Chapter 1 RELIABLE GEOMETRIC COMPUTATIONS WITH ALGEBRAIC PRIMITIVES AND PREDICATES

Chapter1

RELIABLE GEOMETRIC COMPUTATIONS WITH ALGEBRAIC PRIMITIVES AND PREDICATES Mark Foskey

Dinesh Manocha

Tim Culver

John Keyser

and Shankar Krishnan

1.Introduction

The problem of accurate and robust implementation of geometric algorithms has received considerable attention for more than a decade.Despite much progress in computational geometry and geometric modeling,practical imple-mentations of geometric algorithms are prone to error.Much of the dif?culty arises from the fact that reasoning about geometry most naturally occurs in the domain of the real numbers,which can only be represented approximately on a digital computer.Many times,the correctness of geometric algorithms depends on correctly evaluating the signs of arithmetic expressions,and errors due to rounding or imprecise inputs can lead to grossly incorrect results or failure to run to completion.

The proposed solutions to this problem can be classi?ed into inexact and exact approaches[29].The former approach accepts the inaccuracy of the machine representation,and attempts to modify the algorithms,given that constraint, so that they reliably produce acceptable output.The notion of acceptability is dependent on the application.Algorithms developed in this way have been shown to work in speci?c cases.On the other hand,exact geometric com-putation(EGC)requires that every predicate evaluation be correct[35].The exact computation paradigm eliminates numerical error in geometric compu-tations entirely.Unfortunately,exact implementations are often far too slow, especially when we are dealing with nonlinear primitives.Karasick et al.[22] noted that naive implementations can take several orders of magnitude longer than an equivalent?oating-point implementation,an observation that is consis-

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tent with our experience.The goal has been to?nd techniques that reduce the performance penalty to an acceptable level.

As work on exact geometric computation has proceeded,it has become clear that the performance problems can be greatly alleviated.One area that has received less attention is the issue of reliability when dealing with nonlinear algebraic or curved primitives.This area provides numerous interesting chal-lenges for EGC and we address some of them in this paper.

Exact Computation as a Practical Approach.There is no question that EGC is slower than computation relying solely on machine precision arithmetic. The question is whether the slowdown is worth the gain in precision.Indeed, in many scienti?c or engineering applications the input data is inexact,and the question arises whether an exact result is even meaningful.But the main reason for using EGC is not exactness in itself,but rather reliability.A common cause of program failure is that rounding errors lead to inconsistent combinatorial decisions,e.g.about where a point lies with regard to a surface.By making a single interpretation of the data and performing calculations that are consistent with that interpretation,we can avoid this source of failure.Solving the prob-lems of accuracy and consistency is the?rst step towards a general solution to the robustness problem,which also involves handling degeneracies and special cases.

Organization.The rest of this paper is organized as follows.In Sec-tion2we brie?y review the relevant literature.In Section3we present some underlying geometric problems involving curved primitives.We discuss our general approach to EGC for curved primitives in Section4,including methods we use to achieve reasonable speeds for these computations.In Section5we present some results for boundary evaluation and V oronoi computations,and we conclude in Section6.

2.Literature Survey

The issue of robust and accurate computations in geometric applications has been addressed in numerous places,with surveys by Hoffmann[19]and Fortune[16]giving an indication of the variety of work.Yap[34]described the concept of exact geometric computation,and Li and Yap[28]have presented a more recent survey.Some of the earlier inexact approaches were based on geometric tolerances[32]and interval arithmetic[10].

One of the key ideas in accelerating exact computation is the use of?oating point?lters,in which predicates are?rst evaluated using fast?oating point methods and then tested for reliability,by analyzing the size of the possible ?oating point error.If a predicate is unreliable,exact computation is performed.

A good example of this method is the work of Fortune and van Wyk[17].As

Reliable Geometric Computations3 a preprocess,they perform an analysis of the calculations that will be needed by a geometric algorithm,so that the accuracy of these computations can be checked quickly at run time.

A number of researchers have used exact computation for boundary eval-uation.Benouamer,Michelucci,and Peroche[2]implement a solid modeler using a?ltered approach that differs from that of Fortune and van Wyk.Be-nouamer et al.express each sequence of calculations as an expression dag,that is,a directed acyclic graph with operations at internal nodes and constants at the leaves.Calculations are initially performed using interval arithmetic,and if the result is not suf?ciently precise,then exact rational arithmetic is used.

Fortune[15]also used exact arithmetic to implement a polyhedral solid modeler.That work sets an upper limit on the bit-length of accepted input,so that all geometric predicates can be evaluated using arithmetic at some?xed precision.

Yap and Dub′e[35]introduced a general approach they call“precision-driven computation.”Like Benouamer et al.,they also use expression dags,but as a tool to determine in advance the amount of precision needed(that is,the num-ber of digits in a?oating point representation).Precision-driven computation is noteworthy because it is fundamentally distinct from?ltered approaches. However,it is only applicable for closed-form calculations.

Boundary evaluation in solid modeling has been a well studied research topic in the area of polyhedral models.In addition to the results on the subject men-tioned above,we note work of Hoffmann[20]and Requicha and V oelcker[31]. Some algorithms have also been proposed for quadrics or higher degree alge-braic primitives.Casale et al.[4]use trimmed parametric surfaces to generate boundary representations of sculptured solids.Their algorithm uses subdivision methods to evaluate surface intersections,and represents the trimming boundary with piecewise linear segments.Krishnan and Manocha presented algorithms and a system called BOOLE based on the algebraic formulation of the problem [26].BOOLE is based on lower dimensional algorithms for computing the intersections of parametric surfaces and uses a combination of symbolic and numeric algorithms[25].It uses64-bit IEEE?oating point arithmetic.

One area where reliability is particularly challenging and has received rel-atively little study is computation of the medial axis of a polyhedron.There have been a number of approximate approaches,however.Vleugels and Over-mars[33]and Etzion and Rappoport[14]both use recursive subdivision of space to create an arbitrarily close approximation,while Hoff et al.[21]com-pute an approximation at a?xed resolution using graphics hardware.Other authors do not rely on an approximation.Of these,Milenkovic[30]was the ?rst to propose an algorithm for computing the medial axis as a3D geometric object by tracing the seams between the curved faces of the structure.

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3.Nonlinear Geometric Problems

In this section we discuss a number of problems involving curved geometric primitives that arise in geometric applications.

Polynomial Root Isolation.The isolation of complex roots of polynomials is in a sense a geometric problem in the complex plane.Also,the other prob-lems we discuss will depend in an essential way on localizing the real roots of polynomials.

Curve Arrangements.Given a number of algebraic curves in a bounded region of the plane,the goal in the curve arrangement problem is to compute the connected subregions that have no curve passing through them.Each subregion, called a face,is de?ned by piecewise algebraic curves that enclose its boundary. For each of the polynomials de?ning a face,all points in the face will have the same sign with regard to that polynomial.The output of the curve arrangement algorithm is the explicit topological description of each cell.

Boundary Evaluation.In computational solid geometry(CSG)[20],ob-jects are constructed from solid primitives by the boolean operations of union, intersection,and set difference.A complicated object will be represented as a tree,with geometric primitives at the leaves,and boolean operations at the internal nodes.The boundary evaluation problem is the problem of taking a CSG model and constructing from it a representation of its boundary as a set of possibly curved two dimensional surface primitives with adjacency information. The Medial Axis Transformation.The medial axis of a polyhedron is the locus of points that are the centers of spheres contained in the polyhedron and touching the boundary at two or more points.In3dimensions,the medial axis is made up of portions of quadric surfaces intersecting along curves.All of the known practical algorithms for computing the exact medial axis—explicitly constructing all of its surfaces and curves—rely on tracing these curves,starting at the vertices of the polyhedron[5].Combinatorial errors at early stages can cause incorrect curves to be generated,typically resulting in a program failure. The probability for such a failure increases rapidly with the complexity of the polyhedron.

4.Exact Geometric Computation for Curves and Surfaces

The fundamental challenge of EGC in the curvilinear domain is that the coordinates of points determined by intersecting polynomial surfaces will typi-cally be irrational and thus not representable exactly by a rational package.We represent such a point by retaining the polynomials de?ning it,along with an

Reliable Geometric Computations5 axis-aligned box with rational coordinates known to contain only that intersec-tion.There are mechanisms to shrink the box when necessary,to isolate the roots and make comparisons between the points.As a result,the algorithm uses minimal precision to accurately perform the tests.This technique is an example of the distinction between exact arithmetic and exact computation—the only ex-plicit representation of a point is inexact,but all comparisons are made exactly. The library MAPC[24]has been designed to embody these representations for points and curves in two dimensions.

Methods used to isolate points in2D and3D are detailed in[23]and[5]re-spectively.We will brie?y discuss them here to indicate the kind of calculations needed.The fundamental tool we use for reliably localizing algebraic points is the Sturm sequence.For a univariate polynomial f,the Sturm sequence of f is the polynomial remainder sequence of f and f ,with the signs changed according to a simple convention.For any given real number x,the number of sign permanencies PERM(f,x)is the number of times the sign remains the same when successive polynomials in the Sturm sequence are evaluated at x. For two real numbers x

There are generalizations of the Sturm sequence concept for sets of polyno-mials in two and three dimensions,but they are much slower.In the computation of the medial axis,there are times when a point must be localized in3D using the trivariate Sturm sequence[5].However,in most cases it is possible to lo-calize a2D point using only univariate Sturm sequences[23].The idea is to use an alternate method to?nd candidate boxes that may contain one or more points,and then to reduce the problem to a sequence of root determinations on the boundaries of these boxes.

4.1Improving Ef?ciency

To ensure accuracy,Sturm sequence calculations are usually done with exact arithmetic.Since bit lengths arising in a Sturm sequence calculation can be exponential in the degree of the polynomial,these calculations can be quite slow.To improve running times,we have made extensive use of?oating point ?lters.Unfortunately,there is a large gap between the53mantissa bits of a machine double on current hardware and the hundreds of bits that can arise in a Sturm sequence calculation.It is useful to have an arithmetic that is faster than rational arithmetic but that can be?exible in the amount of precision it allows. Aberth and Schaefer[1]have proposed a solution to this problem in what they call range arithmetic,which combines conservative interval arithmetic with variable precision?oating point computation.Each number in their arithmetic is represented by a single?oating point number of arbitrary length,with an associated single-precision radius R.The radius R indicates the width of the

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associated interval,on the scale of the least signi?cant machine word in the representation of the?oating point number.

To guarantee the precision of their results,Aberth and Schaefer perform a calculation at a speci?ed initial precision,keeping track of the loss of accuracy. If the accuracy of the result is insuf?cient,they increase the precision of their representation and recompute the results with increased precision.We?nd that this approach of iterative revision is useful for many geometric problems,where precision-driven computation using expression dags may not be effective. 5.Some Results

In this section,we give examples of how the techniques we have described can be applied to a number of problems.

5.1Polynomial Root Isolation

To isolate complex roots of polynomials,we have used Aberth and Schaefer’s Range library[1]to apply a variant,described in[27],of the Durand-Kerner algorithm[11,9]to a number of polynomials.A similar algorithm has also been proposed by Bini[3].We tested this algorithm on a benchmark set of polynomials from the PoSSo project,available at the following site: http://www-sop.inria.fr/saga/POL

Each class of polynomials is known to be troublesome for many root?nding algorithms.We compared our results with two other packages,Maple and Mu-PAD.The results are given in Table1.1.Maple and MuPAD allow the user to specify the number of digits retained throughout a calculation,but not the (smaller)number of digits that will be reliable in the output.For the purposes of comparison,we speci?ed that calculations be performed with the same number of digits as the maximum used in our calculations with the Range library.Be-cause the Range library performs later calculations with fewer digits than the maximum required,it has a speed advantage when intermediate calculations must be performed at a much higher precision than needed in the?nal result. The particular root-isolation method used also contributes to the speedup.There is,however,an overhead in maintaining the error interval,which becomes more apparent when less precision is needed.These results were previously reported in[27].

We used the following polynomials:

,n=50.

Poly1:Σn i=0x i

i!

Poly2:(x?3c2)2+icx7,0

Poly3:(c2x2?3)2+c2x9,c=1020.

Reliable Geometric Computations7

Case Root Precision MuPAD Maple Range

Poly11078.77 4.7913.17

Poly2120 5.1541.5413.06

Poly380 3.328.539 6.32

Poly430 4.5690.7920.82

Poly53032.2136.31 5.67

Poly63014.0134.310.65

Poly730 6.51713.53 1.23

Poly83012.2118.717 5.26

Poly93071.215 1.26 1.44

Table1.1.Univariate root?nding algorithm applied to nine polynomials from the PoSSo bench-mark suite.The second column indicates the number of required signi?cant digits,speci?ed in advance.The last three columns indicate running times taken by Maple,MuPAD and our al-gorithm.Times are in seconds and measured on an SGI Origin400MHz R12000processor running Irix6.5.

Poly4:x20+cx14+x5+1,c=1012.

Poly5: n i=1(x?i),n=40.

Poly6:(0.01x10+(x?10)2) 20i=1(x?i).

Poly7: 20i=1(x?i)(x?20)2.

Poly8:x14+2cx11+c2x8+4x7?4cx4+4,c=1024.

Poly9:x n?a,n=50,a=1.

5.2Determinant Sign

The problem of ef?ciently computing the sign of the determinant of large rational matrices has not been extensively studied,but there are situations where it can be useful[7].One straightforward approach,using the Range library,is simply to use Gaussian elimination with partial pivoting,repeating the process with progressively higher precision until the sign can be determined reliably. Figure1.1indicates that this method often performs much better than exact methods that use modular arithmetic,when applied to nonsingular matrices. For general matrices,Culver et al.[6]proposed a?lter for computing deter-minant signs exactly.The singular value decomposition,computed at machine precision,can be used to indicate whether the matrix is likely to be singular,what the likely sign of the determinant is,and whether the matrix is well-conditioned enough to ensure that the sign estimate is correct.If the sign estimate is correct, it is used.If the matrix is ill-conditioned and likely to be singular,modular

8246810121416

05

10

15

20

25

30

35

40

45

Figure 1.1.Determinant sign speedup.The speedup factor for the Range library,for various matrices.The horizontal axis gives the order of the matrix,while the vertical axis gives the speedup factor in comparison to an exact modular arithmetic algorithm.The set of matrices includes randomly generated matrices and others arising in geometric problems.The matrices are all nonsingular.

arithmetic is used.Otherwise,Gaussian elimination using the Range library is used.

5.3MAPC

The MAPC library [24],mentioned in Section 4,provides tools for exact manipulation of algebraic points and curves.It uses exact arithmetic based on LiDIA [18]to accurately compute the required Sturm sequences.For high degree polynomials,exact computation of Sturm sequences can be prohibitively slow because of the very large growth in the bit lengths of the coef?cients.Some boundary evaluation computations on algebraic primitives can require Sturm sequence computation for polynomials of degree greater than 80.

MAPC uses a number of techniques to deal with this problem.Of key importance is reducing the number of Sturm sequence computations that must be performed.For instance,?oating point methods can be used to estimate the locations of polynomial roots,which are then con?rmed by a Sturm sequence computation.This is much more ef?cient than repeated bisection using Sturm sequences.

When a Sturm sequence computation is necessary,Aberth and Schaefer’s Range library [1]is used.As with the sign of determinant calculations discussed above,the process of generating the Sturm sequence and computing polynomial signs is performed at successively increasing precision until all the signs can be

Reliable Geometric Computations9

Case1234

Number of Curves3367

Coef?cient Bit size25222562

Number of Faces9113163

Total time without Range 5.29.062.8122.8

Total time with Range 1.8 4.011.09.3

Table1.2.Arrangement of planar algebraic curves.The application?nds all subregions,the segments of curves bounding each subregion,and the connectivity between subregions.The table shows the maximum bit length needed to express the coef?cients of the curves,the number of faces generated by the arrangement,the time taken using the original(exact rational based) code,and the time taken using Range.The curves have maximum degree4.Times are in seconds on a300MHz R12000MIPS processor.

evaluated exactly.Once a?xed precision is reached without success(e.g.40 decimal digits),exact rationals are used instead.

We have used MAPC as a tool in approaching each of the following three geometric problems.We give performance information for each one,with attention to the bene?ts of arbitrary-precision error bounded arithmetic.Again, there is a speed advantage that grows with the complexity of the problem,but a small overhead that becomes apparent with simpler calculations.

Curve Arrangements.The computation of curve arrangements is a useful test case for the MAPC library.In Table1.2we indicate performance results for some example arrangement computations.

Boundary Generation.A motivating application for the MAPC library is the boundary evaluation of(low degree)algebraic solids.MAPC is a core library in the ESOLID system[23]performing such boundary evaluations.In general, computing the boundary representation for a CSG model leads to problems of accuracy and robustness.These problems are exacerbated when the underlying primitives have curved boundaries.To alleviate the reliability problems,the ESOLID system performs performs all geometric tests exactly,using layered ?lters to make the exact computation more ef?cient.

We have tested ESOLID on portions of a real-world model,the Bradley Fighting Vehicle provided courtesy of the Army Research Laboratory.Some example output B-reps are shown in Figure1.2,with comparative timings given in Table1.3.

Figure1.3gives an example of a calculation that can be hard for machine-precision methods.The intersection curve between the two cylinders is not self-crossing,although it appears so at the scale shown.This distinction can be hard for non-exact methods to resolve.

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a b c

d e f

Figure1.2.Boundary computations.Boundary representations of six selected portions of the Bradley Fighting Vehicle,computed by https://www.wendangku.net/doc/7e2772458.html,putations were done exactly,and then output as trimmed NURBS patches for https://www.wendangku.net/doc/7e2772458.html,putation times ranged from about10 seconds to633seconds;further performance details are given in Table1.3.

without Range with Range

Example Total Sturm Total Sturm

Number Time Time Time Time

a10.230.5110.95 1.62

b12.570.2412.69 1.44

c633.42597.3342.99 6.93

d63.158.3461.26 6.36

e250.74190.6273.8615.36

f26.37 1.2928.14 3.63

Table1.3.Timings for the examples from Figure1.2,with and without the incorporation of the Range library.Range is used to improve the ef?ciency of Sturm sequence calculations.The total time and the time spent in Sturm computations is shown.

Reliable Geometric Computations11

Figure1.3.An example of a case that can be dif?cult for machine-precision methods.The plot on the right shows a portion of the intersection curve of the two cylinders,in the parametric domain of one of the cylinders.The curve is very nearly singular,but in fact has two distinct components.

Figure1.4.The“iron maiden pizza box”and a schematic of its medial axis.The top and bottom of the box are removed to show the spikes inside.The model has56faces,and the computation took23minutes.

Medial https://www.wendangku.net/doc/7e2772458.html,puting the medial axis of a polyhedron is a challenging problem because it inherently requires analysis of intersecting curved surfaces. Culver et al.[8]have implemented an exact algorithm for medial axis evaluation that relies both on the MAPC library and on the sign of determinant?lter described in Section5.2,both of which incorporate the Range library.The program has been used to compute the medial axis of complicated polyhedra with as many as250faces[7].Examples of the output are given in Figures1.4 and1.5.In both examples,seams are depicted as straight lines.

6.Conclusions and Future Work

We have found that exact geometric computation can be a practical tool to alleviate reliability problems in geometric computations with algebraic curves

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Figure1.5.The Venus de Milo and a schematic of its medial axis.Seams touching vertices of the polyhedron are omitted for clarity.The polyhedron in this example has250faces,and took 5.6hours to compute.

and surfaces.Some of the initial results related to root?nding,curve arrange-ments,boundary and V oronoi computations are promising and there are many areas for future research.

One important problem is that of dealing with degeneracies,such as the intersection of a line with a polygon only at one vertex,or along an edge.De-generacies can be a source of non-robustness on the one hand,or of serious implementation dif?culties on the other.For simplicity,algorithms often as-sume that primitives are arranged so that there are no degeneracies(i.e.,they are in general position).In practice,however,primitives often are not in gen-eral position,causing implementations of the algorithms to fail.Recasting an algorithm to handle degeneracies tends to result in a situation in which most of the code is to handle special cases.Edelsbrunner and M¨u cke have presented a nice overview of the problem[12].

A number of authors have proposed the idea of symbolic perturbation to solve these problems[12,13].Unfortunately,these algorithms depend on the existence of a decision tree in which each decision rests on the evaluation of an expression that is some known polynomial in the input values.In the non-linear problems we have discussed,the calculation cannot be formulated in this way.

A general approach to the problem of degeneracies,perhaps in the spirit of symbolic perturbation,would be a signi?cant contribution.

Finally,another goal is to perform reliable computations with higher degree primitives(e.g.,bicubic rational parametric patches that are widely used in geometric modeling).Currently,we have handled primitives of algebraic degree four for boundary evaluation and the medial axis computation results in quadric surfaces.

REFERENCES13 7.Acknowledgments

We would like to thank the BRL-CAD group at the Army Research Lab for the use of the Bradley Fighting Vehicle model.This work was supported in part by an ARO Contract DAAD19-99-1-0162,NSF award9876914,DOE ASCI grant and ONR Young Investigator Award.

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Du and F.Hwang,editors,Computing in Euclidean Geometry,pages452–492.World Scienti?c Press,Singapore,1995.

Chapter1会计概论答案

第一章会计透视：会计信息及其使用者▓复习思考题 1．概述会计的性质。 会计是按照会计规范确认、计量、记录一个组织的经济活动，运用特定程序处理加工经济信息，并将处理结果传递给会计信息使用者的信息系统，是组织和总结经济活动信息的主要工具。 会计是一个信息系统，会计处理的各个环节的加工的对象是会计信息。会计信息实际上是一种广义的信息，包含三个层次： 其一，以货币化指标体现的财务信息，它是从动态、静态两个角度，对特定主体经济资源的数量（资产）、归属（负债、所有者权益）、运用效果（收益分配）、增减变化及其结果（财务状况变动及其结果）进行描述； 其二，非货币化的和非数量化的说明性信息，它们不仅仅是对主体的财务状况、经营成果等财务指标的基本说明，而且还包含了大量的主体所处的社会、文化、道德、法律等环境信息，这些信息对于使用者正确判断主体的经营能力、发展前景，往往起到至关重要的作用； 其三，其他用于主体内部管理的信息，这些信息常常由成本会计、管理会计以及内部审计人员提供，主要包括了短期（长期）决策信息、预算信息、责任中心要求及履行情况等情况，虽然与外部性较强的财务会计信息相比，它们更容易为人们所忽略，但在经济管理和财务信息质量控制方面，它们也起了不可低估的作用。不过，在当前的会计报告模式中，所反映的会计信息主要是前两个层次上的信息。 2．企业的获利能力是否为债权人的主要考虑因素？ 债权人关心那些影响自己的债权能否得到按期偿还的因素。他们会对公司的获利能力及清偿能力感兴趣。债权人会从获利能力去衡量未来的现金流量，由于企业的获利能力与现金流量并不一定同步产生，所以对短期债权人来说，企业的获利能力不能成为债权人的主要考虑因素，但对相对长期的债权人来说获利能力应该是值得更加关注的因素。 3．财务报表中体现出来的会计信息用以满足不同使用群体的需求，但并不是所有的使用者都能得到相同的满足的。在实践中，外部财务报表使用者诸如股东、供应商、银行等是如何获得有关公司的财务信息的？若要同时满足不同类别的财务报表使用者的信息需求有什么困难？ 首先，股东是公司法定的所有者，法律上财务报表是为其制作的。法律规定，公司必须定期编制并发布财务报表，为其股东公布财务信息，我国《公司法》对此也有明确的规定。 其次，供应商与公司是商业伙伴关系，不提供商业信用的供应商，由于是钱货两讫，可通过报媒和网络了解公司公开财务的财务信息，如果供应商对公司提供商业信用，供应商可要求企业提供一定的财务信息，但对这些财务信息的准确性、可靠性需要有一定的分析。

(完整版)中国翻译史及重要翻译家

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中国翻译简史

百科知识—中国翻译简史 中国历史上曾经出现了四次翻译高潮： 1东汉至唐宋的佛经翻译 2明末清初的科技翻译 3“五四”时期的西学翻译 4中国历史上第四次翻译高潮（五四以后---当代） 古代佛经翻译（四个阶段） 第一阶段从东汉末年到西晋（起步或草创阶段） 主要是外籍僧人和华籍胡裔僧人，翻译主要靠直译，甚至是“死译”、“硬译”，采取 口授形式，因此可信度不高。 代表人物支谦 支谦，三国时佛经翻译家，又名支越，字恭明。支谦的译述比较丰富：约三十年间，译出佛经《大明度无极经》、《大阿弥陀经》等八十八部、一百一十八卷，创作了《赞菩萨连句梵呗》三契，其翻译以大乘“般若性空”为重点，为安世高、支谶以后译经大师。支谦自译的经也偶尔加以自注，像《大明度无极经》首卷，就是一例。这种 作法足以济翻译之穷，而使原本的意义洞然明白。 特点 1主要力量：外籍僧人和华籍胡裔僧人 2翻译全凭口授 3大多才有直译法 5佛经内容经常采用中国本土道家思想 古代佛经翻译 第二阶段从东晋到隋末（发展期） 释道安总结出了“五失本”、“三不易”的规律； 释道安，南北朝时高僧，翻译家。本姓卫，常山抚柳（河北冀州）人。总结 了汉代以来流行的佛教学说，整理了新译旧译的经典，编纂目录，确立戒规，主 张僧侣以“释”（释迦牟尼）为姓。主要监督翻译了《四阿含》等。主张直译，

不增不减，只做词序调整。翻译佛经在五种情况下会失去本来面目，有三件事决定了译事是很不容易的，因此必须慎之又慎。 彦琮在其论着《辩正论》中提出了翻译要例“十条和对译者的要求“八备”” 彦琮（557—610年），俗姓李，邢台隆尧县双碑人，隋代著名高僧，他精通梵文， 也是我国佛教史上屈指可数的佛经翻译家和佛教著作家。《辩正论》里翻译要例八备十条：就是对做翻译人的具体要求和翻译要求。 鸠摩罗什开始提倡意译； 鸠摩罗什（梵语Kumārajīva ）（公元344 ~ 413 年），音译为鸠摩罗耆婆，又作鸠 摩罗什婆，简称罗什。其父名鸠摩罗炎，母名耆婆，属父母名字的合称，汉语的意思为“童寿”。东晋时后秦高僧，著名的佛经翻译家。与真谛（499—569）、玄奘（602～664）、并称为中国佛教三大翻译家。 慧远等人则对译文的风格和文体问题进行了一定的探索。 慧远，俗姓贾，雁门楼烦（约在今山西朔城区）人。出生于代州（约代县） 主张直译与意译、音译的结合，著有《三法度序》 真谛（449-569）梁陈时代人，翻译《摄大乘论》 古代佛经翻译（唐朝——全盛期） 古代佛经翻译（续） 主要译者多为本国人，他们除了精通佛理以外还精通梵汉两种语言，其译作在质量和数量上都大大超过了前两个阶段。加上唐朝统治者的重视和支持，这一阶段的译经活动达到顶峰，出现了玄奘、不空、义净等著名的僧人译经家。 玄奘提出了佛经翻译中著名的“五不翻”的原则，并为译经者进行了十一种详细的分工。 鸦片战争至甲午战争前 著名的禁烟英雄林则徐决心“师夷之长技以制夷”，开始“日日使人刺探西事，翻译西书”，被誉为“组织翻译活动的先驱”。语言学家马建忠在其《拟设翻译书院议》一文中留下了一些有关翻译的论述。他提出有三类书籍急需翻译，并指出“需要择其善者译之“。此外，他在总结了当时译文中常见的不足之后提出了所谓“善译”的翻译标准，要求译文与原文之间“无毫发出入于其间”。 近代翻译

中国翻译史1

History of Translation Teaching Plan Teaching Contents: 1. An introduction to Chinese translation theory and history 2. An introduction to western countries translation theory and history 中国翻译史的大致分期 1.由汉代到唐宋的上千年的佛经翻译【支谦、道安、鸠摩罗什、昙无谶、法显、谢灵运、真谛、彦琮、慧远、玄奘、不空】 2.明清交替之际的科技翻译【徐光启、利玛窦、汤若望、南怀仁、熊三拔、李之藻等】 3.清末民初的文学和科技翻译【李善兰、华蘅芳、傅兰雅、林纾、严复、梁启超等】 4. 民国时期的翻译【赵元任、朱生豪、林语堂】 5. 新中国成立后的翻译，尤其是改革开放以来的翻译【傅雷、钱钟书、杨绛】 Lecture 1 佛经翻译 I.关于翻译的早期记载 《册府元龟·外臣部·鞮（di）译》记载，周时有越裳国“以三相胥重译而献白雉，曰：‘道路悠远，山川阻深，音使不通，故重译而朝’”。 “五方之民，言语不通，嗜欲不同。达其志，通其欲，东方曰寄，南方曰象，西方曰狄鞮，北方曰译。”《礼记·王制》 翻译的不同称呼:“象寄”、“象胥”、“鞮译”“舌人” 寄send; entrust; rely on 象be like; resemble; image 译translate; interpret 越人歌 今夕何夕兮？ 搴舟中流。 今日何日兮？ 得与王子同舟。 蒙羞被好兮， 不訾诟耻。 心几烦而不绝兮， 知得王子。 山有木兮木有枝， 心悦君兮君不知。 《越人歌》是我国历史上现存的第一首译诗。 秦汉时期对“翻译官”的种种称谓： “行人”、“典客”、“大行令”、“大鸿胪”、“典乐”、“译官令”、“译官丞”等。 到汉朝，我国主要的外事活动是对北方的匈奴用兵，故翻译活动逐渐用“译”来统称了。 II.佛经翻译 佛教创立：公元前六至五世纪 创立地点：古印度 佛教流传：公元65年之前传入中国 我国的佛经翻译

中国翻译史

《英汉翻译教程》 第一章：我国翻译史简介 我国的翻译事业有约两千多年的光辉历史。早在公元前六年西汉哀帝时代，伊存到中国口传一些佛教经句，但还谈不上佛教的翻译。佛经的翻译是在东汉桓帝建和两年（公元148年）开始的，译者是安世高，他是安息人（即波斯），他译了《安般守意经》等三十多部佛经。过些时候，娄迦谶来中国，因为他是月支人，所以又称支娄迦谶。他也译了十多部佛经，但文笔生硬，不易看懂，所以从那时起，大概就有直译和意译这个问题了。他有个学生叫支亮，支亮又有个弟子叫支谦，他们三人号称“三支”，都是当时翻译佛经很有名的人。就在那时，月支派里出现了一个叫竺法护的大翻译家，他译了175部佛经，对于佛法的流传贡献很大。但这些翻译活动还只是民间私人事业。到了符秦时代，释道安设置了“译场”，成了有组织的活动，他本人不懂梵文，惟恐失真，主张严格的直译，在这期间他请来了天竺人（即印度）鸠摩罗什，他全改以前群家的直古风格，主张“意译”，他的译著为我国翻译文学奠定了基础。到南北朝时，一个叫真谛的印度佛教学者应梁武帝之聘来到中国，他译了49部经论，对中国佛教思想有较大影响。 从隋代（公元590年）起到唐代，是我国翻译事业高度发达的时期，隋代有个释彦琮，梵文造诣很深。在他以后出现了古代翻译界的巨星玄奘（与上述鸠摩罗什、真谛一起号称我国佛经三大翻译家），他成为第一个把汉文著作向国外介绍的中国人，他自创了“新译”。 从明代万历年间到清代“清学”时期，佛经翻译呈现一片衰落现象，但却出现了以徐光启、林纾（琴南）、严复（又陵）等为代表的介绍西欧各国科学、文学、哲学的翻译家。徐光启和意大利人利玛窦合作，翻译了欧几里得的《几何原本》、《测量法义》等书。林纾和他的合伙人以口述笔记的方式译了160多部文学作品，其中最著名的有《巴黎茶花女遗事》、《黑奴吁天录》、《块肉余生记》、《王子复仇记》等。严复是我国清末新兴资产阶级启蒙思想家（曾担任过北大校长），等到八国联军战役以后，他避居上海，搞翻译工作，他“曾查过汉晋六朝翻译佛经的方法”，破天荒第一次在《天演论·译例言》里正面提出了信达雅作为译事楷模。 值得一提的是，清末马建忠在他写的《拟设翻译书院议》中发挥了他所认为的“善译”的见解，可以说是试图说明翻译标准的一个开端。他的善译标准包括了三大要求：第一、译者首先要对两种语言素有研究，熟知彼此的异同；第二、弄清原文的意义精神和语气，把它传达出来；第三、译文与原文毫无出入。这些要求是很有道理的，因他本人后来没搞翻译，因此他对“善译”的见解，反被后人忽略了。 “五四”运动是我国近代翻译史的分水岭，“五四”以前最显著的表现是，以严复、林纾等为代表翻译了一系列西方资产阶级学术名著和文学作品。“五四”以后，我国翻译事业开创了一个新的历史时期，开始介绍马列主义经典著作和无产阶级文学作品，《共产党宣言》的译文就发表

中国翻译历史概况

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中西翻译史简介 第一节：中国翻译简史 我国翻译事业约有两千年的历史。佛经翻译始于东汉恒帝建和二年（公元148年）。迄今为止共经历了四次翻译高潮。 一、东汉至唐宋的佛经翻译：我国的佛经翻译，从东汉恒帝末年安世高译经开始，魏 晋南北朝有了进一步发展，到了唐代臻于极盛，北宋时已近式微，元以后则是尾声了。之谦的《法句经序》是我国第一篇有关翻译的论文，?最早涉及了一些重大的翻译原则?（张泽乾，1994）。道安总结了比较完善的直译原则。鸠摩罗什是主张全面意译的第一人。玄奘还提出了?既需求真，又需喻实?的翻译标准，力求忠实与通顺并举。他的?五不翻?原则总结了音译法的规律，即：(1)佛经密语须直译；（2）佛典中的多义词须音译（3）不存在相应概念的词只能音译（4）已经约定俗成的古音译保留（5）为避免语义失真用音译 二、民末清初的科技翻译：明徐光启和意大利人利马杜合作，翻译了欧几里德的《几 何原本》、《测量法义》等书。 三、鸦片战争后至“五四”前的西方政治思想和文学翻译：清林纾和他的合作者 以口述笔记的方式译了一百六十多部文学作品，其中最著名的有《黑奴吁天记》(Uncle Tom’s Cabin)，《块肉余生记》(David Copperfield)，《王子复仇记》(Hamlet)等（现用新译名）。严复所译作品多系西方政治经济学说，如赫胥黎的《天演论》(Evolution and Ethics and Other Essays)，亚当〃斯密的《原富》(An Inquiry Into the Nature and Causes of the Wealth of Nations)，斯宾塞尔的《群己权界论》(On Liberty)、甄克斯的《社会通诠》(The Study of Politics)等、并提出简洁凝练的翻译标准?信、达、雅?(faithfulness, expressiveness and elegance) 。《马氏文通》的作者马建忠于公元1894年在他的《拟设翻译书院议》中发表了他所认为的?善译?的见解，包括三大要求：第一，以者先要对两种语言素有研究，熟知彼此的一统；第二，龙庆原文的意义、精神和语气，把它传达出来；第三，译文与原文毫无出入，?译成之文，适如其所译?。 四、民国时期的翻译事业的繁荣：鲁迅先生认为，?凡是翻译，必须兼顾两个方面， 一则当然其义易解，一则保存原作的丰姿。?并提出了通行的翻译标准：忠实于通顺（faithfulness and smoothness）。瞿秋白论证翻译是可以做到又信又顺的。林语堂提出了?忠实的标准，通顺的标准，美的标准?。傅雷的?重形似而不重神似?的标准。钱钟书提出的?精神姿致依然故我?和?化境?之说。哲学家艾思奇则总结说，?翻译的原则总不外是以‘信’为最根本的东西，‘达’和‘雅’的对于‘信’，就像属性对于本质一样，是分不开的然而是第二义的存在。 五、第五次翻译高潮：无论在翻译的规模和译作的数量上都远远超过了以前任何时期。第二节西方翻译简史：古代翻译活动、近代翻译活动、当代翻译活动 一、古代翻译活动： 西方翻译活动可追溯到公元前三世纪。当时有文字记载的翻译作品已经问世：七十二位犹太学者在自己埃及的亚历山大城翻译了《圣经〃旧约》，即后人所称的《七十子希腊文本》；

张培基《英汉翻译教程》(修订本)配套题库(我国翻译史简 介)

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实践。 二、简要介绍严复“信、达、雅”的翻译标准并谈谈你对这个标准的看法。 【答案】 严复在《天演论》译文的例言中提出了“信、达、雅”的翻译原则和标准。“信”是指对原文和译文两个关联事物的可靠性和一致性，即译文要忠实于原文的内容、风格、思想以及精神，不可歪曲原文，不可遗漏原文的重要内容。“达”是指译文要通达流畅，符合现代汉语表达习惯，符合汉语的语法规范。“雅”是指译文所要达到的文学美感，即文采气质。译文语句要规范、得体、生动、优美，有独特的文学典雅气质。 我认为作为一名合格的译员，首先应该保证前两个标准，即“信”“达”的实现。在翻译时，应确保译文完整准确地传达原文的意思、符合译入语的语法规范，然后在有余力的情况下，再去完善译文，使之更具美感。 三、新中国成立后的翻译工作有哪些特点？ 【答案】 ①翻译工作者在党的领导下，有组织、有计划、有系统地进行工作，逐渐取代了抢译、乱译和重复浪费的现象； ②翻译作品质量大大提高，逐渐克服了粗枝大叶、不负责任的风气； ③翻译工作者为了更好地为社会主义建设服务，开展了批评与自我批评，逐渐消除了过去各种不良现象和无人过问的状况； ④翻译工作者不仅肩负着外译汉的任务，同时为了宣传马列主义、毛泽东思想，介绍我国社会主义革命和建设的经验以及我国优秀的文化遗产，还肩负了汉译外的任务；

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