Abstract Geometric constraint satisfaction using optimization methods
Geometric constraint satisfaction using optimization methods
Jian-Xin Ge1,Shang-Ching Chou*,Xiao-Shan Gao2
Computer Science Department,Wichita State University,Wichita,KS67260-0083,USA
Received9July1999;received in revised form21August1999;accepted17September1999
Abstract
The numerical approach to solving geometric constraint problems is indispensable for building a practical CAD system.The most commonly-used numerical method is the Newton–Raphson method.It is fast,but has the instability problem:the method requires good initial values.To overcome this problem,recently the homotopy method has been proposed and experimented with.According to the report, the homotopy method generally works much better in terms of stability.In this paper we use the numerical optimization method to deal with the geometric constraint solving problem.The experimental results based on our implementation of the method show that this method is also much less sensitive to the initial value.Further,a distinctive advantage of the method is that under-and over-constrained problems can be handled naturally and ef?ciently.We also give many instructive examples to illustrate the above advantages.?Published by Elsevier Science Ltd.
Keywords:Parametric design;Optimization method;Variational geometry
1.Introduction
There are several approaches to solving the geometric constraint problem.The symbolic approach[7,14,21]trans-lates geometric constraints into a system of polynomial equations and solves the system by computer algebra tech-niques such as the Wu–Ritt method or the Grobner basis method[8].It is reliable and complete,but is too slow and space-consuming to solve practical problems.
The propagation approach[1,6,9,15,22,23,26,28,39,41] solves the constraint system by deriving unknown variables or geometric objects from already known ones using a set of prede?ned https://www.wendangku.net/doc/186594855.html,ually the propagation methods are implemented with expert systems or logic programming languages such as Prolog.
The graph analysis approach[5,12,13,25,35,37,40] translates a geometric constraint problem into a graph and ?nds the geometric construction sequence by analyzing the graph.Both the propagation approach and the graph analy-sis approach have their limitation in scope.
On the other hand,the numerical approach [2,4,19,24,27,29,31,36]is a general method for solving the geometric constraint problem.Like the symbolic method, the numerical method?rst translates the constraints into a system of nonlinear equations.Then this equation system is solved by iterative methods instead of exact symbolic computation.
The most commonly used method in the numerical approach is the Newton–Raphson method.It is fast,but has the instability problem:the method is sensitive to the initial values.A small deviation in the initial value can lead to an unexpected or unwanted solution,or to the iteration divergence.To overcome this problem,recently the homo-topy method has been proposed and experimented with[24]. According to the report in Ref.[24],generally the homotopy method works much better in terms of stability.These two methods generally require the number of variables to be the same as the number of equations.If these two numbers are different,i.e.the constraint system is generally over-or under-constrained,some special techniques,such as linear least square and singular value decomposition of a matrix, are required.
In this paper,based on the optimization method we use a numerical method for solving geometric constraint problems.Our experiments with this method show that it is also quite stable.Further,the method can naturally deal with under-and over-constrained problems.We also give many instructive examples to illustrate the above advan-tages.Numerical approaches similar to the optimization method have been introduced and discussed in Refs. [2,4,19].We will discuss the related work in Section2.11.
0010-4485/00/$-see front matter?Published by Elsevier Science Ltd. PII:S0010-4485(99)https://www.wendangku.net/doc/186594855.html,/locate/cad
*Corresponding author.
E-mail addresses:ge@https://www.wendangku.net/doc/186594855.html,(J.-X.Ge);chou@https://www.wendangku.net/doc/186594855.html,(S.-C.Chou);gao@https://www.wendangku.net/doc/186594855.html,(X.-S.Gao)
1On leave from Zhejiang University,Hangzhou,310027,People’s Republic of China.
2On leave from Institute of Systems Sciences,Academia Sinica,Beijing 100080,People’s Republic of China.
2.The optimization method for solving geometric constraint problems
https://www.wendangku.net/doc/186594855.html,ing optimization method for solving a system of equations
Generally,a geometric constraint problem can be?rst translated into a system of equations:
f1 x1;…;x n 0
f2 x1;…;x n 0
…
f m x1;…;x n 0
1
Then the problem is how to solve this system of equations F X 0;where F f1;f2;…;f m T:R n3R m is the equation vector and X x1;x2;…;x n T is the vector of unknown variables.This system of equations can be solved iteratively by the Newton–Raphson method[29].The itera-tion formula is X k?1 X k?J X k ?1F X k ;where J X k is the Jacobi matrix of F X at point X k.
The Newton–Raphson method usually requires that the number of constraints and the number of variables are the same so that the inverse of the Jacobi matrix can be calcu-lated.This requirement makes the method dif?cult to handle under-and over-constrained problems which frequently occur in real applications.
Unlike the other numerical methods,the optimization approach solves the system of equations F X by converting it into?nding X at which the sum of squares
s X
m
i 1
f i X 2 2
is minimal.It is obvious that F X 0has a real solution X?if and only if min s X is0.The problem of solving a system of equations is thus converted into the problem of?nding the minimum of a real multi-variate function.The problem now can be solved by various well-developed numerical optimization methods[10,32,33].
One obvious fact for this approach is that the number of equations m is not necessarily the same as the number of variables n.Thus for this approach it is natural to deal with under-and over-constrained problems.
In this paper,we focus on the numerical aspects of the algorithm to solve the geometric constraint solving problem by the optimization method.We have tested two optimiza-tion methods:the modi?ed Levenberg–Marquardt method and the BFGS method.Next we will brie?y introduce these two methods.
2.2.The modi?ed Levenberg–Marquardt method
By the optimality condition we have the fact that the derivatives g X of s X at the minimum points equal https://www.wendangku.net/doc/186594855.html,ing the chain rule of derivation we have
g X 2J X T F X 3 where J X is the Jacobi matrix of the function vector F X f1;f2;…;f m :Applying the Newton–Raphson itera-
tion formula to Eq.(3)we have the following iteration formula
J T k J k?S k D X k ?J T k F k 4 X k?1 X k?D X k
where S X
m
i 1
f i X 72f i X is a function of second-order derivatives.If we ignore the second-order derivatives we have the Gauss–Newton iteration formula
D X k ? J T k J k ?1J T k F k 5 X k?1 X k?D X k
To ensure that s X decreases with each iteration and also to deal with the singularity of matrix J T k J k;the Levenberg–Marquardt method is usually used with the modi?ed iteration formula
D X k ? J T k J k?l k I ?1J T k F k 6 X k?1 X k?D X k
where I is the unit matrix and l k is a small real number. The selection of l k should ensure that the matrix J T k J k?l k I is positive de?nite.In practice the selection of l k has a great impact on the convergence domain and https://www.wendangku.net/doc/186594855.html,ually l k is initially set to0.01and later is doubled if J T k J k?l k I is not positive de?nite.This method is a locally convergence optimization method and its behavior in our experiments is not satisfactory either in convergence speed and domain. The main problem is that the initial guess of the solution should be very near the solution to ensure that matrix J T k J k is positive de?nite.This problem becomes more serious when processing under-constrained problems,since matrix J T k J k always singular in this case.This makes us resort to the second optimization method to solve the problem.
2.3.The BFGS method
The second method we have tried is the BFGS method which is also called the secant or quasi-Newton method [3,10,33].It is a globally convergent method and thus is a more robust numerical optimization method.This method tries to construct a secant approximation H of the Hessian matrix of function s X :The main algorithm of BFGS is described as follows:
1.Initialization
H0 a unit matrix;X0 the initial value;k 0;
https://www.wendangku.net/doc/186594855.html,pute the derivatives g X and their difference y k at X k
J.-X.Ge et al./Computer-Aided Design31(1999)867–879 868
g k 7s X k ;if?g k??1then X?
X k and stop the iteration
y k g k?g k?1;
https://www.wendangku.net/doc/186594855.html,pute search direction p k and the step to reach a
minimum along the direction p k
p k ?H k g k
l k min l s X k?l p k
D X k l k p k
X k?1 X k?D X k
4.Adjust matrix H
H k?1 H k?1?
y T k H k y k
D X T k y k
23
D X k D X T k
D X T k y k
?H k y k
D X T k?D X k y T k H k
D X T k y k
5.k?1goto(2)
More details of this algorithm can be found in Refs. [3,10,33].There are several ways to improve this algorithm. One improvement is to use the trust region technique in this algorithm to promote convergence from poor starting point guesses[16].Another improvement is to use a different updating formula to avoid storing the secant matrix H to save memory[34].
Compared with the Newton–Raphson method for geometric constraint solving,the optimization method has the following desirable features:
?This method is quite stable as demonstrated by our experimental results.The success of?nding a desired solution by this method is rather insensitive to the initial guess of the solution to the geometric constraint solving problem.Also the solution found by this method is more predictable in contrast to the drastic solution jumping caused by even small changes of the initial value in the Newton–Raphson method.
?Under-and over-constrained problems are naturally handled by this method.In particular,for under-constrained problems,this method will?nd a“visually less changed”solution which is reasonably near the initi-ally sketched diagram.For over-constrained but consis-tent problems,this method will generally still?nd a solution.This feature will be shown in Section2.5. The concept of“visually less changed”is not rigorously de?ned.However,we can give a formal de?nition to a related concept.A solution X is visually least changed if X is a solution to a geometric constraint problem and?X?X0?2is minimal,where X0is the initial guess of the solution. From our experiments,we have found that the optimization method often?nds a solution near the visually least changed solution for under-constrained problems.
In the next section we will show some experimental results of this method.
2.4.Experimental results with the BFGS method
We have developed a system AGP(Associative
J.-X.Ge et al./Computer-Aided Design31(1999)867–879
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Fig.1.Some simple examples.
Geometric Pad)using the BFGS method.3It is an experi-mental sketching system implemented in C ??under the Linux and X/Motif environment.
In AGP,four types of geometric objects are supported:points,lines,circles and arcs.However,only points are internally maintained on which constraints are speci?ed.This is made possible by introducing some auxiliary points under some circumstances.For example when specifying that two circles with centers C 1and C 2are tangent,a new auxiliary tangent point T is introduced and the tangent constraint is internally converted into three constraints:(collinear;C 1T C 2),(onCircle T C 1)and (onCircle T C 2).Finally constraints in the form of (onCircle P i C )i 1;…are converted into (equalDistance P i C P i ?1C i 1;…;k ?1:
In this section we show some examples solved by AGP to demonstrate some features of the optimization method.Fig.1shows some simple examples made by AGP.Fig.1a is one of the Apollonius construction problems .The problem is to construct a circle tangent to three given circles which are speci?ed to have ?xed centers C i i 1;2;3 and to pass through ?xed points P i i 1;2;3 ;respectively.Actually the problem has eight solutions.In the ?gure AGP generated four essentially different circles (in dashed
lines)corresponding the four initially roughly sketched circles.
Fig.1b is the diagram of the Thebault–Taylor theorem proposed as a conjecture in 1938and proved in 1983.The theorem states that given a triangle P 1P 2P 3and a point P 4on P 2P 3;circle C 1is the circumscribed circle of the triangle;circle C 2is the inscribed circle of the triangle;circles C 3and C 4are tangent to line P 2P 3,line P 1P 4,and circle C 1,then the centers C 2,C 3and C 4are collinear.The construction of this diagram is well constrained,but it has 256solutions.In Fig.1c the regular pentagon is speci?ed such that all its ?ve sides are equal and three of its diagonals in dashed lines are equal;the circumscribed circle is speci?ed to pass through ?ve vertices of the pentagon;and the inscribed circle is speci?ed to be tangent to the ?ve sides of the pentagon.Note that this problem is over-constrained.Table 1shows the running statistics of these three exam-ples.4
Since the BFGS method is a globally convergence numer-ical optimization method,the success of ?nding a solution is not very sensitive to the initial value.This preferable feature is demonstrated in Fig.2where the three circles are speci-?ed to be mutually tangent and to be tangent to two neigh-boring sides of a triangle whose three vertices are speci?ed
J.-X.Ge et al./Computer-Aided Design 31(1999)867–879
870Fig.2.The example to demonstrate the insensitivity to the inexact initial guesses of the solutions:(a)and (c)are the initial diagrams constructed by the user;(b)and (d)are the diagrams after computation.
3
This software can be accessed at ftp://https://www.wendangku.net/doc/186594855.html,/pub/agp/agp.tgz.
4
All the running time in this paper is collected by averaging ten conse-cutive execution time on a Pentium Pro 200machine with the Linux oper-ating system.
to be ?xed.Fig.2a and c are the initial diagrams sketched by the user.It is easy to see that the differences between the initial guesses and the exact solutions of this problem,respectively,in Fig.2b and d are rather large.Also this ?gure demonstrates how different initial values lead to different branches of the solutions.
Fig.3is the simplest case for the problem we call the tangent packing problem .The problem is to pack n n ?1 =2circles (n rows of circles)tangent to adjacent circles and/or the adjacent neighboring sides of a given triangle.Fig.3is the case of n 6;i.e.we need to pack 21circles in the triangle.This dif?cult problem contains 174variables (since we introduce auxiliary tangent points)and 6linear equations and 168quadratic equations which could not be block triangularized.Table 2shows the running results for different n of this problem.5
2.5.Under-or over-constrained problems
Under-and over-constrained problems are very common in real applications.For example,engineering drawings are usually under constrained,especially in their early design stages.It is quite inconvenient to require the user to draw the diagram with all the dimensions speci?ed at the beginning.Even for some ?nished engineering drawings under-constrained cases can still occur,since some unimportant dimensions are ignored by the users.Over-constrained problems are not common in engineering drawings.However,the over-constraining technique can be used as a tool to aid the user to draw some complicated ?gures conveniently or to exclude some unwanted solutions.
The optimization method is capable of handling under-and over-constrained problems in a very natural way.The following examples demonstrate this capability.Fig.4shows the process to draw a regular 11-polygon.First the user sketches the diagram as in Fig.4a.Then he/she speci-?es that the bottom side to be ?xed and all the sides of the polygon are equal.At this moment,this problem is under-constrained since the polygon is not totally ?xed.However,the diagram can still be computed satisfying all the constraints in the system as shown in Fig.4b.Finally,the user speci?es that all the diagonals connecting the two next adjacent vertices in the ?gure are equal.After computation we get the regular 11-polygon as shown in Fig.4c.This actually becomes an over-constrained problem,since the
user needs only to specify 8of the 11diagonals to be equal.Of course,this over-constrained problem is consis-tent,meaning that introducing redundant constraints will not con?ict with the existing constraints.Effectively handling under-and over-constrained problems is a preferable feature of a geometric constraint solving system.In this problem,it is rather dif?cult to decide which eight diagonals should be selected to be equal.It is more convenient for the user to specify all the diagonals to be equal.
Sometimes over-constraining can be used to select a solu-tion and exclude others from a ?nite set of solutions to a geometric constraint problem.The next example demon-strates such usage in drawing a regular pentagon.Fig.5a is the initial con?guration of the diagram with two points P 1and P 2?xed.After specifying that ?ve sides of the pentagon are equal and three diagonals P 1P 3,P 2P 5and P 3P 5are equal,the diagram becomes the one in Fig.5b which is a solution we do not want.Actually the problem is well constrained and there are eight solutions to this problem.Next we specify in Fig.5c that points P 1and P 2are ?xed;?ve
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Fig.3.A dif?cult problem.(a)The initial diagram drawn by the user.(b)Diagram generated after all tangent constraints are added.
Table 2
Running statistics for Fig.3with different number of circles #Circles (#rows)#Equations #Variables Time (s)3(2)30300.2286(3)54540.96510(4)8686 3.37915(5)12612611.58721(6)
174
174
23.751
Table 1
Running statistics for Fig.1
#Equations
#Variables Time (s)Fig.1a 44440.623Fig.1b 34340.172Fig.1c
28
24
0.142
5
The case when n 4was given in Ref.[24]which inspires us to consider other cases.
sides of the pentagon are equal;four diagonals P 1P 3,P 2P 5,P 3P 5and P 1P 4are equal.Obviously it becomes an over-constrained problem.After computation we get the desired regular pentagon in Fig.5d.
In the general case under-,well-,and over-constrained problems could be very complicated.It could happen that a seemingly well-constrained diagram actually has in?nite solutions.For example,to specify a regular pentagon we give seven constraints:all the ?ve sides of the pentagon are equal and the four diagonals in Fig.5c are equal.These constraints are independent in the sense that each polynomial corresponding to one constraint is not in the radical ideal of the polynomials corresponding to the other constraints.Since the problem has ?ve points and thus needs seven independent constraints,it seems to be well constrained.But the problem actually has in?nite solutions since the length of each side of the pentagon is not ?xed.This phenomenon occurs for problems with many branches of solutions.Some of the constraints are used to eliminate branches,but not to reduce the degree of freedom of the
J.-X.Ge et al./Computer-Aided Design 31(1999)867–879
872Fig.4.Under-and over-constrained examples.(a)The initial diagram drawn by the user.(b)Diagram generated after specifying that the bottom side is ?xed and the lengths of eleven sides are equal.(c)Diagram gener-ated after specifying that all the diagonals in the ?gure are
equal.
Fig.5.The example to use redundant constraints to select different branches of solutions.(a)Initial diagram drawn by the user.(b)Diagram generated after specifying that ?ve sides of the pentagon are equal and three diagonals are equal.(c)Initial diagram drawn by the user.(d)Diagram generated after specifying that ?ve sides of the pentagon are equal and four diagonals are equal.
diagram.Generally,this kind of problem cannot be solved with the propagation method or the graph analysis method. Obviously the ability of the optimization approach to handle such problems is an advantage over other methods.
2.6.Practical considerations
Our experiments with the optimization method show that this method is quite ef?cient for medium sized geometric constraint solving problems with less than one hundred equations.However,for larger problems the performance is not satisfactory.For example,the problem in Fig.6is to pack19tangent circles in the area separated by two given tangent circles C1and C2.It contains more than170equa-tions,and we solve the problem as a whole in nearly39s. One solution is to use various storage saving techniques to improve the performance[20].Among these methods we tested the method in Ref.[30].The result is quite satisfac-tory.For the six tangent circle packing problem,the method takes only0.84s instead of23.75s(see Table2).However, this method is less unstable that our original method equipped with the trust region technique.In any case this is a good starting point.On one side we could try improve the stability of those very ef?cient but less stable numerical methods by using some techniques,such as the trust region method and stable line search methods.On the other side, we could provide the system with two numerical solvers. These solver are selected so that one is ef?cient but less stable and the other is stable but less ef?cient.When solving a speci?c problem,the system?rst tries the ef?cient solver. If the ef?cient solver could not solve the problem,the stable solver is invoked.
The other solution is to use the decomposition techniques discussed below.Actually the diagram in Fig.6could be constructed sequentially in an order of the size of the circle to be constructed.The construction of each circle is a special case of the Apollonius construction problems.
For those kinds of problems we can use two decomposi-tion techniques to improve the computation performance.One is called equation oriented decomposition technique which turns a system of equations into block triangular form.A system of equations is said to be in block triangular form if it can be divided into subsets of equations:
S1 x1;…;x n
1
;S2 x1;…;x n
1
?n2
;…;S t x1;…;x n
1
?…?n t
: where n i is the number of equations in S i.Such a system of equations can be solved sequentially.Each time S i is solved by the optimization method and the solution is substituted into subsequent sub-systems S k k?i :The block triangu-larization process can be implemented by the algorithms proposed in Refs.[25,37].
Another technique is called cluster oriented decomposi-tion which solves the constraint problems by?rst dividing the diagram into a set of small sub-diagrams called clusters and then assembling these clusters again.A cluster is essen-tially assumed to be a rigid body only having translational and rotational degrees of freedom.This implies that the inner-cluster constraints which only concern geometric objects in the same cluster are invariant with respect to the rigid body transformation,e.g.if an inner-constraint in a cluster is originally satis?ed it will still be satis?ed after the cluster is transformed by any translational and rotational transformation.
First suppose clusters C1;…;C p in the diagram are recog-nized and solved with some methods[1,5,13,35,41].For each cluster C i we introduce a transformation matrix T i
T i
a i?
b i c
b i a i d i
001
H
f f
d
I
g g
e
where a i,b i,c i and d i are unknown variables satisfying a2i?b2i 1:
Like the3D cases[27,36],we?rst translate the inter-cluster constraints,which constrain geometric objects in different clusters,into a system of equations with a i,b i,c i and d i i 1;…;p as unknown variables.For example,an inter-cluster constraint requiring that two clusters C i and C j share a common point P can be written as
T i
x pi
y pi
1
H
f f
d
I
g g
e T j
x pj
y pj
1
H
f f
d
I
g g
e
which essentially represents two linear equations with elements in T i and T j as unknown variables,where x pi;y pi and x pj;y pj are the numerical coordinate values for point P in clusters C i and C j,respectively.The equations obtained in this way,called assembly equations,are then solved by the optimization method.The solution to the system of assembly equations,if it exists,ensures that the inter-clusters will be satis?ed after the transformations are performed on the clusters.Since the inner-cluster constraints are invariant with respect to the transformation, all the constraints in the system are now satis?ed.
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Fig.6.A sequence of Apollonius’construction problems.
Generally,these two decomposition techniques will improve the performance of numerical calculation greatly.It will make the optimization method attractive in some real applications,such as engineering drawing systems in which nearly all problems can be solved sequentially.However,this decomposition technique will not be helpful if the struc-ture of the problem is very “bad”.The diagram in Fig.3is such an example.It is obvious that the system of equations for the problem cannot be structurally block-triangularized and the diagram itself also cannot be clustered.2.7.Problem of inequalities
One of the problems of the optimization method is that the general numerical optimization methods only ?nd local minima of a multi-variate function.It is possible for the function s X in Eq.(2)to have a nonzero local minimum,although there exists a solution X ?to Eq.(1).Furthermore,the general optimization method usually cannot properly handle the critical point (the point at which the gradient vector of the goal function is zero)which is not an minimal point.From our experience,this problem rarely happens for under-or well-constrained problems (actually,we have encountered no such cases so far).However,for over-constrained problems we did encounter such cases.In parti-cular it becomes serious when the constraint problem involves inequalities.
For example,the diagram in Fig.5d is generated from the sketch in Fig.5c by specifying that P 1P 3 P 1P 4 P 2P 5 P 3P 5:This is an over-constrained problem.However,if the initial sketch is Fig.5b with the same constraints,then the optimization iteration will ?nally reach a critical point which is not a solution.
A natural remedy for this problem seems to use inequality constraints.For this example we tried to add an inequality constraint which speci?es that point P 4is above line P 3P 5in Fig.5b.In theory it should get the desired result.Each inequality f X ?0can be transformed into an equality f X ?My 2 0;where y is a newly introduced variable and M is a positive number.It is obvious that we have ?X f X ?0D ?y f X ?My 2 0 :However,this attempt failed in our experiments.The reason is that the introduction of inequalities may lead to some critical points near the solution we want.
Here is a very simple example to demonstrate this situa-tion.Suppose we have an equation x 2?1 0and an inequality x ?0;following the above discussion we construct a function f x ;y to be minimized f x ;y x 2?1 2?M x ?y 2 2
For M 1there are ?ve critical points for this function: 1;^1 ; ^ 2p =2;0 and (0,0)(see Fig.7a–c).But only the ?rst two critical points are the minimum points we want.The other critical points are essentially saddle points which are not local minima.The introduction of these saddle points make the problem especially dif?cult.The
success rate of our numerical solver for this problem is only 33.3%for the initial values of x ;y ? ?5;5 (see Fig.7d).Although we can choose M ?2so that the critical points ^
2p =2:0 are eliminated,the critical point (0,0)cannot be removed.2.8.Constraint hierarchy
The constraint hierarchy can be introduced to geo-metric constraint problems.In mechanical designs,some constraints,especially those related to structural con?gura-tion or performance of the part,are of the highest priority and should be satis?ed unconditionally.Others,such as those for esthetical purposes,are of lower priority and are not necessarily to be satis?ed.Freeman-Benson [11]solves constraint hierarchy problems with an ef?cient local propa-gation method.However,his method cannot handle geometric constraint problems.
We solve this problem with multi-objective optimization methods.As in Ref.[11]we partition all the constraints in the system into a constraint hierarchy with different priority levels.We assume that constraints in lower constraint hierarchy levels have higher priority,and level zero has the highest priority.Following the way in Section 2.1,for each constraint hierarchy level i we could construct an objective function G i X G i X
m i j 0
m ij f 2ij X
where m ij can be used to specify the relative importance of
each constraint in the same hierarchy level.
Now the constraint problem has been transformed into a classic nonlinear multi-objective unconstrained optimiza-tion problem
min{G 0 X ;G 1 X ;…;G k X }:
Several numerical methods can be used to solve the above problem [33,38].We convert this problem into a constrained optimization problem.For simplicity,we only consider two levels of constraints.Constraints in level zero are compulsory and constraints in level one are preferable.First,we solve the problem in level zero by solving follow-ing minimization problem G ?0 min x ?x
n
G 0 X :Since the constraints in this level are mandatory,we must
check that G ?0is less than a prescribed small number 10.If this condition is satis?ed then we proceed to the next level of constraints.One natural condition to satisfy this level of constraint is that no constraints in the previous level (level zero)are violated.So we turn this problem into a constrained optimization problem with the following goal function G ?1 min x ?D
G 1 X
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J.-X.Ge et al./Computer-Aided Design 31(1999)867–879875
-0.8-0.6-0.4-0.2
00.20.4
0.6
0.8
1
1.2
x -1
-0.5
0.5
1
y
12345(a)
0.8
1
1.2
1.4
1.6
-1
-0.5
0.5
1
x
(b)
Fig.7.Problem of unwanted critical point.(a)The graph of function f x ;y in interval ?0:2;1:2 × ?1:2;1:2 :(b)The graph of the function for y 0with x in interval (?1.2,1.2).(c)The graph of the function for x 1with y in interval (?1.2,1.2).(d)The convergence diagram for x ;y ? ?5;5 :The black area consists of the set of the initial points which will lead the numerical solver to the solutions (1,^1).
J.-X.Ge et al./Computer-Aided Design 31(1999)867–879
87600.2
0.4
0.6
0.8
1
-1-0.5
0.5
1
y
(c)
(d)
Fig.7.(continued )
where D {X? G0 X ?G?0?11}and11is a small real number.
Using current general nonlinear constrained optimization techniques[3,10,33],it is not dif?cult to?nd a solution for the above problem.Since constraints in this level are not necessarily to be satis?ed,G?1does not have to be zero.
It is worth pointing out that this technique can be easily adapted to?nd a visually least changed solution discussed in Section2.3.
2.9.Linear constraints
In some applications,such as the user interface design and the architectural layout design,only linear constraints are involved.In this case,we can model the geometric constraint problems with much simpler optimization models.One such model translates the constraints into a linear programming problem
min x c T x
s:t:Ax 0Bx?0
where the conditions correspond to the geometric constraints in the system.For this problem,we can simply set the goal function to be a constant.This problem can be solved by commonly used linear programming algorithms [18,22].The other model is the quadratic programming model where the goal function is the sum of the squares of linear functions induced by linear geometric constraints, thus could be written as
min x x T Ax
s:t:Bx?0:
This problem can be solved by a very ef?cient algorithm called successive quadratic programming(SQP)approach [3,33].We believe that these methods can solve these speci-?c problems much more ef?ciently and robustly.
2.10.Global optimization
The limitation of the optimization method discussed in Section2.7can be overcome with the global optimization method.The global optimization method can be used to determine global minima for a goal function.It is obvious that if there exists a solution X to Eq.(1),the goal function s X in Eq.(2)will always reach its global minimal value of zero at a point which is assumed to be found by the global optimization method.The global optimization will solve the problem by assuring that the minimization process will not trap into a local minimal point or an unwanted critical point. Besides,the global optimization method can be used to ?nd as many solutions to a set of equations as possible by enumerating local minima of the goal function in Eq.(2). The global optimization method is a current research topic in the numerical optimization.Many global opti-mization methods have been developed,including the deterministic method,the stochastic method,the simulated annealing method,the interval method,and the genetic algorithm[17,32,33].Some of these,especially the determi-nistic method,are so well developed that they could be used to solve many dif?cult problems in real applications.
https://www.wendangku.net/doc/186594855.html,parison to some related work
Numerical approaches similar to the optimization method have been introduced and discussed in Refs.[2,4,19].While these papers focused on the mathematical model,the main purpose of our paper is to address the numerical experiment with the optimization method.For the numerical method to solve the geometric constraint problems,one of the most challenging problem is how to?nd a numerical method which is both ef?cient and robust.
In Ref.[4]the authors convert the constraints to an energy function and solve the constraint problem by minimizing the energy function.However,the steepest descent method used in their work suffers from slow convergence because of the zigzagging problem[3],which makes it hard to be used to solve real application problems.In Refs.[2,19]the authors independently proposed a method to convert the constraint problem into a constrained optimization problem.However, both papers gives no detailed information about the numer-ical behavior of the algorithm.
Also the distinctive advantage of the optimization method in handling with under-and over-constrained problems is one of the main focuses of our paper as our experiments with various regular n-polygons have shown(Section2.5). We have made extensive experiments with under-and over-constrained problems and have found that our approach is very natural to deal with these problems. Furthermore,we observe that with this method redundant constraints can be naturally used in practice to select a solu-tion branch from a?nite set of solutions of a well constrained problem(Section2.5).
3.Conclusions
In this paper we use the optimization method to solve geometric constraint problems.Many experimental results show that this method is stable and effective in solving dif?cult geometric constraint problems.In particular,it can be used to solve under-and over-constrained problems naturally.Further more,this method can be extended to a general frame work to cover more general geometric constraint problems in many applications such as CAD. Acknowledgements
This work was supported in part by the NSF Grants CCR-9420857and CCR-9901062and was accomplished at Wichita State University.Ge and Gao were also supported in part by the Chinese National Science Foundation.The
J.-X.Ge et al./Computer-Aided Design31(1999)867–879877
authors wish to thank the reviewers and the editor for their helpful suggestions and advice.
References
[1]Aldefeld B.Variation of geometries based on a geometric-reasoning
https://www.wendangku.net/doc/186594855.html,puter Aided Design 1988;20(3):117–26.
[2]Barford LA.A graphical,language-based editor for generic solid
models represented by constraints,PhD dissertation,Department of Computer Science,Cornell University,1987.
[3]Bazarra MS,Sherali HD,Shetty CM.Nonlinear programming:theory
and algorithms,2.New York:Wiley,1993.
[4]Witkin A,Fleischer K,Barr A.Constraints on parametrized models.
Computer Graphics 1987;21(4):225–32.
[5]Bouma W,Hoffmann CM,Fudos I,Cai J,Paige R.A geometric
constraint https://www.wendangku.net/doc/186594855.html,puter Aided Design 1995;27(6):487–501.[6]Bruderlin B.Rule-based geometric modeling,PhD dissertation,Swiss
Federal Institute of Technology (ETH)Zu
¨rich,1988.[7]Buchanan SA,de Pennington A.Constraint de?nition system:a
computer algebra based approach to solving geometric https://www.wendangku.net/doc/186594855.html,puter Aided Design 1993;25(12):740–50.
[8]Chou S-C.Mechanical geometry theorem proving,Dordrecht:
Kluwer,1987.
[9]Chou S-C,Gao X-S,Zhang J-Z.A ?xpoint approach to automated
geometry theorem proving,WSUCS-95-2,Computer Science Depart-ment,Wichita State University,1995.
[10]Elster KH,editor.Modern mathematical methods of optimization
Berlin:Akademie,1993.
[11]Freeman-Benson B,Maloney J.An incremental constraint solver.
Communications of the ACM 1990;33(1):54–63.
[12]Fudos I,Hoffmann CM.Correctness proof of a geometric constraint
solver,Technical Report CSD93-076,Department of Computer Science of Purdue University,1993.
[13]Fudos I,Hoffmann CM.A graph-constructive approach to solving
systems of geometric constraints.ACM Transactions on Graphics 1997;16(2):179–216.
[14]Gao X-S,Chou S-C.Solving geometric constraint problems.II.A
symbolic approach and decision of https://www.wendangku.net/doc/186594855.html,puter Aided Design 1998;30(2):115–22.
[15]Gao X-S,Chou S-C.Solving geometric constraint problems,I.A
global propagation https://www.wendangku.net/doc/186594855.html,puter Aided Design 1998;30(1):47–54.
[16]Gay DM.Algorithm 611—subroutines for unconstrained minimiza-tion using a model/trust-regin approach.ACM Transactions on Math-ematical Software 1983;9:503–24.
[17]Horst R,Pardalos PM,Thai NV.Introduction to global optimization,
Dordrecht:Kluwer,1995.
[18]Ignizio JP.Linear programming,Englewood Cliffs,NJ:Prentice-Hall,
1994.
[19]Kalra D,Barr A.Constraint-based ?gure-maker.Eurographics’90
1990:413–24.
[20]Kelley CT.Iterative methods for optimization,Department of Mathe-matics,North Carolina State University,https://www.wendangku.net/doc/186594855.html,/eos/users/c/ctkelley/www/darts.html,to be published by SIAM in 1999,Draft of May 4,1998.
[21]Kondo K.Algebraic method for manipulation of dimensional
relationships in geometric models.Geometric Aided Design 1992;24(3):141–7.
[22]Kramer G.Solving geometric constraint systems,Cambridge,MA:
MIT Press,1992.
[23]Kramer G.Geometric constraint engine.Arti?cial Intelligence
1992;58:327–60.
[24]Lamure H,Michelucci D.Solving geometric constraints by homo-topy.IEEE Transactions on Visualization and Computer Graphics 1996;2(1):28–34.
[25]Latheam RS,Middleditch AE.Connectivity analysis:a tool for
processing geometric https://www.wendangku.net/doc/186594855.html,puter Aided Design 1994;28(11):917–28.
[26]Lee JY,Kim K.Geometric reasoning for knowledge-based para-metric design using graph https://www.wendangku.net/doc/186594855.html,puter Aided Design 1996;28(10):831–41.
[27]Lee K,Andrews G.Inference of the positions of components in an
assembly:part https://www.wendangku.net/doc/186594855.html,puter Aided Design 1985;17(1):20–4.
[28]Leler W.Constraint programming languages,Reading,MA:Addison-Wesley,1988.
[29]Light R,Gossard D.Modi?cation of geometric models through varia-tional geometry.Geometric Aided Design 1982;14:208–14.
[30]Lin DC,Nocedal J.On the limited memory bfgs method for large
scale optimization.Mathematical Programming 1989;45:503–628.[31]Lin VC,Gossard DC,Light RA.Variational geometry in computer-aided https://www.wendangku.net/doc/186594855.html,puter Graphics 1981;15(3):171–7.
[32]More JJ,Wright SJ.Optimization software guide,SIAM,1993.[33]Nemhauser GL,Rinnooy Kan AHG,Todd MJ,editors.Optimization
Amsterdam:Elsevier,1989.
[34]Nocedal J.Updating quasi-Newton matrices with limited storage,
Mathematics of Computation,1980;35,773–82.
[35]Owen J.Algebraic solution for geometry from dimensional
constraints,ACM Symp.Found.of Solid Modeling,Austin TX,1991,p.397–407.
[36]Rocheleau DN,Lee K.System for interactive assembly modeling.
Computer Aided Design 1987;19(1):65–72.
[37]Serrano D,Gossard D.Constraint management in MCAE.In:Gero J,
editor.Arti?cial intelligence in engineering:design,Amsterdam:Elsevier,1988.
[38]Schnierderjans MJ.Goal programming:methodology and applica-tions,Dordrecht:Kluwer,1995.
[39]Suzuki H,Ando H,Kimura F.Geometric constraints and reasoning
for geometrical CAD https://www.wendangku.net/doc/186594855.html,puter and Graphics 1990;14(2):211–24.
[40]Todd P.A k -tree generalization that characterizes consistency of
dimensioned engineering drawings.SIAM Journal of Discussions in Mathematics 1989;2:255–61.
[41]Verroust A,Schonek F,Roller D.Rule-oriented method for parame-trized computer-aided https://www.wendangku.net/doc/186594855.html,puter Aided Design 1992;24(3):531–40.
J.-X.Ge et al./Computer-Aided Design 31(1999)867–879
878Jianxin Ge is an associate professor in Applied Mathematics Department at Zhejiang University,China,He received his BS in 1988,MS in 1990,and Ph.D.in 1993,all in Computer Science and Engi-neering at Zhejiang University.His research interests are in the computer aided design (CAD)and include 3D surface and solid modeling,computer graphics,geometric constraint satisfaction,and numerical
computation.
J.-X.Ge et al./Computer-Aided Design 31(1999)867–879
879
Xiaoshan Gao was born in Hebei province of China in 1963.He got his Ph.D.from the Chinese Academy of Sciences in 1988.His research interests include automated reasoning,symbolic computation,compu-ter graphics and intelligence CAD,and computer aided education.He has published one monograph and more than 40research papers.He has won a ?rst class award in natural sciences and an Outstanding Young Scientist Award of 1997from the Chinese Academy of
Sciences.He is a recipient of the Excellent Youth Grant from the Chinese Academy of Sciences.He is a recipient of the Excellent Youth Grant from the Chinese NSF for
1998–2000.
Shang-Ching Chou ,currently a Professor at the CS Department of Wichita State University,received a Ph.D.at University of Texas at Austin in 1985.Since then he has been supported by NSF for 15conse-cutive years for his research in automated geometric
reasoning.
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毕业论文写作要求与格式规范 关于《毕业论文写作要求与格式规范》，是我们特意为大家整理的，希望对大家有所帮助。 (一)文体 毕业论文文体类型一般分为：试验论文、专题论文、调查报告、文献综述、个案评述、计算设计等。学生根据自己的实际情况，可以选择适合的文体写作。 (二)文风 符合科研论文写作的基本要求：科学性、创造性、逻辑性、
实用性、可读性、规范性等。写作态度要严肃认真，论证主题应有一定理论或应用价值;立论应科学正确，论据应充实可靠，结构层次应清晰合理，推理论证应逻辑严密。行文应简练，文笔应通顺，文字应朴实，撰写应规范，要求使用科研论文特有的科学语言。 (三)论文结构与排列顺序 毕业论文，一般由封面、独创性声明及版权授权书、摘要、目录、正文、后记、参考文献、附录等部分组成并按前后顺序排列。 1.封面：毕业论文(设计)封面具体要求如下： (1)论文题目应能概括论文的主要内容，切题、简洁，不超过30字，可分两行排列;
(2)层次：大学本科、大学专科 (3)专业名称：机电一体化技术、计算机应用技术、计算机网络技术、数控技术、模具设计与制造、电子信息、电脑艺术设计、会计电算化、商务英语、市场营销、电子商务、生物技术应用、设施农业技术、园林工程技术、中草药栽培技术和畜牧兽医等专业，应按照标准表述填写; (4)日期：毕业论文(设计)完成时间。 2.独创性声明和关于论文使用授权的说明：需要学生本人签字。 3.摘要：论文摘要的字数一般为300字左右。摘要是对论文的内容不加注释和评论的简短陈述，是文章内容的高度概括。主要内容包括：该项研究工作的内容、目的及其重要性;所使用的实验方法;总结研究成果，突出作者的新见解;研究结论及其意义。摘要中不列举例证，不描述研究过程，不做自我评价。
公文格式规范与常见公文写作
公文格式规范与常见公文写作 一、公文概述与公文格式规范 党政机关公文种类的区分、用途的确定及格式规范等，由中共中央办公厅、国务院办公厅于2012年4月16日印发，2012年7月1日施行的《党政机关公文处理工作条例》规定。之前相关条例、办法停止执行。 （一）公文的含义 公文，即公务文书的简称，属应用文。 广义的公文，指党政机关、社会团体、企事业单位，为处理公务按照一定程序而形成的体式完整的文字材料。 狭义的公文，是指在机关、单位之间，以规范体式运行的文字材料，俗称“红头文件”。 ?（二）公文的行文方向和原则 ?、上行文下级机关向上级机关行文。有“请示”、“报告”、和“意见”。 ?、平行文同级机关或不相隶属机关之间行文。主要有“函”、“议案”和“意见”。 ?、下行文上级机关向下级机关行文。主要有“决议”、“决定”、“命令”、“公报”、“公告”、“通告”、“意见”、“通知”、“通报”、“批复”和“会议纪要”等。 ?其中，“意见”、“会议纪要”可上行文、平行文、下行文。?“通报”可下行文和平行文。 ?原则： ?、根据本机关隶属关系和职权范围确定行文关系 ?、一般不得越级行文 ?、同级机关可以联合行文 ?、受双重领导的机关应分清主送机关和抄送机关 ?、党政机关的部门一般不得向下级党政机关行文 ?(三) 公文的种类及用途 ?、决议。适用于会议讨论通过的重大决策事项。 ?、决定。适用于对重要事项作出决策和部署、奖惩有关单位和人员、变更或撤销下级机关不适当的决定事项。
?、命令（令）。适用于公布行政法规和规章、宣布施行重大强制性措施、批准授予和晋升衔级、嘉奖有关单位和人员。 ?、公报。适用于公布重要决定或者重大事项。 ?、公告。适用于向国内外宣布重要事项或者法定事项。 ?、通告。适用于在一定范围内公布应当遵守或者周知的事项。?、意见。适用于对重要问题提出见解和处理办法。 ?、通知。适用于发布、传达要求下级机关执行和有关单位周知或者执行的事项，批转、转发公文。 ?、通报。适用于表彰先进、批评错误、传达重要精神和告知重要情况。 ?、报告。适用于向上级机关汇报工作、反映情况，回复上级机关的询问。 ?、请示。适用于向上级机关请求指示、批准。 ?、批复。适用于答复下级机关请示事项。 ?、议案。适用于各级人民政府按照法律程序向同级人民代表大会或者人民代表大会常务委员会提请审议事项。 ?、函。适用于不相隶属机关之间商洽工作、询问和答复问题、请求批准和答复审批事项。 ?、纪要。适用于记载会议主要情况和议定事项。?（四）、公文的格式规范 ?、眉首的规范 ?（）、份号 ?也称编号，置于公文首页左上角第行，顶格标注。“秘密”以上等级的党政机关公文，应当标注份号。 ?（）、密级和保密期限 ?分“绝密”、“机密”、“秘密”三个等级。标注在份号下方。?（）、紧急程度 ?分为“特急”和“加急”。由公文签发人根据实际需要确定使用与否。标注在密级下方。 ?（）、发文机关标志（或称版头） ?由发文机关全称或规范化简称加“文件”二字组成。套红醒目，位于公文首页正中居上位置（按《党政机关公文格式》标准排
ctex 宏包说明 ctex
ctex宏包说明 https://www.wendangku.net/doc/186594855.html,? 版本号：v1.02c修改日期：2011/03/11 摘要 ctex宏包提供了一个统一的中文L A T E X文档框架，底层支持CCT、CJK和xeCJK 三种中文L A T E X系统。ctex宏包提供了编写中文L A T E X文档常用的一些宏定义和命令。 ctex宏包需要CCT系统或者CJK宏包或者xeCJK宏包的支持。主要文件包括ctexart.cls、ctexrep.cls、ctexbook.cls和ctex.sty、ctexcap.sty。 ctex宏包由https://www.wendangku.net/doc/186594855.html,制作并负责维护。 目录 1简介2 2使用帮助3 2.1使用CJK或xeCJK (3) 2.2使用CCT (3) 2.3选项 (4) 2.3.1只能用于文档类的选项 (4) 2.3.2只能用于文档类和ctexcap.sty的选项 (4) 2.3.3中文编码选项 (4) 2.3.4中文字库选项 (5) 2.3.5CCT引擎选项 (5) 2.3.6排版风格选项 (5) 2.3.7宏包兼容选项 (6) 2.3.8缺省选项 (6) 2.4基本命令 (6) 2.4.1字体设置 (6) 2.4.2字号、字距、字宽和缩进 (7) ?https://www.wendangku.net/doc/186594855.html, 1
1简介2 2.4.3中文数字转换 (7) 2.5高级设置 (8) 2.5.1章节标题设置 (9) 2.5.2部分修改标题格式 (12) 2.5.3附录标题设置 (12) 2.5.4其他标题设置 (13) 2.5.5其他设置 (13) 2.6配置文件 (14) 3版本更新15 4开发人员17 1简介 这个宏包的部分原始代码来自于由王磊编写cjkbook.cls文档类，还有一小部分原始代码来自于吴凌云编写的GB.cap文件。原来的这些工作都是零零碎碎编写的，没有认真、系统的设计，也没有用户文档，非常不利于维护和改进。2003年，吴凌云用doc和docstrip工具重新编写了整个文档，并增加了许多新的功能。2007年，oseen和王越在ctex宏包基础上增加了对UTF-8编码的支持，开发出了ctexutf8宏包。2009年5月，我们在Google Code建立了ctex-kit项目1，对ctex宏包及相关宏包和脚本进行了整合，并加入了对XeT E X的支持。该项目由https://www.wendangku.net/doc/186594855.html,社区的开发者共同维护，新版本号为v0.9。在开发新版本时，考虑到合作开发和调试的方便，我们不再使用doc和docstrip工具，改为直接编写宏包文件。 最初Knuth设计开发T E X的时候没有考虑到支持多国语言，特别是多字节的中日韩语言。这使得T E X以至后来的L A T E X对中文的支持一直不是很好。即使在CJK解决了中文字符处理的问题以后，中文用户使用L A T E X仍然要面对许多困难。最常见的就是中文化的标题。由于中文习惯和西方语言的不同，使得很难直接使用原有的标题结构来表示中文标题。因此需要对标准L A T E X宏包做较大的修改。此外，还有诸如中文字号的对应关系等等。ctex宏包正是尝试着解决这些问题。中间很多地方用到了在https://www.wendangku.net/doc/186594855.html,论坛上的讨论结果，在此对参与讨论的朋友们表示感谢。 ctex宏包由五个主要文件构成：ctexart.cls、ctexrep.cls、ctexbook.cls和ctex.sty、ctexcap.sty。ctex.sty主要是提供整合的中文环境，可以配合大多数文档类使用。而ctexcap.sty则是在ctex.sty的基础上对L A T E X的三个标准文档类的格式进行修改以符合中文习惯，该宏包只能配合这三个标准文档类使用。ctexart.cls、ctexrep.cls、ctexbook.cls则是ctex.sty、ctexcap.sty分别和三个标准文档类结合产生的新文档类，除了包含ctex.sty、ctexcap.sty的所有功能，还加入了一些修改文档类缺省设置的内容（如使用五号字体为缺省字体）。 1https://www.wendangku.net/doc/186594855.html,/p/ctex-kit/
文档书写格式规范要求
学生会文档书写格式规范要求 目前各部门在日常文书编撰中大多按照个人习惯进行排版，文档中字体、文字大小、行间距、段落编号、页边距、落款等参数设置不规范，严重影响到文书的标准性和美观性，以下是文书标准格式要求及日常文档书写注意事项，请各部门在今后工作中严格实行： 一、文件要求 1.文字类采用Word格式排版 2.统计表、一览表等表格统一用Excel格式排版 3.打印材料用纸一般采用国际标准A4型（210mm×297mm），左侧装订。版面方向以纵向为主，横向为辅，可根据实际需要确定 4.各部门的职责、制度、申请、请示等应一事一报，禁止一份行文内同时表述两件工作。 5.各类材料标题应规范书写，明确文件主要内容。 二、文件格式 （一）标题 1.文件标题：标题应由发文机关、发文事由、公文种类三部分组成，黑体小二号字,不加粗，居中，段后空1行。 （二）正文格式 1. 正文字体：四号宋体，在文档中插入表格，单元格内字体用宋体，字号可根据内容自行设定。 2.页边距：上下边距为2.54厘米；左右边距为 3.18厘米。
3.页眉、页脚：页眉为1.5厘米；页脚为1.75厘米； 4.行间距：1.5倍行距。 5.每段前的空格请不要使用空格，应该设置首先缩进2字符 6.年月日表示：全部采用阿拉伯数字表示。 7.文字从左至右横写。 （三）层次序号 (1)一级标题：一、二、三、 (2)二级标题：（一）（二）（三） (3)三级标题：1. 2. 3. (4)四级标题：（1）（2）（3） 注：三个级别的标题所用分隔符号不同，一级标题用顿号“、”例如：一、二、等。二级标题用括号不加顿号，例如：（三）（四）等。三级标题用字符圆点“.”例如：5. 6.等。 （四）、关于落款： 1.对外行文必须落款“湖南环境生物专业技术学院学生会”“校学生会”各部门不得随意使用。 2.各部门文件落款需注明组织名称及部门“湖南环境生物专业技术学院学生会XX部”“校学生会XX部” 3.所有行文落款不得出现“环境生物学院”“湘环学院”“学生会”等表述不全的简称。 4.落款填写至文档末尾右对齐，与前一段间隔2行 5.时间落款：文档中落款时间应以“2016年5月12日”阿拉伯数字
政府公文写作格式规范
政府公文写作格式 一、眉首部分 （一）发文机关标识 平行文和下行文的文件头，发文机关标识上边缘至上页边为62mm，发文机关下边缘至红色反线为28mm。 上行文中，发文机关标识上边缘至版心上边缘为80mm，即与上页边距离为117mm，发文机关下边缘至红色反线为30mm。 发文机关标识使用字体为方正小标宋_GBK，字号不大于22mm×15mm。 （二）份数序号 用阿拉伯数字顶格标识在版心左上角第一行，不能少于2位数。标识为“编号000001” （三）秘密等级和保密期限 用3号黑体字顶格标识在版心右上角第一行，两字中间空一字。如需要加保密期限的，密级与期限间用“★”隔开，密级中则不空字。 （四）紧急程度 用3号黑体字顶格标识在版心右上角第一行，两字中间空一字。如同时标识密级，则标识在右上角第二行。 （五）发文字号 标识在发文机关标识下两行，用3号方正仿宋_GBK字体剧
中排布。年份、序号用阿拉伯数字标识，年份用全称，用六角括号“〔〕”括入。序号不用虚位，不用“第”。发文字号距离红色反线4mm。 （六）签发人 上行文需要标识签发人，平行排列于发文字号右侧，发文字号居左空一字，签发人居右空一字。“签发人”用3号方正仿宋_GBK，后标全角冒号，冒号后用3号方正楷体_GBK标识签发人姓名。多个签发人的，主办单位签发人置于第一行，其他从第二行起排在主办单位签发人下，下移红色反线，最后一个签发人与发文字号在同一行。 二、主体部分 （一）标题 由“发文机关+事由+文种”组成，标识在红色反线下空两行，用2号方正小标宋_GBK，可一行或多行居中排布。 （二）主送机关 在标题下空一行，用3号方正仿宋_GBK字体顶格标识。回行是顶格，最后一个主送机关后面用全角冒号。 （三）正文 主送机关后一行开始，每段段首空两字，回行顶格。公文中的数字、年份用阿拉伯数字，不能回行，阿拉伯数字：用3号Times New Roman。正文用3号方正仿宋_GBK，小标题按照如下排版要求进行排版：
tabularx宏包中改变弹性列的宽度
tabularx宏包中改变弹性列的宽度\hsize 分类：latex 2012-03-07 21:54 12人阅读评论(0) 收藏编辑删除 \documentclass{article} \usepackage{amsmath} \usepackage{amssymb} \usepackage{latexsym} \usepackage{CJK} \usepackage{tabularx} \usepackage{array} \newcommand{\PreserveBackslash}[1]{\let \temp =\\#1 \let \\ = \temp} \newcolumntype{C}[1]{>{\PreserveBackslash\centering}p{#1}} \newcolumntype{R}[1]{>{\PreserveBackslash\raggedleft}p{#1}} \newcolumntype{L}[1]{>{\PreserveBackslash\raggedright}p{#1}} \begin{document} \begin{CJK*}{GBK}{song} \CJKtilde \begin{tabularx}{10.5cm}{|p{3cm} |>{\setlength{\hsize}{.5\hsize}\centering}X |>{\setlength{\hsize}{1.5\hsize}}X|} %\hsize是自动计算的列宽度，上面{.5\hsize}与{1.5\hsize}中的\hsize前的数字加起来必须等于表格的弹性列数量。对于本例，弹性列有2列，所以“.5+1.5=2”正确。 %共3列，总列宽为10.5cm。第1列列宽为3cm，第3列的列宽是第2列列宽的3倍，其宽度自动计算。第2列文字左右居中对齐。注意：\multicolum命令不能跨越X列。 \hline 聪明的鱼儿在咬钩前常常排祠再三& 这是因为它们要荆断食物是否安全&知果它们认为有危险\\ \hline 它们枕不会吃& 如果它们判定没有危险& 它们就食吞钩\\ \hline 一眼识破诱饵的危险，却又不由自主地去吞钩的& 那才正是人的心理而不是鱼的心理& 是人的愚合而不是鱼的恳奋\\
2-1论文写作要求与格式规范(2009年修订)
广州中医药大学研究生学位论文基本要求与写作规范 为了进一步提高学位工作水平和学位论文质量，保证我校学位论文在结构和格式上的规范与统一，特做如下规定： 一、学位论文基本要求 （一）科学学位硕士论文要求 1.论文的基本科学论点、结论，应在中医药学术上和中医药科学技术上具有一定的理论意义和实践价值。 2.论文所涉及的内容，应反映出作者具有坚实的基础理论和系统的专门知识。 3.实验设计和方法比较先进，并能掌握本研究课题的研究方法和技能。 4.对所研究的课题有新的见解。 5.在导师指导下研究生独立完成。 6.论文字数一般不少于3万字，中、英文摘要1000字左右。 （二）临床专业学位硕士论文要求 临床医学硕士专业学位申请者在临床科研能力训练中学会文献检索、收集资料、数据处理等科学研究的基本方法,培养临床思维能力与分析能力,完成学位论文。 1.学位论文包括病例分析报告及文献综述。 2.学位论文应紧密结合中医临床或中西结合临床实际，以总结临床实践经验为主。 3.学位论文应表明申请人已经掌握临床科学研究的基本方法。 4.论文字数一般不少于15000字，中、英文摘要1000字左右。 （三）科学学位博士论文要求 1.研究的课题应在中医药学术上具有较大的理论意义和实践价值。 2.论文所涉及的内容应反映作者具有坚实宽广的理论基础和系统深入的专门知识，并表明作者具有独立从事科学研究工作的能力。 3.实验设计和方法在国内同类研究中属先进水平，并能独立掌握本研究课题的研究方法和技能。
4.对本研究课题有创造性见解，并取得显著的科研成果。 5.学位论文必须是作者本人独立完成，与他人合作的只能提出本人完成的部分。 6.论文字数不少于5万字，中、英摘要3000字；详细中文摘要(单行本)1万字左右。 （四）临床专业学位博士论文要求 1.要求论文课题紧密结合中医临床或中西结合临床实际，研究结果对临床工作具有一定的应用价值。 2.论文表明研究生具有运用所学知识解决临床实际问题和从事临床科学研究的能力。 3.论文字数一般不少于3万字，中、英文摘要2000字；详细中文摘要(单行本)5000字左右。 二、学位论文的格式要求 （一）学位论文的组成 博士、硕士学位论文一般应由以下几部分组成，依次为：1.论文封面；2. 原创性声明及关于学位论文使用授权的声明；3.中文摘要；4.英文摘要；5.目录； 6.引言； 7.论文正文； 8.结语； 9.参考文献；10.附录；11.致谢。 1.论文封面：采用研究生处统一设计的封面。论文题目应以恰当、简明、引人注目的词语概括论文中最主要的内容。避免使用不常见的缩略词、缩写字，题名一般不超过30个汉字。论文封面“指导教师”栏只写入学当年招生简章注明、经正式遴选的指导教师1人，协助导师名字不得出现在论文封面。 2．原创性声明及关于学位论文使用授权的声明（后附）。 3.中文摘要：要说明研究工作目的、方法、成果和结论。并写出论文关键词3～5个。 4.英文摘要：应有题目、专业名称、研究生姓名和指导教师姓名，内容与中文提要一致，语句要通顺，语法正确。并列出与中文对应的论文关键词3～5个。 5.目录：将论文各组成部分(1～3级)标题依次列出，标题应简明扼要，逐项标明页码，目录各级标题对齐排。 6.引言：在论文正文之前，简要说明研究工作的目的、范围、相关领域前人所做的工作和研究空白，本研究理论基础、研究方法、预期结果和意义。应言简
公文写作毕业论文写作要求和格式规范
（公文写作）毕业论文写作要求和格式规范
中国农业大学继续教育学院 毕业论文写作要求和格式规范 壹、写作要求 （壹）文体 毕业论文文体类型壹般分为：试验论文、专题论文、调查方案、文献综述、个案评述、计算设计等。学生根据自己的实际情况，能够选择适合的文体写作。 （二）文风 符合科研论文写作的基本要求：科学性、创造性、逻辑性、实用性、可读性、规范性等。写作态度要严肃认真，论证主题应有壹定理论或应用价值；立论应科学正确，论据应充实可靠，结构层次应清晰合理，推理论证应逻辑严密。行文应简练，文笔应通顺，文字应朴实，撰写应规范，要求使用科研论文特有的科学语言。 （三）论文结构和排列顺序 毕业论文，壹般由封面、独创性声明及版权授权书、摘要、目录、正文、后记、参考文献、附录等部分组成且按前后顺序排列。 1．封面：毕业论文（设计）封面（见文件5）具体要求如下： （1）论文题目应能概括论文的主要内容，切题、简洁，不超过30字，可分俩行排列； （2）层次：高起本，专升本，高起专； （3）专业名称：现开设园林、农林经济管理、会计学、工商管理等专业，应按照标准表述填写； （4）密级：涉密论文注明相应保密年限； （5）日期：毕业论文完成时间。 2．独创性声明和关于论文使用授权的说明：（略）。
3．摘要：论文摘要的字数壹般为300字左右。摘要是对论文的内容不加注释和评论的简短陈述，是文章内容的高度概括。主要内容包括：该项研究工作的内容、目的及其重要性；所使用的实验方法；总结研究成果，突出作者的新见解；研究结论及其意义。摘要中不列举例证，不描述研究过程，不做自我评价。 论文摘要后另起壹行注明本文的关键词，关键词是供检索用的主题词条，应采用能够覆盖论文内容的通用专业术语，符合学科分类，壹般为3～5个，按照词条的外延层次从大到小排列。 4．目录（目录示例见附件3）：独立成页，包括论文中的壹级、二级标题、后记、参考文献、和附录以及各项所于的页码。 5．正文：包括前言、论文主体和结论 前言：为正文第壹部分内容，简单介绍本项研究的背景和国内外研究成果、研究现状，明确研究目的、意义以及要解决的问题。 论文主体：是全文的核心部分，于正文中应将调查、研究中所得的材料和数据加工整理和分析研究，提出论点，突出创新。内容可根据学科特点和研究内容的性质而不同。壹般包括：理论分析、计算方法、实验装置和测试方法、对实验结果或调研结果的分析和讨论，本研究方法和已有研究方法的比较等方面。内容要求论点正确，推理严谨，数据可靠，文字精炼，条理分明，重点突出。 结论：为正文最后壹部分，是对主要成果的归纳和总结，要突出创新点，且以简练的文字对所做的主要工作进行评价。 6．后记：对整个毕业论文工作进行简单的回顾总结，对给予毕业论文工作提供帮助的组织或个人表示感谢。内容应尽量简单明了，壹般为200字左右。 7．参考文献：是论文不可或缺的组成部分。它既可反映毕业论文工作中取材广博程度，又可反映文稿的科学依据和作者尊重他人研究成果的严肃态度，仍能够向读者提供有关
配合前面的ntheorem宏包产生各种定理结构
%=== 配合前面的ntheorem宏包产生各种定理结构,重定义一些正文相关标题===% \theoremstyle{plain} \theoremheaderfont{\normalfont\rmfamily\CJKfamily{hei}} \theorembodyfont{\normalfont\rm\CJKfamily{song}} \theoremindent0em \theoremseparator{\hspace{1em}} \theoremnumbering{arabic} %\theoremsymbol{} %定理结束时自动添加的标志 \newtheorem{definition}{\hspace{2em}定义}[chapter] %\newtheorem{definition}{\hei 定义}[section] %!!!注意当section为中国数字时，[sction]不可用！ \newtheorem{proposition}{\hspace{2em}命题}[chapter] \newtheorem{property}{\hspace{2em}性质}[chapter] \newtheorem{lemma}{\hspace{2em}引理}[chapter] %\newtheorem{lemma}[definition]{引理} \newtheorem{theorem}{\hspace{2em}定理}[chapter] \newtheorem{axiom}{\hspace{2em}公理}[chapter] \newtheorem{corollary}{\hspace{2em}推论}[chapter] \newtheorem{exercise}{\hspace{2em}习题}[chapter] \theoremsymbol{$\blacksquare$} \newtheorem{example}{\hspace{2em}例}[chapter] \theoremstyle{nonumberplain} \theoremheaderfont{\CJKfamily{hei}\rmfamily} \theorembodyfont{\normalfont \rm \CJKfamily{song}} \theoremindent0em \theoremseparator{\hspace{1em}} \theoremsymbol{$\blacksquare$} \newtheorem{proof}{\hspace{2em}证明} \usepackage{amsmath}%数学 \usepackage[amsmath,thmmarks,hyperref]{ntheorem} \theoremstyle{break} \newtheorem{example}{Example}[section]
论文写作格式规范与要求(完整资料).doc
【最新整理，下载后即可编辑】 广东工业大学成人高等教育 本科生毕业论文格式规范（摘录整理） 一、毕业论文完成后应提交的资料 最终提交的毕业论文资料应由以下部分构成： （一）毕业论文任务书（一式两份，与论文正稿装订在一起）（二）毕业论文考核评议表（一式三份，学生填写表头后发电子版给老师） （三）毕业论文答辩记录（一份, 学生填写表头后打印出来，答辩时使用） （四）毕业论文正稿（一式两份，与论文任务书装订在一起），包括以下内容： 1、封面 2、论文任务书 3、中、英文摘要（先中文摘要，后英文摘要，分开两页排版） 4、目录 5、正文（包括：绪论、正文主体、结论） 6、参考文献 7、致谢 8、附录（如果有的话） （五）论文任务书和论文正稿的光盘
二、毕业论文资料的填写与装订 毕业论文须用计算机打印，一律使用A4打印纸，单面打印。 毕业论文任务书、毕业论文考核评议表、毕业论文正稿、答辩纪录纸须用计算机打印，一律使用A4打印纸。答辩提问记录一律用黑色或蓝黑色墨水手写，要求字体工整，卷面整洁；任务书由指导教师填写并签字，经主管院领导签字后发出。 毕业论文使用统一的封面，资料装订顺序为：毕业论文封面、论文任务书、考核评议表、答辩记录、中文摘要、英文摘要、目录、正文、参考文献、致谢、附录（如果有的话）。论文封面要求用A3纸包边。 三、毕业论文撰写的内容与要求 一份完整的毕业论文正稿应包括以下几个方面： （一）封面（见封面模版） （二）论文题目（填写在封面上，题目使用2号隶书，写作格式见封面模版） 题目应简短、明确，主标题不宜超过20字；可以设副标题。（三）论文摘要（写作格式要求见《摘要、绪论、结论、参考文献写作式样》P1～P2） 1、中文“摘要”字体居中，独占一页
Groff 应用
使用Groff 生成独立于设备的文档开始之前 了解本教程中包含的内容和如何最好地利用本教程，以及在使用本教程的过程中您需要完成的工作。 关于本教程 本教程提供了使用Groff(GNU Troff)文档准备系统的简介。其中介绍了这个系统的工作原理、如何使用Groff命令语言为其编写输入、以及如何从该输入生成各种格式的独立于设备的排版文档。 本教程所涉及的主题包括： 文档准备过程 输入文件格式 语言语法 基本的格式化操作 生成输出 目标 本教程的主要目标是介绍Groff，一种用于文档准备的开放源码系统。如果您需要在应用程序中构建文档或帮助文件、或为客户和内部使用生成任何类型的打印或屏幕文档(如订单列表、故障单、收据或报表)，那么本教程将向您介绍如何开始使用Groff以实现这些任务。 在学习了本教程之后，您应该完全了解Groff的基本知识，包括如何编写和处理基本的Groff输入文件、以及如何从这些文件生成各种输出。
先决条件 本教程的目标读者是入门级到中级水平的UNIX?开发人员和管理员。您应 该对使用UNIX命令行Shell和文本编辑器有基本的了解。 系统要求 要运行本教程中的示例，您需要访问运行UNIX操作系统并安装了下面这些软件的计算机(请参见本教程的参考资料部分以获取相关链接)： Groff。Groff分发版中包括groff前端工具、troff后端排版引擎和本教 程中使用的各种附属工具。 自由软件基金会将Groff作为其GNU Project中的一部分进行了发布，所 发布的源代码符合GNU通用公共许可证(GPL)并得到了广泛的移植，几乎对于所有的UNIX操作系统、以及非UNIX操作系统(如Microsoft?Windows?)都有相应 的可用版本。 在撰写本教程时，最新的Groff发布版是Version 1.19.2，对于学习本教 程而言，您至少需要Groff Version 1.17。 gxditview。从Version 1.19.2开始，Groff中包含了这个工具，而在以 前的版本中，对其进行了单独的发布。 PostScript Previewer，如ghostview、gv或showpage。 如果您是从源代码安装Groff，那么请参考Groff源代码分发版中的自述 文件，其中列举了所需的任何额外的软件，而在编译和安装Groff时可能需要 使用这些软件。 介绍Groff 用户通常在字处理软件、桌面发布套件和文本布局应用程序等应用程序环 境中创建文档，而在这些环境中，最终将对文档进行打印或导出为另一种格式。整个文档准备过程，从创建到最后的输出，都发生在单个应用程序中。文档通
TeX 使用指南(常见问题)
TeX 使用指南 常见问题（一） 1.\makeatletter 和\makeatother 的用法？ 答：如果需要借助于内部有\@字符的命令，如\@addtoreset，就需要借助于另两个命令 \makeatletter, \makeatother。 下面给出使用范例，用它可以实现公式编号与节号的关联。 \begin{verbatim} \documentclass{article} ... \makeatletter % '@' is now a normal "letter" for TeX \renewcommand\theequation{\thesection.\arabic{equation}} \@addtoreset{equation}{section} \makeatother % '@' is restored as a "non-letter" character for TeX \begin{document} ... \end{verbatim} 2.比较一下CCT与CJK的优缺点？ 答：根据王磊的经验，CJK 比CCT 的优越之处有以下几点： 1）字体定义采用LaTeX NFSS 标准，生成的DVI 文件不必像CCT 那样需要用patchdvi 处理后才能预览和打印。而且一般GB 编码的文件也不必进行预处理就可直接用latex 编译。2）可使用多种TrueType 字体和Type1 字体，生成的PDF 文件更清楚、漂亮。 3）能同时在文章中使用多种编码的文字，如中文简体、繁体、日文、韩文等。 当然，CCT 在一些细节上，如字体可用中文字号，字距、段首缩进等。毕竟CJK 是老外作的吗。 谈到MikTeX 和fpTeX, 应该说谈不上谁好谁坏，主要看个人的喜好了。MikTeX 比较小，不如fpTeX 里提供的TeX 工具，宏包全，但一般的情况也足够了。而且Yap 比windvi 要好用。fpTeX 是teTeX 的Windows 实现，可以说各种TeX 的有关软件基本上都包括在内。 3.中文套装中如何加入新的.cls文件？ 答：放在tex文件的同一目录下，或者miktex/localtexmf/tex/latex/下的某个子目录下，可以自己建一个。 4.怎样象第几章一样，将参考文献也加到目录？ 答：在参考文献部分加入 \addcontentsline{toc}{chapter}{参考文献}
论文的写作格式及规范
论文的写作格式及规范
附件9： 科学技术论文的写作格式及规范 用非公知公用的缩写词、字符、代号，尽量不出现数学式和化学式。 2作者署名和工作单位标引和检索，根据国家有关标准、数据规范为了提高技师、高级技师论文的学术质量，实现论文写的科学化、程序化和规范化，以利于科技信息的传递和科技情报的作评定工作，特制定本技术论文的写作格式及规范。望各位学员在注重科学研究的同时，做好科技论文撰写规范化工作。 1 题名 题名应以简明、确切的词语反映文章中最重要的特定内容，要符合编制题录、索引和检索的有关原则，并有助于选定关键词。 中文题名一般不宜超过20 个字，必要时可加副题名。英文题名应与中文题名含义一致。 题名应避免使作者署名是文责自负和拥有著作权的标志。作者姓名署于题名下方，团体作者的执笔人也可标注于篇首页地脚或文末，简讯等短文的作者可标注于文末。 英文摘要中的中国人名和地名应采用《中国人名汉语拼音字母拼写法》的有关规定；人名姓前名后分写，姓、名的首字母大写，名字中间不加连字符；地名中的专名和通名分写，每分写部分的首字母大写。 作者应标明其工作单位全称、省及城市名、邮编( 如“齐齐哈尔电业局黑龙江省齐齐哈尔市(161000) ”)，同时，在篇首页地脚标注第一作者的作者简介，内容包括姓名，姓别，出生年月，学位，职称，研究成果及方向。
3摘要 论文都应有摘要（3000 字以下的文章可以略去）。摘要的：写作应符合GB6447-86的规定。摘要的内容包括研究的目的、方法、结果和结论。一般应写成报道性文摘，也可以写成指示性或报道-指示性文摘。摘要应具有独立性和自明性，应是一篇完整的短文。一般不分段，不用图表和非公知公用的符号或术语，不得引用图、表、公式和参考文献的序号。中文摘要的篇幅：报道性的300字左右，指示性的100 字左右，报道指示性的200字左右。英文摘要一般与中文摘要内容相对应。 4关键词 关键词是为了便于作文献索引和检索而选取的能反映论文主题概念的词或词组，一般每篇文章标注3?8个。关键词应尽量从《汉语主题词表》等词表中选用规范词——叙词。未被词表收录的新学科、新技术中的重要术语和地区、人物、文献、产品及重要数据名称，也可作为关键词标出。中、英文关键词应一一对应。 5引言 引言的内容可包括研究的目的、意义、主要方法、范围和背景等。 应开门见山，言简意赅，不要与摘要雷同或成为摘要的注释，避免公式推导和一般性的方法介绍。引言的序号可以不写，也可以写为“ 0”，不写序号时“引言”二字可以省略。 6论文的正文部分 论文的正文部分系指引言之后，结论之前的部分，是论文的核心， 应按GB7713--87 的规定格式编写。 6.1层次标题
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