CN104123739A - Coding and decoding methods of polyhedron composed of face elements and stereoscopic puzzle - Google Patents
Coding and decoding methods of polyhedron composed of face elements and stereoscopic puzzle Download PDFInfo
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- CN104123739A CN104123739A CN201310148268.5A CN201310148268A CN104123739A CN 104123739 A CN104123739 A CN 104123739A CN 201310148268 A CN201310148268 A CN 201310148268A CN 104123739 A CN104123739 A CN 104123739A
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Abstract
The invention discloses a coding method of a polyhedron composed of face elements to convert structural information of the polyhedron to an assembling code. The coding method comprises the following steps: Step a, a reference vertex is coded and each last face element which is coded for the first time is marked; Step b, the next reference vertex is searched along an annular route formed by vertexes of the last face elements which are coded for the first time and an expanded spiral route, and coding is carried out according to the route information; and the step a and the step b are repeated until coding is finished. The invention also discloses a corresponding decoding method capable of restoring the assembling code to a predetermined polyhedron shape. The invention also discloses a corresponding stereoscopic puzzle. By reading the assembling code, the face elements of an entity are assembled to form a predetermined real polyhedron stereoscopic shape. By replacing a three-dimensional assembly drawing and an unfolding drawing with the code, manufacturing costs can be reduced. Assembling order information is also provided and can be used in manufacturing and assembling of puzzles, models, teaching aids and the like.
Description
Technical field
The present invention relates to a kind of polyhedral coding and coding/decoding method and cubic pasteup, particularly a kind of polyhedral coding being formed by bin part and coding/decoding method and cubic pasteup.
Background technology
In the real three-dimensional shape of structure, in order to describe correct installation method, conventionally use three-dimensional assembly drawing.This three-dimensional assembly drawing combines the perspective pattern of structure element, and is marked with assembling sequence.It draws more complicated, and cost of manufacture is higher.
For the polyhedron three-dimensional shape forming with face structural detail, conventionally with the stretch-out view of structural surface, polyhedral structure is described, for example: shown in " Fig. 6-2 ... launch schematic diagram " in Chinese patent 201120379415.6 " regular polygon combination magic square that can be interconnected ".Draw still more complicated of this stretch-out view, and can not directly indicate assembled order.In the time that polyhedral structure complicates, as concaver, structure, large-scale combined moulding etc. with hole, or face structure is while being with figuratum printed matter, represents it is more difficult by stretch-out view, and, when assembled, be difficult to determine assembled order according to stretch-out view.
Summary of the invention
The object of the invention is to: a kind of polyhedral coding method being made up of bin part is provided, by the flow process of coding method, polyhedral structural information is converted to assembled coding.The present invention also provides corresponding coding/decoding method, by the flow process of coding/decoding method, assembled coding is reduced to predetermined polyhedron-shaped.The present invention also provides corresponding cubic pasteup, by reading assembled coding, by the step of coding/decoding method, the bin part of entity is assembled into predetermined real polyhedron three-dimensional shape.
Object of the present invention is achieved through the following technical solutions:
The polyhedral coding method being made up of bin part, using a polyhedral summit as the first reference point, forms bin part as the first reference plane using one of the first reference point, and polyhedron is encoded, and it is characterized in that, comprises the following steps:
A. the first reference point is encoded, and using the last bin part of encoding first as the second reference plane;
Described encodes and comprises the first reference point, and since the first reference plane, according to the first sense of rotation, all formation bin parts of traversal the first reference point, encode according to the information of bin part; Described information comprises the not coding maker of bin part and forms the index value at angle;
When polyhedral all bin parts be all encoded out-of-date, end-of-encode;
The first described sense of rotation is clockwise or counter clockwise direction; Coding described in this step can also comprise the first sense of rotation; This coding method can be arranged a first fixing sense of rotation, and in the time that the fixed-direction of the first sense of rotation and agreement is identical, coding can omit the first sense of rotation to reduce coding output length;
Described not coding maker is the mark whether bin part was encoded;
Described formation angle is the angle at the first reference point of bin part; The index value at described formation angle is the data for searching bin part and formation angle, for example, be numbering, predefine numerical value, memory address etc.; Element is not while encoding first face to face, can omit angle index value, to reduce coding output length;
B. the circuit forming along the summit of the second reference plane, searching route terminal and the 3rd reference plane, and encode according to routing information;
Described circuit, is taking the first reference point as starting point, according to the second sense of rotation, and the non-closed path that all summits of traversal the second reference plane form; Described path termination is the summit with uncoded formation bin part; The 3rd described reference plane is the bin part in first orientation that points to the end path of path termination; Described routing information comprises path information;
In the time searching for less than path termination, end-of-encode;
The second described sense of rotation is clockwise or counter clockwise direction, identical or different with the first sense of rotation; Coding described in this step can also comprise the second sense of rotation; This coding method can be arranged a second fixing sense of rotation, and in the time that the fixed-direction of the second sense of rotation and agreement is identical, coding can omit the second sense of rotation to reduce coding output length;
Described path information can comprise path step-length numerical value, also can comprise the mark that represents path extreme value, for example the longest or the shortest mark;
Described routing information can also comprise the information on the summit of path process, while being used in decoding, verifies that whether path is correct;
Described first orientation is the left side or the right; In the time that search pattern only limits to the summit of the second reference plane, in the 3rd reference plane on the right side in the path that turns clockwise, or being rotated counterclockwise the 3rd reference plane in left side in path, be equal to the second reference plane; Coding described in this step can also comprise first orientation; This coding method can be arranged a fixing first orientation, and in the time that the constant bearing of first orientation and agreement is identical, coding can omit first orientation to reduce coding output length;
C. using path termination as the first reference point, using the 3rd reference plane as the first reference plane, re-execute step a and subsequent step thereof.
On the basis of the above, this coding method also can be done following improvement:
In step a, also comprise the angle information that is adjacent face according to bin part and encode;
Described angle information can comprise numerical value or scope or the concavo-convex mark of angle, for bin part being loaded into the position that meets angle information in the time decoding.
This improved procedure can be specified the angle relation of bin part and adjacent surface; Can reduce to angular range or concavo-convex encoding flag the data volume that coding is exported.
On the basis of the above, this coding method also can be done following improvement:
In step b, circuit is extended to the spiral routes with the second sense of rotation rotation, and in spiral routes searching route terminal;
The described spiral routes that extends to is that the inferior last term point from current search route starts, by the reverse direction of the second sense of rotation, around the adjacent vertex on most end summit; When finding first not when the summit in route, take this summit as new most end summit, by new most end summit repetitive operation to determine the next summit of route process; In the time that all adjacent vertexs on most end summit are all on route, search pattern is ended.
The effect of this improved procedure is, in the time that complicated polyhedron is encoded, if original route finishes and searches for less than the summit with uncoded formation bin part, can extend route, and again find the summit with uncoded formation bin part at extension route, thereby reduce because coding finishes to cause the uncoded situation of part bin part in advance.
On the basis of the above, this coding method also can be done following improvement:
Select many group initial parameters and execution parameter, the many groups of output polyhedron coded data, sorts many group codings data, selects the prepreerence coding of sequence as final output encoder;
Described initial parameter can comprise the first reference point, can also comprise the first reference plane;
Described execution parameter can comprise the first sense of rotation in step a, can also comprise the second sense of rotation in step b, can also comprise the position of the path termination in step b, can also comprise the first orientation in step b;
The quantity that the key word of described sequence comprises output formation face, can also comprise the length that coding is exported.
This improved procedure can be selected the coding through optimizing from many group codings.
Utilize the coded data of above method output, can, by the reverse mode that reads coded data, polyhedron coded data be decoded:
The polyhedral coding/decoding method being made up of bin part, by reading coded data, decodes to polyhedron coded data, it is characterized in that, comprises the following steps:
D. read one section of summit construction data group, the not solution code mark that this data group comprises one group of bin part and angle index value; Since the first reference plane, according to the first sense of rotation, decode whole formation faces of the first reference point according to vertex data group; And the bin part of the last decoding first of mark is as the second reference plane;
E. read stretch footpath data, this packet is containing path information; Since the first reference point, according to the second sense of rotation, all summits of traversal the second reference plane, and search pattern is extended to the spiral routes with the second sense of rotation rotation, decode path termination according to path data; And using the bin part in first orientation in end path that points to path termination on path as the 3rd reference plane;
F. using path termination as the first reference point, using the 3rd reference plane as the first reference plane, re-execute steps d and subsequent step thereof;
When all coded datas all read when complete, decoding finishes;
The initial value of the first described reference point is virtual initial reference point, and the initial value of the first described reference plane is the virtual formation face of of initial reference point;
The first described sense of rotation is clockwise or counter clockwise direction; Described construction data group can also comprise the first sense of rotation; In the time that construction data group does not comprise the first sense of rotation, using the first fixing sense of rotation of arranging as the first sense of rotation;
The described code mark of not separating is whether bin part is the mark of decoding first;
Described angle index value is the data for searching bin part and formation angle; Element is while decoding first face to face, according to angle index value loading surface element with form angle; Whether element is not while decoding first face to face, ignores and loads an already present bin part, can be correct according to angle index value checking bin part;
Described summit construction data group can also comprise the angle information of bin part; Described angle information can comprise numerical value or scope or the concavo-convex mark of angle, in the time of decoding, bin part is loaded into the position that meets angle information;
The second described sense of rotation is clockwise or counter clockwise direction; Described path data can also comprise the second sense of rotation; In the time that path data does not comprise the second sense of rotation, using the second fixing sense of rotation of arranging as the second sense of rotation;
The described spiral routes that extends to is that the inferior last term point from current search route starts, by the reverse direction of the second sense of rotation, around the adjacent vertex on most end summit; When finding first not when the summit in route, take this summit as new most end summit, by new most end summit repetitive operation to determine the next summit of route process; In the time that all adjacent vertexs on most end summit are all on route, search pattern is ended;
Described path information can comprise path step-length numerical value or represent the mark of path extreme value; When path packets of information is during containing path step-length numerical value, taking the summit that arrives after described step-length numerical value from starting point as path termination; When path packets of information is during containing the mark of extreme value, have and do not load the summit that forms bin part as path termination using first or last on search pattern;
Described routing information can also comprise the information on the summit of path process, while being used in decoding, verifies that whether path is correct;
Described first orientation is the left side or the right; In the time that search pattern only limits to the summit of the second reference plane, in the 3rd reference plane on the right side in the path that turns clockwise, or being rotated counterclockwise the 3rd reference plane in left side in path, be equal to the second reference plane; Described path data can also comprise first orientation; In the time that path data does not comprise first orientation, using the fixing first orientation of arranging as first orientation.
Utilize above-mentioned coding method and coding/decoding method, except can processing polyhedral structure data, the bin part of entity can also be assembled into actual polyhedron three-dimensional shape in computer process:
The polyhedron cubic pasteup being made up of bin part, according to polyhedron decoding code, is assembled into the polyhedron-shaped of solid by the bin part of entity.It is characterized in that:
Cubic pasteup is made up of multiple bin parts and decoding code; The angle of described bin part has angle index value; Described decoding code is spaced and is formed by multiple summits structure code-group and path code; Not solution code mark and angle index value that described summit structure code-group comprises one group of bin part; Described path code packages is containing path information;
The assembling method of picture mosaic is similar to the polyhedral coding/decoding method that utilizes computer process, comprises the following steps:
G. read one section of summit structure code-group; Since the first reference plane, according to the first sense of rotation, according to summit code-group assembled go out whole formation faces of the first reference point; And the last assembled bin part of mark is as the second reference plane;
H. read stretch footpath code; Since the first reference point, according to the second sense of rotation, all summits of traversal the second reference plane, and search pattern is extended to the spiral routes with the second sense of rotation rotation, according to path code search outbound path terminal; And using the bin part in first orientation in end path that points to path termination on path as the 3rd reference plane;
I. using path termination as the first reference point, using the 3rd reference plane as the first reference plane, re-execute step g and subsequent step thereof;
When all decoding codes all read when complete, assembled end;
The initial value of the first described reference point is virtual initial reference point, and the initial value of the first described reference plane is the virtual formation face of of initial reference point;
The first described sense of rotation is clockwise or counter clockwise direction; Described structure code-group can also comprise the first sense of rotation; When structure code-group is not while comprising the first sense of rotation, using the first fixing sense of rotation of arranging as the first sense of rotation;
The described code mark of not separating is whether bin part is assembled first mark;
Described angle index value is the information for searching bin part and formation angle; Element is while decoding first face to face, according to the assembled bin part of angle index value with form angle; Whether element is not while decoding first face to face, ignores an assembled already present bin part, can be correct according to angle index value checking bin part;
Described summit structure code-group can also comprise the angle information of bin part; Described angle information can comprise numerical value or scope or the concavo-convex mark of angle, in when decoding by the assembled bin part position to meeting angle information;
The second described sense of rotation is clockwise or counter clockwise direction; Described path code can also comprise the second sense of rotation; In the time that path code does not comprise the second sense of rotation, using the second fixing sense of rotation of arranging as the second sense of rotation;
The described spiral routes that extends to is that the inferior last term point from current search route starts, by the reverse direction of the second sense of rotation, around the adjacent vertex on most end summit; When finding first not when the summit in route, take this summit as new most end summit, by new most end summit repetitive operation to determine the next summit of route process; In the time that all adjacent vertexs on most end summit are all on route, search pattern is ended;
Described path information can comprise path step-length numerical value or represent the mark of path extreme value; When path packets of information is during containing path step-length numerical value, taking the summit that arrives after described step-length numerical value from starting point as path termination; When path packets of information is during containing the mark of extreme value, have and do not load the summit that forms bin part as path termination using first or last on search pattern;
Described routing information can also comprise the information on the summit of path process, while being used in decoding, verifies that whether path is correct;
Described first orientation is the left side or the right; In the time that search pattern only limits to the summit of the second reference plane, in the 3rd reference plane on the right side in the path that turns clockwise, or being rotated counterclockwise the 3rd reference plane in left side in path, be equal to the second reference plane; Described path code can also comprise first orientation; In the time that path code does not comprise first orientation, using the fixing first orientation of arranging as first orientation.
On the basis of the above, this polyhedron cubic pasteup also can be done following improvement:
The angle index value at identical angle is identical;
Described identical angle can comprise, the angle of the same position of multiple identical bin parts;
Described identical angle can also comprise, multiple angles with identical rotational symmetry of same bin part.
This improved procedure can reduce the quantity of angle index value, is conducive to find fast when assembled corresponding bin part and assembled angle.
On the basis of the above, this polyhedron cubic pasteup also can be done following improvement:
Angle index value is the apparent parameter of bin part and corresponding angles;
Described apparent parameter can comprise shape or size; Wherein can comprise having rotational symmetric n-shaped bin part N time, its angle index value is N; Wherein can also comprise, angle index value is number of degrees size or the scope at angle;
Described apparent parameter can also comprise word, pattern or color; Wherein can comprise, angle index value is word or pattern, and the angle of bin part has the mark of angle index value, and the angle index value in decoding code is corresponding word or pattern; Wherein can also comprise, angle index value is color, and the angle of bin part has corresponding color mark, and the angle index value in decoding code is color pattern.
This improved procedure has been optimized the angle index value of entity, is conducive to find fast when assembled corresponding bin part and assembled angle.
On the basis of the above, this polyhedron cubic pasteup also can be done following improvement:
On the angle of bin part, have the mark of assembled serial number, the angle index value of bin part comprises corresponding serial number;
Described serial number is the numbering of order of representation, for example, 1,2,3..., a, b, c..., etc.
This improved procedure is conducive to when assembled find fast corresponding bin part and assembled angle, and intuitively shows assembled order.
On the basis of the above, this polyhedron cubic pasteup also can be done following improvement:
The angle of bin part has the fragment of decoding code; Comprising, the angle of bin part has the code snippet of the bin part of the summit structure code-group corresponding with its serial number; The code snippet of described bin part can also comprise the code snippet of bin part continuous with it and that there is no angle index value, can also comprise the path code snippet continuous with it;
The angle of described bin part can also have the code snippet of the first sense of rotation; The first angle of the summit structure code-group at the described Shi Qi place, angle with the first sense of rotation code snippet;
Described code snippet can be word or pattern, wherein can comprise, path code is word or pattern.
This improved procedure is dispersed in decoding code on bin part, by bin part with decoding code combination together with.
The invention has the beneficial effects as follows: a kind of polyhedral coding method being made up of bin part is provided, by the flow process of coding method, polyhedral structural information can be converted to assembled coding.The present invention also provides corresponding coding/decoding method, by the flow process of coding/decoding method, assembled coding can be reduced to predetermined polyhedron-shaped.The present invention also provides corresponding cubic pasteup, by reading assembled coding, by the step of coding/decoding method, the bin part of entity can be assembled into predetermined real polyhedron three-dimensional shape.The present invention substitutes three-dimensional assembly drawing and stretch-out view with coding, can reduce cost of manufacture, and assembled order information is provided, and can be used for the making of picture mosaic, model, teaching aid etc. and assembled.
Brief description of the drawings
Fig. 1 is the process flow diagram that polyhedron is carried out to text code.
Fig. 2 is the process flow diagram of output vertex tectonic information cross-talk flow process.
Fig. 3 is the process flow diagram of outgoing route message segment sub-process.
Fig. 4 is the process flow diagram that polyhedron is carried out to text decoding.
Fig. 5 is the schematic diagram that opposite element arranges angle index value.
Fig. 6 is the schematic diagram that figuratum bin part is arranged to angle index value.
Fig. 7 is the schematic diagram that the bin part to there being 2 rotational symmetries arranges angle index value.
Fig. 8 is the schematic diagram that the bin part to there being 6 rotational symmetries arranges angle index value.
Fig. 9 is the schematic diagram of pentagonal prism being implemented to coding.
Figure 10 is cube coding schematic diagram.
Figure 11 is regular dodecahedron coding schematic diagram.
Figure 12 is truncated cube coding schematic diagram.
Figure 13 is that little oblique side cuts half icosahedron coding schematic diagram.
Figure 14 is lozenge element schematic diagram.
Figure 15 is the assembled parallelepipedon coding schematic diagram of lozenge element.
Figure 16 is the assembled granatohedron coding schematic diagram of lozenge element.
Figure 17 is the convex polyhedron coding schematic diagram of cube and four rib job mixs.
Figure 18 is that cube is removed the concave polyhedron coding schematic diagram that four rib vertebras form.
Figure 19 is the schematic diagram that illustrates a summit of decoding.
Figure 20 illustrates the schematic diagram of finding next the first reference point and the first reference plane by circuit and helix route.
Figure 21 is pentagonal prism assembled the 1st step schematic diagram of decoding.
Figure 22 is pentagonal prism assembled the 2nd step schematic diagram of decoding.
Figure 23 is pentagonal prism assembled the 3rd step schematic diagram of decoding.
Figure 24 is pentagonal prism assembled the 4th step schematic diagram of decoding.
Figure 25 is pentagonal prism assembled the 5th step schematic diagram of decoding.
Figure 26 is pentagonal prism assembled the 6th step schematic diagram of decoding.
Figure 27 is pentagonal prism assembled the 7th step schematic diagram of decoding.
Figure 28 is that cube is removed concave polyhedron assembled the 1st step schematic diagram of decoding that four rib vertebras form.
Figure 29 is that cube is removed concave polyhedron assembled the 2nd step schematic diagram of decoding that four rib vertebras form.
Figure 30 is that cube is removed concave polyhedron assembled the 3rd step schematic diagram of decoding that four rib vertebras form.
Figure 31 is that cube is removed concave polyhedron assembled the 4th step schematic diagram of decoding that four rib vertebras form.
Figure 32 is that cube is removed concave polyhedron assembled the 5th step schematic diagram of decoding that four rib vertebras form.
Figure 33 is that cube is removed concave polyhedron assembled the 6th step schematic diagram of decoding that four rib vertebras form.
Figure 34 is that cube is removed concave polyhedron assembled the 7th step schematic diagram of decoding that four rib vertebras form.
Figure 35 is that cube is removed concave polyhedron assembled the 8th step schematic diagram of decoding that four rib vertebras form.
Figure 36 is that cube is removed concave polyhedron assembled the 9th step schematic diagram of decoding that four rib vertebras form.
Figure 37 is the 1st the bin part schematic diagram with irregular pattern.
Figure 38 is the 2nd the bin part schematic diagram with irregular pattern.
Figure 39 is the 3rd the bin part schematic diagram with irregular pattern.
Figure 40 is the 4th the bin part schematic diagram with irregular pattern.
Figure 41 is the 5th the bin part schematic diagram with irregular pattern.
Figure 42 is the 6th the bin part schematic diagram with irregular pattern.
Figure 43 is the 7th the bin part schematic diagram with irregular pattern.
Figure 44 is the schematic diagram of the polyhedron cubic pasteup assembled by the bin part with irregular pattern.
Figure 45 is the 4th the bin part schematic diagram with decoding fragment pattern.
Figure 46 is the 7th the bin part schematic diagram with decoding fragment pattern.
Embodiment
In the following discussion, for the present invention is described up hill and dale, a large amount of details has been proposed.But those of ordinary skill in the art should understand also can realize the present invention in the situation that there is no specific detail.Below in conjunction with accompanying drawing, typical embodiment of the present invention is described in further detail.
Fig. 1 is a process flow diagram that polyhedron is carried out to text code.Key step comprises:
Step 100: program starts, input parameter comprises polyhedral structure data, initial the first reference point, the first initial reference plane etc., and the variable using in predefine flow process.
Step 110: call output vertex tectonic information cross-talk flow process, export one section of summit tectonic information section text code.
Step 120: testing process end mark.
Step 130: if flow process end mark is set up, end-of-encode, returns results.
Step 140: if flow process end mark is not set up, call outgoing route message segment sub-process, output stretch footpath message segment text code.
Step 150: testing process end mark, if flow process end mark is not set up, jumps to the step of calling output vertex tectonic information cross-talk flow process.
Step 160: if flow process end mark is set up, end-of-encode, returns to coding result.
Fig. 2 is the process flow diagram of output vertex tectonic information cross-talk flow process.Key step comprises:
Step 170: sub-process starts.
Step 180: since the first reference plane, travel through clockwise the formation face of the first reference point.
In the present embodiment, in the time traveling through the first initial reference point, comprise the first initial reference plane, in the time of remaining other first reference points of traversal, not comprise the first reference plane.Can avoid so first coded faces always to encode, with Optimized Coding Based structure and length.
In the present embodiment, agreement in a clockwise direction as fixing around direction, and all coding summits all with this fixing directional ring around, can omit like this output ring around direction, reduce the output length of coding.If be not fixing direction around direction, in the time that starting, traversal around direction, for example, can represent (Clockwise) clockwise by output character " C " by output ring, output " A " represents (Anticlockwise) counterclockwise.
Step 190: detect whether formation face is uncoded.
Step 200: if formation face is not uncoded, output null character string is as the encoded mark of this face, and the circulation of continuation traversal.Do not export in the present embodiment the index value at the angle of the formation face of having encoded, in other embodiments, can export the information of describing formation face and angle yet, in the time of decoding, can verify that whether decode procedure is correct.
Step 210: the angle information of exporting this face and front one side.
In the present embodiment, only output represents whether angle is the mark " ^ " of re-entrant angle, to reduce the output length of coding.Also can export the angle numerical value of angle, for example " 120 ° "; Also can export the quadrature at the angle place representing with " I ", " II ", " III ", " IV " etc.Only export in the present embodiment and the angle information of front one side, also can export the angle information of all adjacent surfaces of this face, concrete instruction erection method while being beneficial to decode, but can increase the output length of coding.
Step 220: the angle index value of exporting this face.
In the present embodiment, the angle index value of output can be the index value that forms the angle of face in polyhedral structure data, or other predefined numerical value or texts, as long as can find corresponding bin part and angle by this angle index value.In the time of polyhedron-shaped coding the to entity, angle index value can be various words or pattern or other marks, as long as can find by this mark the bin part of corresponding entity, and finds corresponding angle.
Step 230: the value of revising the not coding maker of this face.
Step 240: this face of mark is the second reference plane.
Step 250: continue the traversal circulation of the formation face of the first reference point.
Step 260: output text is optimized, can deletes and not affect the continuous coding maker of the end of decoded result.
Step 270: detect whether all faces were all output at least 1 time.
Step 280: if all faces were all output at least 1 time, setting procedure end mark.
Step 290: sub-process finishes, returns to main flow.
Fig. 3 is the process flow diagram of outgoing route message segment sub-process.Ergodic algorithm in the present embodiment, can take into account circuit and spiral routes, and its original route is the summit of the second reference plane, and after original route finishes, extends to spiral route.Key step comprises:
Step 300: sub-process starts, the variable using in definitim flow also carries out initialization.Wherein, while calling this sub-process at every turn, all will to summit whether the mark in route carry out initialization.
Step 310: the inferior last term point of original route is set, taking the first reference point as starting point.
Step 320: the most end summit that the anticlockwise next summit that the second reference plane is set is original route.
In the present embodiment, agreement is using counterclockwise as fixing sense of rotation, and all non-closed path are all with this fixing direction rotation, can omit like this output sense of rotation, reduces the output length of coding.
Step 330: the mark in route that most end summit in original route and time last term point are set.
Step 340: the formation face on traversal most end summit.
Step 350: whether the formation face that detects most end summit is what not encoded.
Step 360: continue the traversal circulation of the formation face on most end summit.
Step 370: if most end summit does not have the formation face of not encoding, from inferior last term point, travel through clockwise the adjacent vertex on most end summit.
Step 380: detect adjacent vertex whether in route.
Step 390: continue the traversal circulation of the adjacent vertex on most end summit.
Step 400: if all adjacent vertexs on most end summit all on route, setting procedure end mark.
Step 410: sub-process finishes, returns to main flow.
Step 420: if most end summit has the formation face of not encoding, start outgoing route message segment.In the present embodiment, using character " | " as the initial mark of routing information section.
In the present embodiment, if described in step 320, the output length of agreement counterclockwise to encode with minimizing as fixing sense of rotation.If sense of rotation is not fixing direction, be at this step output beginning flag " | " afterwards, output sense of rotation, for example " C " or " A ".
Step 430: output terminal step number.
In the present embodiment, use a kind of method of optimizing output: if be counted as 1, ignore output counting, otherwise the counting that output represents with negative value; Can in the time of decoding, whether be negative value afterwards by character " | " like this, judge whether routing information section finishes, thereby can omit the tectonic information section beginning flag repeating subsequently, to reduce special separator, Optimized Coding Based structure, and reduce the length of output encoder.
In the present embodiment, select first summit with the formation face of not exporting as path termination, and the counting on outgoing route summit.Can select to omit the counting on outgoing route summit, only using beginning flag " | " as shortest path mark, to reduce the output length of coding.Also other summits with the formation face of not exporting on can selection schemer are as path termination, and the counting on outgoing route summit.
Step 440: it is next the first reference point that most end summit is set.
Step 450: the face that path ends left side is set is the 3rd reference plane, is also next the first reference plane.
In the present embodiment, agreement is using left side as fixing first orientation, and the 3rd all reference planes is all in this fixing orientation, can omit like this end of output orientation, reduces the output length of coding.If first orientation is not fixing orientation, in the time that finishing, this step export first orientation, for example, represent left side (Left) with output character " L ", output " R " represents right side (Right).
Step 460: sub-process finishes, returns to main flow.
Step 470,480: be new most end summit if adjacent vertex not in route, arranges this adjacent vertex, and former most end summit be set for time last term point.
Step 490: the mark of most end summit in route is set.
Step 500: path vertices is counted, and jumped to and detect most end summit and whether there is the step of the formation face of not exporting.
Utilize the coded data of above method output, can, by reverse mode, coded data be decoded.Fig. 4 is a process flow diagram that polyhedron is carried out to text decoding.Key step comprises:
Step 510: program starts, input parameter comprises coded data, with polyhedral bin part structured data of angle index value etc., and the variable using in predefined process.Note, in the time of assembled summit first, the first reference point and the first reference plane are virtual not designated values.
Step 520: read the coding of the continuous summit construction data group of first paragraph, and be decomposed into list.Due to the first paragraph not belt path message segment of encoding, therefore read separately.
Step 530: according to table data, by the clockwise direction of agreement in the time encoding, the formation face on this summit of decoding.
If list items, with not separating code mark, loads the structured data of a structural surface by the angle index value in coding; If list items comprises the mark of re-entrant angle, load this face and arrive and the position of front one side in re-entrant angle; And the last face loading of mark is the second reference plane;
If list items without not separating code mark, is ignored a decoded formation face.
In the present embodiment using agreement fixed-direction as the first sense of rotation, if construction data group has comprised the first sense of rotation, should be undertaken assembled by the first sense of rotation in construction data group.
Only decode according to the mark of re-entrant angle in the present embodiment, the particular location of bin part can utilize the structured data of the structured data of bin part and assembled part to carry out space calculating to determine.If angle information also comprises angle numerical value and the angular range of angle, decoding process can also be decoded by angle numerical value and angular range.
Step 540: detect coding and whether read end.
Step 550: if coding reads end, decode procedure finishes.
Step 560: read the hybrid coding of stretch footpath data and summit construction data group, first extract path data, analysis path data, take out path step number.
Step 570: according in the counter clockwise direction of when coding agreement around the second reference plane, the initial terminal vertex of initialization circuit and helix route and time terminal vertex.
In the present embodiment using agreement fixing sense of rotation as the second sense of rotation, if path data has also comprised specific the second sense of rotation, the second sense of rotation in data is around the second reference plane by path.
Step 580: detect path counting and whether reached path step number.
Step 590: if path counting has reached path step number, using terminal vertex as the first reference point, using the face in path ends left side as the first reference plane, re-execute the step of decoding summit structural surface.
In the present embodiment using agreement left side as first orientation, if path data has also comprised specific first orientation, the first orientation in data is selected next the first reference plane by path.
Step 600: if path counting does not reach path step number, search next step summit of route.If path data also comprises the list of path vertices, can verify the whether identical path data in current summit.
Step 610: extend route, and jump to detection path and count the step that whether has reached path step number.
The angle index value of bin part, for searching bin part and corresponding angle, if polyhedral each structural surface is not identical, each angle of structural surface is not identical yet, is tackled the angle of each face and is distributed different angle index values to distinguish.If polyhedral bin part or angle are identical, for convenience of decoding and assembled, identical angle index value is distributed at the angle that can be the same position of identical face, for distributing identical angle index value in the angle with rotational symmetry of face.
In Fig. 5, although quadrilateral element has the angle at two angles to equate, owing to there is no rotational symmetry, decoding and when assembled two angles can not exchange use, therefore can be each angle and distribute different angle index values.
In Fig. 6, although be with figuratum regular hexagon element shape to have rotational symmetry, pattern has been done restriction to its symmetry, therefore for different angle index values is distributed at each angle.
In Fig. 7, be with equally figuratum regular hexagon element because pattern has rotational symmetry 2 times, identical angle index value can be distributed in two relative angles therefore with rotational symmetry.
In Fig. 8, there is rotational symmetric regular hexagon element 6 times, can be 6 angles and distribute identical angle index value unitedly.If in one group of bin part, only have a kind of rotational symmetric regular hexagon element that has 6 times of size, face numbering and angle numbering merging can be numbered to " 6 ".Do not have equally the figuratum equilateral triangle with the single size length of side, square, regular pentagon etc., in program, can respectively angle index value be made as to " 3 ", " 4 ", " 5 " etc.
Fig. 9 is the embodiment schematic diagram to pentagonal prism polyhedron coding.In the present embodiment, bin part is to have rotational symmetric positive N shaped element part N time, and the angle index value of square and regular pentagon is respectively " 4 " and " 5 ".Selected initial the first reference point (700), initial the first reference plane (701); Around the first reference point (700), export clockwise all formation faces (701,702,703), coding output " 5,4,4 "; Taking the first reference point (700) as starting point, counterclockwise around the second reference plane (703), find the summit (704) that first has the formation face of not encoding, its path is 1, the path " | " that therefore output is ignored; Taking path ends summit (704) as the first reference point, path ends left surface (703) is the first reference plane, output formation face (705,701,703), coding " 4,, ", be optimized for " 4 "; In like manner, find next first reference point (706), outgoing route length " | ", output comprises the coding " 4 " of new formation face (707); Find next first reference point (708), outgoing route length " | ", output comprises the coding " 4 " of new formation face (709); From initial vertax (708), all formation faces along first summit (710) of route are exported, second summit (711) in path has not the formation face (712) of output, therefore outgoing route length " |-2, "; In like manner, export last formation face (712) and be encoded to " 5 ".Comprehensive above output, according to the coding of the present embodiment flow process output is finally:
“5，4，4|4|4|4|-2，5”
Can find out from above-mentioned coding, the Output rusults of the present embodiment program substitutes polyhedron stretch-out view with the coding of textual form, and the information of assembled order is provided.
If the input parameter in coding flow process is selected different initial the first reference points and initial the first reference plane, the present embodiment flow process will obtain different Output rusults, and the coding of for example one group of initial first reference point (700) and initial the first reference plane (703) output is:
“4，5，4|5|4|-2，4|4”
Select another to organize initial the first reference point (700) and initial the first reference plane (702), the coding of the present embodiment flow process output is:
“4，4，5|4|5|-2，4|-2，4”
Can increase on stream new step, from above several group codings, select more preferential conduct finally to export.Should preferentially select the coding of output construction face quantity maximum, in the present embodiment, because the quantity of the structural surface of exporting is identical, can consider to use other key word sequences, for example, while considering assembled decoding, first select the face of size maximum as first assembled, flow process will be exported " 5; 4,4|4|4|4|-2,5 " as net result.
In addition, the summit that can arrange to have the formation face of output not using first on search pattern is as path termination, at this moment can omit path, and using routing information section beginning flag character " | " as shortest path mark, coding can further be reduced to:
“5，4，4|4|4|4|5”
When to this code decoding, correct decoding, as path termination, also can be carried out in the summit that has the formation face of decoding not using first on search pattern.
In Figure 10, the cube being made up of square, due to the symmetry of structure, starts all to export identical coding from arbitrary initial the first reference point and initial the first reference plane, and the output of the present embodiment flow process is:
“4，4，4|4|4|-2，4”
In Figure 11, the regular dodecahedron being made up of regular pentagon, starts coding from arbitrary initial the first reference point and initial the first reference plane, and the output of the present embodiment flow process is:
“5，5，5|5|5|5|-2，5|5|-2，5|-2，5|-2，5|-3，5”
In Figure 12, the truncated cube being formed by triangle and octagon, from selected initial the first reference point (720) and initial the first reference plane (721), the coding of the output of the present embodiment flow process is:
“8，3，8|3|8|3|8|3|8|-3，3|8|3|-3，3|-3，3”
In the coding of above-mentioned output, the output that has comprised 2 places " |-3 ", be the present embodiment flow process after traveled through leg-of-mutton 2 summits of last output, in the spiral routes of extending, find next the first reference point, and path code exported.
In Figure 13, the little oblique side's icosidodecahedron being formed by triangle, square, regular pentagon, from selected initial the first reference point (730) and initial the first reference plane (731), the coding of the output of the present embodiment flow process is:
“5，4，3，4|3，4|3，4|3，4|3|4，5|4|5|4|5|4|5|4|5|-2，4，3|4|3，4|3|4|3，4|3|4|3，4|3|4|3，4|3|4|3|4，5|-2，4|5|-2，4|5|-2，4|5|-2，4|5|-3，4，3|4|3|4|3|4|3|4|3|-2，，5”
In the structural code of the final stage summit of above-mentioned coding, the output that has comprised 1 place ",, ", wherein continuous two list separators have represented to export the coding maker of an already present formation face.In the time of decoding, the continuous decoded mistake of list separator presentation surface element, skip an already present bin part.
In Figure 14, lozenge element has Rotational Symmetry angle 2 times, and the index value that one of them angle (801) can be set is A, and the index value of another angle (802) is B, other index value also can be set, as long as can distinguish and find this two kinds of angles.
For the rhombohedron in Figure 15, from initial the first reference point (811) and initial the first reference plane (812), the coding of the output of the present embodiment flow process is:
“A，A，A|A|B|-2，B”
Equally, for granatohedron in Figure 16, from initial the first reference point (821) and initial the first reference plane (822), the coding of the output of the present embodiment flow process is:
“A，A，A，A|B|A，A|-2，A，A|-2，A，A|-2，A”
In Figure 17, the convex polyhedron being combined into by cube and rectangular pyramid, from initial the first reference point (901) and initial the first reference plane (902), the coding of the output of the present embodiment flow process is:
“4，4，4|4|3，3|3|3，4”
In Figure 18, remove by cube the concave polyhedron that rectangular pyramid forms, from initial the first reference point (911) and initial the first reference plane (912), the coding of the output of the present embodiment flow process is:
“4，4，4|4|3，^3|^3|^3，4”
From above 2 coding contrasts, the present embodiment flow process has added the mark that represents re-entrant angle in the coding of concave polyhedron.If accurately describe the angle relation between adjacent surface, can accurately export the angle number of degrees including concave, convex angle.
Figure 19 for example understands the decoding process to a summit.If the coding of the construction data group reading be " 4;; 3 " from current the first reference point (1100) and the first reference plane (1101), decoding process will be in the direction of the clock (1103) load first foursquare bin part (1104).Reading after continuous 2 separators ",, ", decoding process will be skipped an already present formation face (1102).Then loading a gore element (1105), has decoded in summit.
Figure 20 illustrated find the flow process of next the first reference point and the first reference plane by circuit and helix route.If the routing information reading coding be " |-4 ... ", from current the first reference point (1200) and the second reference plane (1201), decoding process will be obtained first route summit (1202) by counter clockwise direction.Respectively along follow-up route summit (1203,1204), reaching the 4th route summit (1206) afterwards, take this summit as next the first reference point, taking last directed walk left surface (1205) as next the first reference plane.The path step number indicated if encoded further strengthens, and decoding program will further extend helix route (1250) as shown in phantom in FIG., and step number is found next the first reference point and the first reference plane by path.
Figure 21-Figure 27 is the embodiment schematic diagram to the decoding of pentagonal prism polyhedron.The output encoder of the coding flow process shown in corresponding diagram 9:
“5，4，4|4|4|4|-2，5”
For clear narration decoding process, in the pentagonal prism polyhedron in Figure 21-Figure 27 and Fig. 9, summit pentagonal prism polyhedron spins upside down, can be with reference to corresponding reference numerals.In Figure 21, selected initial the first reference point (700), determines first formation face from first section of coding " 5,4,4 " first arbitrarily, corresponding initial the first reference plane (701).At Figure 22, Tu23Zhong, assembled remaining 2 bin parts in order, comprising last assembled bin part (703).Because a triangular pyramidal taking the first reference point as summit can be determined in the angle of three faces, therefore the shape on the assembled summit of 3 faces is fixed, and does not need the angle parameter between face and face to mate.
In Figure 24, according to next section coding " | 4 ", decoding process is in the end in the summit of assembled bin part (703), select and the counterclockwise adjacent summit of the first reference point (700), as next the first reference point (704), load a facing element that angle index value is " 4 ".Equally, at Figure 25, Tu26Zhong, from follow-up continuous 2 sections " | 4 " codings, 2 bin parts after assembled.
In Figure 27, from next section coding " |-2,5 ", decoding process, along circuit counterclockwise, from current the first reference point (708), finds next the first reference point (711) by 2 footpath, step step numbers, assembled last bin part.If this section of coding is the coding without path step-length, as the embodiment with shortest path mark in Fig. 9, its corresponding code snippet is " | 5 ", at circuit through first assembled complete summit (in Figure 26 710), while arriving second not assembled complete summit (711), the summit that has the bin part of not decoding using this is as next the first reference point, the coming to the same thing of decoding.
Above-mentioned decode procedure, also can decode by the step of specifying, and by reading coding, by bin part reality, that have angle index value, is reduced into coding represented polyhedron-shaped really.
Figure 28-Figure 36 is the embodiment schematic diagram of cube being removed to the concave polyhedron decoding of four rib vertebras formation.The output encoder of the concave polyhedron cataloged procedure shown in corresponding Figure 18:
“4，4，4|4|3，^3|^3|^3，4”
In Figure 28, selected initial the first reference point (911), determines first bin part from first section of coding " 4,4,4 " first arbitrarily, corresponding initial the first reference plane (912).At Figure 29, Tu30Zhong, assembled remaining 2 faces in order.In Figure 31, from next section coding " | 4 " assembled next face of decoding.
In Figure 32, from next section coding " | 3, ^3 ", decoding process is at assembled the 5th face; In Figure 33, by the mark that is re-entrant angle of the angle in coding, assembled one is the 6th face of re-entrant angle with the 5th face angle.For the first current reference point (as in Figure 31 1301), because the shape of having decoded is fixed, its vacant locations is also fixed position, and therefore its vacant locations forms the angle of virtual; The angle of adding 2 bin parts to the angle of virtual, can form 2 kinds of protruding or recessed stable space triangular tapers.Therefore, need assembled completely according to coding summit, and adjacent surface is these two conditions of re-entrant angle, calculates by bin part structured data, or by the bin part of assembled entity, can determine the loading position of the 5th and the 6th bin part.Can also, according to the coding that comprises accurate output angle numerical value, carry out assembled decoding or check assembled shape.
Afterwards, decoding process is by identical decoding step, can be assembled goes out remaining, in Figure 34, corresponding coding " | ^3 ", as Figure 35, Tu36Zhong, corresponding coding " | ^3,4 ".
Figure 37-Figure 43 is the bin part schematic diagram with irregular pattern, different from the regular polygon element with rotational symmetry, can not be using general " 4 ", " 5 " etc. as angle index value, and the angle of bin part should have corresponding with it index value.Can use the apparent parameters such as word, pattern or color as angle index value, these apparent parameters can directly be marked on the angle of bin part, can be marked at the front of bin part, also can be marked at reverse side; Also can be printed on the instructions of entity cubic pasteup apparent parameter as mark.
In the present embodiment, using the serial number of layout again as angle index value, and on the thumbnail of instructions or on the angle of bin part, mark angle index.According to the output flow process of Fig. 9 with as the target shape with predetermined pattern of Figure 44, in Figure 37, the angle index value " 1 " of shown bin part is labeled on corresponding angle (1511); In Figure 38, the angle index value " 2 " of shown bin part is labeled on corresponding angle (1521); In Figure 39, the angle index value " 3 " of shown bin part is labeled on corresponding angle (1531); In Figure 40, the angle index value " 4 " of shown bin part is labeled on corresponding angle (1541); In Figure 41, the angle index value " 5 " of shown bin part is labeled on corresponding angle (1551); In Figure 42, the angle index value " 6 " of shown bin part is labeled on corresponding angle (1561); In Figure 43, the angle index value " 7 " of shown bin part is labeled on corresponding angle (1571).
According to the output flow process of Fig. 9, the angle index value in decoding code is replaced by:
“1，2，3|4|5|6|-2，7”
Or the code of shortest path mark:
“1，2，3|4|5|6|7”
According to above decoding code, can be oppositely according to coding/decoding method, bin part is assembled into and is with figuratum polyhedron three-dimensional shape as Figure 44 predetermined.
Also can use other apparent parameters as angle index value, for example angle index value " 1 ", " 2 ", " 3 ", " 4 ", " 5 ", " 6 ", " 7 " can be replaced with to corresponding color value: red, orange, yellow, green, blue, blue, purple, by the mode of mark or instructions, angle index value is corresponding with the angle of bin part, and decoding code is replaced by " red; orange; Huang | green | green grass or young crops | indigo plant |-2; purple ", color value wherein can replace with corresponding pattern, can reduce predetermined three-dimensional shape according to coding/decoding method equally.This improved procedure has been optimized the angle index value of entity, is conducive to find fast corresponding bin part and assembled angle when assembled, can also increase the interest of picture mosaic simultaneously.
In Figure 37-Figure 43, the index value at the angle of bin part is serial number, can have actual serial number mark on the angle of solid face element, can also be with the fragment of decoding code.
In Figure 37, the angle with serial number is with corresponding code snippet " 1 ".In Figure 38, the angle with serial number is with corresponding code snippet " 2 ".In Figure 39, the angle with serial number is with corresponding code snippet " 3 ".In Figure 40, the angle with serial number is with corresponding code snippet " | 4 ", and wherein, code snippet " | " is that default path length is 1 path code.In Figure 41, the angle with serial number is with corresponding code snippet " | 5 ".In Figure 42, the angle with serial number is with corresponding code snippet " | 6 ".In Figure 43, the angle with serial number is with corresponding code snippet " |-2,7 ".
When structure angle corresponding in code snippet is with the mark of decoded mistake, and during without angle index, continuous separator in the encode fragment of the as shown in figure 13 little oblique side's icosidodecahedron of example ";; ", this code snippet can merge to same summit structure code-group before or after the code snippet with angle index value in.
In the time of the assembled bin part with code snippet, select corresponding bin part and angle according to serial number, by reading angle institute with code snippet, according to coding/decoding method, bin part is assembled into and is with figuratum polyhedron three-dimensional shape as Figure 44 predetermined.This improved procedure together with decoding code combination, can save independent instructions by bin part, saves cost.
In the above-described embodiments, there is place code snippet continuous path code before with the angle of serial number; In other schemes, also can there is place code snippet continuous path code afterwards, for example, the code snippet in Figure 39, Figure 40, Figure 41, Figure 42, Figure 43 can change respectively " 3| ", " 4| ", " 5| ", " 6|-2 ", " 7 " into, is equivalent for decoding process.
Can also further code snippet be represented with pattern.In Figure 45, be the bin part corresponding with Figure 40, path code " | " in its code snippet is special circular pattern, in like manner, the path code of the bin part corresponding with Figure 41, Figure 42 can be also same circular pattern code.In Figure 46, path code is the text that circular pattern adds upper pathway step number, can also omit path step number text, carrys out searching route terminal with aforesaid paths minimum value.
The above embodiment is preferred embodiment of the present invention; embodiments of the present invention are not limited to this; under enlightenment of the present invention; according to ordinary skill knowledge and the customary means of this area; do not departing under the above-mentioned basic fundamental thought of the present invention prerequisite; the present invention can also make equivalent modifications, replacement or the change of other various ways, all belongs to protection scope of the present invention.Protection scope of the present invention is covered by claim and equivalents thereof.
Claims (10)
1. the polyhedral coding method being made up of bin part, using a polyhedral summit as the first reference point, forms bin part as the first reference plane using one of the first reference point, and polyhedron is encoded, and it is characterized in that, comprises the following steps:
A. the first reference point is encoded, and using the last bin part of encoding first as the second reference plane;
Described encodes and comprises the first reference point, and since the first reference plane, according to the first sense of rotation, all formation bin parts of traversal the first reference point, encode according to the information of bin part; Described information comprises the not coding maker of bin part and forms the index value at angle;
B. the circuit forming along the summit of the second reference plane, searching route terminal and the 3rd reference plane, and encode according to routing information;
Described circuit, is taking the first reference point as starting point, according to the second sense of rotation, and the non-closed path that all summits of traversal the second reference plane form; Described path termination is the summit with uncoded formation bin part; The 3rd described reference plane is the bin part in first orientation that points to the end path of path termination; Described routing information comprises path information;
C. using path termination as the first reference point, using the 3rd reference plane as the first reference plane, re-execute step a and subsequent step thereof.
2. coding method according to claim 1, is characterized in that:
In step a, also comprise the angle information that is adjacent face according to bin part and encode.
3. coding method according to claim 1, is characterized in that:
In step b, circuit is extended to the spiral routes with the second sense of rotation rotation, and in spiral routes searching route terminal.
4. according to one of coding method described in claim 1-3, it is characterized in that:
Select many group initial parameters and execution parameter, the many groups of output polyhedron coded data, sorts many group codings data, selects the prepreerence coding of sequence as final output encoder.
5. the polyhedral coding/decoding method being made up of bin part, by reading coded data, decodes to polyhedron coded data, it is characterized in that, comprises the following steps:
D. read one section of summit construction data group, the not solution code mark that this data group comprises one group of bin part and angle index value; Since the first reference plane, according to the first sense of rotation, decode whole formation faces of the first reference point according to vertex data group; And the bin part of the last decoding first of mark is as the second reference plane;
E. read stretch footpath data, this packet is containing path information; Since the first reference point, according to the second sense of rotation, all summits of traversal the second reference plane, and search pattern is extended to the spiral routes with the second sense of rotation rotation, decode path termination according to path data; And using the bin part in first orientation in end path that points to path termination on path as the 3rd reference plane;
F. using path termination as the first reference point, using the 3rd reference plane as the first reference plane, re-execute steps d and subsequent step thereof.
6. the polyhedron cubic pasteup being made up of bin part, according to polyhedron decoding code, is assembled into the polyhedron-shaped of solid by the bin part of entity.It is characterized in that:
Cubic pasteup is made up of multiple bin parts and decoding code; The angle of described bin part has angle index value; Described decoding code is spaced and is formed by multiple summits structure code-group and path code; Not solution code mark and angle index value that described summit structure code-group comprises one group of bin part; Described path code packages is containing path information;
The assembling method of picture mosaic comprises the following steps:
G. read one section of summit structure code-group; Since the first reference plane, according to the first sense of rotation, according to summit code-group assembled go out whole formation faces of the first reference point; And the last assembled bin part of mark is as the second reference plane;
H. read stretch footpath code; Since the first reference point, according to the second sense of rotation, all summits of traversal the second reference plane, and search pattern is extended to the spiral routes with the second sense of rotation rotation, according to path code search outbound path terminal; And using the bin part in first orientation in end path that points to path termination on path as the 3rd reference plane;
I. using path termination as the first reference point, using the 3rd reference plane as the first reference plane, re-execute step g and subsequent step thereof.
7. polyhedron cubic pasteup according to claim 6, is characterized in that:
The angle index value at identical angle is identical.
8. polyhedron cubic pasteup according to claim 6, is characterized in that:
Angle index value is the apparent parameter of bin part and corresponding angles.
9. polyhedron cubic pasteup according to claim 6, is characterized in that:
On the angle of bin part, have the mark of assembled serial number, the angle index value of bin part comprises corresponding serial number.
10. polyhedron cubic pasteup according to claim 9, is characterized in that:
The angle of bin part has the fragment of decoding code; Comprising, the angle of bin part has the code snippet of the bin part of the summit structure code-group corresponding with its serial number.
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Application publication date: 20141029 |