CN102044076A - Distance measuring method for regular octahedron - Google Patents
Distance measuring method for regular octahedron Download PDFInfo
- Publication number
- CN102044076A CN102044076A CN2010105266145A CN201010526614A CN102044076A CN 102044076 A CN102044076 A CN 102044076A CN 2010105266145 A CN2010105266145 A CN 2010105266145A CN 201010526614 A CN201010526614 A CN 201010526614A CN 102044076 A CN102044076 A CN 102044076A
- Authority
- CN
- China
- Prior art keywords
- tag
- dir
- distance
- 2dir
- regular octahedron
- 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
Links
Images
Landscapes
- Image Analysis (AREA)
- Image Processing (AREA)
Abstract
The invention discloses a distance measuring method for a regular octahedron. The distance measurement of the regular octahedron can be converted into the analysis of six distance extension directions, and distance direction regions are divided. The distance in each distance region is only related to the region, and is independent of other regions. The distance measurement of the regular octahedron is realized; and distance computational formulas are four arithmetic operation, namely addition, subtraction, multiplication and division, so the distance measuring method has small computation amount.
Description
Technical field
The present invention relates to technical field of distance measurement, particularly relate to the regular octahedron distance measurement method.
Background technology
In fields such as geographical information technology, Computer Image Processing and computer program development, image need be carried out digitized processing, wherein a kind of means commonly used are grid systems.
Traditional grid system is based on rectangular node, and coordinate representation is simple, convenience of calculation, thereby be widely used.But development along with fields such as global remote sensing image database, Flame Image Process new technology, the novel dot matrix arrangement mode of regular hexagon grid CCD and developments of games, the uniform grid system that comprises other shapes such as plane trigonometry uniform grid system, regular hexagon grid system has obtained paying close attention to and having dropped into preliminary application gradually, has obtained better effects.Triangular grid system can expand to positive gengon and make up the Global Grid subdivision model, comprises positive tetrahedron, regular octahedron, regular dodecahedron, regular dodecahedron etc.For example, owing to regular octahedron is made up of eight identical equilateral triangles, thereby the use triangular grid system will be very convenient.
Yet, do not have a kind of method that can realize the regular octahedron range observation now.
Summary of the invention
For solving the problems of the technologies described above, the embodiment of the invention provides a kind of regular octahedron distance measurement method, and to solve the problem that prior art can't realize the regular octahedron range observation, technical scheme is as follows:
A kind of regular octahedron distance measurement method comprises:
In the regular octahedron stretch-out view, arrange triangular network;
The triangular network unit is carried out the regional analysis of six propagation directions and generates regional distribution chart;
Draw the regular octahedron distance calculating method at regional distribution chart.
Preferably, the described regional analysis that the triangular network unit is carried out six propagation directions comprises:
What obtain six propagation directions is initially just penetrating the district;
Obtain two and derive and just penetrate the district by the described direct diffraction in district of initially just penetrating;
Just penetrate district's diffraction and obtain other and derive and just penetrate the district by described deriving;
The a plurality of zones of formation are cut apart in the overlapping region that utilizes angular bisector just to penetrate the district to deriving;
The range observation that the distance in each zone equals to arrive the minimum value and value of all directions in this zone and each intra-zone is only relevant with this zone.
Preferably, describedly draw the regular octahedron distance calculating method at areal distribution and comprise:
For 8 triangles in the regular octahedron stretch-out view are encoded to 0-7 respectively;
Described triangle intermediate cam network element is carried out three-dimensional coordinate to be represented;
Draw the regular octahedron distance calculating method at coordinate relation in the zone.
Preferably, describedly draw the regular octahedron distance calculating method at coordinate relation in the zone and be:
Adopt the method for recompile, the coding of a triangular network unit is made as 0, and then derives the coding of another triangular network unit, establish the T that is encoded to behind another triangular network unit recompile, then
Work as t
A＜4 o'clock:
If t＜4, then T=(t-t
A+ 4) %4;
If t＞3, then T=(t-t
A+ 4) %4+4;
Work as t
A＞3 o'clock:
If t＜4, then T=(t
A-t+4) %4+4;
If t＞3, then T=(t
A-t+4) %4;
According to different T values, draw different regular octahedron distance calculating methods.
Preferably, described regular octahedron distance calculating method is respectively according to eight kinds of different situations of a-h:
A, when T=0, the computing method of distance D have following six kinds of situations:
(1), if i＞K+1 and j≤N+DIR_TAG and k≤M+DIR_TAG, then distance D=i-K-1;
(2), if i＞K+DIR_TAG and j≤N and k＞M+DIR_TAG, then distance D=N+DIR_TAG-j;
(3), if i≤K+DIR_TAG and j≤N+DIR_TAG and k＞M+1, then distance D=k-M-1;
(4), if i≤K and j＞N+DIR_TAG and k＞M+DIR_TAG, then distance D=K+1-i;
(5), if i≤K+DIR_TAG and j＞N+1 and k≤M+DIR_TAG, then distance D=j-N-1;
(6), if i＞K+DIR_TAG and j＞N+1 and k≤N, then distance D=M+1-k;
B, when T=1, following three kinds of situations are arranged:
(1), if j＞M+N+1, then distance D=M+K+DIR_TAG+1-k;
(2), if k＞K+M+1, then distance D=M+N+DIR_TAG+1-j;
(3), if j≤M+N+1 and k≤K+M+1, then distance D=M+i;
C, when T=2, following four kinds of situations are arranged:
(1), as if i≤M+DIR_TAG and k＞K+DIR_TAG, then:
1., if K 〉=M, then distance D=K+2M+N+DIR_TAG+2-j;
2., as if K＜M, then:
I, if i≤K+DIR_TAG, then distance D=K+2M+N+DIR_TAG+2-j;
II, if i＞K+DIR_TAG, then distance D=K+M+DIR_TAG+k;
(2), as if i≤M+DIR_TAG and k≤K+DIR_TAG, then:
1., if i≤k, then distance D=K+M+DIR_TAG+i;
2., if i＜k, then distance D=K+M+DIR_TAG+k;
(3), as if i＞M+DIR_TAG and k≤K+DIR_TAG, then:
1., if K≤M, then distance D=2K+M+N+DIR_TAG+2-j;
2., as if K＞M, then:
I, if k＞M, then distance D=K+M+DIR_TAG+i;
II, if k≤M, then distance D=2K+M+N+DIR_TAG+2-j;
(4), as if i＞M+DIR_TAG and k＞K+DIR_TAG, then:
1., if K 〉=M, then distance D=K+2M+N+DIR_TAG+2-j;
2., if K＜M, then distance D=2K+M+N+DIR_TAG+2-j;
D, when T=3, following three kinds of situations are arranged:
(1), if j＞M+DIR_TAG, then distance D is K+M+DIR_TAG+1-i;
(2), if j≤M+DIR_TAG and i≤K+M+1, then distance D=K+k;
(3), if i＞K+M+1, then distance D=K+N+DIR_TAG+1-j;
E, when T=4, following three kinds of situations are arranged:
(1), if i＞M+N+1, then distance D=K+N+DIR_TAG+1-k;
(2), if i≤M+N+1 and k≤K+N+1, then distance D=N+j;
(3), if k＞K+N+1, then distance D=M+N+DIR_TAG+1-i;
F, when T=5, following four kinds of situations are arranged:
(1), as if k≤N+DIR_TAG and j≤M+DIR_TAG, then:
1., if j≤k, then distance D=M+N+DIR_TAG+j;
2., if j＞k, then distance D=M+N+DIR_TAG+k;
(2), as if k＞N+DIR_TAG and j≤M+DIR_TAG, then:
1., as if M＞N, then:
I, if j≤N+DIR_TAG, then distance D=K+2M+N+DIR_TAG+2-i;
II, if j＞N+DIR_TAG, then distance D=M+N+DIR_TAG+k;
2., if M≤N, then distance D=K+2M+N+DIR_TAG+2-i;
(3), as if k≤N+DIR_TAG and j＞M+DIR_TAG, then:
1., if M＞N, then distance D=K+M+2N+DIR_TAG+2-i;
2., as if M≤N, then:
I, if k≤M+DIR_TAG, then distance D=K+M+DIR_TAG+2N+2-i;
II, if k＞M+DIR_TAG, then distance D=M+N+DIR_TAG+j;
(4), as if k＞N+DIR_TAG and j＞M+DIR_TAG, then:
1., if M＞N, then distance D=K+M+2N+2+DIR_TAG-i;
2., if M≤N, then distance D=K+2M+N+2+DIR_TAG-i;
G, when T=6, following four kinds of situations are arranged:
(1), as if i＞K+N+1, then:
1., if k＞j, then distance D=MIN (K+2M+N+1+DIR_TAG+j, K+2M+2N+2DIR_TAG+2-j, K＞N? (K+M+2N+DIR_TAG+1+i): (2K+M+N+DIR_TAG+1+i), 2K+2M+N+2DIR_TAG+2-k);
2., if k≤j, then distance D=MIN (K+2M+N+1+DIR_TAG+k, K+2M+2N+2DIR_TAG+2-j, K＞N? (K+M+2N+DIR_TAG+1+i): (2K+M+N+DIR_TAG+1+i), 2K+2M+N+2DIR_TAG+2-k);
(2), as if i≤K+N+1 and j≤K+M+1 and k≤M+N+1, then:
1., as if M＞N, then:
I, if K＞M, then distance D=MIN (K+2M+N+DIR_TAG+1+j, K+M+2N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i);
II, if K≤M, then:
A, if K＞N, then distance D=MIN (K+M+2N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i, 2K+M+N+DIR_TAG+1+j);
B, if K≤N, then distance D=MIN (K+M+2N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+i, 2K+M+N+DIR_TAG+1+j);
2., as if M≤N, then:
I, if K＞M, then:
A, if K＞N, then distance D=MIN (K+2M+N+DIR_TAG+1+j, K+2M+N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i);
B, if K≤N, then distance D=MIN (K+2M+N+DIR_TAG+1+j, K+2M+N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+i);
II, if K≤M, then distance D=MIN (K+2M+N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+j, 2K+M+N+DIR_TAG+1+i);
(3), as if k＞M+N+1, then:
1., if i＞j, distance D=MIN ((M＞N) then? K+M+2N+DIR_TAG+1+k:K+2M+N+DIR_TAG+1+k, 2K+M+2N+2DIR_TAG+2-j, 2K+M+N+DIR_TAG+1+j, 2K+2M+N+2DIR_TAG+2-i);
2., if i≤j, distance D=MIN ((M＞N) then? K+M+2N+DIR_TAG+1+k:K+2M+N+DIR_TAG+1+k, 2K+M+2N+2DIR_TAG+2-j, 2K+M+N+DIR_TAG+1+i, 2K+2M+N+2DIR_TAG+2-i);
(4), as if j＞K+M+1, then:
1., if i＞k, distance D=MIN ((K＞M) then? (K+2M+N+DIR_TAG+1+j): 2K+M+N+DIR_TAG+1+j, K+2M+2N+2DIR_TAG+2-i, K+M+2N+DIR_TAG+1+k, K+M+2N+2DIR_TAG+2-k);
2., if i≤k, distance D=MIN ((K＞M) then? K+2M+N+DIR_TAG+1+j:2K+M+N+DIR_TAG+1+j, K+2M+2N+2DIR_TAG+2-i, K+M+2N+DIR_TAG+1+i, 2K+M+2N+2DIR_TAG+2-k);
H, when T=7, following four kinds of situations are arranged:
(1), as if i≤N+DIR_TAG and j＞K+DIR_TAG, then:
1., if K＞N, then distance D=K+M+2N+DIR_TAG+2-k;
2., as if K≤N, then:
I, if i＞K+DIR_TAG, then distance D=2K+N+2DIR_TAG+j;
II, if i≤K+DIR_TAG, then distance D=K+M+DIR_TAG+2N+2-k;
(2), as if i＞N+DIR_TAG and j＞K+DIR_TAG, then:
1., if K＞N, then distance D=K+M+2N+DIR_TAG+2-k;
2., if K≤N, then distance D=2K+M+N+DIR_TAG+2-k;
(3), as if i＞N+DIR_TAG and j≤K+DIR_TAG, then:
1., as if K＞N, then:
I, if j≤N+DIR_TAG, then distance D=2K+M+N+DIR_TAG+2-k;
II, if j＞N+DIR_TAG, then distance D=K+N+DIR_TAG+i;
2., if K≤N, then distance D=2K+M+N+DIR_TAG+2-k;
(4), as if i≤N+DIR_TAG and j≤K+DIR_TAG, then:
1., if j＜i, then distance D=K+N+DIR_TAG+j;
2., if j 〉=i, then distance D=K+N+DIR_TAG+i.
By using above technical scheme, regular octahedron distance measurement method provided by the invention can be converted to the regular octahedron range observation analysis of 6 extended distance directions, produce the range direction area dividing, the distance of each distance areas inside is only relevant with this zone, and is irrelevant with other zones.Not only realized the range observation of regular octahedron, and since the distance calculation formula all be add, subtract, the multiplication and division arithmetic, calculated amount is little.
Description of drawings
In order to be illustrated more clearly in the embodiment of the invention or technical scheme of the prior art, to do to introduce simply to the accompanying drawing of required use in embodiment or the description of the Prior Art below, apparently, the accompanying drawing that describes below only is some embodiment that put down in writing among the present invention, for those of ordinary skills, can also obtain other accompanying drawing according to these accompanying drawings.
Fig. 1 is the code pattern of the regular octahedron stretch-out view of the embodiment of the invention;
Fig. 2 is the three-dimensional coordinate synoptic diagram of embodiment of the invention positive triangle;
Fig. 3 is the leg-of-mutton three-dimensional coordinate synoptic diagram of embodiment of the invention negative sense;
Fig. 4 is the synoptic diagram of embodiment of the invention triangular network cell abutment relation;
Fig. 5 is the triangular network synoptic diagram of embodiment of the invention regular octahedron stretch-out view;
Fig. 6 is the synoptic diagram of six propagation directions of embodiment of the invention triangular network unit;
Fig. 7 is the areal map of the embodiment of the invention at the A direction analysis formation of forward triangular network unit;
Fig. 8 is the areal map of the embodiment of the invention at the A direction analysis formation of negative sense triangular network unit;
Fig. 9 is the areal map of the embodiment of the invention at the B direction analysis formation of forward triangular network unit;
Figure 10 is the areal map of the embodiment of the invention at the B direction analysis formation of negative sense triangular network unit;
Figure 11 is the areal map of the embodiment of the invention at the C direction analysis formation of forward triangular network unit;
Figure 12 is the areal map of the embodiment of the invention at the C direction analysis formation of negative sense triangular network unit;
Figure 13 is the areal map of the embodiment of the invention at the D direction analysis formation of forward triangular network unit;
Figure 14 is the areal map of the embodiment of the invention at the D direction analysis formation of negative sense triangular network unit;
Figure 15 is the areal map of the embodiment of the invention at the E direction analysis formation of forward triangular network unit;
Figure 16 is the areal map of the embodiment of the invention at the E direction analysis formation of negative sense triangular network unit;
Figure 17 is the areal map of the embodiment of the invention at the F direction analysis formation of forward triangular network unit;
Figure 18 is the areal map of the embodiment of the invention at the F direction analysis formation of negative sense triangular network unit.
Embodiment
In order to make those skilled in the art person understand technical scheme among the present invention better, below in conjunction with the accompanying drawing in the embodiment of the invention, technical scheme in the embodiment of the invention is clearly and completely described, obviously, described embodiment only is the present invention's part embodiment, rather than whole embodiment.Based on the embodiment among the present invention, the every other embodiment that those of ordinary skills obtained should belong to the scope of protection of the invention.
As shown in Figure 1, encode for each triangle and limit in the regular octahedron stretch-out view.Four top triangles are encoded to 0,1,2,3 respectively, four following triangles are encoded to 4,5,6,7 respectively.Wherein, the triangle of coding 0-3 is a positive triangle, and the triangle of coding 4-7 is the negative sense triangle.Each Atria limit is encoded to I, J, K respectively according to counter clockwise direction.Be understandable that shown in Figure 1 only is a kind of in the multiple coded system.Need to prove, which kind of coded system no matter, to algorithm of the present invention and result all less than influence.
For each triangular network unit in the accurate location regular octahedron triangle, need align octahedral each triangle intermediate cam network element and carry out three-dimensional coordinate and represent.
Be that example describes to be encoded to 1 positive triangle below.
As shown in Figure 2, establishing the coordinate that is encoded to certain triangular network unit in 1 the triangle is { t, i, j, k}; Wherein, t is the leg-of-mutton coding of regular octahedron, in this example, and t=1.Be understandable that t ∈ [0,7]; I (i＞0) represents the unit distance farthest of this grid cell and limit I, and in like manner, j (j＞0) represents the unit distance of this network element and limit J, and k (k＞0) represents the unit distance of this network element and limit K.The coordinate that can get the triangular network unit that black region is represented among Fig. 2 according to above definition for 1,4,6,8}.
Be understandable that other positive triangle coded systems are identical with triangle shown in Figure 2.
Be that example describes to be encoded to 4 negative sense triangle below.
As shown in Figure 3, establishing the coordinate that is encoded to certain triangular network unit in 4 the triangle is { t, i, j, k}; Wherein, t is the leg-of-mutton coding of regular octahedron, is understandable that t ∈ [0,7]; I (i＞0) represents the unit distance of this grid cell and limit I, and in like manner, j (j＞0) represents the unit distance of this network element and limit J, and k (k＞0) represents the unit distance of this network element and limit K.The coordinate that can get the triangular network unit that black region is represented among Fig. 2 according to above definition for 4,3,5,7}.
Be understandable that other negative sense triangle coded systems are identical with triangle shown in Figure 3.
A kind of inventor's the distance measuring method based on the plane trigonometry grid is now disclosed:
If any triangle gridding unit is CA in the triangle gridding cellular system, the triangle gridding unit of adjacency is CNCA with it
i, referring to Fig. 4 because with triangular network unit adjacent have 12, so 1≤i≤12.
Distance between any two triangle gridding unit is:
1, CA and the distance of self are zero, promptly DIST (CA, CA)=0;
2, CA and be 1 unit length, i.e. DIST (CNCA in abutting connection with the distance of triangle gridding unit
i, CA)=1, i ∈ 1,2 ..., 12};
3, CB and CA adjacency not, the triangle gridding unit of establishing with the CB adjacency is CNCB
i, i ∈ 1,2 ..., 12},, then CB to the distance of CA than CNCB
iTo the big unit of minimum value and value of CA, that is:
DIST(CB，CA)＝MIN{DIST(CNCB
i，CA)|1≤i≤12}+1。
But the triangle gridding subdivision that is based on regular octahedron is open and flat to the plane, can't constitute the continuous two dimensional surface space of a sealing, the distance measuring method that therefore can not directly use based on the plane trigonometry grid calculates the distance between any triangle gridding on the regular octahedron.But the basic theories of plane trigonometry distance measuring is still set up for regular octahedron triangle gridding subdivision.Lack though regular octahedron launches the flat topology structure, the range distribution rule of the dimension on three limits of triangle gridding unit is constant.Therefore the distance measuring of regular octahedron can be equivalent to the analysis with the propagation direction on limit.The equal space line analysis is carried out on each limit of regular octahedron, can be found to be divided into the some subregions relevant with the limit.The subregion difference, the aspect effect difference.The distance of each subregion equals to arrive the minimum value and value of all directions in this zone.
As shown in Figure 5, at first in the regular octahedron surface, triangular network is set.Align octahedral 6 summits called after P1, P8, P10, P13, P15 and P30 respectively.
As shown in Figure 6, establishing certain forward triangular network unit is a, need to prove, this triangular network unit can be any one triangular network unit in the regular octahedron triangular network.According to three limits of triangular network unit a and the extended line on limit can be 6 propagation directions with tessellation, can distinguish called after A-F direction, be that every and triangular network unit a are the zone of limit adjacency, propagation direction is parallel with this limit, every and initial triangle only is that the summit is adjacent, and then propagation direction is parallel to the limit that this summit faces toward.Propagation direction as A among Fig. 7 is parallel with the limit at a P19, P21 place, but develops towards the limit at a P5, P6 place, and the propagation direction of B is parallel with the limit at a P19, P20 place among Fig. 8, but develops towards the limit at a P13, P25 place.Need to prove, for clear display, other triangular network unit are left out among Fig. 6, only stay the triangular network unit a of black.To analyze respectively all directions below.
At first, the A direction is analyzed.
As shown in Figure 7, be encoded to the little triangle that surrounds by thick straight line in 1 the triangle and also be triangular network unit a.Then the extended line on these three limits, triangular network unit intersects respectively at each rib of regular octahedron.If three summits of this triangular network unit are P19, P20 and P21, the limit of establishing P20, P21 place is a1, and the limit of establishing P19, P20 place is a2, and the limit of establishing P19, P21 place is a3.(coding of Fig. 7 intermediate cam shape is with (0), (1), (2), (3), (4), (5), (6), (7) expression with being encoded to 1 for the extended line of limit a1, coding is identical with Fig. 7 among Fig. 8-18, no longer represent) the limit at triangle mid point P1, P13 place intersect, establishing intersection point is P6.The extended line of limit a1 is folded to along triangular network through some P6 and is encoded in 2 the triangle, and continue to prolong and P13, intersect on the limit at P15 place, if intersection point is P14, and be folded to through P14 and be encoded in 6 the triangle, with P15, intersect on the limit at P30 place, and establishing intersection point is P28, and be folded to through P28 and be encoded in 7 the triangle, with P8, intersect on the limit at P30 place, if intersection point is P29, and is folded to through P29 and is encoded in 4 the triangle, with P8, intersect on the limit at P10 place, if intersection point is P9, and be folded to through P9 and be encoded in 0 the triangle, with a P1, intersect on the limit at P10 place, and establishing intersection point is P4, turning back through P4 is encoded in 1 the triangle, intersects with a P20.The extended line of limit a2 and limit a3 also prolongs in each triangle of regular octahedron according to the triangular network trend and intersects with corresponding limit, and intersection point and extended line all mark in the drawings, are not repeated at this.
Among Fig. 7, for convenience, now adopt frontier point to represent the zone, from then on Qu Yu a frontier point begins, and the solid line in Fig. 7 is demarcated to another frontier point, and finally gets back to initial frontier point.Demarcating around the zone that forms around frontier point promptly is the zone that the present invention will represent.For example, the P20P5P7P17P18P15P28P26P6P21P20 zone is the set in following three zones: center on the zone that forms by line segment P5P6, P6P20, P20P5; Line segment P5P6, P6P28, P28P15, P15P7, P7P5 are around the zone that forms; Line segment P7P15, P15P18, P18P7 are around the zone that forms.
What the A direction was formed in P20P5P7P17P18P15P28P26P6P21P20 zone is initially just penetrating the district, this moment is section P15P28 along the line, line segment P15P18 reflects, and P7P22P24P30P13P15P7 and P14P15P1P8P9P29P28P26P14 form the complete district of just penetrating on A1 and the A2 direction respectively.Ultimate range 2K+3M+2N+2 〉=2K+2M+2N+2 in the P7P22P24P30P13P15P7 zone wherein, therefore, the distance of the extended area that this zone is farther is invalid, and the analysis of this sub-direction can be limited in the one's respective area; The analysis that in like manner can demonstrate,prove the A2 direction can directly be limited in the P7P22P24P30P13P15P7 zone.Obviously there are the overlapping region in P7P22P24P30P13P15P7 and P14P15P1P8P9P29P28P26P14, and the distance in the overlapping region is analyzed, and can obtain subregion shown in Figure 7.Wherein the A2-3 zone only and if only if N＜(K+M+N+1)/2 existence, and its concrete shape is not total triangle as shown in FIG., also can be quadrilateral, and the limit that is had more is the part of P22P24.Following relation is promptly arranged:
During K＞N, be quadrilateral;
During K≤N, be triangle.
According to above analysis principle, analyze at the A direction of negative sense triangular network unit, can obtain subregion as shown in Figure 8.For easy, can divide another name at forward triangular network unit A direction regional analysis and be forward A direction regional analysis and negative sense A direction regional analysis at the A direction regional analysis of negative sense triangular network unit.
Below each subregion is made an explanation:
For brief introduction is represented, introduce the formulate propagation direction:
With
Wherein,
The expression propagation direction is for to expand towards C from an A or B, and its equal space line is parallel with AB;
The expression propagation direction is expansion from an A towards line segment BC, and equal space line is parallel with BC.
With
The propagation direction of expression direction D.Formula
With
Expression is put the pairing distance of E along the propagation direction of direction D.
The A direction is analyzed, can be obtained the zoning map (as shown in Figure 7 and Figure 8, wherein Fig. 7 is a forward, and Fig. 8 is a negative sense) of A direction.Each subregion is as shown in the table.
Analysis to the B direction:
Only analyze the forward situation herein, as shown in Figure 9, what the B direction was formed in P21P6P14P13P25P21 zone is initially just penetrating the district, this moment is section P13P14 along the line, line segment P13P25 reflects, and P6P14P28P29P30P10P13P6 and P12P13P1P15P16P27P25P12 form the complete district of just penetrating on B1 and the B2 direction respectively.Wherein, the part in P6P14P28P29P30P10P13P6 zone can further be divided into P13P25P30P15P8P2P1P10P13 direction and two complete districts of just penetrating of P28P29P4P10P12P30P28, the ultimate range 2K+3M+3N+2 in two zones 〉=2K+2M+2N+2.Therefore, the distance of farther extended area is invalid, and the analysis of this sub-direction can be limited in the one's respective area.
It is the P4P10P11P12P13P25P30P29P23P4 zone that there are the overlapping region in obvious P13P25P30P15P8P2P1P10P13 and P28P29P4P10P12P30P28, because of
So along P1P30 this zone is divided into two parts, its left part is that effective propagation direction of B1-7 is the pairing direction of P28P29P4P10P12P30P28, and all the other zones are the P13P25P30P15P8P2P1P10P13 direction.It should be explained that,
The expression propagation direction is B1, and is parallel with P10P30, towards a P9 expansion.The P28P29P30 zone is analyzed, and there are two propagation directions in the B1 direction in this zone, comprises that the propagation direction of P6P14P28P29P30P10P13P6 is
With the propagation direction of P13P25P30P15P8P2P1P10P13 be
Because
Therefore in should the zone
Direction is invalid.It should be explained that,
The distance that is illustrated in this direction point P30 is K+2M+2N+3.
The overlapping region of P12P13P1P15P16P27P25P12 and P6P14P28P29P30P10P13P6 is P6P13P25P26P14P6, and the propagation direction of this area B is
With
Because
And
Therefore the angular bisector along P15P13P30 is two parts, wherein angular bisector upper section with this area dividing
Direction is invalid, and lower portion
Direction is invalid.
P12P13P1P15P16P27P25P12 will produce two and derive and just penetrate the district, comprise P13P6P1P3P10P9P8P22P29P30P27P15P14P13 and P27P15P14P13P6P5P1P3P2P16P27.Wherein, the P13P6P1P3P10P9P8P22P29P30P27P15P14P13 zone is P13P14P15P27P16P2P3P1P5P13 with the overlapping region in P27P15P14P13P6P5P1P3P2P16P27 zone.Because
And with
Equate, so the angular bisector of P1P15P8 is divided into two parts, angular bisector upper portion with the overlapping region
The P15P16 direction is invalid, lower portion
Direction is invalid.In like manner can handle P13P6P1P3P10P9P8P22P29P30P27P15P14P13 and P13P25P30P15P8P2P1P10P13, the overlay region of P13P25P30P15P8P2P1P10P13 and P13P6P1P3P10P9P8P22P29P30P27P15P14P13.Form as the area dividing among Fig. 9 at last.
B direction at negative sense triangular network unit is analyzed, and can obtain subregion as shown in figure 10.Each subregion basic condition of Fig. 9 and Figure 10 is as shown in the table:
Analysis to the C direction:
As shown in figure 11, P20P21P12P25P27P30P29P22P24P20 be the C direction initially just penetrating the district.Just penetrate the district by this and will be split into two and derive and just penetrate the district, comprising P24P30P25P13P15P7P22P23P24 and P25P27P16P2P8P10P24P30P25.Obviously the ultimate range in these two zones is 2K+2M+3N+2 〉=2K+2M+2N+2, and therefore in the bearing of trend in this two zone, the C direction is with invalid.This two is derived and just penetrate the district and analyze, and the positive area that can obtain among Fig. 9 is divided.Figure 12 divides for negative area.Each subregion basic condition of Figure 11 and Figure 12 is as shown in the table:
Analysis to the D direction:
As shown in figure 13, P20P11P24P10P9P4P20 is for initially just penetrating the district.Produce two extensions respectively and just penetrating the district, comprise P4P10P11P12P13P25P30P28P29P23P4 and P11P24P22P18P8P2P1P3P10.The lap in this two zone is P4P10P11P24P23P9P4, and obviously P8P10P30 angle angular bisector is two parts with this area dividing, and upper-side area is the D2 direction, and downside is the D1 direction.
The P4P10P11P12P13P25P30P28P29P23P4 zone will produce two derives and just penetrates the district, comprises P29P30P24P10P11P12P13P6P14P26P28P29 and P10P13P1P15P8P30P10.Two zones of deriving are overlapped, and P15P30P13 angle bisector is divided into two parts with the overlapping region, and the left side is the diffraction direction of P10P13P1P15P8P30P10, and the right side is the P29P30P24P10P11P12P13P6P14P26P28P29 diffraction direction.
The P11P24P22P18P8P2P1P3P10 zone will produce two derives and just penetrates the district, comprises P22P8P10P1P5P7P22, and P10P8P30P15P13P1P10.This two zone will be cut apart along the P1P8P15 angular bisector, and upper portion is a P10P8P30P15P13P1P10 extension direction, and lower portion (being D1-3) is a P22P8P10P1P5P7P22 extension direction.It should be noted that when K＞(K+M+N+1)/2 the D1-3 zone will comprise the part that drops on the P1P15P13 zone (among Figure 10 because of K＜(K+M+N+1)/2, do not reflect this point).But the D direction is invalid direction in P1P15P13, therefore not impact analysis result.Therefore D direction positive area is divided as shown in figure 13, and negative area is divided as shown in figure 14.Each subregion situation is as shown in the table:
Analysis to the E direction:
As shown in figure 15, initially just penetrate the district for P19P20P4P29P8P16P2P3P19, existing two to derive and just penetrate the district, comprising P9P29P28P14P15P1P8P9 and P2P8P10P30P25P27P2.Obviously be easy to prove that two outside extended areas of just penetrating the district of deriving are the dead space.Further analysis can obtain forward subregion among Figure 15.Figure 16 divides for negative area.Each subregion situation such as following table:
Analysis to the F direction:
As shown in figure 17, initially just penetrate the district for P19P5P7P1P2P3P19, existing two to derive and just penetrate the district, comprising P3P1P13P15P27P2P3 and P5P1P10P8P22P7P5.Obviously the angular bisector of P8P1P15 is divided into two parts with the overlapping region.P1P15P8P30P10P13P1 and P16P27P25P12P13P1P15P16 are just penetrated in deriving of P3P1P13P15P27P2P3.Both overlapping regions are cut-off rule with the angular bisector of P13P15P30.The deriving of P5P1P10P8P22P7P5 just penetrated the district and is P1P10P13P30P15P8P1 and P18P8P1P10P11P24P22.Wherein the cut-off rule of the overlay region of P1P10P13P30P15P8P1 and P1P15P8P30P10P13P1 and P16P27P25P12P13P1P15P16 is respectively P13P30P10 and P8P30P15 angular bisector as shown in figure 12.The cut-off rule of P1P10P13P30P15P8P1 and P18P8P1P10P11P24P22 is the angular bisector of P30P8P10, and promptly the angular bisector lower zone is F2-5.Notice that F2-5 will be extended in the P10P13P30 zone when K＞(K+M+N+1)/2.When M＜(K+M+N+1)/2, F1-5 is extended in the P10P13P30 zone.Figure 17 is a F direction forward region check off fruit, and Figure 18 divides for negative area.Each subregion basic condition is as shown in the table:
The line segment that 1P3P is parallel with P4P6, P point be on this line segment more arbitrarily
At above analysis result, draw the distance calculation formula of regular octahedron below.
Suppose that certain triangle intermediate cam network element A coordinate is { t
A, i
A, j
A, k
A, another triangle intermediate cam network element B coordinate be t, i, j, k}, then the distance calculating method between triangular network unit A and the B is as follows:
At first carries out recompile, the leg-of-mutton coding in A place, triangular network unit is made as 0, and with the triangle recompile at triangular network unit B place, the recompile method is as follows:
If be encoded to T behind the triangle recompile of B place, then
Work as t
A＜4 o'clock:
As t＜4, T=(t-t then
A+ 4) %4;
As t＞3, T=(t-t then
A+ 4) %4+4.
Work as t
A＞3 o'clock:
As t＜4 o'clock, T=(t then
A-t+4) %4+4;
As t＞3 o'clock, T=(t then
A-t+4) %4.
Need to prove, more than " % " representative in four formula get remainder and calculate.
When A place triangle is positive triangle, make DIR_TAG=0; When A place triangle is the negative sense triangle, make DIR_TAG=1.
Behind the recompile, establish:
This moment B coordinate be T, i, j, k}, then the distance D computing method of AB are as follows:
1, when T=0, the triangular network unit B is in and is encoded in 0 the positive triangle, and the computing method of the distance D of AB are had following six kinds of situations:
(1), as i＞K+1 and j≤N+DIR_TAG and k≤M+DIR_TAG, distance D=i-K-1;
(2), as i＞K+DIR_TAG and j≤N and k＞M+DIR_TAG, then distance D=N+DIR_TAG-j;
(3), as i≤K+DIR_TAG and j≤N+DIR_TAG and k＞M+1, then distance D=k-M-1;
(4), as i≤K and j＞N+DIR_TAG and k＞M+DIR_TAG, then distance D=K+1-i;
(5), as i≤K+DIR_TAG and j＞N+1 and k≤M+DIR_TAG, then distance D=j-N-1;
(6), as i＞K+DIR_TAG and j＞N+1 and k≤N, then distance D=M+1-k.
2, when T=1, following three kinds of situations are arranged:
(1), as j＞M+N+1, distance D=M+K+DIR_TAG+1-k then;
(2), as k＞K+M+1, distance D=M+N+DIR_TAG+1-j then;
(3), as j≤M+N+1 and k≤K+M+1, then distance D=M+i.
3, when T=2, following four kinds of situations are arranged:
(1), as i≤M+DIR_TAG and k＞K+DIR_TAG, then:
1., during as K 〉=M, distance D=K+2M+N+DIR_TAG+2-j then;
2., during as K＜M, then:
I, as i≤K+DIR_TAG, distance D=K+2M+N+DIR_TAG+2-j then;
II, as i＞K+DIR_TAG, distance D=K+M+DIR_TAG+k then;
(2), as i≤M+DIR_TAG and k≤K+DIR_TAG, then:
1., during as i≤k, distance D=K+M+DIR_TAG+i then;
2., during as i＜k, distance D=K+M+DIR_TAG+k then;
(3), as i＞M+DIR_TAG and k≤K+DIR_TAG, then
1., during as K≤M, distance D=2K+M+N+DIR_TAG+2-j then;
2., during as K＞M, then:
I, as k＞M, distance D=K+M+DIR_TAG+i then;
II, as k≤M, distance D=2K+M+N+DIR_TAG+2-j then;
(4), as i＞M+DIR_TAG and k＞K+DIR_TAG, then:
1., as K 〉=M, distance D=K+2M+N+DIR_TAG+2-j then;
2., as K＜M, distance D=2K+M+N+DIR_TAG+2-j then.
4, when T=3, following three kinds of situations are arranged:
(1), as j＞M+DIR_TAG, then distance D is K+M+DIR_TAG+1-i;
(2), as j≤M+DIR_TAG and i≤K+M+1, then distance D=K+k;
(3), as i＞K+M+1, distance D=K+N+DIR_TAG+1-j then.
5, when T=4, following three kinds of situations are arranged:
(1), as i＞M+N+1, distance D=K+N+DIR_TAG+1-k then;
(2), as i≤M+N+1 and k≤K+N+1, then distance D=N+j;
(3), as k＞K+N+1, distance D=M+N+DIR_TAG+1-i then.
6, when T=5, following four kinds of situations are arranged:
(1), as k≤N+DIR_TAG and j≤M+DIR_TAG, then:
1., as j≤k, distance D=M+N+DIR_TAG+j then;
2., as j＞k, distance D=M+N+DIR_TAG+k then;
(2), as k＞N+DIR_TAG and j≤M+DIR_TAG, then:
1., as M＞N, then:
I, as j≤N+DIR_TAG, distance D=K+2M+N+DIR_TAG+2-i then;
II, as j＞N+DIR_TAG, distance D=M+N+DIR_TAG+k then;
2., as M≤N, distance D=K+2M+N+DIR_TAG+2-i then;
(3), as k≤N+DIR_TAG and j＞M+DIR_TAG, then:
1., as M＞N, distance D=K+M+2N+DIR_TAG+2-i then;
2., as M≤N, then:
I, as k≤M+DIR_TAG, distance D=K+M+DIR_TAG+2N+2-i then;
II, as k＞M+DIR_TAG, distance D=M+N+DIR_TAG+j then;
(4), as k＞N+DIR_TAG and j＞M+DIR_TAG, then:
1., as M＞N, distance D=K+M+2N+2+DIR_TAG-i then;
2., as M≤N, distance D=K+2M+N+2+DIR_TAG-i then.
7, when T=6, following four kinds of situations are arranged:
(1), as i＞K+N+1, then:
1., as k＞j, distance D=MIN (K+2M+N+1+DIR_TAG+j, K+2M+2N+2DIR_TAG+2-j, K＞N then? (K+M+2N+DIR_TAG+1+i): (2K+M+N+DIR_TAG+1+i), 2K+2M+N+2DIR_TAG+2-k);
Need to prove, in the following formula " K＞N? (K+M+2N+DIR_TAG+1+i): (2K+M+N+DIR_TAG+1+i) " be the condition selection calculation command in the C language, promptly statement 1? order 1: order 2, its implication is as follows: while statement 1 is a true time, fill order 1, not person's fill order 2.In following formula, " K＞N? (K+M+2N+DIR_TAG+1+i): (2K+M+N+DIR_TAG+1+i) " expression, when K＞N is a true time, carry out K+M+2N+DIR_TAG+1+i; Otherwise, carry out 2K+M+N+DIR_TAG+1+i.
2., as k≤j, distance D=MIN (K+2M+N+1+DIR_TAG+k, K+2M+2N+2DIR_TAG+2-j, K＞N then? (K+M+2N+DIR_TAG+1+i): (2K+M+N+DIR_TAG+1+i), 2K+2M+N+2DIR_TAG+2-k);
(2), as i≤K+N+1 and j≤K+M+1 and k≤M+N+1, then:
1., as M＞N, then:
I, as K＞M, distance D=MIN (K+2M+N+DIR_TAG+1+j, K+M+2N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i) then;
II, as K≤M, then:
A, as K＞N, distance D=MIN (K+M+2N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i, 2K+M+N+DIR_TAG+1+j) then;
B, as K≤N, distance D=MIN (K+M+2N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+i, 2K+M+N+DIR_TAG+1+j) then;
2., as M≤N, then:
I, as K＞M, then:
A, as K＞N, then distance D=MIN (K+2M+N+DIR_TAG+1+j, K+2M+N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i);
B, as K≤N, then distance D=MIN (K+2M+N+DIR_TAG+1+j, K+2M+N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+i);
II, as K≤M, then distance D=MIN (K+2M+N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+j, 2K+M+N+DIR_TAG+1+i);
(3), as k＞M+N+1, then:
1., as i＞j, distance D=MIN ((M＞N) then? K+M+2N+DIR_TAG+1+k:K+2M+N+DIR_TAG+1+k, 2K+M+2N+2DIR_TAG+2-j, 2K+M+N+DIR_TAG+1+j, 2K+2M+N+2DIR_TAG+2-i);
2., as i≤j, distance D=MIN ((M＞N) then? K+M+2N+DIR_TAG+1+k:K+2M+N+DIR_TAG+1+k, 2K+M+2N+2DIR_TAG+2-j, 2K+M+N+DIR_TAG+1+i, 2K+2M+N+2DIR_TAG+2-i);
(4), as j＞K+M+1, then:
1., as i＞k, distance D=MIN ((K＞M) then? (K+2M+N+DIR_TAG+1+j): 2K+M+N+DIR_TAG+1+j, K+2M+2N+2DIR_TAG+2-i, K+M+2N+DIR_TAG+1+k, K+M+2N+2DIR_TAG+2-k);
2., as i≤k, distance D=MIN ((K＞M) then? K+2M+N+DIR_TAG+1+j:2K+M+N+DIR_TAG+1+j, K+2M+2N+2DIR_TAG+2-i, K+M+2N+DIR_TAG+1+i, 2K+M+2N+2DIR_TAG+2-k).
8, when T=7, following four kinds of situations are arranged:
(1), as i≤N+DIR_TAG and j＞K+DIR_TAG, then:
1., as K＞N, distance D=K+M+2N+DIR_TAG+2-k then;
2., as K≤N, then:
I, as i＞K+DIR_TAG, distance D=2K+N+2DIR_TAG+j then;
II, as i≤K+DIR_TAG, distance D=K+M+DIR_TAG+2N+2-k then;
(2), as i＞N+DIR_TAG and j＞K+DIR_TAG, then:
1., as K＞N, distance D=K+M+2N+DIR_TAG+2-k then;
2., as K≤N, distance D=2K+M+N+DIR_TAG+2-k then;
(3), as i＞N+DIR_TAG and j≤K+DIR_TAG, then:
1., as K＞N, then:
I, as j≤N+DIR_TAG, distance D=2K+M+N+DIR_TAG+2-k then;
II, as j＞N+DIR_TAG, distance D=K+N+DIR_TAG+i then;
2., as K≤N, distance D=2K+M+N+DIR_TAG+2-k then;
(4), as i≤N+DIR_TAG and j≤K+DIR_TAG, then:
1., as j＜i, distance D=K+N+DIR_TAG+j then;
2., as j 〉=i, distance D=K+N+DIR_TAG+i then.
Regular octahedron distance measurement method of the present invention can be analyzed according to the different diffraction zone of the unit of triangular network, and then draws the regular octahedron range observation formula under the zones of different situation, realizes the range observation of regular octahedron.Because only add, subtract, the multiplication and division arithmetic, thereby calculated amount is little.
As seen through the above description of the embodiments, those skilled in the art can be well understood to the present invention and can realize by the mode that software adds essential general hardware platform.Based on such understanding, the part that technical scheme of the present invention contributes to prior art in essence in other words can embody with the form of software product, this computer software product can be stored in the storage medium, as ROM/RAM, magnetic disc, CD etc., comprise that some instructions are with so that a computer equipment (can be a personal computer, server, the perhaps network equipment etc.) carry out the described method of some part of each embodiment of the present invention or embodiment.
The present invention can be used in numerous general or special purpose computingasystem environment or the configuration.For example: personal computer, server computer, handheld device or portable set, plate equipment, multicomputer system, the system based on microprocessor, set top box, programmable consumer-elcetronics devices, network PC, small-size computer, mainframe computer, comprise distributed computing environment of above any system or equipment or the like.
The above only is the specific embodiment of the present invention; should be as pointing out, for those skilled in the art, under the prerequisite that does not break away from the principle of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.
Claims (5)
1. a regular octahedron distance measurement method is characterized in that, comprising:
In the regular octahedron stretch-out view, arrange triangular network;
The triangular network unit is carried out the regional analysis of six propagation directions and generates regional distribution chart;
Draw the regular octahedron distance calculating method at regional distribution chart.
2. method according to claim 1 is characterized in that, the described regional analysis that the triangular network unit is carried out six propagation directions comprises:
What obtain six propagation directions is initially just penetrating the district;
Obtain two and derive and just penetrate the district by the described direct diffraction in district of initially just penetrating;
Just penetrate district's diffraction and obtain other and derive and just penetrate the district by described deriving;
The a plurality of zones of formation are cut apart in the overlapping region that utilizes angular bisector just to penetrate the district to deriving;
The range observation that the distance in each zone equals to arrive the minimum value and value of all directions in this zone and each intra-zone is only relevant with this zone.
3. method according to claim 1 is characterized in that, describedly draws the regular octahedron distance calculating method at areal distribution and comprises:
For 8 triangles in the regular octahedron stretch-out view are encoded to 0-7 respectively;
Described triangle intermediate cam network element is carried out three-dimensional coordinate to be represented;
Draw the regular octahedron distance calculating method at coordinate relation in the zone.
4. method according to claim 3 is characterized in that, describedly draws the regular octahedron distance calculating method at coordinate relation in the zone and is:
Adopt the method for recompile, the coding of a triangular network unit is made as 0, and then derives the coding of another triangular network unit, establish the T that is encoded to behind another triangular network unit recompile, then
Work as t
A＜4 o'clock:
If t＜4, then T=(t-t
A+ 4) %4;
If t＞3, then T=(t-t
A+ 4) %4+4;
Work as t
A＞3 o'clock:
If t＜4, then T=(t
A-t+4) %4+4;
If t＞3, then T=(t
A-t+4) %4;
According to different T values, draw different regular octahedron distance calculating methods.
5. method according to claim 4 is characterized in that, described regular octahedron distance calculating method is respectively according to eight kinds of different situations of a-h:
A, when T=0, the computing method of distance D have following six kinds of situations:
(1), if i＞K+1 and j≤N+DIR_TAG and k≤M+DIR_TAG, then distance D=i-K-1;
(2), if i＞K+DIR_TAG and j≤N and k＞M+DIR_TAG, then distance D=N+DIR_TAG-j;
(3), if i≤K+DIR_TAG and j≤N+DIR_TAG and k＞M+1, then distance D=k-M-1;
(4), if i≤K and j＞N+DIR_TAG and k＞M+DIR_TAG, then distance D=K+1-i;
(5), if i≤K+DIR_TAG and j＞N+1 and k≤M+DIR_TAG, then distance D=j-N-1;
(6), if i＞K+DIR_TAG and j＞N+1 and k≤N, then distance D=M+1-k;
B, when T=1, following three kinds of situations are arranged:
(1), if j＞M+N+1, then distance D=M+K+DIR_TAG+1-k;
(2), if k＞K+M+1, then distance D=M+N+DIR_TAG+1-j;
(3), if j≤M+N+1 and k≤K+M+1, then distance D=M+i;
C, when T=2, following four kinds of situations are arranged:
(1), as if i≤M+DIR_TAG and k＞K+DIR_TAG, then:
1., if K 〉=M, then distance D=K+2M+N+DIR_TAG+2-j;
2., as if K＜M, then:
I, if i≤K+DIR_TAG, then distance D=K+2M+N+DIR_TAG+2-j;
II, if i＞K+DIR_TAG, then distance D=K+M+DIR_TAG+k;
(2), as if i≤M+DIR_TAG and k≤K+DIR_TAG, then:
1., if i≤k, then distance D=K+M+DIR_TAG+i;
2., if i＜k, then distance D=K+M+DIR_TAG+k;
(3), as if i＞M+DIR_TAG and k≤K+DIR_TAG, then:
1., if K≤M, then distance D=2K+M+N+DIR_TAG+2-j;
2., as if K＞M, then:
I, if k＞M, then distance D=K+M+DIR_TAG+i;
II, if k≤M, then distance D=2K+M+N+DIR_TAG+2-j;
(4), as if i＞M+DIR_TAG and k＞K+DIR_TAG, then:
1., if K 〉=M, then distance D=K+2M+N+DIR_TAG+2-j;
2., if K＜M, then distance D=2K+M+N+DIR_TAG+2-j;
D, when T=3, following three kinds of situations are arranged:
(1), if j＞M+DIR_TAG, then distance D is K+M+DIR_TAG+1-i;
(2), if j≤M+DIR_TAG and i≤K+M+1, then distance D=K+k;
(3), if i＞K+M+1, then distance D=K+N+DIR_TAG+1-j;
E, when T=4, following three kinds of situations are arranged:
(1), if i＞M+N+1, then distance D=K+N+DIR_TAG+1-k;
(2), if i≤M+N+1 and k≤K+N+1, then distance D=N+j;
(3), if k＞K+N+1, then distance D=M+N+DIR_TAG+1-i;
F, when T=5, following four kinds of situations are arranged:
(1), as if k≤N+DIR_TAG and j≤M+DIR_TAG, then:
1., if j≤k, then distance D=M+N+DIR_TAG+j;
2., if j＞k, then distance D=M+N+DIR_TAG+k;
(2), as if k＞N+DIR_TAG and j≤M+DIR_TAG, then:
1., as if M＞N, then:
I, if j≤N+DIR_TAG, then distance D=K+2M+N+DIR_TAG+2-i;
II, if j＞N+DIR_TAG, then distance D=M+N+DIR_TAG+k;
2., if M≤N, then distance D=K+2M+N+DIR_TAG+2-i;
(3), as if k≤N+DIR_TAG and j＞M+DIR_TAG, then:
1., if M＞N, then distance D=K+M+2N+DIR_TAG+2-i;
2., as if M≤N, then:
I, if k≤M+DIR_TAG, then distance D=K+M+DIR_TAG+2N+2-i;
II, if k＞M+DIR_TAG, then distance D=M+N+DIR_TAG+j;
(4), as if k＞N+DIR_TAG and j＞M+DIR_TAG, then:
1., if M＞N, then distance D=K+M+2N+2+DIR_TAG-i;
2., if M≤N, then distance D=K+2M+N+2+DIR_TAG-i;
G, when T=6, following four kinds of situations are arranged:
(1), as if i＞K+N+1, then:
1., if k＞j, then distance D=MIN (K+2M+N+1+DIR_TAG+j, K+2M+2N+2DIR_TAG+2-j, K＞N? (K+M+2N+DIR_TAG+1+i): (2K+M+N+DIR_TAG+1+i), 2K+2M+N+2DIR_TAG+2-k);
2., if k≤j, then distance D=MIN (K+2M+N+1+DIR_TAG+k, K+2M+2N+2DIR_TAG+2-j, K＞N? (K+M+2N+DIR_TAG+1+i): (2K+M+N+DIR_TAG+1+i), 2K+2M+N+2DIR_TAG+2-k);
(2), as if i≤K+N+1 and j≤K+M+1 and k≤M+N+1, then:
1., as if M＞N, then:
I, if K＞M, then distance D=MIN (K+2M+N+DIR_TAG+1+j, K+M+2N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i);
II, if K≤M, then:
A, if K＞N, then distance D=MIN (K+M+2N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i, 2K+M+N+DIR_TAG+1+j);
B, if K≤N, then distance D=MIN (K+M+2N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+i, 2K+M+N+DIR_TAG+1+j);
2., as if M≤N, then:
I, if K＞M, then:
A, if K＞N, then distance D=MIN (K+2M+N+DIR_TAG+1+j, K+2M+N+DIR_TAG+1+k, K+M+2N+DIR_TAG+1+i);
B, if K≤N, then distance D=MIN (K+2M+N+DIR_TAG+1+j, K+2M+N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+i);
II, if K≤M, then distance D=MIN (K+2M+N+DIR_TAG+1+k, 2K+M+N+DIR_TAG+1+j, 2K+M+N+DIR_TAG+1+i);
(3), as if k＞M+N+1, then:
1., if i＞j, distance D=MIN ((M＞N) then? K+M+2N+DIR_TAG+1+k:K+2M+N+DIR_TAG+1+k, 2K+M+2N+2DIR_TAG+2-j, 2K+M+N+DIR_TAG+1+j, 2K+2M+N+2DIR_TAG+2-i);
2., if i≤j, distance D=MIN ((M＞N) then? K+M+2N+DIR_TAG+1+k:K+2M+N+DIR_TAG+1+k, 2K+M+2N+2DIR_TAG+2-j, 2K+M+N+DIR_TAG+1+i, 2K+2M+N+2DIR_TAG+2-i);
(4), as if j＞K+M+1, then:
1., if i＞k, distance D=MIN ((K＞M) then? (K+2M+N+DIR_TAG+1+j): 2K+M+N+DIR_TAG+1+j, K+2M+2N+2DIR_TAG+2-i, K+M+2N+DIR_TAG+1+k, K+M+2N+2DIR_TAG+2-k);
2., if i≤k, distance D=MIN ((K＞M) then? K+2M+N+DIR_TAG+1+j:2K+M+N+DIR_TAG+1+j, K+2M+2N+2DIR_TAG+2-i, K+M+2N+DIR_TAG+1+i, 2K+M+2N+2DIR_TAG+2-k);
H, when T=7, following four kinds of situations are arranged:
(1), as if i≤N+DIR_TAG and j＞K+DIR_TAG, then:
1., if K＞N, then distance D=K+M+2N+DIR_TAG+2-k;
2., as if K≤N, then:
I, if i＞K+DIR_TAG, then distance D=2K+N+2DIR_TAG+j;
II, if i≤K+DIR_TAG, then distance D=K+M+DIR_TAG+2N+2-k;
(2), as if i＞N+DIR_TAG and j＞K+DIR_TAG, then:
1., if K＞N, then distance D=K+M+2N+DIR_TAG+2-k;
2., if K≤N, then distance D=2K+M+N+DIR_TAG+2-k;
(3), as if i＞N+DIR_TAG and j≤K+DIR_TAG, then:
1., as if K＞N, then:
I, if j≤N+DIR_TAG, then distance D=2K+M+N+DIR_TAG+2-k;
II, if j＞N+DIR_TAG, then distance D=K+N+DIR_TAG+i;
2., if K≤N, then distance D=2K+M+N+DIR_TAG+2-k;
(4), as if i≤N+DIR_TAG and j≤K+DIR_TAG, then:
1., if j＜i, then distance D=K+N+DIR_TAG+j;
2., if j 〉=i, then distance D=K+N+DIR_TAG+i.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN2010105266145A CN102044076A (en) | 2010-10-29 | 2010-10-29 | Distance measuring method for regular octahedron |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN2010105266145A CN102044076A (en) | 2010-10-29 | 2010-10-29 | Distance measuring method for regular octahedron |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN102044076A true CN102044076A (en) | 2011-05-04 |
Family
ID=43910190
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN2010105266145A Pending CN102044076A (en) | 2010-10-29 | 2010-10-29 | Distance measuring method for regular octahedron |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN102044076A (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4941114A (en) * | 1987-03-26 | 1990-07-10 | Kabushiki Kaisha Toshiba | Triangular mesh generation method |
| US6073068A (en) * | 1996-12-05 | 2000-06-06 | Caterpillar Inc. | Method for determining the elevation of a point on a work site represented in a triangular irregular network |
| FR2826719A1 (en) * | 2001-07-02 | 2003-01-03 | Gilbert Alexandre Dibon | Map overlay grid sheet for determining the distance of a planned journey, has plastic transparent overlay sheet containing a printed grid of crossing lines which form a multitude of equilateral triangles |
| CN1967596A (en) * | 2006-08-14 | 2007-05-23 | 东南大学 | Construction method of triangulation of 3D scattered point set in 3D scan system |
| CN101192307A (en) * | 2006-11-17 | 2008-06-04 | 鸿富锦精密工业（深圳）有限公司 | Point cloud triangular topological relations construction method |
| CN101685008A (en) * | 2008-09-23 | 2010-03-31 | 中国科学院地理科学与资源研究所 | Triangular grid system, three-dimensional coordinate system and distance measuring method |
-
2010
- 2010-10-29 CN CN2010105266145A patent/CN102044076A/en active Pending
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4941114A (en) * | 1987-03-26 | 1990-07-10 | Kabushiki Kaisha Toshiba | Triangular mesh generation method |
| US6073068A (en) * | 1996-12-05 | 2000-06-06 | Caterpillar Inc. | Method for determining the elevation of a point on a work site represented in a triangular irregular network |
| FR2826719A1 (en) * | 2001-07-02 | 2003-01-03 | Gilbert Alexandre Dibon | Map overlay grid sheet for determining the distance of a planned journey, has plastic transparent overlay sheet containing a printed grid of crossing lines which form a multitude of equilateral triangles |
| CN1967596A (en) * | 2006-08-14 | 2007-05-23 | 东南大学 | Construction method of triangulation of 3D scattered point set in 3D scan system |
| CN101192307A (en) * | 2006-11-17 | 2008-06-04 | 鸿富锦精密工业（深圳）有限公司 | Point cloud triangular topological relations construction method |
| CN101685008A (en) * | 2008-09-23 | 2010-03-31 | 中国科学院地理科学与资源研究所 | Triangular grid system, three-dimensional coordinate system and distance measuring method |
Non-Patent Citations (2)
| Title |
|---|
| 《测绘学报》 20050225 袁文,等 一种新的球面三角投影：等角比投影（EARP） 第34卷, 第01期 2 * |
| 《遥感学报》 20090115 袁文,等 基于等角比例投影的球面三角四叉树剖分模型 第13卷, 第01期 2 * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106780738B (en) | Path site optimization method based on environmental sensitive area of power transmission and transformation project | |
| US9886791B2 (en) | Three-dimensional information processing device | |
| Zhu et al. | Parking simulation of three-dimensional multi-sized star-shaped particles | |
| Su et al. | Uncertainty-aware visualization and proximity monitoring in urban excavation: a geospatial augmented reality approach | |
| CN103226844A (en) | Three-dimensional geological tunnel modeling method based on spatial data structure system | |
| CN107102991A (en) | A kind of shaft tower parametric modeling method in three-dimension GIS system | |
| CN108959333A (en) | Gas ductwork method for automatic modeling and system based on augmented reality | |
| CN103970837A (en) | Discontinuous DEM classified manufacturing method based on urban land and vertical planning | |
| CN102044076A (en) | Distance measuring method for regular octahedron | |
| CN116662473A (en) | Space database establishment method, device, equipment and storage medium | |
| Bhargava et al. | Triangulated irregular network model from mass points | |
| Kennie et al. | Digital terrain modelling | |
| CN111368468A (en) | Method for solving two-dimensional boundary of centralized village based on mathematical method and programming algorithm | |
| CN110096564A (en) | A kind of route independent positioning method, apparatus and system based on BIM+GIS | |
| van Toll et al. | The explicit corridor map: Using the medial axis for real-time path planning and crowd simulation | |
| CN109597870A (en) | A kind of assessment method of geodata availability | |
| CN114627254B (en) | Composite geographic information data plane coordinate decryption method and model | |
| CN113609691B (en) | Intersection modeling processing method oriented to intelligent traffic simulation | |
| Yin et al. | Visibility analysis for three-dimension urban landscape | |
| Zong et al. | Symbolic expressions of differences between Earth radii | |
| Li et al. | Study on a general cutting algorithm of complex blocks | |
| Chao et al. | Crystal-modeler: A tool for geometric analysis and three-dimensional modeling of crystal forms based on rectangular coordinates in space | |
| Zhu et al. | A new 3D visible space index for evaluating urban openness | |
| Kallay | Defining edges on a round earth | |
| CN103034782A (en) | Coarse-set-based multi-granularity space direction relation uncertainty evaluation method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C12 | Rejection of a patent application after its publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20110504 |