CN106709969A - Partition-based Delaunay triangulated network growth algorithm - Google Patents
Partition-based Delaunay triangulated network growth algorithm Download PDFInfo
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Abstract
The invention discloses a partition-based Delaunay triangulated network growth algorithm. The algorithm comprises the following steps: determining a minimum rectangular bounding box of a discrete point set, determining average distances of discrete points in horizontal and vertical directions, determining a discrete point number scope in a rectangular ring, generating an initial rectangular ring, completing division of the discrete point minimum rectangular bounding box, performing initial network construction based on a rectangular ring set, completing network construction of all the discrete points, and optimizing a generated triangulated network. According to the invention, the data computation processing efficiency is high, the data processing process is objective and fair and is little affected by manual factors, at the same time, on one hand, the work efficiency of data computation work can be effectively improved, on the other hand, the calculation precision of the generation computation work of the Delaunay triangulated network can be effectively guaranteed, and the work efficiency and the reliability of generation of the Delaunay triangulated network are guaranteed.
Description
Technical field
The present invention be a kind of Delaunay triangulation network growth algorithm based on subregion, relate generally to network forming region division and
Gradually network forming based on subregion
Background technology
TIN (Triangulated irregular network) as in two dimensional surface domain it is any from
A kind of graphical representation means and analysis tool of scatterplot collection network forming, with geometry it is good, data structure is simple the characteristics of, and
And compared with regular grid it is stronger to irregular area data point distribution adaptability, therefore ground, finite element analysis etc. neck
Domain is widely used, and the key of use above is that triangulation and structure how are preferably carried out to discrete point
Net, Delaunay triangulation network causes that it is used in the generation of TIN because of the uniqueness and reasonability of its network forming.
With the extensive use of Delaunay Triangulation method, the algorithm has obtained the concern of numerous scholars in recent decades
And research, generating the triangulation network subdivision algorithms of many maturations, the algorithm of wherein main flow has the triangulation network to divide and rule algorithm, Incremental insertion
Algorithm, triangulation growth algorithm.
Divide and conquer builds subnet by the way that point set region recurrence is divided, and then carries out subnet and merges the final triangle of generation
Net, but the algorithm design higher of network forming efficiency is complicated and takes more internal memory in a recursive process, and incremental inserting algorithm is main
On the basis of the initial triangulation network is generated, the form for carrying out Incremental insertion builds the triangulation network, is realized simply with algorithm, in occupancy
The characteristics of depositing few, but as the triangle increased where judging insertion point of the triangulation network will occupy the substantial amounts of time, therefore
Network forming efficiency is not high.Triangulation growth algorithm is mainly based upon base side and finds the process for thirdly building the triangulation network, and divides and rules
Algorithm is simple compared to realizing, without carrying out the recursive generation of a large amount of subnets and merging, being compared with incremental algorithm has same
Shortcoming be exactly algorithm realize it is inefficient particularly when discrete point is more, it is necessary to devote a tremendous amount of time retrieval suitable
Thirdly.
In sum, in order to improve the operating efficiency of network forming operation and ensure the correctness of network forming, in the urgent need to exploitation one
Kind improved Delaunay triangulation network growth algorithm, with meet it is actually used the need for.Therefore carried out based on growth algorithm here
Network forming, and consider how to reduce and spend in the retrieval suitable time thirdly, with improve growth algorithm network forming efficiency simultaneously
Ensure the correctness of network forming.
The content of the invention
The invention aims to provide a kind of Delaunay triangulation network growth algorithm based on subregion.
To reach above-mentioned purpose, the present invention is implemented according to following technical scheme：
A kind of Delaunay triangulation network growth algorithm based on subregion, comprises the following steps：
The first step, the minimum rectangle bounding box for determining discrete point set, the n discrete point coordinate form that importing is collected is such as
The point data of p (x, y), stores in discrete point set, if horizontal direction is X-axis, level is to the right positive direction, and vertical direction is
Y-axis, is vertically upward positive direction, compare in discrete point set x coordinate a little be worth to minimax x respectively xmin、
xmax, while compare y-coordinate a little be worth to minimax y-coordinate value respectively ymin、ymax, according to xmin、xmax、ymin、
ymaxObtain four coordinate values of angle point of minimum rectangle bounding box, respectively a (xmin,ymin) in the lower left corner, b (xmax,ymax) on the right side
Upper angle, c (xmin,ymax) in the upper left corner, d (xmax,ymin) in the lower right corner；
Second step, discrete point is determined in average distance both horizontally and vertically, according to xminWith xmaxThe absolute value of difference
Obtain minimum rectangle bounding box length dx, y in the horizontal directionminWith ymaxDifference thoroughly deserve minimum rectangle encirclement
Box length dy in vertical direction, the product according to dx and dy obtains the area S of minimum rectangle bounding box, area and discrete points
The ratio of amount is worth to the average area occupied by each discrete point, and the length in the space that each point is occupied is obtained after extraction of square root, makees
It is the average distance d between any two points：If d is discrete point average distance ax in the horizontal direction, according to dx and
The ratio of dy, and discrete point average distance ax in the horizontal direction is calculated discrete point average departure in vertical direction
From ay：
3rd step, discrete points scope in straight-flanked ring is determined, if n discrete point is evenly distributed on a square area
It is interior, by being divided into for square area ruleRow andRow are that square area is made up of a series of small square,
A discrete point is included in each small square in the regular grid of generation, often row or each column are includedIndividual discrete point, the
The d obtained in two steps：Average distance between discrete point is each small foursquare side length, by the 1st row,Row, the 1st row, theThe union in the region where row is set to a straight-flanked ring i.e. outermost of regular grid, then the rectangle
Comprising about in ringIndividual discrete point, andThe adjacent small foursquare set in inside of small square where individual discrete point
In small foursquare quantity will be less than or equal toThen calculate successively from outside to inside small just in gathering with internal small square
The medium and small foursquare quantity of the square small square set in adjacent inside is the quantity of discrete point, inner most when n is even number
The medium and small foursquare quantity of small square set is that the quantity of discrete point is 4, the inner most small square set when n is odd number
Medium and small foursquare quantity is that the quantity of discrete point is 1, it is known that when line width col width is all a discrete point average distance, successively
The discrete points included in the small square set in inside for obtaining are up toFor n discrete point being randomly distributed
Minimum rectangle bounding box, if be equally divided intoRow andRow, internal small square is calculated according to method same above successively
The quantity of the quantity of the medium and small rectangle of shape set and the discrete point for being included, it is known that the distribution of discrete point will be greatly uneven, because
This is in order to ensure after dividing in the small rectangular set in inside that is calculated successively all comprising a number of discrete point, it is known that internal
Can only be at most distributed in the region that small rectangular set is occupiedIndividual discrete point, in just can guarantee that the small rectangular set in others inside
There is an an appropriate number of discrete point, therefore set and contain up in a union i.e. straight-flanked ring in the corresponding region of internal small rectangular setIndividual discrete point, the calculating of the Delaunay triangulation network growth algorithm time complexity based on subregion for convenience, by minimum
Discrete points are set to
4th step, generation initial rectangular ring, using minimum rectangle bounding box as initial rectangular ring external boundary, ax, ay make
It is step-length when external boundary is inside contracted generates inner boundary in the horizontal direction and the vertical direction, by four x coordinates of angle point of external boundary
Value inside contracts the step-length in a horizontal direction, and y-coordinate value inside contracts the step-length in a vertical direction, generates four angle points, four
Angle point constitutes the inner boundary of initial rectangular ring clockwise, according to four coordinate values of angle point of external boundary, compares and obtains external boundary
The x of minimum and maximum, y-coordinate value, respectively xextermin、xextermax、yextermin、yextermax, similarly obtain four angles of inner boundary
Minimax x, the y-coordinate value of point, respectively xinnermin、xinnermax、yinnermin、yinnermax, take in discrete point set a bit
P (x, y), if xextermin≤x<xinnerminOr xinnermax<x≤xextermax, and yinnermax≤y<yextermaxOr yextermin≤y<
yinnermin, then the point is illustrated in initial rectangular ring, all discrete points in traversal discrete point set repeat above discrete point and sit
Scale value deterministic process, obtains all discrete points in initial rectangular ring, if zoom factor k, between 0.25-2, k × ax makees
Step-length when being scaled for inner boundary on level is square, k × ay is used as step-length in vertical direction.If discrete points are less thanThen by the x coordinate value of four angle points of inner boundary inside contract a level it is square on step-length, y-coordinate value inside contracts a Vertical Square
Upward step-length, if discrete points are more thanTo then be put outside the x coordinate value of four angle points of inner boundary a level it is square on
Step-length, puts the step-length in a vertical direction outside y-coordinate value, after the inner boundary angular coordinate adjustment of initial rectangular ring, repeat with
It is upper judge all discrete points whether the process in initial rectangular ring, the points that include of initial rectangular ring are calculated, if the points exist
Minimal pointWith maximum number of pointsBetween, then it is eligible.If not in minimal pointWith maximum number of pointsBetween,
Then change the calculating process of initial rectangular ring inner boundary coordinate value according to more than, in the initial rectangular ring inner boundary angle point for having changed
Change the inner boundary coordinate value of initial rectangular ring on the basis of coordinate again, judge the point of the discrete point in initial rectangular ring
Number, repeats above procedure, until the points in initial rectangular ring are in minimal pointWith maximum number of pointsBetween, generation is just
Beginning straight-flanked ring, is loaded into straight-flanked ring set；
5th step, the division for completing discrete point minimum rectangle bounding box, the inner boundary of initial rectangular ring are set to next
The external boundary of the straight-flanked ring that will be generated, the first of the new straight-flanked ring is generated according to the process that straight-flanked ring inner boundary is generated in the 4th step
Whether beginning inner boundary, calculates the discrete points in current newly-generated straight-flanked ring, judge discrete points in minimal pointWith
Maximum number of pointsBetween, if not existing, according to circumstances repeat to change the calculating process of inner boundary coordinate in the 4th step, and judge
The points of the discrete point in the new straight-flanked ring, until the discrete point in newly-generated straight-flanked ring is counted in minimal pointWith
Maximum number of pointsBetween, newly-generated straight-flanked ring is loaded into straight-flanked ring set, according to initial rectangular ring, current newly-generated
Straight-flanked ring in points and discrete point set in points, calculate residue and be not loaded into points in straight-flanked ring, repeat more than
Straight-flanked ring generating process, so that the rectangle ring type for carrying out minimum rectangle bounding box from outside to inside is divided, when residue is not loaded into
Points in straight-flanked ring 3 withBetween when, the inner boundary of the straight-flanked ring that will be newly generated is used as next square that will be generated
The external boundary of shape ring, four angle points of inner boundary are center that the average value of four angle points of external boundary is rectangle where external boundary
Point, the point that all residues are not loaded into straight-flanked ring is loaded into the straight-flanked ring, and now minimum rectangle bounding box is divided and finished, will
The straight-flanked ring is loaded into straight-flanked ring set, and straight-flanked ring set generation is finished；
6th step, initial network forming is carried out based on straight-flanked ring set, according to the straight-flanked ring set that the 5th step is generated, by set
The maximum straight-flanked ring of index value is set to inner loop as initial network forming region, and the maximum straight-flanked ring of index value is inside
Time big straight-flanked ring of ring and index value, and be set to inner loop adjacent ring union as initially thirdly retrieving area, root
It is the central point of initial network forming area external boundary according to the angular coordinate of initial network forming area inner boundary, finds out the nearest point of distance center point
p1With range points p1Nearest point p2, respectively as the beginning and end of a line of the triangulation network, using the side as initial baseline
It is loaded into baseline set, initial baseline only stores index value of the beginning and end in discrete point set, according to initial baseline
The cosine value of the angle that each is put and initial baseline is constituted in initial thirdly retrieval area is calculated, the minimum point of cosine value is found out i.e.
The maximum point of angle thirdly, triangle is loaded into triangle sets as initial baseline, and newly-generated side is loaded into
In baseline set, index value of the left and right triangle on newly-generated side in triangle sets is recorded, if left triangle or right three
Angular temporary nothing is then set to -1, record triangle corresponding three while index value be three while index value in baseline set, according to
The other both sides of newly-generated triangle, repeat search procedure above thirdly, if this side is suitable thirdly in network forming area
New triangle is then generated in the corresponding straight-flanked ring of inner loop, triangle is loaded into triangle sets, the triangle of generation
The side of shape is loaded into baseline set, records index value of the corresponding left and right triangle in the side in triangle sets, if left three
Angular or right triangle wouldn't exist then be set to -1, while record triangle corresponding three while index value be three while in baseline set
Index value in conjunction, new three are not generated if being not thirdly suitably in the corresponding straight-flanked ring of inner loop in network forming area if this side
It is angular, the baseline is loaded into tentative baseline set, according to the baseline newly increased in baseline set, repeat generation triangle above
The process of shape, when the baseline amount in the baseline amount in baseline set and tentative baseline set is not further added by, initial network forming is complete
Into；
7th step, the network forming for completing all discrete points, the corresponding straight-flanked ring of adjacent ring of inner loop during by initial network forming
The inner loop of this network forming is set to, next adjacent ring of the corresponding straight-flanked ring of inner loop of this time network forming is set to this network forming
The adjacent ring of inner loop, inner loop as network forming area, the union of the adjacent ring of inner loop and inner loop as thirdly retrieving area,
It is suitable thirdly in thirdly retrieval area retrieval since the baseline in the tentative baseline set of initial network forming generation, repeat with
Upper network forming process, updates baseline set, after the baseline in tentative baseline set participates in network forming to be finished then newly-increased from this network forming
Plus baseline start to repeat above network forming process, generate new tentative baseline set, update baseline set, triangle sets, weight
Above procedure is answered so as to carry out network forming by ring from inside to outside, when index value of the corresponding straight-flanked ring of inner loop in straight-flanked ring set
Be 0, when the index value of the corresponding straight-flanked ring of adjacent ring of inner loop in straight-flanked ring set is 1, based on tentative baseline set and
In thirdly retrieval area retrieval, thirdly, whether direct construction network does not consider further that thirdly in network forming area baseline in baseline set,
Tentative baseline collection is not regenerated, and newly-generated triangle and baseline are loaded into baseline set and triangle sets respectively, when
Baseline in baseline set is not further added by, i.e., all discrete points have participated in network forming, and network forming is completed；
8th step, optimizes the triangulation network of generation, is all sides of the triangulation network according to the baseline set generated after the completion of network forming
Set, it is the baseline at 0 to take index value, is set to current basic line, obtains the index value of its corresponding left and right triangle i.e. with current
Baseline is index value of two triangles of common edge in triangle sets, if two index values are not -1, in triangle
The triangle at manipulative indexing value is found in shape set, the triangle of current left and right two is set to, is calculated and is worked as front left and right two three
The angle value at the angle that summit and current basic line outside angular middle current basic line are constituted, asks it and is not needed if more than 180 °
Optimize, otherwise two summits in two triangles of connection outside current basic line summit, generate new baseline, and it is and newborn
Two other summit outside into baseline summit respectively constitutes two new triangles, and by the corresponding index value of current basic line and
The index value of its corresponding left and right triangle is set to the index value of newly-generated baseline as its index value in baseline set
And the index value of the left and right triangle of newly-generated baseline, when the index value and current triangle corresponding three of the first two triangle
The index value on side is set to index value and new life of the two newly-generated index values of triangle as it in triangle sets
Into corresponding three side of two triangles index value, newly-generated baseline and triangle are then inserted into it in baseline respectively
At set index value corresponding with triangle sets, baseline and triangle original in gathering is substituted, repeat above procedure, until
All Baseline Surveys in baseline set are finished, and ultimately generate Delaunay triangulation network.
Further, in the described first step, the 3rd step, discrete points n is 3 -+∞.
Further, in described second step, area S and discrete points n according to discrete point set minimum rectangle bounding box
After being calculated the average distance d between any two points, average distance d is set to discrete point average distance ay in the Y direction, root
According to the length dy (difference of Y-coordinate) and width dx (difference of X-coordinate) ratio relation of Rectangular Bounding Volume, discrete point is calculated
Average distance ax in the X direction, above computing formula is as follows：
Further, the zoom factor k in the 4th described step is 0.25-2.
Further, the discrete points scope that each straight-flanked ring in the straight-flanked ring set that the 5th described step is obtained is included
ForThe discrete points scope that wherein the maximum straight-flanked ring of index value is included is
Further, in the 6th described step, the described formula for judging calculating cosine value when thirdly is：
Wherein ps(xs, ys)pe(xe, ye) it is respectively the beginning and end of baseboard, ptemp(xtemp, ytemp) wait to judge
Discrete point.
Data operation treatment effeciency of the present invention is high, data handling procedure objective and fair, be affected by human factors it is small, while one
Aspect can effectively improve the operating efficiency of data operation work, on the other hand can effectively ensure that Delaunay triangulation network is generated
The computational accuracy of operation, it is ensured that the operating efficiency and reliability of Delaunay triangulation network generation.
Brief description of the drawings
Describe the present invention in detail with reference to the accompanying drawings and detailed description
Fig. 1：Implementing procedure figure of the present invention；
Fig. 2：For algorithm realizes flow chart；
Fig. 3：Discrete point set subregion design sketch；
Fig. 4：It is different discrete point retrieval area network forming effect contrast figures；
Fig. 5：Gradually network forming design sketch；
Fig. 6：This algorithm and traditional algorithm network forming comparison diagram；
Fig. 7：This algorithm and traditional algorithm network forming time contrast table.
Specific embodiment
For technological means, creation characteristic, reached purpose and effect for making present invention realization are easy to understand, with reference to
Specific embodiment, is expanded on further the present invention.
A kind of Delaunay triangulation network growth algorithm based on subregion, comprises the following steps as shown in Fig. 1-7：
The first step, the minimum rectangle bounding box for determining discrete point set.The n discrete point coordinate form that importing is collected is such as
The point data of p (x, y), stores in discrete point set, if horizontal direction is X-axis, level is to the right positive direction, and vertical direction is
Y-axis, is vertically upward positive direction.Compare in discrete point set x coordinate a little be worth to minimax x respectively xmin、
xmax, while compare y-coordinate a little be worth to minimax y-coordinate value respectively ymin、ymax.According to xmin、xmax、ymin、
ymaxObtain four coordinate values of angle point of minimum rectangle bounding box, respectively a (xmin,ymin) in the lower left corner, b (xmax,ymax) on the right side
Upper angle, c (xmin,ymax) in the upper left corner, d (xmax,ymin) in the lower right corner.
Second step, determine discrete point in average distance both horizontally and vertically.According to xminWith xmaxThe absolute value of difference
Obtain minimum rectangle bounding box length dx, y in the horizontal directionminWith ymaxDifference thoroughly deserve minimum rectangle encirclement
Box length dy in vertical direction, the product according to dx and dy obtains the area S of minimum rectangle bounding box, area and discrete points
The ratio of amount is worth to the average area occupied by each discrete point, and the length in the space that each point is occupied is obtained after extraction of square root, makees
It is the average distance d between any two points：If d is discrete point average distance ax in the horizontal direction, according to dx
Discrete point in vertical direction average is calculated with the ratio of dy, and discrete point average distance ax in the horizontal direction
Apart from ay：
3rd step, determine discrete points scope in straight-flanked ring.If n discrete point is evenly distributed on a square area
It is interior, by being divided into for square area ruleRow andRow are that square area is made up of a series of small square,
A discrete point is included in each small square in the regular grid of generation, often row or each column are includedIndividual discrete point, the
The d obtained in two steps：Average distance between discrete point is each small foursquare side length.By the 1st row,Row, the 1st row, theThe union in the region where row is set to a straight-flanked ring i.e. outermost of regular grid, then the rectangle
Comprising about in ringIndividual discrete point, andThe adjacent small foursquare set in inside of small square where individual discrete point
In small foursquare quantity will be less than or equal toThen calculate successively from outside to inside small just in gathering with internal small square
The medium and small foursquare quantity of the square small square set in adjacent inside is the quantity of discrete point, inner most when n is even number
The medium and small foursquare quantity of small square set is that the quantity of discrete point is 4, the inner most small square set when n is odd number
Medium and small foursquare quantity is that the quantity of discrete point is 1.Understand when line width col width is all a discrete point average distance, successively
The discrete points included in the small square set in inside for obtaining are up toFor n discrete point being randomly distributed
Minimum rectangle bounding box, if be equally divided intoRow andRow, internal small square is calculated according to method same above successively
The quantity of the medium and small rectangle of shape set and the discrete point that is included quantity (in some small rectangles will not comprising discrete point or comprising
Multiple discrete points), it is known that the distribution of discrete point will be greatly uneven, therefore in order to ensure divide after be calculated successively in
A number of discrete point is all included in the small rectangular set in portion, it is known that can only at most divide in the region that internal small rectangular set is occupied
ClothIndividual discrete point, just can guarantee that in the small rectangular set in others inside there is an appropriate number of discrete point.Therefore set internal small
The union in the corresponding region of rectangular set is to contain up in a straight-flanked ringIndividual discrete point, for convenience based on subregion
The calculating of Delaunay triangulation network growth algorithm time complexity, the union by the corresponding region of internal small rectangular set is one
The smallest discrete points included in straight-flanked ring are set to
4th step, generation initial rectangular ring.Using minimum rectangle bounding box as initial rectangular ring external boundary, ax, ay make
It is step-length when external boundary is inside contracted generates inner boundary in the horizontal direction and the vertical direction.By four x coordinates of angle point of external boundary
Value inside contracts the step-length in a horizontal direction, and y-coordinate value inside contracts the step-length in a vertical direction, generates four angle points, four
Angle point constitutes the inner boundary of initial rectangular ring clockwise.According to four coordinate values of angle point of external boundary, compare and obtain external boundary
The x of minimum and maximum, y-coordinate value, respectively xextermin、xextermax、yextermin、yextermax, similarly obtain four angles of inner boundary
Minimax x, the y-coordinate value of point, respectively xinnermin、xinnermax、yinnermin、yinnermax.Take in discrete point set a bit
P (x, y), if xextermin≤x<xinnerminOr xinnermax<x≤xextermax, and yinnermax≤y<yextermaxOr yextermin≤y<
yinnermin, then the point is illustrated in initial rectangular ring, all discrete points in traversal discrete point set repeat above discrete point and sit
Scale value deterministic process, obtains all discrete points in initial rectangular ring.If zoom factor k, between 0.25-2, k × ax makees
Step-length when being scaled for inner boundary on level is square, k × ay is used as step-length in vertical direction.If discrete points are less thanThen by the x coordinate value of four angle points of inner boundary inside contract a level it is square on step-length, y-coordinate value inside contracts a Vertical Square
Upward step-length.If discrete points are more thanTo then be put outside the x coordinate value of four angle points of inner boundary a level it is square on
Step-length, puts the step-length in a vertical direction outside y-coordinate value.Initial rectangular ring inner boundary angular coordinate adjustment after, repeat with
It is upper judge all discrete points whether the process in initial rectangular ring, the points that include of initial rectangular ring are calculated, if the points exist
Minimal pointWith maximum number of pointsBetween, then it is eligible.If not in minimal pointWith maximum number of pointsIt
Between, then change the calculating process of initial rectangular ring inner boundary coordinate value according to more than, in the initial rectangular ring inner boundary for having changed
Change the inner boundary coordinate value of initial rectangular ring on the basis of angular coordinate again, judge discrete point in initial rectangular ring
Points, repeat above procedure, until the points in initial rectangular ring are in minimal pointWith maximum number of pointsBetween, generation
Initial rectangular ring, is loaded into straight-flanked ring set.
5th step, on the basis of initial rectangular ring complete discrete point minimum rectangle bounding box division.By initial rectangular
The inner boundary of ring is set to the external boundary of next straight-flanked ring that will be generated, according to the mistake that straight-flanked ring inner boundary is generated in the 4th step
The initial inner boundary of the Cheng Shengcheng new straight-flanked rings.The discrete points in current newly-generated straight-flanked ring are calculated, discrete point is judged
Whether number is in minimal pointAnd maximum number of pointsBetween, if not existing, according to circumstances repeat to change inner boundary in the 4th step
The calculating process of coordinate, and judge the points of discrete point in the new straight-flanked ring, until discrete in newly-generated straight-flanked ring
Point points are in minimal pointAnd maximum number of pointsBetween, newly-generated straight-flanked ring is loaded into straight-flanked ring set.According to
The points in points and discrete point set in initial rectangular ring, current newly-generated straight-flanked ring, calculate residue and are not loaded into square
Points in shape ring, repeat above straight-flanked ring generating process, so that the straight-flanked ring for carrying out minimum rectangle bounding box from outside to inside
Formula is divided.When residue be not loaded into points in straight-flanked ring 3 withBetween when, the inner boundary of the straight-flanked ring that will be newly generated
Used as the external boundary of next straight-flanked ring that will be generated, four angle points of inner boundary are for the average value of four angle points of external boundary
The central point of rectangle where external boundary, the point that all residues are not loaded into straight-flanked ring is loaded into the straight-flanked ring, now minimum
Rectangular Bounding Volume is divided and finished, and the straight-flanked ring is loaded into straight-flanked ring set, and straight-flanked ring set generation is finished.
6th step, initial network forming is carried out based on straight-flanked ring set.According to the straight-flanked ring set that the 5th step is generated, by set
Used as initial network forming region (being set to inner loop), the maximum straight-flanked ring of index value is inner loop and rope to the maximum straight-flanked ring of index value
Draw the union of time big straight-flanked ring (being set to the adjacent ring of inner loop) of value as initially thirdly retrieving area.According to initial network forming area
The angular coordinate of inner boundary is the central point of initial network forming area external boundary, finds out the nearest point p of distance center point1With range points p1
Nearest point p2, respectively as the beginning and end of a line of the triangulation network, the side is loaded into baseline as initial baseline
In set, initial baseline only stores index value of the beginning and end in discrete point set.Initial the is calculated according to initial baseline
The cosine value of the angle that each point is constituted with initial baseline in three point retrieval areas, finds out the i.e. angle maximum of the minimum point of cosine value
Point thirdly, triangle is loaded into triangle sets as initial baseline, and newly-generated side is loaded into baseline set,
Index value of the left and right triangle on newly-generated side in triangle sets is recorded, is temporarily set without if if left triangle or right triangle
Be -1, record triangle corresponding three while index value be three while index value in baseline set.According to newly-generated triangle
The other both sides of shape, repeat search procedure above thirdly, if it is thirdly inner loop correspondence in network forming area that this side is suitable
Straight-flanked ring in then generate new triangle, triangle is loaded into triangle sets, the side of the triangle of generation is loaded into
In baseline set, index value of the corresponding left and right triangle in the side in triangle sets is recorded, if left triangle or right triangle
Shape wouldn't exist and then be set to -1, at the same record triangle corresponding three while index value be three while index in baseline set
Value, does not generate new triangle, by this if being not thirdly suitably in the corresponding straight-flanked ring of inner loop in network forming area if this side
Baseline is loaded into tentative baseline set.According to the baseline newly increased in baseline set, repeat to generate the process of triangle above,
When the baseline amount in the baseline amount in baseline set and tentative baseline set is not further added by, initial network forming is completed.
7th step, on the basis of initial network forming completion, complete the network forming of all discrete points.Inside during by initial network forming
The corresponding straight-flanked ring of adjacent ring of ring is set to the inner loop of this network forming, this time network forming the corresponding straight-flanked ring of inner loop it is next
Individual adjacent ring is set to the adjacent ring of the inner loop of this network forming, inner loop as network forming area, the adjacent ring of inner loop and inner loop
Union as thirdly retrieving area.Area is thirdly being retrieved since the baseline in the tentative baseline set of initial network forming generation
Retrieval is suitable thirdly, repeats above network forming process, updates baseline set, when the baseline in tentative baseline set participates in network forming
After finishing, then above network forming process is repeated since the baseline that this network forming is newly increased, generate new tentative baseline set, updated
Baseline set, triangle sets.Above procedure is repeated so as to carry out network forming by ring from inside to outside, when the corresponding straight-flanked ring of inner loop
Index value in straight-flanked ring set is 0, and the index value of the corresponding straight-flanked ring of adjacent ring of inner loop in straight-flanked ring set is 1
When, based on the baseline in tentative baseline set and baseline set, in thirdly retrieval area retrieval, thirdly, direct construction network is no longer examined
Consider thirdly whether in network forming area, tentative baseline collection is not regenerated, newly-generated triangle and baseline are loaded into baseline respectively
In set and triangle sets.When the baseline in baseline set is not further added by, i.e., all discrete points have participated in network forming, and network forming is complete
Into.
8th step, optimizes the triangulation network of generation.Baseline set according to being generated after the completion of network forming is all sides of the triangulation network
Set, it is the baseline at 0 to take index value, is set to current basic line, obtains the index value of its corresponding left and right triangle i.e. with current
Baseline is index value of two triangles of common edge in triangle sets, if two index values are not -1, in triangle
The triangle at manipulative indexing value is found in shape set, the triangle of current left and right two is set to.Calculate and work as front left and right two three
The angle value at the angle that summit and current basic line outside angular middle current basic line are constituted, asks it and is not needed if more than 180 °
Optimize, otherwise two summits in two triangles of connection outside current basic line summit, generate new baseline, and it is and newborn
Two other summit outside into baseline summit respectively constitutes two new triangles, and by the corresponding index value of current basic line and
The index value of its corresponding left and right triangle is set to the index value of newly-generated baseline as its index value in baseline set
And the index value of the left and right triangle of newly-generated baseline, when the index value and current triangle corresponding three of the first two triangle
The index value on side is set to index value and new life of the two newly-generated index values of triangle as it in triangle sets
Into corresponding three side of two triangles index value, newly-generated baseline and triangle are then inserted into it in baseline respectively
At set index value corresponding with triangle sets, baseline and triangle original in gathering is substituted, repeat above procedure, until
All Baseline Surveys in baseline set are finished, and ultimately generate Delaunay triangulation network.
In the present embodiment, in the described first step, the 3rd step, discrete points n is 3 -+∞.
In the present embodiment, in described second step, according to the area S and discrete points of discrete point set minimum rectangle bounding box
After n is calculated the average distance d between any two points, average distance d is set to discrete point average distance ay in the Y direction,
Length dy (difference of Y-coordinate) and width dx (difference of X-coordinate) ratio relation according to Rectangular Bounding Volume, are calculated discrete
Point average distance ax in the X direction, above computing formula is as follows：
In the present embodiment, the zoom factor k in the 4th described step is 0.25-2.
In the present embodiment, the discrete points model that each straight-flanked ring in the straight-flanked ring set that the 5th described step is obtained is included
Enclose forThe discrete points scope that wherein the maximum straight-flanked ring of index value is included is
In the present embodiment, in the 6th described step, the described formula for judging calculating cosine value when thirdly is：Wherein
ps(xs, ys)pe(xe, ye) it is respectively the beginning and end of baseboard, ptemp(xtemp, ytemp) it is discrete point to be judged.
Data operation treatment effeciency of the present invention is high, data handling procedure objective and fair, be affected by human factors it is small, while one
Aspect can effectively improve the operating efficiency of data operation work, on the other hand can effectively ensure that Delaunay triangulation network is generated
The computational accuracy of operation, it is ensured that the operating efficiency and reliability of Delaunay triangulation network generation.
It should be understood by those skilled in the art that, the present invention is not limited to the above embodiments, above-described embodiment and explanation
Merely illustrating the principles of the invention described in book, without departing from the spirit and scope of the present invention, the present invention also has
Various changes and modifications, these changes and improvements all fall within the protetion scope of the claimed invention.The claimed scope of the invention
By appending claims and its equivalent thereof.
Claims (6)
1. a kind of Delaunay triangulation network growth algorithm based on subregion, it is characterised in that described based on subregion
Delaunay triangulation network growth algorithm comprises the following steps：
The first step, the minimum rectangle bounding box for determining discrete point set, importing collect n discrete point coordinate form such as p (x,
Y) point data, stores in discrete point set, if horizontal direction is X-axis, level is to the right positive direction, and vertical direction is Y-axis,
Be vertically upward positive direction, compare in discrete point set x coordinate a little be worth to minimax x respectively xmin、xmax, together
When compare y-coordinate a little be worth to minimax y-coordinate value respectively ymin、ymax, according to xmin、xmax、ymin、ymaxObtain
Four coordinate values of angle point of minimum rectangle bounding box, respectively a (xmin,ymin) in the lower left corner, b (xmax,ymax) in the upper right corner, c
(xmin,ymax) in the upper left corner, d (xmax,ymin) in the lower right corner；
Second step, discrete point is determined in average distance both horizontally and vertically, according to xminWith xmaxDifference thoroughly deserves
Minimum rectangle bounding box length dx, y in the horizontal directionminWith ymaxThe minimum rectangle bounding box that thoroughly deserves of difference exist
Length dy in vertical direction, the product according to dx and dy obtains the area S of minimum rectangle bounding box, area and discrete point quantity
Than the average area being worth to occupied by each discrete point, the length in the space that each point is occupied is obtained after extraction of square root, as appointing
The average distance d anticipated between 2 points：If d is discrete point average distance ax in the horizontal direction, according to dx's and dy
Ratio, and discrete point average distance ax in the horizontal direction is calculated discrete point average distance in vertical direction
ay：
3rd step, determine discrete points scope in straight-flanked ring, if n discrete point is evenly distributed in a square area, will
The square area is regular to be divided intoRow andRow are that square area is made up of a series of small square, generation
A discrete point is included in each small square in regular grid, often row or each column are includedIndividual discrete point, in second step
The d for obtaining：Average distance between discrete point is each small foursquare side length, by the 1st row,Row, the
1 row, theThe union in the region where row is set to a straight-flanked ring i.e. outermost of regular grid, then included in the straight-flanked ring
AboutIndividual discrete point, andIt is small just in the adjacent small foursquare set in inside of small square where individual discrete point
Square quantity will be less than or equal toThe small square for then calculating successively from outside to inside in gathering with internal small square is adjacent
The inside medium and small foursquare quantity of small square set be discrete point quantity, the inner most small square when n is even number
It is 4 to gather the medium and small foursquare quantity i.e. quantity of discrete point, the inner most small medium and small pros of square set when n is odd number
The quantity of shape is that the quantity of discrete point is 1, it is known that when line width col width is all a discrete point average distance, what is obtained successively is interior
The discrete points included in the small square set in portion are up toThe minimum rectangle of the n discrete point for being randomly distributed
Bounding box, if be equally divided intoRow andRow, in calculating internal small rectangular set successively according to method same above
The quantity of the quantity of small rectangle and the discrete point for being included, it is known that the distribution of discrete point will be greatly uneven, therefore in order to protect
All comprising a number of discrete point in the small rectangular set in inside that card is calculated successively after dividing, it is known that internal small rectangular set
Can only be at most distributed in the region that conjunction is occupiedIndividual discrete point, just can guarantee that in the small rectangular set in others inside there is appropriate number
The discrete point of amount, therefore set and contain up in a union i.e. straight-flanked ring in the corresponding region of internal small rectangular setIt is individual from
Scatterplot, the calculating of the Delaunay triangulation network growth algorithm time complexity based on subregion, smallest discrete is counted for convenience
It is set to
4th step, generation initial rectangular ring, using minimum rectangle bounding box as initial rectangular ring external boundary, ax, ay are used as outer
Border inside contracts step-length when generating inner boundary in the horizontal direction and the vertical direction, by the x coordinate value of four angle points of external boundary
Step-length in one horizontal direction of contracting, y-coordinate value inside contracts the step-length in a vertical direction, generates four angle points, four angle points
The inner boundary of initial rectangular ring is constituted clockwise, according to four coordinate values of angle point of external boundary, compares the minimum for obtaining external boundary
With maximum x, y-coordinate value, respectively xextermin、xextermax、yextermin、yextermax, similarly obtain four angle points of inner boundary
Minimax x, y-coordinate value, respectively xinnermin、xinnermax、yinnermin、yinnermax, take in discrete point set a point p (x,
Y), if xextermin≤x<xinnerminOr xinnermax<x≤xextermax, and yinnermax≤y<yextermaxOr yextermin≤y<
yinnermin, then the point is illustrated in initial rectangular ring, all discrete points in traversal discrete point set repeat above discrete point and sit
Scale value deterministic process, obtains all discrete points in initial rectangular ring, if zoom factor k, between 0.25-2, k × ax makees
Step-length when being scaled for inner boundary on level is square, k × ay is used as step-length in vertical direction.If discrete points are less thanThen by the x coordinate value of four angle points of inner boundary inside contract a level it is square on step-length, y-coordinate value inside contracts a Vertical Square
Upward step-length, if discrete points are more thanTo then be put outside the x coordinate value of four angle points of inner boundary a level it is square on
Step-length, puts the step-length in a vertical direction outside y-coordinate value, after the inner boundary angular coordinate adjustment of initial rectangular ring, repeat with
It is upper judge all discrete points whether the process in initial rectangular ring, the points that include of initial rectangular ring are calculated, if the points exist
Minimal pointWith maximum number of pointsBetween, then it is eligible.If not in minimal pointWith maximum number of pointsBetween,
Then change the calculating process of initial rectangular ring inner boundary coordinate value according to more than, in the initial rectangular ring inner boundary angle point for having changed
Change the inner boundary coordinate value of initial rectangular ring on the basis of coordinate again, judge the point of the discrete point in initial rectangular ring
Number, repeats above procedure, until the points in initial rectangular ring are in minimal pointWith maximum number of pointsBetween, generation is just
Beginning straight-flanked ring, is loaded into straight-flanked ring set；
5th step, complete discrete point minimum rectangle bounding box division, by the inner boundary of initial rectangular ring be set to it is next will
The external boundary of the straight-flanked ring of generation, according in the 4th step generate straight-flanked ring inner boundary process generate the new straight-flanked ring it is initial in
Whether border, calculates the discrete points in current newly-generated straight-flanked ring, judge discrete points in minimal pointAnd maximum
PointsBetween, if not existing, according to circumstances repeat to change the calculating process of inner boundary coordinate in the 4th step, and judge at this
The points of the discrete point in new straight-flanked ring, until the discrete point in newly-generated straight-flanked ring is counted in minimal pointAnd maximum
PointsBetween, newly-generated straight-flanked ring is loaded into straight-flanked ring set, according to initial rectangular ring, current newly-generated square
The points in points and discrete point set in shape ring, calculate the points that residue is not loaded into straight-flanked ring, repeat above rectangle
Ring generating process, so that the rectangle ring type for carrying out minimum rectangle bounding box from outside to inside is divided, when residue is not loaded into rectangle
Points in ring 3 withBetween when, the inner boundary of the straight-flanked ring that will be newly generated is used as next straight-flanked ring that will be generated
External boundary, four angle points of inner boundary are the central point that the average value of four angle points of external boundary is rectangle where external boundary, institute
There is the remaining point not being loaded into straight-flanked ring to be loaded into the straight-flanked ring, now minimum rectangle bounding box is divided and finished, by the square
Shape ring is loaded into straight-flanked ring set, and straight-flanked ring set generation is finished；
6th step, initial network forming is carried out based on straight-flanked ring set, according to the straight-flanked ring set that the 5th step is generated, will be indexed in set
Be worth maximum straight-flanked ring as initial network forming region, and be set to inner loop, the maximum straight-flanked ring of index value be inner loop and
Time big straight-flanked ring of index value, and be set to inner loop adjacent ring union as area is initially thirdly retrieved, according to first
The angular coordinate of beginning network forming area inner boundary is the central point of initial network forming area external boundary, finds out the nearest point p of distance center point1With
Range points p1Nearest point p2, respectively as the beginning and end of a line of the triangulation network, loaded the side as initial baseline
To in baseline set, initial baseline only stores index value of the beginning and end in discrete point set, is calculated according to initial baseline
The cosine value of the angle that each point is constituted with initial baseline, finds out the minimum point i.e. angle of cosine value in initial thirdly retrieval area
Maximum point thirdly, triangle is loaded into triangle sets as initial baseline, and newly-generated side is loaded into baseline
In set, index value of the left and right triangle on newly-generated side in triangle sets is recorded, if left triangle or right triangle
Temporarily without being then set to -1, record triangle corresponding three while index value be three while index value in baseline set, according to new life
Into triangle other both sides, repeat more than search procedure thirdly, if this side is suitable thirdly in network forming area is
New triangle is then generated in the corresponding straight-flanked ring of portion's ring, triangle is loaded into triangle sets, the triangle of generation
While being loaded into baseline set, index value of the corresponding left and right triangle in the side in triangle sets is recorded, if left triangle
Or right triangle wouldn't exist then be set to -1, while record triangle corresponding three while index value be three while in baseline set
Index value, if this side is suitable be not thirdly in the corresponding straight-flanked ring of inner loop in network forming area if do not generate new triangle
Shape, the baseline is loaded into tentative baseline set, according to the baseline newly increased in baseline set, repeats generation triangle above
Process, when the baseline amount in the baseline amount in baseline set and tentative baseline set is not further added by, initial network forming is completed；
7th step, the network forming for completing all discrete points, the corresponding straight-flanked ring of adjacent ring of inner loop during by initial network forming are set to
The inner loop of this time network forming, next adjacent ring of the corresponding straight-flanked ring of inner loop of this time network forming is set to the inside of this network forming
The adjacent ring of ring, inner loop as network forming area, the union of the adjacent ring of inner loop and inner loop as thirdly retrieving area, from first
It is suitable thirdly in thirdly retrieval area retrieval that baseline in the tentative baseline set of beginning network forming generation starts, and repeats above structure
Network process, updates baseline set, after the baseline in tentative baseline set participates in network forming to be finished, then newly increased from this network forming
Baseline starts to repeat above network forming process, generates new tentative baseline set, updates baseline set, triangle sets, repeat with
Upper process so as to by ring carry out network forming from inside to outside, when index value of the corresponding straight-flanked ring of inner loop in straight-flanked ring set is 0,
When index value of the corresponding straight-flanked ring of adjacent ring of inner loop in straight-flanked ring set is 1, based on tentative baseline set and baseline
In thirdly retrieval area retrieval thirdly, whether direct construction network does not consider further that thirdly in network forming area, no longer for baseline in set
Generation tentative baseline collection, newly-generated triangle and baseline are loaded into baseline set and triangle sets respectively, work as baseline
Baseline in set is not further added by, i.e., all discrete points have participated in network forming, and network forming is completed；
8th step, optimizes the triangulation network of generation, is the set on all sides of the triangulation network according to the baseline set generated after the completion of network forming,
It is the baseline at 0 to take index value, is set to current basic line, and the index value for obtaining its corresponding left and right triangle is with current basic line
Index value of two triangles of common edge in triangle sets, if two index values are not -1, in triangle sets
In find triangle at manipulative indexing value, be set to the triangle of current left and right two, calculate when in two triangles of front left and right
The angle value at the angle that summit and current basic line outside current basic line are constituted, asks it and need not be carried out if more than 180 ° excellent
Change, otherwise connect two summits outside current basic line summit in two triangles, generate new baseline, and with newly-generated baseline
Two other summit outside summit respectively constitutes two new triangles, and the corresponding index value of current basic line is corresponding with it
The index value of left and right triangle be set to index value of the index value of newly-generated baseline as it in baseline set and new
The index value of the left and right triangle of baseline is generated, when the rope on corresponding three side of the index value and current triangle of the first two triangle
Draw value and be set to index value and newly-generated two of the two newly-generated index values of triangle as it in triangle sets
The index value on corresponding three side of individual triangle, newly-generated baseline and triangle be then inserted into it in baseline set respectively and
At the corresponding index value of triangle sets, baseline and triangle original in gathering is substituted, above procedure is repeated, until baseline set
All Baseline Surveys in conjunction are finished, and ultimately generate Delaunay triangulation network.
2. a kind of Delaunay triangulation network growth algorithm based on subregion according to claim 1, it is characterised in that described
The first step, the 3rd step in, discrete points n be 3 -+∞.
3. a kind of Delaunay triangulation network growth algorithm based on subregion according to claim 1, it is characterised in that described
Second step in, area S and discrete points n according to discrete point set minimum rectangle bounding box are calculated flat between any two points
After d, average distance d is set to discrete point average distance ay in the Y direction, the length dy (Y according to Rectangular Bounding Volume
The difference of coordinate) and width dx (difference of X-coordinate) ratio relation, discrete point average distance ax in the X direction is calculated,
Above computing formula is as follows：
4. a kind of Delaunay triangulation network growth algorithm based on subregion according to claim 1, it is characterised in that described
The 4th step in zoom factor k be 0.25-2.
5. a kind of Delaunay triangulation network growth algorithm based on subregion according to claim 1, it is characterised in that described
The straight-flanked ring set that obtains of the 5th step in the discrete points scope that includes of each straight-flanked ring beWherein index
The discrete points scope that the maximum straight-flanked ring of value is included is
6. a kind of Delaunay triangulation network growth algorithm based on subregion according to claim 1, it is characterised in that described
The 6th step in, it is described judge calculating cosine value when thirdly formula be：
Wherein ps(xs,ys)pe(xe,ye) it is respectively the beginning and end of baseboard, ptemp(xtemp,ytemp) it is to be judged discrete
Point.
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