CN104504202B - A kind of interactive computer aids in paper folding design method - Google Patents
A kind of interactive computer aids in paper folding design method Download PDFInfo
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- CN104504202B CN104504202B CN201410815053.9A CN201410815053A CN104504202B CN 104504202 B CN104504202 B CN 104504202B CN 201410815053 A CN201410815053 A CN 201410815053A CN 104504202 B CN104504202 B CN 104504202B
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Abstract
The present invention relates to computer interaction design field, more particularly to a kind of interactive computer auxiliary paper folding design method.Interactive computer auxiliary paper folding design method comprises the following steps：Input threedimensional model；Extract the three-dimensional framework of the threedimensional model；According to the three-dimensional framework, the threedimensional model is resolved into semantic multiple basic bodies；The multiple basic body is fitted with solid, similar geometry body corresponding with each basic body is found；Adjusting needs the joint face of connection between the similar geometry body.The paper folding pattern that the design method provided using the present invention is produced allows to cut out and pasted, and highly difficult, the high complexity mode for individual paper folding pattern do not cut out compared with tradition is more suitable for domestic consumer, is particularly suitable for children.
Description
Technical field
The present invention relates to computer interaction design field, more particularly to a kind of interactive computer auxiliary paper folding design side
Method.
Background technology
Paper folding is a kind of sacrifice art originating from East Asia, and that widespread is Japanese paper folding " Origami " the most, is to make
With a common plane paper do not cut out do not paste in the case of be folded into threedimensional model.Although modern many paper folding art are big
Teacher can be only with a piece of paper with regard to that can fold the paper folding moulding for visually making us very much being pleasantly surprised, but this art is with high
Difficulty and complexity, are not appropriate for ordinary populace, are particularly not suitable for children.
One active multidisciplinary research field, including mathematics, art are already turned into based on computer assisted paper folding
And computer science.But, most research work is all to concentrate on how to generate three-dimensional folding that is complicated, having artistry
Pattern formula, or some specific designs of applied mathematics principle analysis.Which how few people not to have superb paper folding for if being concerned about
The ordinary people of technology develops a kind of paper folding design system of strong applicability.In addition, existing interactive computer design system is all
It is that the artist with certain professional knowledge or adult fan design to be, and is not suitable for not possessing the general of these technical ability
Logical masses, are particularly not suitable for children.
The content of the invention
Paper folding design method, Ke Yibang are aided in the technical problem to be solved in the present invention is to provide a kind of interactive computer
Help almost the user without professional knowledge by Arbitrary 3 D modelling into the paper folding pattern easily folded.
In order to solve the above-mentioned technical problem, paper folding design method, bag are aided in the invention provides a kind of interactive computer
Include following steps：
Input threedimensional model；
Extract the three-dimensional framework of the threedimensional model；
According to the three-dimensional framework, the threedimensional model is resolved into semantic multiple basic bodies；
The multiple basic body is fitted with solid, similar geometry body corresponding with each basic body is found；
Adjusting needs the joint face of connection between the similar geometry body；
Deploy the paper folding pattern that the similar geometry body after the adjustment obtains the approximate threedimensional model.
Preferably, the threedimensional model is three-dimensional grid model.
Preferably, the three-dimensional framework includes：Only connect the end joint of one section of bone, two sections of connection and be differently directed bone
The star joints that more than two sections of L-type joint and connection are differently directed bone.
Preferably, it is described according to the three-dimensional framework, the threedimensional model is resolved into semantic multiple basic bodies
The step of specifically include：
According to the three-dimensional framework, generate two disjoint cut surfaces in L-type joint and split the threedimensional model
As two parts；
In the tri patch intersected with the cut surface, the tri patch nearest with the L-type joint is found；
Find all triangular facets that the tri patch intersected with the cut surface and with the L-type joint recently is connected
Piece；
All tri patch formation triangular facet loop that the tri patch nearest with the L-type joint is connected；
The threedimensional model is partitioned into two parts by the triangular facet loop at the L-type.
Preferably, according to the three-dimensional framework, two intersecting cut surfaces are generated by the threedimensional model in L-type joint
Two parts are partitioned into, the direction of the cut surface intersecting to two carries out progressive alternate adjustment, until two cut surfaces are described
It is non-intersect inside threedimensional model.
Preferably, it is described to be fitted the multiple basic body with solid, find similar geometry corresponding with each basic body
Body step includes：Determine the solid direction；Rebuild the solid surface；And according to the solid direction, described
Solid surface fitting generates the similar geometry body.
Preferably, include the step of the determination solid direction：Check the three-dimensional bone in each basic body
Frame structure, if comprising the star joint, the solid direction determines three of the solid using PCA
Axially.
Preferably, include the step of the determination solid direction：Check described three in each basic body
Skeleton structure is tieed up, if only using the direction of the bone comprising one section of bone for Main way, another two is axially using two dimension
PCA is determined.
Preferably, the step of reconstruction solid surface is specifically included：
It is determined that determining global oriented bounding box on three axial directions of the solid in direction；
The basic body is resolved into by multiple components using equidistant cut surface on three axial directions；
It is determined that the local direction bounding box of the multiple component after decomposing；
Local direction bounding box fitting is generated into the solid surface.
The above-mentioned technical proposal of the present invention has the following advantages that：The interactive computer auxiliary paper folding design that the present invention is provided
Method inputs high-resolution three-dimensional grid model as system, and a series of paper folding samples are generated in the case where the interaction of user is instructed
Formula.These paper folding patterns can easily be folded into basic three-dimensional micromodule, such as cube truncated cone or other six faces very much
Body, then sticks these basic modules paper―folding model together approximate with regard to the threedimensional model profile that can be made with input.Using
The paper folding pattern that the design method that the present invention is provided is produced allows to cut out and pasted, individual paper folding do not cut out compared with tradition
Highly difficult, the high complexity mode of pattern is more suitable for domestic consumer, is particularly suitable for children.
Brief description of the drawings
Fig. 1 is the method flow diagram that interactive computer provided in an embodiment of the present invention aids in paper folding design method；
Fig. 2 is the joint schematic diagram in three-dimensional framework provided in an embodiment of the present invention；
Fig. 3 is the determination schematic diagram in truncated cone direction provided in an embodiment of the present invention；
Fig. 4 a, Fig. 4 b, Fig. 4 c, Fig. 4 d are the process schematics provided in an embodiment of the present invention that basic body is fitted to truncated cone；
Fig. 5 is the adjustment schematic diagram of connection surface provided in an embodiment of the present invention.
Fig. 6 a, Fig. 6 b, Fig. 6 c, Fig. 6 d, Fig. 6 e, Fig. 6 f are interactive computer auxiliary paper folding provided in an embodiment of the present invention
The system handling process of design method；
Embodiment
The embodiment to the present invention is described in further detail with reference to the accompanying drawings and examples.Following examples
For illustrating the present invention, but it is not limited to the scope of the present invention.
As shown in figure 1, aiding in the method flow of paper folding design method for interactive computer provided in an embodiment of the present invention
Figure.
A kind of interactive computer auxiliary paper folding design method that the present invention is provided, comprises the following steps：S1, input are three-dimensional
Model；S2, the three-dimensional framework for extracting threedimensional model；S3, according to three-dimensional framework, threedimensional model is resolved into semantic multiple
Basic body；S4, with solid multiple basic bodies are fitted, find similar geometry body corresponding with each basic body；S5, adjustment are similar
The joint face of connection is needed between solid；Similar geometry body after S6, expansion adjustment obtains the paper folding sample of approximate three-dimensional model
Formula.
Further, three-dimensional grid model is extracted into the three-dimensional framework of three-dimensional grid model as input, and user's
Under necessity is instructed, three-dimensional grid model is resolved into the basic body of semantic information according to above-mentioned three-dimensional framework.Intended with solid
Each basic body of conjunction approximate three-dimensional grid model finds several in similar geometry body corresponding with each basic body, the present embodiment
What body is not limited thereto by taking pre-defined folding multi-face body-cube truncated cone as an example.When being necessary, further rectify
The joint face of just adjacent cube truncated cone, to guarantee well stably to paste.Finally, these cube truncated cones are deployed
Printed into two-dimentional folding pattern, and by the folding line that can instruct to fold.These paper folding patterns can be easily
It is cut, folds, pastes, produces the paper―folding model of an approximate original three-dimensional model.
Further, design method provided in an embodiment of the present invention is using pre-defined folding multi-face body-cube
Truncated cone, is fitted each basic body of approximate three-dimensional grid model.Because the cube truncated cone similar to happy high building blocks is made
Children are especially suitable for for basic folded style to use, and in addition, approximate are come using a cube to each piece of bone
It is also that comparison is rational.Also, this cube truncated cone is also closely similar with happy high building blocks, being adapted to most child makes
With.Carry out an approximate basic body using cube truncated cone H, following conformance error need to be minimized：
Wherein, S in formula (1)jIt is a cube truncated cone H surface, viIt is to carry out approximately basic using cube truncated cone H
A point on body, d (vi, Sj) represent viWith SjThe distance between.
Further, in step s 2, three-dimensional framework includes：Only connect end joint, the two sections of differences of connection of one section of bone
Point to the L-type joint of bone and connect more than the two sections star joints for being differently directed bone.As shown in Fig. 2 real for the present invention
Joint schematic diagram in the three-dimensional framework of example offer is provided.The method that three-dimensional grid model skeleton is extracted using grid contraction, is passed through
Remove small structure to be simplified, extract the three-dimensional framework of input three-dimensional grid model.According to obtain input three-dimensional grid mould
The three-dimensional framework of type, can resolve into the three-dimensional grid model of input multiple basic bodies with semantic information.
Further, step S3 is specifically included：According to the three-dimensional framework of input three-dimensional grid model, each L-type joint
Cut surface is decomposed each basic body of threedimensional model；Wherein, cut surface is the angle for two sections of bones formation that L-type joint is connected
Divide face equally.It is assumed that the cut surface at the l of L joints is P_l, cut surface decomposes each base of three-dimensional grid model using following specific steps
Body：
S31, initialization tri patch integrate S as empty set；
The tri patch t_a of the tri patch middle-range abscission joint l that S32, determination are intersected with cut surface P_l recently, will
Tri patch t_a is put into tri patch collection S；
S33, determination are intersected with cut surface P_l, and the tri patch being joined directly together with the tri patch in tri patch collection S
T_b, tri patch t_b is put into tri patch collection S；
S34, repeat step S33, until it is all intersect with cut surface P_l and with the tri patch in tri patch collection S
The tri patch being joined directly together is found, and the tri patch for the condition that meets is put into tri patch collection S.
Wherein, each connected tri patch formation triangular facet loop in tri patch collection S enters the basic body at the l of joint
Row is decomposed.Further, the three-dimensional grid model of input is carried out with cut surface in other L-type joints using same method
Decompose, obtain each basic body with semantic information, used when remaining to be fitted.
Further, in practical operation, above-mentioned decomposition method fails sometimes, such as is carried out in L-type joint three-dimensional
When two adjacent cut surfaces of model segmentation intersect inside the three-dimensional grid model of input.Carried out in L-type joint three-dimensional
The cut surface of model segmentation is non-intersect, the coincidence that the joint face after segmentation can be complete, and then further carries out the behaviour such as pasting
Make.When two cut surfaces intersect inside the three-dimensional grid model of input, the decomposition of basic body is carried out using above-mentioned decomposition method
When, the generation for the situation such as the basic body after being decomposed can be caused imperfect, it is impossible to can not be obtained after complete coincidence and then stickup
Complete threedimensional model reproduces.When the design method provided using the present invention is operated, if detected in L-type joint
When two adjacent cut surfaces for carrying out threedimensional model segmentation intersect inside the three-dimensional grid model of input, two intersecting to cut
The direction of face carries out progressive alternate adjustment, until two cut surfaces are non-intersect inside the threedimensional model.Or use householder
The direction of the dynamic cut surface to inside input three-dimensional grid model and position are adjusted, to obtain more accurate segmentation result,
And then more it is similar to the paper―folding model of input three-dimensional grid model.
Further, the problem of input three-dimensional grid model basic body approximate with the fitting of cube truncated cone, with investigation
The classical problem of bounding box (Oriented Bounding Box, OBB) is closely similar.Step S4 includes：S41, determine cube
Truncated cone direction；And S42, reconstruction cube frusto-conical surface.
Further, in step S41, the court of cube truncated cone is determined according to the basic body of input three-dimensional grid model
To typically by the apex coordinate progress principal component analytical method (Principal upward to three reference axis of cube truncated cone
Component Analysis, PCA) determine.But, determine cube truncated cone direction, above-mentioned cube if only using PCA
Truncated cone determines that the method in direction can in particular cases produce deviation some, such as the Main way that PCA is analyzed and semanteme
On direction have deviation, as shown in figure 3, being the determination schematic diagram in truncated cone direction provided in an embodiment of the present invention.Using the present invention
The design method that embodiment is provided carries out operating process, has obtained the bone information of each block assembly, can determine semanteme
The direction of information be used as cube truncated cone mainly towards.Further, the three dimensional skeletal structure in each basic body is checked, if
Comprising star joint, cube truncated cone direction is determined using PCA；Check the three-dimensional framework in each basic body
Structure, if only using the direction of bone comprising one section of bone for Main way, another two direction is using two-dimentional principal component analysis
Method is determined.This conditional PCA methods can preferably be fitted each basic body of input three-dimensional grid model, such as Fig. 3
It is shown.
Further, it is that provided in an embodiment of the present invention be fitted basic body is cut as shown in Fig. 4 a, Fig. 4 b, Fig. 4 c, Fig. 4 d
The process schematic of cone.Step S42 is specifically included：As shown in fig. 4 a it is determined that being determined on three axial directions of cube truncated cone in direction
Global oriented bounding box, specially determines the position of each axially upper farthest grid vertex, and then determines that global direction is surrounded
Six surfaces of box；Basic body is resolved into by multiple components using equidistant cut surface on each axial direction as shown in Figure 4 b；Such as
The local direction bounding box of each component after decomposing is determined shown in Fig. 4 c；Finally local direction bounding box is intended as shown in figure 4d
Symphysis is into cube truncated cone.
Further, the cube truncated cone of each fitting basic body is that two relatively independent, adjacent cubes are cut
Cone needs the surface being affixed not to be substantially parallel what can directly be pasted.Therefore, adjacent two cubes cut phase for convenience
Paste, it is necessary to adjust two adjacent cubical joint faces.The step S4 of the design method provided in the present invention, with step S5
Between also include step S6：Joint face between the adjacent cube truncated cone of adjustment, makes adjacent cube truncated cone need stickup
Two surfaces it is parallel to each other.
Further, two adjacent cube truncated cones are denoted as Ha and Hb, their connection surface, which is two, to be needed to glue
The face sticked together is denoted as Sa and Sb respectively.If joint face Sa is parallel with joint face Sb, need not further it be adjusted
It is whole to be just secured at together.If joint face Sa and joint face SB are not parallel, by two adjacent cube truncated cones
Larger one of volume is used as main truncated cone.It is assumed that the cube truncated cone Ha main truncated cone of volume great thing, as shown in figure 5, being this
The adjustment schematic diagram for the connection surface that inventive embodiments are provided, is adjusted using following specific steps：
S61, adjustment cube truncated cone Ha joint face：When joint face Sa only with joint face Sb connection surfaces each other, then adjust
Joint face S ' a new whole joint face Sa to cube truncated cone Ha, make the new joint face S ' a of cube truncated cone Ha vertical parallel to two
The cut surface of cube truncated cone；
S62, adjustment cube truncated cone Hb joint face：What extension cube truncated cone Hb all and joint face Sb intersected
Side, is allowed to intersect with the joint face S ' a that cube truncated cone Ha is new, the new joint face S ' b of cube truncated cone Hb is formed, after adjustment
Joint face S ' a are parallel with S ' b；
New joint face S ' a and S ' b of S63, comparison size, if new joint face S ' a and S ' b area ratio exists
0.7~1.43, then joint face S ' b new cube truncated cone Hb size is adjusted to the joint face S ' new with cube truncated cone Ha
A is equally big.If new joint face S ' a and S ' b area ratio is outside the above range, new joint face S ' a and S ' b sizes
Deviation is larger, without the adjustment of connection surface, regenerates suitable truncated cone and is pasted.
Joint face S ' a after adjustment and S ' b be parallel to each other and size as, can directly be pasted, and then complete
Cube truncated cone Ha and Hb stickup.Multiple cube truncated cones with semantic basic body will be fitted and be launched into two-dimentional paper folding sample
Formula, and the two-dimentional paper folding pattern of output is cut out, folded and pasted, you can obtain final with inputting precision three-dimensional model
Similar paper―folding model.
Further, Fig. 6 a, Fig. 6 b, Fig. 6 c, Fig. 6 d, Fig. 6 e, Fig. 6 f are interactive calculating provided in an embodiment of the present invention
Machine aids in the system handling process of paper folding design method.Interactive computer auxiliary paper folding design side provided in an embodiment of the present invention
The system handling process of method is concretely comprised the following steps：The threedimensional model of input as shown in Figure 6 a；The three-dimensional of input is extracted as shown in Figure 6 b
The three-dimensional framework of model；As fig. 6 c, cut surface is used in obtained three-dimensional framework L-type joint, by the three-dimensional mould of input
Type resolves into multiple with semantic basic body；(cut such as Fig. 6 d and using folding polyhedron in the present embodiment with cube
Exemplified by cone), approach and be fitted each basic body；And need the surface connected to be adjusted obtained each folding multi-face body,
It is allowed to that the model approximate with inputting threedimensional model can be obtained as illustrated in figure 6e after pasting；Most each folding multi-face body exhibition at last
Open as the foldable pattern of two dimension, and the folding line for being known that folding is printed as shown in Figure 6 f.What is obtained carries folding line
The paper―folding model for instructing, allowing to be tailored and pasting, highly difficult, the high complexity for individual paper folding pattern do not cut out compared with tradition
Mode is more suitable for domestic consumer, particularly children
In summary, the interactive computer auxiliary paper folding design method that the present invention is provided decomposes complicated threedimensional model
Into the making simple solid of task；Paper folding task is made up of many independent small tasks of permission team unity；Polylith is several
The folding process of what body directly can timely feed back to domestic consumer, shorten Production Time and can during paper folding with
When be adjusted.For given threedimensional model, it is creasy that the design method provided by the present invention can produce several prints
The paper for folding visual guide is made, three-dimensional paper―folding model can be formed after every paper is rolled well along folding line has each of semanteme
Part-structure.The paper folding pattern that the design method provided using the present invention is produced allows to cut out and pasted, compared with tradition not
Highly difficult, the high complexity mode for individual paper folding pattern cut out is more suitable for domestic consumer, is particularly suitable for children.
Finally it should be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although
The present invention is described in detail with reference to the foregoing embodiments, it will be understood by those within the art that：It still may be used
To be modified to the technical scheme described in foregoing embodiments, or equivalent substitution is carried out to which part technical characteristic；
And these modification or replace, do not make appropriate technical solution essence depart from various embodiments of the present invention technical scheme spirit and
Scope.
Claims (9)
1. a kind of interactive computer aids in paper folding design method, it is characterised in that comprise the following steps：
Input threedimensional model；
Extract the three-dimensional framework of the threedimensional model；
According to the three-dimensional framework, the threedimensional model is resolved into semantic multiple basic bodies；
The multiple basic body is fitted with solid, similar geometry body corresponding with each basic body is found；
Adjusting needs the joint face of connection between the similar geometry body；
Deploy the paper folding pattern that the similar geometry body after the adjustment obtains the approximate threedimensional model.
2. interactive computer according to claim 1 aids in paper folding design method, it is characterised in that the threedimensional model
For three-dimensional grid model.
3. interactive computer according to claim 1 aids in paper folding design method, it is characterised in that the three-dimensional framework
Including：Only connect more than two sections differences in L-type joint and connection that the end joint of one section of bone, two sections of connection are differently directed bone
Point to the star joint of bone.
4. interactive computer according to claim 3 aids in paper folding design method, it is characterised in that described in the basis
Three-dimensional framework, the step of threedimensional model is resolved into semantic multiple basic bodies specifically includes：
According to the three-dimensional framework, generate two disjoint cut surfaces in L-type joint and be partitioned into the threedimensional model
Two parts；
In the tri patch intersected with the cut surface, the tri patch nearest with the L-type joint is found；
Find all tri patch that the tri patch intersected with the cut surface and with the L-type joint recently is connected；
All tri patch formation triangular facet loop that the tri patch nearest with the L-type joint is connected；
The threedimensional model is partitioned into two parts by the triangular facet loop at the L-type.
5. interactive computer according to claim 4 aids in paper folding design method, it is characterised in that the generation two
The step of disjoint cut surface, specifically includes：
According to the three-dimensional framework, generate two intersecting cut surfaces in L-type joint and the threedimensional model is partitioned into two
Part, the direction of the cut surface intersecting to two carries out progressive alternate adjustment, until two cut surfaces are in the threedimensional model
Portion is non-intersect.
6. interactive computer according to claim 5 aids in paper folding design method, it is characterised in that described to use solid
The multiple basic body is fitted, finding similar geometry body step corresponding with each basic body includes：Determine the solid side
To；Rebuild the solid surface；And it is described similar several according to the solid direction, solid surface fitting generation
He Ti.
7. interactive computer according to claim 6 aids in paper folding design method, it is characterised in that in the determination institute
The step of stating solid direction includes：The three dimensional skeletal structure in each basic body is checked, if including the star joint, institute
State three axial directions that solid direction determines the solid using PCA.
8. interactive computer according to claim 6 aids in paper folding design method, it is characterised in that in the determination institute
The step of stating solid direction includes：The three dimensional skeletal structure in each basic body is checked, if only comprising one section of bone,
The direction of the bone is used for Main way, another two is axially determined using the PCA of two dimension.
9. the interactive computer auxiliary paper folding design method according to claim any one of 6-8, it is characterised in that described
The step of rebuilding the solid surface specifically includes：
It is determined that determining global oriented bounding box on three axial directions of the solid in direction；
The basic body is resolved into by multiple components using equidistant cut surface on three axial directions；
It is determined that the local direction bounding box of the multiple component after decomposing；
Local direction bounding box fitting is generated into the solid surface.
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| CN108044997B (en) * | 2017-11-20 | 2023-07-14 | 浙江工业大学 | Paper folding deformation structure with bistable characteristic |
| CN113822989A (en) * | 2021-09-26 | 2021-12-21 | 浙大城市学院 | Digital design and manufacturing method of boneless festive lantern |
| CN114722488A (en) * | 2022-03-16 | 2022-07-08 | 江苏大学 | Modeling method for fitting generalized cylinder curved surface based on water elastic paper folding derivative structure |
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