CN105590333A - Method for determination of point-surface topological relation on the basis of delta-shaped region equation - Google Patents

Method for determination of point-surface topological relation on the basis of delta-shaped region equation Download PDF

Info

Publication number
CN105590333A
CN105590333A CN201510854514.8A CN201510854514A CN105590333A CN 105590333 A CN105590333 A CN 105590333A CN 201510854514 A CN201510854514 A CN 201510854514A CN 105590333 A CN105590333 A CN 105590333A
Authority
CN
China
Prior art keywords
delta
point
shaped region
region
monitoring point
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201510854514.8A
Other languages
Chinese (zh)
Inventor
吴会胜
文聪聪
蔺丽芳
宋冬梅
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
China University of Petroleum East China
Original Assignee
China University of Petroleum East China
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by China University of Petroleum East China filed Critical China University of Petroleum East China
Priority to CN201510854514.8A priority Critical patent/CN105590333A/en
Publication of CN105590333A publication Critical patent/CN105590333A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/20—Drawing from basic elements, e.g. lines or circles

Abstract

The present invention provides a method for determination of a point-surface topological relation on the basis of a delta-shaped region equation. The method comprises the steps: S1, building a delta-shaped region equation; S2, determining a determination method of the delta-shaped region topological relation; S3, dividing a planar region into the delta-shaped region, and storing identification numbers and vertex coordinates thereof of the delta-shaped region in order; and S4, substituting monitoring points into the delta-shaped region equation generated in the step S3, and determining the topological relation of the monitoring points and the planar region. The method for determination of the point-surface topological relation on the basis of a delta-shaped region equation is applicable to the planar regions with arbitrary shapes, with versatility; the method for determination of the point-surface topological relation on the basis of a delta-shaped region equation is able to determine the point-surface containing and decomposed state and determine whether the points are on the boundary of the surface. The method for determination of the point-surface topological relation on the basis of the delta-shaped region equation reduces the algorithm complexity to a certain degree, and when monitoring points are stored in a first delta-shaped region or the boundary, the required calculated amount is minimum.

Description

A kind of method based on delta domain equation judging point and face topological relation
Technical field
The invention belongs to spatial data processing technology field, relate in particular to a kind of based on deltaThe method of domain equation judging point and face topological relation.
Background technology
The spatial data forming based on point, line, surface three class geographical entities is being described geographical spaceIn the process of things or phenomenon, topological relation plays an important role, and it is to describe sky that topology is expressedBetween be related to the important method of consistency between datagraphic; The topological relation of spatial data comprises adjacencyRelation, incidence relation and inclusion relation, the topological relation of point-like entity and planar entity mainly refers toInclusion relation and incidence relation. The judgement of point and face topological relation is significant: one, energyEnough spatial relations clearly reflecting between point-like entity and planar entity, are conducive to carry outGeographical entity is rebuild; Two, as the basis that judges line and face, face and face topological relation; Three,The foundation of the correlation space data manipulations such as geographical entity is chosen, information inquiry, spatial analysis,For example mouse is clicked and is chosen planar entity, clicks planar entity attribute information, point and the face checkedThe operations such as Overlap Analysis.
In spatial data structure, planar entity is described with polygonal region conventionally, therefore,Point and the described spatial relationship of topological relation of face are equivalent to some the relation with polygonal region,The topological relation of so-called judging point and face determines that point is in polygon or in Polygonal BoundaryUpper or at outside of polygon. Existing numerous the grinding of determination methods about point with polygon position relationshipStudy carefully, representative algorithm is as follows: ray method, the ray and the polygon that set out by calculating monitoring pointThe intersection point number judging point on border is inner or outside at polygon; Equal-area method, passes through monitoring pointWhether the triangle area sum forming that is connected with Polygonal Boundary point equates with area of a polygonDetermine its position relationship; Preset angle configuration, is similar to equal-area method, by monitoring point and polygonWhether the connected angle sum forming of boundary point is that 360 degree are determined its position relationship; PolygonSubdivision method, first such algorithm is split into some sub-figures by certain mode by shape changeable(such as convex polygon, trapezoidal etc.) is then for example, by certain rule (tree construction) storage and inspectionThe position relationship of measuring point and sub-figure. In addition, also have determining method based on Polygonal Boundary direction,Vector multiply each other method and on above-mentioned algorithm basis improved computational methods.
The existing determination methods of comprehensive analysis, exists following not enough: 1. time complexity is high,For example ray algorithm, although this algorithm need not carry out pretreatment to polygon, easily realizes,Its time complexity is O (N); 2. use limitation, some algorithms are confined to particular typePolygon, for example equal-area method and preset angle configuration are only applicable to convex polygon; 3. judging efficiency is notHeight, particularly for complex polygon, some determination methods in the time carrying out, exist memory cost large,The problem of inefficiency.
Summary of the invention
The object of the present invention is to provide a kind of efficiency higher, be applicable to any planar region and pointTopological relation determination methods, be intended to solve the inefficiency of point and face topological relation determination methodsAnd use limited problem.
The present invention is achieved in that a kind of based on delta domain equation judging point and face topologicalThe method of relation, comprises that step is as follows:
S1, structure delta domain equation
The construction basis of delta domain equation is: rear all subregion area sum is divided in former regionRemain unchanged and equal former region area. Describe in conjunction with shown in Fig. 1, triangle Δ abc,Apex coordinate is respectively a (x1, y1), b (x2, y2), c (x3, y3), and monitoring point is o(x, y), divides according to former region the rule that the rear gross area remains unchanged and equals former region areaRule, if fruit dot o (x, y) is in triangle or on a triangle limit, meets formula1：
SΔabc＝SΔabo+SΔaco+SΔbco
Formula 1
S Δ abc represents the area of triangle Δ abc, and S Δ abo represents the area of triangle Δ abo,S Δ aco represents the area of triangle Δ aco, and S Δ bco represents the area of triangle Δ bco.
According to triangle area computing formula, derive the gore taking apex coordinate as parameterLong-pending formula expression. With the example that is calculated as of S Δ abc, its area formula as shown in Equation 2:
SΔabc＝1/2*Lab*h
Formula 2
Lab represents the length of the limit ab of triangle Δ abc, and h represents the summit of triangle Δ abcC is to the distance on ab limit;
Calculate according to the apex coordinate of triangle Δ abc limit ab length L ab computing formula asShown in formula 3;
Lab＝((x1-x2)2+(y1-y2)2)1/2
Formula 3
Calculate the calculating of summit c to the distance h on ab limit according to the apex coordinate of triangle Δ abcFormula is as shown in Equation 4:
h＝|x1*y2+x2*y3+x3*y1-x1*y3-x2*y1-x3*y2|/((x2-x1)2+(y1-y2)2)1/2
Formula 4
|| represent to take absolute value;
Bring formula 3 and formula 4 into formula 2, obtain the triangle area based on apex coordinateFormula, as shown in Equation 5;
SΔabc＝1/2*|x1*y2+x2*y3+x3*y1-x1*y3-x2*y1-x3*y2|
Formula 5
In like manner can obtain S Δ abo, S Δ aco, S Δ bco, its expression formula is as formula 6-8 instituteShow;
SΔabo＝1/2*|x1*y2+x2*y+x*y1-x1*y-x2*y1-x*y2|
Formula 6
SΔaco＝1/2*|x1*y+x*y3+x3*y1-x1*y3-x*y1-x3*y|
Formula 7
SΔbco＝1/2*|x*y2+x2*y3+x3*y-x*y3-x2*y-x3*y2|
Formula 8
Bring formula 5, formula 6, formula 7, formula 8 into formula 1, can obtain formula 9,Leg-of-mutton region equation.
|x1*y2+x2*y3+x3*y1-x1*y3-x2*y1-x3*y2|＝|x1*y2+x2*y+x*y1-x1*y-x2*y1-x*y2|+|x1*y+x*y3+x3*y1-x1*y3-x*y1-x3*y|+|x*y2+x2*y3+x3*y-x*y3-x2*y-x3*y2|
Formula 9
S2, determine point and the determination methods of delta-shaped region topological relation
According to the delta domain equation building in S1, by coordinate (x, the y) band of monitoring pointEnter delta domain equation, if do not meet the equality condition of formula 9, show this monitoring point notIn delta-shaped region, point is from state with delta-shaped region; Otherwise, show this monitoring pointIn delta-shaped region or on border, then by monitoring point substitution Atria bar limit institute respectivelyLinear equation, if meet arbitrary linear equation, show that this monitoring point is at deltaOn border, territory, if all do not meet three linear equations, represent that this monitoring point is at deltaInside, territory.
S3, planar region is divided into delta-shaped region, and stores successively the mark of delta-shaped regionKnow number and apex coordinate
The principle that planar region is divided into delta-shaped region is: each delta of dividingTerritory all belongs to the scope in planar region; All delta-shaped region scope sums of dividing equal faceShape regional extent.
First judge the shape of planar zone boundary, be then protruding polygon according to planar zone boundaryShape situation or be concave polygon situation and operate respectively, sets forth in conjunction with Fig. 2.
(1) judge the concavity and convexity on all summits, planar region according to storage order, if existedConcave point, planar zone boundary is concave polygon, and by judgement order respectively storage concavity summit andConcave vertex; If there is no concave point, planar zone boundary is convex polygon.
The method that judges summit, planar region concavity and convexity is as follows: according to the storage on summit, planar regionGet sequentially, successively three summit (V that order is connectedi，Vi+1，Vi+2), form with intermediate pointVi+1For the angle ∠ V on summitiVi+1Vi+2If, ∠ ViVi+1Vi+2Be greater than 180 degree, summit Vi+1For concave point; Otherwise, summit Vi+1For salient point.
(2) be convex polygon situation for planar zone boundary shape, explain in conjunction with Fig. 3State:
1. according to the storage order on summit, planar region, with first summit or an arbitrary summitFor fixing point (Vn), connect and the non-conterminous point of fixing point successively, by shape changeable Region DecompositionBecome several subregions.
Polygon vertex storage order V in shown in Fig. 31V2V3V4V5V6By first summit V1AsFixing point, connects and non-conterminous some V of fixing point successively1V3、V1V4、V1V5。
2. judge successively fixing point VnTwo summit (V with other sequential storagei、Vi+1) beNo conllinear, if a) conllinear not represents that the subregion that these three summits form is deltaTerritory, stores this leg-of-mutton identification number ID and apex coordinate; If b) conllinear, continues to getNext summit (Vi+2), judge VnWith Vi+1And Vi+2Whether conllinear, and carry out a or bOperation; Be fixed successively a VnWith conllinear judgement and the corresponding operating on other summits, work as instituteThere is summit to be all judged the operation that stops this step after end.
In shown in Fig. 3, first judge V1、V2、V3Whether conllinear, V in this example1、V2、V3Then judge V point-blank,1、V3、V4Whether conllinear, V in this example1、V3、V4Do not store triangle Δ V point-blank,1V3V4ID be 1, and store summit V1、V3、V4Coordinate, judged all summits according to aforesaid operations method, can be by planar districtTerritory is divided into Δ V1V3V4、ΔV1V4V5With Δ V1V5V6Three delta-shaped regions.
(3) be concave polygon situation for planar zone boundary shape, explain in conjunction with Fig. 4State:
1. by the concave vertex of storage in step (1), extract a concave vertex according to storage order (Vi), and connect two summit (V that are adjacenti-1，Vi+1), if the concave vertex extractingFor first summit V in planar region1, V0Be designated last summit in planar region;Judge Vi、Vi-1And Vi+1Whether conllinear, if conllinear not forms a delta-shaped region;If conllinear, by the summit V of storage in step (1)iDelete, if storage in (1)Number of vertex be 3, polygonal region completes the division of delta-shaped region, otherwise, repeat 1.Operation;
Zone boundary polygon in shown in Fig. 4, the storage order of its concave vertex is V1V3V4V6V7, first delta-shaped region Δ V of formation7V1V2。
Whether the delta-shaped region that 2. determining step is produced in 1. comprises other tops in planar regionPoint, determination methods is the method for describing in S2, is about to not comprise three summits of delta-shaped regionEvery other summit bring this delta domain equation into, judge that other summits are at this deltaOverseas portion is still on inside or border.
If the delta-shaped region of step in 1. do not comprise other arbitrary summits (not in inside or limitBoundary), store this leg-of-mutton identification number ID and apex coordinate, and delete summit ViDepositStorage; Judge with Vi-1And Vi+1The concavity and convexity at angle forming for summit, and upgrade it in step (1)In the storage of corresponding concavity and convexity, then repeat 1. to operate;
If the delta-shaped region of step in 1. comprises other arbitrary summits (in inside or border),Give up and process this concave vertex Vi, then repeat 1. to operate;
If the summit of the storage in step (1) adds up to 3, show to only have a triangleRegion, polygonal region completes the division of delta-shaped region.
The deletion order of the planar region concave vertex in shown in Fig. 4: V1，V3，V4，V6；The delta-shaped region of dividing is respectively: Δ V7V1V2，ΔV2V3V4，ΔV2V4V5，ΔV5V6V7， ΔV5V7V2。
S4, by the leg-of-mutton region equation producing in monitoring point substitution S3, judge monitoring pointTopological relation with planar region
(1) according to the storage order of the delta-shaped region in S3, extract a delta-shaped region,Carry out monitoring point and this triangle according to the determination methods of S2 mid point and delta-shaped region topological relationThe judgement of shape region topology relation.
(2) if judge monitoring point in this triangle inside, show that this monitoring point is at faceShape intra-zone, the topological relation judgement in monitoring point and planar region finishes.
(3) if judge monitoring point on leg-of-mutton border, further judge placeTriangle border whether be the border in planar region: if the border in planar region showsThis monitoring point is on the border in planar region, otherwise, show that this monitoring point is at planar intra-zone,The topological relation judgement in monitoring point and planar region finishes.
(4), if judge monitoring point not on this triangle inside or border, also judge whetherHave and be not judged to other delta-shaped region, if do not had, show that monitoring point is at planar region exterior,The topological relation judgement in monitoring point and planar region finishes; Otherwise, separately get a delta-shaped regionOperate, repeat (1) operation.
Than the shortcoming and defect of prior art, the present invention has following beneficial effect: thisBrightly provide the topological relation judgement side that a kind of efficiency is higher, be used in any planar region and pointMethod, can be applicable to the planar region of arbitrary shape, has versatility; The present invention not only canJudging point and face comprise and from state, and whether applicable judging point on the border of face;The present invention has reduced algorithm complex to a certain extent, when existing monitoring point in first of storageWhen individual delta-shaped region inside or border condition, needed amount of calculation minimum.
Brief description of the drawings
Figure 1 shows that for building delta-shaped region graph of equation example;
Figure 2 shows that the flow chart that planar region is divided into delta-shaped region;
Schematic diagram is divided in the Delta Region that Figure 3 shows that planar region, convex polygon border;
Schematic diagram is divided in the Delta Region that Figure 4 shows that planar region, concave polygon border;
Figure 5 shows that a little and judge schematic diagram with complicated planar region topology relation.
Detailed description of the invention
In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction withDrawings and Examples, are further elaborated to the present invention. Should be appreciated that this place retouchesThe specific embodiment of stating only, in order to explain the present invention, is not intended to limit the present invention.
Planar region in this example as shown in Figure 5, has 13 summits, and summit is by the inverse timePin storage, V1For initial vertex, V13For stopping summit; Monitoring point is A and B.
Example operation one: build delta domain equation according to formula 9, the function of mainly usingModule is
privatedoubleTriangleAreaEquation(doublex,doubley,doublex1,doubley1,doublex2,doubley2,doublex3,doubley3)：x1、y1、x2、Y2, x3, y3 are triangular apex coordinate; X, y are monitoring point coordinate.
Example operation two: determine the determination methods of putting with delta-shaped region topological relation, mainly useTo function module be:
privateintTopologyPointTriangle(doublex,doubley,doublex1,doubley1,doublex2,doubley2,doublex3,doubley3)：x1、y1、x2、Y2, x3, y3 are triangular apex coordinate; X, y are monitoring point coordinate; Return of value 0 representsPoint is in delta-shaped region inside, and 1 represents that point is on delta-shaped region border, and 2 represent that point is at triangleShape region exterior; This function call TriangleAreaEquation () function completes main calculatingFunction.
privateboolPointAtLine(doublex1,doubley1,doublex2,doubley2,Doublex3, doubley3): for judging 3 whether conllinear; X1, y1, x2, y2, x3,Y3 is apex coordinate to be measured; Return of value true represents conllinear, and false represents not conllinear.
Example operation three: according to the storage order on the summit in planar region, judge successively summitConcavity and convexity, the function module of mainly using is: privateboolConvexOrConcave(doublex1,doubley1,doublex2,doubley2,doublex3,doubley3)：x1、Y1, x2, y2, x3, y3 are three apex coordinates; Return of value true represents that summit is convexity,False represents that summit is concavity. Concave crown point and concave vertex are stored in respectively to one-dimension array, operationResult: recessed vertical array ArrayConcave[V2,V4,V8,V9]; Concave vertex arrayArrayConvex[V1,V3,V5,V6,V7,V10,V11,V12,V13]. The storage order array on summitConvex[V1,V2,V3,V4,V5,V6,V7,V8,V9,V10,V11,V12,V13]。
(1) to concave vertex V1Operate, connect and V1Two adjacent summit V2WithV13, first utilize function PointAtLine () to judge V13、V1And V2Not conllinear, shows energyEnough form delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV13V1V2In do not comprise other summits, therefore preserving this leg-of-mutton ID is 1, preserve V13、V1And V2Apex coordinate, in array ArrayConvex, delete V1; Utilize functionV is deleted in ConvexOrConcave () judgement1Rear V2And V13Concavity and convexity, can draw V2And V13Concavity and convexity do not change, therefore the event memory on summit is: recessed vertical arrayArrayConcave[V2,V4,V8,V9]; Concave vertex arrayArrayConvex[V3,V5,V6,V7,V10,V11,V12,V13]; The storage order array on summitConvex[V2,V3,V4,V5,V6,V7,V8,V9,V10,V11,V12,V13]。
(2) to concave vertex V3Operate, connect and V3Two adjacent summit V2WithV4, first utilize function PointAtLine () to judge V2、V3And V4Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV2V3V4In do not comprise other summits, therefore preserving this leg-of-mutton ID is 2, preserve V2、V3And V4Apex coordinate, in array ArrayConvex, delete V3; Utilize functionV is deleted in ConvexOrConcave () judgement3Rear V2And V4Concavity and convexity, can draw V2And V4Concavity and convexity do not change, therefore the event memory on summit is: recessed vertical arrayArrayConcave[V2,V4,V8,V9]; Concave vertex arrayArrayConvex[V5,V6,V7,V10,V11,V12,V13]; The storage order array on summitConvex[V2,V4,V5,V6,V7,V8,V9,V10,V11,V12,V13]。
(3) to concave vertex V5Operate, connect and V5Two adjacent summit V4WithV6, first utilize function PointAtLine () to judge V4、V5And V6Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV4V5V6In comprise summit V8, give up and process V5, the event memory on summit is constant.
(4) to concave vertex V6Operate, connect and V6Two adjacent summit V5WithV7, first utilize function PointAtLine () to judge V5、V6And V7Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judge ΔV5V6V7In comprise summit V8, give up and process V6, the event memory on summit is constant.
(7) to concave vertex V7Operate, connect and V7Two adjacent summit V6WithV8, first utilize function PointAtLine () to judge V6、V7And V8Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV6V7V8In do not comprise other summits, therefore preserving this leg-of-mutton ID is 3, preserve V6、V7And V8Apex coordinate, in array ArrayConvex, delete V7; Utilize functionV is deleted in ConvexOrConcave () judgement7Rear V6And V8Concavity and convexity, can draw V6And V8Concavity and convexity do not change, therefore the event memory on summit is: recessed vertical arrayArrayConcave[V2,V4,V8,V9]; Concave vertex arrayArrayConvex[V5,V6,V10,V11,V12,V13]; The storage order array on summitConvex[V2,V4,V5,V6,V8,V9,V10,V11,V12,V13]。
(8) to concave vertex V10Operate, connect and V10Two adjacent summit V9WithV11, first utilize function PointAtLine () to judge V9、V10And V11Conllinear, deletes topPoint V10Storage, therefore the event memory on summit is: recessed vertical arrayArrayConcave[V2,V4,V8,V9]; Concave vertex arrayArrayConvex[V5,V6,V11,V12,V13]; The storage order array on summitConvex[V2,V4,V5,V6,V8,V9,V11,V12,V13]。
(9) to concave vertex V11Operate, connect and V11Two adjacent summit V9WithV12, first utilize function PointAtLine () to judge V9、V11And V12Not conllinear, shows energyEnough form delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV9V11V12In do not comprise other summits, therefore preserving this leg-of-mutton ID is 4, preserveV9、V11And V12Apex coordinate, in array ArrayConvex, delete V11; Utilize letterV is deleted in number ConvexOrConcave () judgement11Rear V9And V12Concavity and convexity, can drawV9And V12Concavity and convexity do not change, therefore the event memory on summit is: concave crown is countedGroup ArrayConcave[V2,V4,V8,V9]; Concave vertex arrayArrayConvex[V5,V6,V12,V13]; The storage order array on summitConvex[V2,V4,V5,V6,V8,V9,V12,V13]。
(10) to concave vertex V12Operate, connect and V12Two adjacent summit V9And V13, first utilize function PointAtLine () to judge V9、V12And V13Not conllinear, showsCan form delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV9V12V13In do not comprise other summits, therefore preserving this leg-of-mutton ID is 5, preserveV9、V12And V13Apex coordinate, in array ArrayConvex, delete V12; Utilize letterV is deleted in number ConvexOrConcave () judgement12Rear V9And V13Concavity and convexity, can drawV13Concavity and convexity do not change, V9Become concave vertex by concave crown point, therefore depositing of summitStorage result is: recessed vertical array ArrayConcave[V2,V4,V8]; Concave vertex arrayArrayConvex[V5,V6,V13,V9]; The storage order array on summitConvex[V2,V4,V5,V6,V8,V9,V13]。
(11) to concave vertex V13Operate, connect and V13Two adjacent summit V9And V2, first utilize function PointAtLine () to judge V9、V13And V2Not conllinear, showsCan form delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV9V13V2In do not comprise other summits, therefore preserving this leg-of-mutton ID is 6, preserve V9、V13And V2Apex coordinate, in array ArrayConvex, delete V13; Utilize functionV is deleted in ConvexOrConcave () judgement13Rear V9And V2Concavity and convexity, can draw V9Concavity and convexity do not change, V2Become concave vertex by concave crown point, therefore the storage on summitResult is: recessed vertical array ArrayConcave[V4,V8]; Concave vertex arrayArrayConvex[V5,V6,V9,V2]; The storage order array on summitConvex[V2,V4,V5,V6,V8,V9]。
(12) to concave vertex V9Operate, connect and V9Two adjacent summit V8WithV2, first utilize function PointAtLine () to judge V8、V9And V2Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV8V9V2Middle summit V4, give up and process V9, the event memory on summit is constant.
(13) to concave vertex V2Operate, connect and V2Two adjacent summit V9WithV4, first utilize function PointAtLine () to judge V9、V2And V4Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV9V2V4In do not comprise other summits, therefore preserving this leg-of-mutton ID is 7, preserve V9、V2And V4Apex coordinate, in array ArrayConvex, delete V2; Utilize functionV is deleted in ConvexOrConcave () judgement2Rear V9And V4Concavity and convexity, can draw V9And V2Concavity and convexity do not change, therefore the event memory on summit is: recessed vertical arrayArrayConcave[V4,V8]; Concave vertex array ArrayConvex[V5,V6,V9]; Depositing of summitStorage order array Convex[V4,V5,V6,V8,V9]。
(14) to concave vertex V5Operate, connect and V5Two adjacent summit V4WithV6, first utilize function PointAtLine () to judge V5、V4And V6Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV4V5V6In comprise summit V8, give up and process V5, the event memory on summit is constant.
(15) to concave vertex V6Operate, connect and V6Two adjacent summit V5WithV8, first utilize function PointAtLine () to judge V5、V6And V8Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV5V6V8In do not comprise other summits, therefore preserving this leg-of-mutton ID is 8, preserve V5、V6And V8Apex coordinate, in array ArrayConvex, delete V6; Utilize functionV is deleted in ConvexOrConcave () judgement6Rear V5And V8Concavity and convexity, can draw V5Concavity and convexity do not change, V8Become concave vertex by concave crown point, therefore the storage on summitResult is: recessed vertical array ArrayConcave[V4]; Concave vertex arrayArrayConvex[V5,V9,V8]; The storage order array Convex[V on summit4,V5,V8,V9]。
(16) to concave vertex V9Operate, connect and V9Two adjacent summit V8WithV4, first utilize function PointAtLine () to judge V8、V9And V4Not conllinear, showing canForm delta-shaped region; Then utilize TopologyPointTriangle () function to judgeΔV8V9V4In do not comprise other summits, therefore preserving this leg-of-mutton ID is 9, preserve V8、V9And V4Apex coordinate, in array ArrayConvex, delete V9; Utilize functionV is deleted in ConvexOrConcave () judgement9Rear V8And V4Concavity and convexity, can draw V8Concavity and convexity do not change, V4Become concave vertex by concave crown point, therefore the storage on summitResult is: recessed vertical array ArrayConcave[]; Concave vertex arrayArrayConvex[V5,V8,V4]; The storage order array Convex[V on summit4,V5,V8]。
(16) judge and only remain 3 summits, therefore preserve Δ V5V8V4ID be 10,Preserve V5、V8And V4Apex coordinate; Delta-shaped region EO is divided in planar region.
Example operation four: according to 10 delta-shaped regions preserving in example operation threeΔV13V1V2、ΔV2V3V4、ΔV6V7V8、ΔV9V11V12、ΔV9V12V13、ΔV9V13V2、ΔV9V2V4、ΔV5V6V8、ΔV8V9V4With Δ V5V8V4, and the seat of monitoring point A and BMark, utilizes function TopologyPointTriangle () to judge successively monitoring point and delta-shaped regionTopological relation, deterministic process is as follows:
(1) monitoring point A, B and Δ V13V1V2Topological relation judgement, result be from;
(2) monitoring point A, B and Δ V2V3V4Topological relation judgement, result be from;
(3) monitoring point A, B and Δ V6V7V8Topological relation judgement, result is that A is at Δ V6V7V8Inside, shows that monitoring point A is at planar intra-zone; B and Δ V6V7V8From;
(4) monitoring point B and Δ V9V11V12Topological relation judgement, result be from;
(5) monitoring point B and Δ V9V12V13Topological relation judgement, result be from;
(6) monitoring point B and Δ V9V13V2Topological relation judgement, result be from;
(7) monitoring point B and Δ V9V2V4Topological relation judgement, result be from;
(8) monitoring point B and Δ V5V6V8Topological relation judgement, result be from;
(9) monitoring point B and Δ V8V9V4Topological relation judgement, result be from;
(10) monitoring point B and Δ V5V8V4Topological relation judgement, result be from, showMonitoring point B is at planar region exterior.
The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention,All any amendments of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc.,Within all should being included in protection scope of the present invention.

Claims (5)

1. the method based on delta domain equation judging point and face topological relation, its spyLevy and be, it is as follows that the method comprising the steps of:
S1, structure delta domain equation;
S2, determine point and the determination methods of delta-shaped region topological relation;
S3, planar region is divided into delta-shaped region, and stores successively the mark of delta-shaped regionKnow number and apex coordinate;
S4, by the leg-of-mutton region equation producing in monitoring point substitution step S3, judgement prisonThe topological relation in measuring point and planar region.
2. as claimed in claim 1 based on delta domain equation judging point and face topological passThe method of system, is characterized in that, in step S1, and the apex coordinate of definition triangle Δ abcBe respectively a (x1, y1), b (x2, y2), c (x3, y3), monitoring point is o (x, y),Building delta domain equation is:
|x1*y2+x2*y3+x3*y1-x1*y3-x2*y1-x3*y2|＝|x1*y2+x2*y+x*y1-x1*y-x2*y1-x*y2|+|x1*y+x*y3+x3*y1-x1*y3-x*y1-x3*y|+|x*y2+x2*y3+x3*y-x*y3-x2*y-x3*y2|。
3. as claimed in claim 1 based on delta domain equation judging point and face topological passSystem method, it is characterized in that, described step S2 specifically comprises: by the coordinate of monitoring point (x,Y) bring delta domain equation into, if do not meet the equality condition of delta-shaped region equation,Show that this monitoring point is not in delta-shaped region, point is from state with delta-shaped region; Otherwise,Show that this monitoring point is in delta-shaped region or on border, then by monitoring point substitution three respectivelyThe linear equation at place, three limits of dihedral, if meet arbitrary linear equation, shows this monitoringPoint, on delta-shaped region border, if all do not meet three linear equations, represents this monitoringPoint is in delta-shaped region inside.
4. as claimed in claim 1 based on delta domain equation judging point and face topological passThe method of system, is characterized in that, in step S3, planar region is divided into deltaThe principle in territory is: each delta-shaped region of dividing all belongs to the scope in planar region; DrawAll delta-shaped region scope sums of dividing equal planar regional extent.
5. as claimed in claim 1 based on delta domain equation judging point and face topological passThe method of system, is characterized in that, described step S4 specifically comprises:
(1), according to the storage order of the delta-shaped region in step S3, extract a triangleRegion, monitors according to the determination methods of step S2 mid point and delta-shaped region topological relationPut the judgement with this delta-shaped region topological relation;
(2) if judge monitoring point in this triangle inside, show that this monitoring point is at faceShape intra-zone, the topological relation judgement in monitoring point and planar region finishes;
(3) if judge monitoring point on leg-of-mutton border, further judge placeTriangle border whether be the border in planar region: if the border in planar region showsThis monitoring point is on the border in planar region, otherwise, show that this monitoring point is at planar intra-zone,The topological relation judgement in monitoring point and planar region finishes;
(4), if judge monitoring point not on this triangle inside or border, also judge whetherHave and be not judged to other delta-shaped region, if do not had, show that monitoring point is at planar region exterior,The topological relation judgement in monitoring point and planar region finishes; Otherwise, separately get a delta-shaped regionOperate i.e. repeating step (1) operation.
CN201510854514.8A 2015-11-28 2015-11-28 Method for determination of point-surface topological relation on the basis of delta-shaped region equation Pending CN105590333A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201510854514.8A CN105590333A (en) 2015-11-28 2015-11-28 Method for determination of point-surface topological relation on the basis of delta-shaped region equation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201510854514.8A CN105590333A (en) 2015-11-28 2015-11-28 Method for determination of point-surface topological relation on the basis of delta-shaped region equation

Publications (1)

Publication Number Publication Date
CN105590333A true CN105590333A (en) 2016-05-18

Family

ID=55929888

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201510854514.8A Pending CN105590333A (en) 2015-11-28 2015-11-28 Method for determination of point-surface topological relation on the basis of delta-shaped region equation

Country Status (1)

Country Link
CN (1) CN105590333A (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106273496A (en) * 2016-08-30 2017-01-04 大连理工大学 A kind of complicated break area automatic division method increased during material manufactures
CN109816716A (en) * 2019-01-11 2019-05-28 北京摩拜科技有限公司 Generation method, device and the server of parking area
WO2020019512A1 (en) * 2018-07-26 2020-01-30 平安科技（深圳）有限公司 Robot positioning detection method and apparatus and computer readable storage medium
CN113375614A (en) * 2021-06-29 2021-09-10 北京微纳星空科技有限公司 Unmanned equipment monitoring method and device, electronic equipment and storage medium

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004078867A (en) * 2002-08-16 2004-03-11 Eiji Kurihara Method for determining inside and outside of polygon
CN102663789A (en) * 2012-04-19 2012-09-12 上海巨唐信息科技有限公司 Method for performing triangularization on polygon containing holes and islands in two-dimensional plane
CN102982562A (en) * 2012-10-19 2013-03-20 浙江中正智能科技有限公司 Method for judging whether target point is positioned inside polygon area
CN104143214A (en) * 2013-05-07 2014-11-12 北京四维图新科技股份有限公司 Electronic map polygon triangulation method and device

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004078867A (en) * 2002-08-16 2004-03-11 Eiji Kurihara Method for determining inside and outside of polygon
CN102663789A (en) * 2012-04-19 2012-09-12 上海巨唐信息科技有限公司 Method for performing triangularization on polygon containing holes and islands in two-dimensional plane
CN102982562A (en) * 2012-10-19 2013-03-20 浙江中正智能科技有限公司 Method for judging whether target point is positioned inside polygon area
CN104143214A (en) * 2013-05-07 2014-11-12 北京四维图新科技股份有限公司 Electronic map polygon triangulation method and device

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
ZHONGSHULLUO: "求判断点是否在三角形内的最佳算法", 《HTTP://BLOG.CSDN.NET/LUOYUSHI2010/ARTICLE/DETAILS/8845556》 *
知乎用户: "如何判断点在多边形内部", 《HTTPS://WWW.ZHIHU.COM/QUESTION/27505636》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106273496A (en) * 2016-08-30 2017-01-04 大连理工大学 A kind of complicated break area automatic division method increased during material manufactures
WO2020019512A1 (en) * 2018-07-26 2020-01-30 平安科技（深圳）有限公司 Robot positioning detection method and apparatus and computer readable storage medium
CN109816716A (en) * 2019-01-11 2019-05-28 北京摩拜科技有限公司 Generation method, device and the server of parking area
CN113375614A (en) * 2021-06-29 2021-09-10 北京微纳星空科技有限公司 Unmanned equipment monitoring method and device, electronic equipment and storage medium

Similar Documents

Publication Publication Date Title
Zhou et al. Edge bundling in information visualization
Han et al. Point cloud simplification with preserved edge based on normal vector
Crane et al. A survey of algorithms for geodesic paths and distances
Zhang et al. Online structure analysis for real-time indoor scene reconstruction
Chen et al. Computing the minimum distance between a point and a NURBS curve
CN105590333A (en) Method for determination of point-surface topological relation on the basis of delta-shaped region equation
Abdelkader et al. VoroCrust: Voronoi meshing without clipping
Dzitsiuk et al. De-noising, stabilizing and completing 3D reconstructions on-the-go using plane priors
Wortmann Surveying design spaces with performance maps: A multivariate visualization method for parametric design and architectural design optimization
JP2011018328A (en) Method and apparatus for dividing three-dimensional model and image processing system including three-dimensional model division apparatus
CN104318100A (en) Method for thinning thick point-cloud on basis of feature sensitive projection operator
Zhang et al. Resolving topology ambiguity for multiple-material domains
Governi et al. 3D geometry reconstruction from orthographic views: A method based on 3D image processing and data fitting
Qin et al. Mass-driven topology-aware curve skeleton extraction from incomplete point clouds
CN104346481A (en) Community detection method based on dynamic synchronous model
Xiao et al. Building segmentation and modeling from airborne LiDAR data
TW201738774A (en) Unsupervised feature selection method and device
CN101114379A (en) Method for judging point whether or not situated in polygon
Xin et al. Efficiently computing geodesic offsets on triangle meshes by the extended Xin–Wang algorithm
WO2020043070A1 (en) Customer flow line and customer flow hot zone determining method and apparatus
Shen et al. A progressive method for the collapse of river representation considering geographical characteristics
Hao et al. Slice-based building facade reconstruction from 3D point clouds
EP3711027B1 (en) System and method for drawing beautification
Wang et al. 2D point-in-polygon test by classifying edges into layers
Phan et al. Triangulation based skeletonization and trajectory recovery for handwritten character patterns

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20160518

RJ01 Rejection of invention patent application after publication