CN103927783B - A kind of THREE DIMENSIONAL TRIANGULATION NET builds and fills out the figure segmentation method between hollowing out - Google Patents

Abstract

The present invention relates to a kind of THREE DIMENSIONAL TRIANGULATION NET and build the figure segmentation method filling out between hollowing out.The present invention cuts method direct construction THREE DIMENSIONAL TRIANGULATION NET based on figure, is considered as network forming problem optimizing labelling problem.First obtain initial land form scatterplot and reality landform scatterplot, after being merged, estimate each point normal vector；Scatterplot after being combined uses incremental inserting algorithm structure tetrahedron to decompose space, and we want the triangulation network obtained i.e. to be included in tetrahedron；Intersect each triangular facet area information in information and tetrahedron according to each discrete test is vectorial and tetrahedral, add weights in s t figure；Solve final surface with minimal cut maximum-flow algorithm, between i.e. obtaining filling out and hollowing out, each tetrahedron volume in space is added and i.e. obtains filling out the quantity of earth work dug.The method is without projecting to two dimensional surface, it is to avoid two-dimensional projection's method builds the deficiency of the triangulation network；Being calculated earthwork by tetrahedron, precision is higher.

Description

A kind of THREE DIMENSIONAL TRIANGULATION NET builds and fills out the figure segmentation method between hollowing out

Technical field

The invention belongs to field of three-dimension modeling, particularly relate to a kind of THREE DIMENSIONAL TRIANGULATION NET build fill out between hollowing out figure cut Method.

Background technology

In Geotechnical Engineering, relate generally to fill out hollow out between the measurement of the cubic metre of earth and stone.The measurement of the cubic metre of earth and stone, calculating are Quantities budget in engineering construction, establishment detail design and the important evidence of reasonable arrangement job site.Existing Cubic metre of earth and stone computational methods have the method for section, square mesh method and DTM method.

Method of section computational accuracy is relevant with the length of section spacing, and spacing is the least, and precision is the highest；Method of section meter Choosing of when calculating earthwork it is noted that transverse section, choosing of section has considerable influence to precision；But this side Method is computationally intensive, especially becomes apparent from the case of scope bigger required precision height.

The precision of square mesh method calculating earthwork depends on the size gathering packing density, simultaneously with grid Size is relevant, and grid is the least, and precision is the highest；It is suitable that some hypsography minor grades change mild place Use square mesh method.

DTM method can be well adapted for complicated irregular terrain profiles, it is thus possible to preferably express real terrain surface specifications, Sciagraphy is used to build initial land form TIN and real model TIN respectively；Fill with triangular prism method or Grid Method and open Designing a model and difference space between real model in excavation border, calculates earthwork afterwards.This side Method computational accuracy is high, but there is also some problems: when building TIN with sciagraphy, and different perspective planes builds TIN there are differences the TIN of mistake (even), precision is had considerable influence；Sciagraphy can not build more Complicated real model (there is overlap on perspective plane)；Triangular facet can be carried out when calculating volume by triangular prism method Decompose, precision is had considerable influence.

Summary of the invention

The technical problem to be solved is that providing a kind of THREE DIMENSIONAL TRIANGULATION NET to build the figure filling out between hollowing out cuts Method.With it, complicated Geotechnical Engineering can be built threedimensional model more accurately, higher to obtain The quantity of earth work of precision.

In order to achieve the above object, the present invention cuts method based on figure, is considered as network forming problem optimizing labelling problem.First First obtain initial land form scatterplot and reality landform scatterplot, after being merged, estimate each point normal vector；After being combined Scatterplot uses incremental inserting algorithm structure tetrahedron to decompose space, and we want the triangulation network obtained i.e. to wrap It is contained in tetrahedron；Each triangular facet area in information and tetrahedron is intersected according to each discrete test is vectorial and tetrahedral Information, adds weights in s-t figure；Final surface is solved with minimal cut-maximum-flow algorithm, between i.e. obtaining filling out and hollowing out, Each tetrahedron volume in space is added and i.e. obtains filling out the quantity of earth work dug.

Specifically, the inventive method comprises the steps:

(1) first obtain the real landform scatterplot filled out between hollowing out to be measured, measure scatterplot border cuts according to reality And the subdivision initial land form triangulation network obtains initial land form scatterplot；

(2) each discrete test vector is estimated after reality is measured scatterplot and the merging of initial land form scatterplot；

(3) the measurement scatterplot after being combined uses incremental inserting algorithm to build tetrahedron to filling out between excavation and filling hollows out Row decomposes；

(4) s-t figure is built, including normal vector energy term and triangle area energy term, according to each scatterplot normal direction Measure and intersect each triangular facet area information in information and tetrahedron with tetrahedral, add weights in s-t figure；

(5) final surface is solved with minimal cut-maximum-flow algorithm, between i.e. obtaining filling out and hollowing out, each by space Tetrahedron volume is added and i.e. obtains filling out the quantity of earth work dug.

The present invention builds the method for energy function: to fill out hollow out between carry out Delaunay Tetrahedron subdivision, will The tetrahedral dual graph of Delaunay (i.e. Voronoi diagram) is as the node of s-t figure and directed edge, and s-t schemes bag Include normal vector energy term and triangle area energy term.

Fill out and hollow out surface energy function E (S)=λ_normalE_normal(S)+λ_areaE_area(S)；

S digs spatial surface for filling out；

E_normal(S) it is the energy term of normal vector；

E_area(S) it is the energy term of triangle area；

λ_normalFor normal vector energy term weight；λ_areaFor area item energy term weight.

The present invention proposes to utilize normal vector to add the weights of s-t figure with the tetrahedral information that intersects.Utilize tetrahedron Summit P and shift value σ determine tetrahedron, add its t weights；The triangular facet intersected with normal vector correspond to s-t In directed edge, add limit weights；Last tetrahedron that normal vector passes adds s weights.

After proposition max-flow min-cut algorithm of the present invention re-flags the node in s-t figure, will be not by s and t The vertex ticks of labelling is t, retains between tetrahedron corresponding to t node be and fill out and hollow out.The inventive method is to envelope Close the scene Direct Three-dimensional triangulation network to build, it is not necessary to project to two dimensional surface, it is to avoid two-dimensional projection's method builds triangle The deficiency of net；Between direct construction goes out to fill out and hollows out, can show more intuitively and fill out the spatial dimension dug；By four sides Body calculates earthwork, it is to avoid the decomposition of DTM method intermediate cam shape, and precision is higher.

Accompanying drawing explanation

Fig. 1 is that reality measures scatterplot.1 is Measured Boundary point, and 2 is surface scatterplot, and 3 is features of terrain scatterplot.

Fig. 2 is encryption features of terrain scatterplot schematic diagram.1 for measuring scatterplot, and 2 is the point of encryption, and 3 is ground before encryption Shape feature scatterplot, 4 is features of terrain scatterplot after encryption.

Fig. 3 is for cutting out and encrypt original scatterplot schematic diagram according to Measured Boundary.1 is initial land form figure, and 2 for measuring limit Boundary, 3 is initial land form scatterplot.

After Fig. 4 is for merging reality scatterplot and initial land form scatterplot, estimate discrete test vector schematic diagram.1 is initial land form Scatterplot, 2 is that reality measures scatterplot, and 3 is discrete test vector.

Fig. 5 is that THREE DIMENSIONAL TRIANGULATION NET based on s-t figure rebuilds schematic diagram.1 is the triangular facet passed by normal vector, and 2 are Voronoi polyhedron, 3 is Delaunay tetrahedron, and 4 is the three-dimensional triangulation net surface rebuild, and 5 is normal vector Terminal, 6 is the normal vector of tetrahedron top, and 7 is tetrahedron top, and 8 is that tetrahedron top is anti-along normal vector Point after direction translation σ distance.

Fig. 6 hollows out a THREE DIMENSIONAL TRIANGULATION NET reconstruction flow chart for filling out.

Fig. 7 is that filling out of structure hollows out a schematic diagram.

Detailed description of the invention

The present invention is to cut the THREE DIMENSIONAL TRIANGULATION NET network construction method of method, techniqueflow based on Delaunay tetrahedron and figure As shown in Figure 6.Initial land form scatterplot and reality landform scatterplot is utilized space to be carried out Delaunay tetrahedron and divides Solving, summit and the directed edge of the tetrahedral dual graph of Delaunay (i.e. Voronoi diagram) correspond in s-t figure Summit and directed edge, vertex representation Delaunay tetrahedron, directed edge represent band directive triangular facet. The computational problem filled out between hollowing out is considered as energy function minimization problem by us, and energy function includes normal vector energy Item and triangle area energy term, add the weights of s-t figure according to normal information and triangle area information, Solution procedure is exactly to find the minimal cut of s-t figure, and the labelling tetrahedron of global optimization is s or t.

Based on principles above, embodiments of the present invention are described in detail with reference to the attached drawings.

1. obtain scatterplot data

The real surface in 1.1 pairs of certain regions measures, and obtains reality and measures scatterplot and Measured Boundary scatterplot, if There is Feature line in the side slope after excavation, obtains the measurement scatterplot of features of terrain, as shown in Figure 1.Obtain ground The purpose of shape pattern measurement scatterplot is to express threedimensional model more accurately, thus obtains and fill out excavation number more accurately Amount.

1.2 encryption landform pattern measurement points, make the average distance of adjacent landform pattern measurement point survey for reality surface / 3rd of amount point average distance, it is therefore an objective to recover the shape of landform more accurately, as shown in Figure 2.

The 1.3 subdivision initial land form triangulation networks, it is therefore an objective to less triangle can be more accurately close to measuring limit Boundary, projects to X/Y plane by Measured Boundary and the initial land form triangulation network, the triangulation network summit that will fall in border Take out, measure scatterplot as initial land form, as shown in Figure 3.Subdivision algorithm is the limit splitting each triangle, takes The midpoint of triangle edges is as cut-point, and finds triangle t1 and t2 at this place, limit, the coordinate of cut-point Have the meansigma methods on 4 summits altogether for triangle t1 and t2, such a triangle be divided into four less Triangle.

Reality is measured scatterplot and initial land form is measured and estimated each discrete test vector after scatterplot merges, such as Fig. 4 by 1.4 Shown in.To this end, for each some p in a cloud, obtain and its k the most close consecutive points, then pass through Least square is that these points calculate a part plan P.This plane can be expressed as follows:

$P(n,d)=\underset{(n,d)}{\arg \min }\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{(n\·p_i-d)}^2$

Wherein n is the normal vector of plane P, and d is the P distance to zero.

2. build Delaunay tetrahedron

Building the tetrahedral purpose of Delaunay is to decompose space, initial land form is measured scatterplot with existing Actual measured amount scatterplot takes incremental inserting algorithm to build Delaunay tetrahedron.The tetrahedral dual graph of Delaunay The summit of (i.e. Voronoi diagram) and directed edge correspond to summit and the directed edge of s-t figure.The summit table of s-t figure Show that tetrahedron, directed edge represent the directive triangular facet of band.

3. add the weights of s-t

3.1 add weights according to normal vector.S-t figure principle based on resurfacing is illustrated in Fig. 5, and black is real Heart round dot P represents tetrahedron top, and black dotted lines L is the normal vector n of solid black round dot P, and black is hollow Round dot P' is tetrahedron top move σ distance along the opposite direction of normal vector after point.The four sides at P' point place, location Body T', is connected it with the t end points in s-t figure and gives its t weights, according to said method adding all of t weights； Find the triangular facet T passed by normal vector along normal vector n from P point_iUntil the tetrahedron passed through is nothing Limit tetrahedron or be t tetrahedron, interpolation T_iThe weights of the directed edge of corresponding s-t figure；Normal vector n passes through Last tetrahedron T and s-t figure in s be connected, and give s weights, method is added all of successively Limit weights and s weights.

3.2 add weights according to triangle area.Calculate the area of each triangle in Delaunay tetrahedron, will It joins in directed edge corresponding in s-t figure as weights, calculates each triangle of Delaunay tetrahedron simultaneously The meansigma methods of area, joins in all of t weights as weights.

3.3 reasonable distribution λ_normalAnd λ_areaWeight, so far s-t figure structure completes.

4. solve between filling out and hollowing out

Max-flow min-cut algorithm is utilized to re-flag the state that in s-t figure, each summit is connected with s and t, through weight After new labelling, the summit not being connected with s and t is defined as t summit, and in such s-t figure, each summit is divided into two classes: S summit and t summit.We retain the Delaunay tetrahedron of t vertex correspondence, these retained tetrahedrons It is between filling out and hollowing out, as shown in Figure 7.Filling out earth excavation amount V is exactly each tetrahedron volume sum, earth volume It is calculated as follows:

$V=\underset{i\∈I}{\mathrm{\Σ}}{v}_i=\frac{1}{3}\underset{i\∈I}{\mathrm{\Σ}}{s}_i{h}_i$

I for fill out hollow out between tetrahedral set；

v_iIt it is a tetrahedral volume；

s_iFor tetrahedron base area；

h_iFor tetrahedral height.

Claims (3)

1. a THREE DIMENSIONAL TRIANGULATION NET builds and fills out the figure segmentation method between hollowing out, it is characterised in that comprise the steps:

(1) first obtain the real landform scatterplot filled out between hollowing out to be measured, measure scatterplot border cuts according to reality And the subdivision initial land form triangulation network obtains initial land form scatterplot；

(2) each discrete test vector is estimated after reality is measured scatterplot and the merging of initial land form scatterplot；

(3) measurement scatterplot after being combined use incremental inserting algorithm build tetrahedron to fill out hollow out between carry out point Solve；

(4) s-t figure is built, including normal vector energy term and triangle area energy term, Delaunay tetrahedron The summit of dual graph and directed edge correspond to the summit in s-t figure and directed edge, vertex representation Delaunay tetra- Face body, directed edge represents the directive triangular facet of band；

Utilize tetrahedron top P and shift value σ to determine tetrahedron, add its t weights；Intersect with normal vector Triangular facet correspond to the directed edge in s-t, adds limit weights；Last tetrahedron that normal vector passes adds S weights；

(5) final surface is solved with minimal cut-maximum-flow algorithm, between i.e. obtaining filling out and hollowing out, each by space Tetrahedron volume is added and i.e. obtains filling out the quantity of earth work dug.

2. the method for claim 1, it is characterised in that the method building energy function is: to space Carry out Delaunay Tetrahedron subdivision, tetrahedral for Delaunay dual graph as the node of s-t figure and is had Xiang Bian, s-t figure includes normal vector energy term and triangle area energy term；Fill out and hollow out a surface energy function E (S)=λ_normalE_normal(S)+λ_areaE_area(S), S digs spatial surface for filling out；E_normal(S) it is the energy of normal vector Quantifier；E_area(S) it is the energy term of triangle area；λ_normalFor normal vector energy term weight；λ_areaFor area Item energy term weight.

3. method as claimed in claim 1 or 2, it is characterised in that re-flag with max-flow min-cut algorithm After node in s-t figure, will be not t by the vertex ticks of s and t labelling, retain the tetrahedron that t node is corresponding It is between filling out and hollowing out.