimensional model gridding file, each edge of diabolo, the index of storage respective vertices, calculate
The Euclidean distance on limit also stores；
C, face data structure
Read the triangular facet relation of three-dimensional model gridding file, the index on three summits of storage.
A kind of three-dimensional topology information extracting method described based on Reeb figure, it is characterised in that:
Step 2 demarcates source point, uses the space length on limit as weight, utilizes summit in the triangular facet relation of three-dimensional model gridding
Triangular facet relation also uses dijkstra's algorithm to calculate three-dimensional model gridding summit other each points on model surface to source point
Shortest path as geodesic distance；It is implemented as follows:
(1) source point is demarcated
Initially setting up virtual standard geodetic source point, the selection of this geodetic source point has the farthest method of peak method, space length, according to
The difference of the aspect of model chooses suitable source point scaling method, and vertical model is used peak method, the strip mould to accumbency
Type uses space length solstics method, specific as follows:
A, peak method
The peak selecting three-dimensional model gridding is expressed as benchmark source point, peak system of selection:
Vselected=max{vn(y) | n=1,2 ..., N}
Wherein VselectedRepresenting selected source point, max{} is maximizing, vnY () represents the y-coordinate component on the n-th summit,
N is the summit sum of triangular mesh；
B, space length solstics method
Select theorem in Euclid space in farthest 2 one as the method for source point, be expressed as:
Vselected=max{ | | vi-vj||2| i=1,2 ..., N；J=1,2 ..., N}
Wherein VselectedRepresenting selected source point, max{} is maximizing, | | vi-vj| | represent vertex viAnd vjSpace away from
From, i and j represents summit numbering respectively, and N is the summit sum of triangular mesh；(2), after demarcating source point, the sky on limit is used
Between length as weight, utilize the triangular facet relation on summit and use dijkstra's algorithm to calculate the grid vertex geodetic to source point
Distance, specific as follows:
After demarcating source point, find the geodesic curve to this source point of all summits in triangular mesh, and then calculate geodesic distance, profit
The concrete grammar asking for geodesic distance with dijkstra algorithm is as follows:
For the shortest route problem of single source point, the non-directed graph G and source point V of a given cum rights, in asking from V to G its
He shortest path a little, in the processing procedure of triangular mesh, the weights between 2 are the Euclidean distance of point-to-point transmission；
Introducing an auxiliary vector E, the value of each component E [i] in E is starting point v0To terminal viCurrent shortest path
Length, the original state of E [i] formulates according to the following rules: if from v0To viThere is connection, be then defined as the weights connected, no
Then it is defined as infinite ∞, it is assumed that S is the set of the terminal having tried to achieve shortest path, then next shortest path, if this road
The terminal in footpath is z, or is (v0, z), or centre is through the path of the some arrival summit z of S, specifically calculates process
As follows:
A, setting up an adjacency matrix arcs for replacing weighted-graph G, matrix element arcs [i] [j] represents and connects (vi, vj)
Weights, if this connection does not exists, then replace with infinite ∞, set up a vertex set having found shortest path simultaneously
Closing S, its original state is empty set, initializes auxiliary vector according to the following formula:
E [i]=arcs [0] [i]
B, selection vertex viIf meeting E [i]=arcs [0] [i], have found a new shortest path, updating S；
If C meets E []+arcs [] [i] < E [k], then revise from v by formula E [k]=E [k]+arcs [] [k]0Set out vertex vk
Shortest path；D, repetitive operation B, C, until from v0Start to all shortest paths on remaining all summit all to find.
A kind of three-dimensional topology information extracting method described based on Reeb figure, it is characterised in that:
Step 3 use the geodesic distance on summit as Morse functional value.
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