asymptote_geometry_en
dynamo节点中文翻译
1.Analyze['ænə,laɪz]对..进行分析2.Built in内置3.Core核心4.Display显示5.Geometry几何图形6.Office办公7.Operators[ˈɒpəreɪtə(r)s]运算符8.Revit9.analysis extensions[ɪk'stenʃ(ə)n;ek-]分析扩展bel['leɪb(ə)l]标注、标签11.Daylighting['deɪlaɪt]光照12.Render['rendə]渲染13.Site location[lə(ʊ)'keɪʃ(ə)n]设置场地位置14.15.All false检测所有元素是否为假16.All true检测素有元素是否为真17.Contains[kən'teinz]是否包含指定图元18.Contains key是否包含指定关键点19.Count表中项数20.Count false错误项数数量21.Count true正确项数数量22.Equels确定两个实例是否相等23.Flatten['flæt(ə)n]摊平24.Get keys获取关键点25.Get values['væljʊz]获取关键值26.Group by function['fʌŋ(k)ʃ(ə)n]通过函数编组27.Import from csv通过文本输入28.Index of['ɪndeks]..中的索引29.Insert[ɪn'sɜːt]插入30.Is homogeneous[,hɒmə(ʊ)'dʒiːnɪəs; -'dʒen-]是否相同的31.32.33.Is rectangular[rek'tæŋgjʊlə]是否相同矩形34.Is uniform depth是否均匀深度35.Loop while循环36.Map映射37.Map to映射到38.Maximum item by key['mæksɪməm]最大项目的关键点39.Minimum item by key最小项目关键点40.Newton root find1d no deriv发现根源不导出41.Newton root find1d with deriv发现根源导出42.Normalize depth['nɔ:məlaɪz]标准化深度43.Rank最深的列表深度44.Remove if not删除列表中非指定成员45.Removed key删除指定关键点46.Reorder重新排序47.Set difference差集48.Set intersection交集49.Set union并集50.Sort by function通过函数确定排序51.Sort index by value将数列升序排列52.True for all所有为真53.True for any部分为真54.Color颜色55.Color range2D颜色范围56.Date time日期时间57.Day of week星期几58.evaluate[ɪ'væljʊeɪt]评估59.formula['fɔːmjʊlə]公式60.Input输入61.List列表62.Location[lə(ʊ)'keɪʃ(ə)n]地点63.Logic['lɒdʒɪk]逻辑64.Math数学65.Object对象66.Scripting[skrɪpt]脚本67.Sting字符串68.Thread[θred]线路69.Time span时间跨度70.Units[ˈjuːnɪts]单位71.View观察72.Web网络73.File文件74.Arc[ɑːk]弧75.Bounding box[baʊnd]范围框76.Circle圆77.Cone[kəʊn]圆锥78.Coordinate system[kəʊ'ɔ:dɪneɪt]坐标系79.Cuboid['kjuːbɒɪd]立方体80.Curve曲线81.Cylinder['sɪlɪndə]圆柱体82.Edge[edʒ]边缘83.Ellipse[ɪ'lɪps]椭圆84.Ellipse arc椭圆弧85.Face面86.Geometry几何图形87.Helix螺旋88.Index group指标组89.Line直线90.Mesh网格91.nurbs curve非均匀曲线92.Nurbs surface非均匀表面93.Plane平面94.Point点95.Poly curve Poly曲线96.Poly surface Poly表面97.Polygon多变形98.Rectangle['rektæŋg(ə)l]矩形99.Solid实体1.Sphere[sfɪə]球体2.Surface表面3.Topology[tə'pɒlədʒɪ]拓扑4.Uv5.Vector向量6.Vertex['vɜːteks]顶点7.Tessellation[,tesi'leiʃən]曲面细分8.Selection选择9.View视图10.Analysis[ə'nælɪsɪs]分析11.Application应用应用程序12.12.Elements['elimənts]基础13.13.References['refərənsɪz]参照14.14.Transaction[træn'zækʃ(ə)n]交易、回报15.15.Views视口16.17.Adaptive component[ə'dæptɪv][kəm'pəʊnənt]自适应构件18.Category['kætɪg(ə)rɪ]类别19.Curtain panel['kɜːt(ə)n]['pæn(ə)l]幕墙嵌板20.Curve by points曲线点21.Curve element曲线图形、元素22.Direct shape[dəˈrekt][ʃeɪp]直接形状23.Divided path[dɪ'vaɪdɪd][pɑːθ]分割路径24.Divided surface分割表面25.Element元素26.Family族27.Family instance['ɪnst(ə)ns]族实例28.Family type族类型29.Floor楼板30.Floor type楼板类型31.Form表格32.Grid网格33.import instance导入实例34.Level标高35.Material[mə'tɪərɪəl]材质36.Model curve模型曲线37.Model text模型文本38.Model text type模型文本类型39.Mullion['mʌljən]竖挺40.Parameter[pə'ræmɪtə]参数41.Reference plane['ref(ə)r(ə)ns]参照平面42.Sketch plane草图平面43.Structural framing['strʌktʃ(ə)r(ə)l]['f reɪmɪŋ]结构框架44.Structural type结构类型45.Sun settings太阳设置46.Topography[tə'pɒgrəfɪ]地形46.Wall墙体47.Wall type墙体类型48.axonometric view[,æksənəu'metrik]三项投影视图49.Ceiling plan view['siːlɪŋ]楼层平面视图(天花板)50.Drafting view['drɑːftɪŋ]制图视图50.Foor plan view楼层平面视图51.Perspective view[pə'spektɪv]透视图52.Section view['sekʃiəu]剖面视图53.Sheet图纸54.Structural plan view结构平面视图55.View视图56.View3D三维视图。
实用CAD术语对照表
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 n alignment allocate Altitude ambient color ambient light angular dimension angular unit annotation anonymous block anti-aliasing aperture apparent intersections append Application key appload Apply approximation points arc Architectual Ticks area Argument Arrange icons array arrowhead ASCII aseadmin aseexport aselinks aserows aseselect asesqled Aspect aspect ratio assign Assist associative dimension associative hatches attach attdef attdisp attedit attenuation attenuation of light attext attredef
序号
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
英文词汇
Creo 4.0 Parametric Congfig配置文件选项详细说明
yes, no
assemble_module_in_rep 检索指定表示中 CSA 的已组装模块。
atb_search_path
延伸ATB更新和ATB检查状况命令的搜索路径。
attach_menumanager
设置主 Creo 窗口的菜单管理器附件。
yes, no
auto_center_dimension
类别 \ \ \
\ \ \ \ \ \
\ \
\ \ \ \ \ \
Creo 4.0 Parametric 配置选项
名称
说明
值
默认值
convert_to_wf3_replace 转换为 Wildfire3 的替换功能。
yes, no
no
cosmetic_thread_match_tole 设置公差，该值在分析中用于将标准螺纹类型和标
e
的范围。'2D' 仅适用于 2D 模型，'ALL' 适用于
所有模型。
ecadcollab_auto_redef_cuts 自动重新定义受协作更改影响的 ECAD 切口
yes, no
edge_tess_quality
设置弧形网格化的精度级别。
high, medium, low
enable_3dmodelspace_browse 是 - 启动 Creo 时在浏览器中显示“3D 模型空间 yes, no
anlfeat_update_on_redefine 重新定义后强制对分析特征进行完整更新 (如同新 yes, no
特征)
arc_radius_limit
在数控程序文件的 CIRCLE 语句中设置半径的上限
。该值必须为正值。否则，将使用 10*零件尺寸。
数据库st函数 空间对象线路自定义切割方法
数据库中的st函数以及空间对象线路自定义切割方法是目前在地理信息系统和数据处理领域中比较热门的话题。
作为一种高级的数据库功能，st函数可以帮助用户处理和分析地理空间数据，而空间对象线路自定义切割方法则可以帮助用户更灵活地处理线状地理空间对象。
在本篇文章中，我将从简到繁地介绍这两个主题，让你能够更深入地理解它们的概念、用法和意义。
一、st函数1. st函数是什么？st函数是一种用于处理空间数据的数据库函数，它能够对空间对象进行空间分析和空间操作，例如空间查询、几何运算、距离计算等。
2. st函数的使用场景在地理信息系统中，st函数被广泛应用于地图制图、地理空间分析、位置导航等领域，它能够帮助用户快速准确地处理各种空间数据，提高数据的可视化和分析效率。
3. st函数的优势和局限尽管st函数在空间数据处理方面有着诸多优势，但它也存在一些局限性，如不同数据库系统之间的兼容性、性能表现等方面需要用户注意。
二、空间对象线路自定义切割方法1. 空间对象线路自定义切割方法的定义空间对象线路自定义切割方法是一种用户根据实际需求，自定义划分线状地理空间对象的方法，以便更灵活地处理和展现地理空间信息。
2. 切割方法的实现步骤用户可以通过指定线路、节点等地理元素，进行自定义的切割操作，以满足特定的地理信息处理需求。
3. 切割方法的应用场景空间对象线路自定义切割方法适用于道路交通分析、地块划分、环境规划等领域，它能够为用户提供更个性化、精准的地理数据处理解决方案。
总结与展望通过对st函数和空间对象线路自定义切割方法的深入介绍，我们可以看到它们的重要性和应用前景。
随着地理信息技术的不断发展，对空间数据处理的需求也越来越复杂和多样化，因此掌握这两个主题的知识将对我们未来的工作和研究具有重要意义。
个人观点及理解作为地理信息技术的从业者，我深知st函数和空间对象线路自定义切割方法在实际工作中的重要性。
它们能够帮助我们更快速、更精准地处理和分析地理空间数据，为地理信息技术的应用提供了强大的支持。
数学专业英语词汇
横坐标Abscissa 横轴Abscissa axis 绝对值Absolute value Absolutely convergent Absolutely convergent series Acceptance region Acute angle 绝对收敛绝对收敛级数接受区域锐角锐角三角形加法Acute triangle Addition 伴随矩阵代数Adjoint matrix Algebra 角Angle 圆心角Angle at the centre Angle in a circular segment Anti-clockwise Anti-symmetric matrix Arc cosecant 圆周角反时针方向反对称矩阵反余割反余弦Arc cosine 反余切Arc cotangent Areal element Argument 面积元素幅角算术中项结合律Arithmetic mean Associative law Asymptote 渐近线渐近线Asymptotic line Augmented matrix Auxiliary line Average 增广矩阵辅助线平均值轴Axis 横坐标轴纵坐标轴对称轴Axis of abscissas Axis of ordinates Axis of symmetry Basis 基贝叶斯定理伯努利试验二元Bayes’ Theorem Bernouill’s trial Binary 二项分布二项式定理二元正态分布分块对角矩阵旋转体Binomial distribution Binomial Theorem Bivariate normal distribution Block diagonal matrix Body of rotation Bounded 有界的上有界的下有界的有界区域 Bounded above Bounded below Bounded region有界变量无限的Bounded variable Boundless 微积分Calculus 消去律Cancellation law Canonical form Casual 标准型随机的圆心Center of a circle Central limit Theorem Central moment Certain event 中心极限定理中心矩必然事件链式法则基变换Chain rule Change of base Characteristic equation Characteristic root Characteristic value Characteristic vector Chybyshev inequality Chi square distribution Circle 特征方程特征根特征值特征向量切比雪夫不等式2 分布 圆 圆锥 Circular cone圆柱 Circular cylinderCircular ring圆环 圆周 CircumferenceClass interval组距 组限 Class limits组平均 组中值 顺时针的 闭区间 闭集 Class meanClass midpointClockwiseClosed intervalClosed set系数 Coefficient相关系数 余子式 列 Coefficient of correlationCofactorColumn列秩 Column rank列向量 公分母 公差 Column vectorCommon denominatorCommon differenceCommon divisorCommon factorCommon logarithmCommon multipleCommon ratioCommutative lawComplement minor 公约数 公因子 常用对数 公倍数 公比 交换律 余子式补集Complementary set Complex number Composite function Composition 复数复合函数 复合复合事件 复利Compound event Compound interest Concave 凹凸Convex 条件收敛 条件概率条件概率密度 条件概率分布 条件概率函数 置信区间 置信水平 共轭复数 连通域常数Conditional convergence Conditional probability Conditional probability density Conditional probability distribution Conditional probability function Confidence interval Confidence level Conjugate complex number Connect domain Constant 约束条件 连续性左连续右连续连续点连续分布连续随机变量 收敛Constraint condition Continuity Continuity from the left Continuity from the right Continuity point Continuous distribution Continuous random variable Converge 收敛性收敛域依概率收敛 收敛半径 逆命题卷积Convergence Convergence domain Convergence in probability Convergence radius Converse proposition Convolution 坐标Coordinate 坐标轴坐标平面 坐标系坐标变换 共面Coordinate axis Coordinate planes Coordinate system Coordinate transformation Coplane 互素Coprime 推论Corollary 相关系数 余割Correlation coefficient Cosecant 余弦Cosine 余切Cotangent 可列 Countable可列可加性 协方差协方差矩阵 准则Countable additivity Covariance Covariance matrix Criterion 临界值立方体立方根立方Critical value Cube Cube root Cubic 三次插值 立方根三次样条函数 曲线Cubic interpolation Cubic root Cubic splines Curve 曲线Curve line 曲面Curve surface Cusp 尖点曲线的尖点 柱Cusp of a curve Cylinder 柱面Cylindrical surface D’Alembert’s criterion Data procession Decade 达朗贝尔准则 数据处理 十进制推论Deduction 定积分定二次型 定义Definite integral Definite quadratic form Definition 退化双曲线 次数Degenerate hyperbola Degree 置信度多项式的次数 密度函数 分母Degree of confidence Degree of polynomial Density function Denominator Denumerable Derivative 可列的导数左导数右导数行列式偏差Derivative on the left Derivative on the right Determinant Deviation 对角线对角阵矩阵的对角化 直径Diagonal line Diagonal matrix Diagonalization of matrix Diameter 菱形Diamond 差、差分 差分方程 可微的 Difference Difference equation Differentiable微分Differential 微积分Differential and integral calculus Differential coefficient Differential equation Differential equation of first order Differential equation of higher order Differential of area Differential operation Differentials of higher order Differentiate 微商微分方程一阶微分方程 高阶微分方程 面积元素 微分运算 高阶微分 求微分微分积分方程 数值逼近 维Differention integral equation Digital approximation Dimension 有向直线最速下降方向 狄利克雷函数 不连通的 不连续点第一类不连续点 第二类不连续点 离散Directed line Direction of steepest descent Dirichlet’s function Disconnected Discontinuity point Discontinuity point of the first kind Discontinuity point of the second kind Discrete 离散分布离散随机变量 判别式Discrete distribution Discrete random variable Discriminant 不相交事件 相异根Disjiont events Distinct root 分布Distribution 分布函数 分配律Distribution function Distributive law 发散Diverge 发散级数多项式相除法 因子Divergent series Division algorithm for polynomial Divisor 域Domain 收敛域Domain of convergence Domain of definition Domain of integration Dot product 定义域积分区域 内积二重积分 二重极限 双精度Double integral Double limit Double precision 二重根Double root 对偶Dual 对偶律Dualization law 有效估计 Efficiency estimation有效估计量特征多项式特征值Efficiency estimator Eigenpolynomial Eigenvalue特征向量弹性Eigenvector Elasticity元素Element柱的母线面积元素矩阵的元素集合的元素基本事件初等函数初等数学初等变换消元法Element of cylinder Element of area Element of matrix Element of set Elementary event Elementary function Elementary mathematics Elementary transformation Elimination椭圆Ellipse 椭球Ellipsoid椭圆柱面经验方差经验分布函数空集Elliptic cylinderEmpirical variance Empirical distribution function Empty set端点Endpoint 总体Ensemble总体均值可数Ensemble average Enumerable可数无穷等概率Enumerable infinite Equal probability Equal ratio等比等可能事件方程Equally likely event Equationn次方程等腰三角形相似变换等边三角形等价Equation of n-th order Equicrural triangle Equiform transformation Equilateral triangle Equivalence等价变换等价关系误差Equivalence transformation Equivalent relationError误差分析误差检验测量误差估计Error analysisError checkError of measurement Estimate区间估计相关的估计量回归系数估计Estimate by a interval Estimate of correlation Estimate of regression coefficient总体比例估计 总体方差估计 估计量Estimate of population proportion Estimate of population variance Estimator 欧几里德空间 偶数Euclidean space Even 偶函数Even function 偶数Even number 事件Event 小概率事件 幂级数展开 期望Event of small probability Expansion into power-series Expectation 试验Experiment 显函数Explicit function Exponent 指数指数曲线 指数曲线 指数分布 指数函数 开立方Exponent curve Exponential curve Exponential distribution Exponential function Extraction of cubic root Extraction of square root Extremal 开平方极值极值点Extreme point 极值Extreme value 因子Factor 阶乘Factorial 因式分解 曲线族Factoring Family of curve Fiducial interval Fiducial limit 置信区间 置信限定义域Field of definition Field of rational numbers Finite 有理数域 有限的有限区间 有限开区间 一阶矩Finite interval Finite open interval First moment 拟和Fitting 曲线拟和 多项式拟和 直线拟和 浮点运算 焦点Fitting of a curve Fitting of a polynomial Fitting of a straight line Floating point operation Focus 公式Formula 四则运算 分数Four arithmetic operation Fraction 分数线 Fraction stroke相对误差 分数Fractional error Fractional number Frequency 频率边界点Frontier point 满秩Full rank 函数Function 一元函数 一次函数 多元函数 n 元函数 基本函数 基本解Function of a single variable Function of first degree Function of many variables Function of n-variables Fundamental function Fundamental solution Fundamental system of solutions Fundamental theorem Gamma distribution Gamma function 基础解系 基本定理 分布函数高斯分布 母线Gaussian distribution Generator 几何平均 几何分布 几何平均 几何级数 几何级数 几何Geometric average Geometric distribution Geometric mean Geometric series Geometrical series Geometry 空间几何 黄金分割 拟和优度拟和优度检验 斜率Geometry of space Golden cut Goodness of fit Goodness of fit test Gradient 图示法Graphical method Great circle of a sphere Greatest common factor Greatest lower bound Greatest value 球的大圆 最大公因子 下确界最大值分组误差区间分半搜索 调和级数 高阶导数 高阶差分高阶微分方程 高阶微分 高阶Grouping error Half interval search Harmonic series Higher derivative Higher difference Higher differential equation Higher differentiation Higher order 高次项Higher term 高阶导数高阶常微分方程 Higher-order derivative Higher-order ordinary differential equation高阶偏微分方程高阶偏导数直方图Higher-order partial differential equation Higher-order partial derivative Histogram齐次Homogeneous齐次微分方程齐次方程齐次函数齐次线性微分方程齐次线性方程齐次多项式n次齐次多项式水平渐近线水平线Homogeneous differential equation Homogeneous equation Homogeneous function Homogeneous linear differential equation Homogeneous linear equation Homogeneous polynomial Homogeneous polynomial of degree n Horizontal asymptoteHorizontal line水平面Horizontal plane 双曲线Hyperbola双曲面Hyperboloid单叶双曲面双叶双曲面超几何分布假设Hyperboloid of one sheet Hyperboloid of two sheets Hypergeometric distribution Hypothesis假设检验幂等矩阵单位元素单位矩阵病态Hypothesis testing Idempotent matrix Identical element Identity matrixIll-condition病态方程病态矩阵虚轴Ill-conditioned equation Ill-conditioned matrix Imaginary axis虚数Imaginary number 虚根Imaginary root虚数单位隐式Imaginary unit Implicit隐函数Implicit function不可能事件广义积分广义二重积分倾角Impossible event Improper integral Improper double integral Inclination angle夹角Included angle集合的包含不相容Inclusion of sets Incompatible不相容事件不定积分不定二次型独立Incompatible event Indefinite integral Indefinite quadratic form Independence随机变量独立性Independence of random variable独立事件独立随机事件 独立随机变量 自变量 Independent event Independent random event Independent random variable Independent variable Indeterminate form Index of a quadratic form Index of inertia 未定式二次型的指数 惯性指数 不等式Inequality 无限自由度 无穷间断点 无穷区间 无穷极限 无穷级数 无穷集 Infinite degree of freedom Infinite discontinuity Infinite interval Infinite limit Infinite series Infinite set 无穷大量 无穷小量 拐点Infinitely large quantity Infinitely small quantity Inflection point 固有误差 非齐次 Inherent error Inhomogeneous Initial condition Initial value 初始条件 初值内点Inner point 内积Inner product 向量内积 内径Inner product of vector Inradius 内切圆 Inscribed circle 瞬时Instantaneous 整数Integer 可积的 Integrable 积分Integral 整式Integral expression Integral mean value Integration 积分中值 积分法部分分式积分法 分部积分法 换元积分法 截距Integration by partial fraction Integration by parts Integration by substitution Intercept 内点Interior point 内积Interior product Intermediate value theorem Interpolation 介值定理 插值插值多项式 交Interpolation polynomial Intersection 集合的交 交点 Intersection of sets Intersection point区间Interval 区间估计收敛区间反三角函数 反函数Interval estimation Interval of convergence Inverse circular function Inverse function Inverse interpolation Inverse logarithm Inverse mapping Inverse matrix 逆插值反对数逆映射逆矩阵倒数Inverse of a number Inverse operation Inverse proposition Inverse sine 逆运算逆命题反正弦反对称Inverse symmetric Inverse theorem Inverse transformation Invertible 逆定理逆变换可逆可逆矩阵无理数Invertible matrix Irrational 无理数Irrational number Irrelevance 不相关不可逆Irreversible 等腰直角三角形 等腰梯形等腰三角形 累次积分迭代Isosceles right triangle Isosceles trapezoid Isosceles triangle Iterated integral Iteration 雅可比行列式 联合密度联合分布联合分布函数 联合概率密度 联合概率分布 约当标准型 约当矩阵跳跃间断点 拐点Jacobian Joint density Joint distribution Joint distribution function Joint probability density Joint probability distribution Jordan canonical form Jordan matrix Jump discontinuity Knee 已知Known 拉格朗日方程 拉格朗日乘数 拉格朗日插值 结合律Lagrange equation Lagrange multiplier Lagrange interpolation Law of association Law of commutation Law of distribution Law of large number交换律分配律大数定律主对角线首项元素最小公倍数 最小二乘法 左连续Leading diagonal Leading element Least common multiple Least square method Left continuous Left derivative 左导数左极限Left limit 左乘法Left multiplication Leibniz’s formula Lemma 莱布尼兹公式 引理弧长Length of arc 线段长度峰度Length of segment Leptokurtosis 显著水平似然方程似然函数极限Level of significance Likelihood equation Likelihood function Limit 极限分布线段Limiting distribution Line segment 线性代数线性相关线性相关线性微分方程 线性方程线性表示线性函数线性无关线性回归线性表示线性空间线性变换线性相关线性无关局部极大值 局部极小值 对数Linear algebras Linear correlation Linear dependence Linear differential equation Linear equation Linear expression Linear function Linear independence Linear regression Linear representation Linear space Linear transformation Linearly dependent Linearly independent Local maximum Local minimum Logarithm 对数函数对数的底纵轴Logarithm function Logarithmic base Longitudinal axis Lower bound 下界下三角矩阵 最小公倍数 菱形Lower triangular matrix Lowest common multiple Lozenge 马克劳林级数 长轴 Maclaurin series Major axis优化Majorization 尾数Mantissa 多值函数映射Many-value function Map 边缘密度边缘分布临界值Marginal density Marginal distribution Marginal value 数学期望数学归纳法 乘方Mathematical expectation Mathematical induction Mathematical power Mathematical statistics Matrix 数理统计矩阵二次型的矩阵 系数矩阵矩阵的迹最大的Matrix of a quadratic form Matrix of coefficients Matrix trace Maximal 最大值Maximal value 最大Maximum 最大似然最大似然估计 最大点Maximum likelihood Maximum likelihood estimate Maximum point 平均值Mean 平均数Mean number 均方差Mean square deviation Mean square error Mean value 均方误差平均值均值向量平均速度精确度Mean vector Mean velocity Measure of precision Median point 中点、重心 配方法Method of completing the square Method of geometry Method of iteration Method of least squares Method of maximum likelihood Method of minimum squares Method of moment Method of optimization Method of parabolas Method of random sampling Method of steepest descent Method of substitution Method of variation of constants Method of weighted mean Metric space几何方法迭代法最小二乘法 最大似然法 最小二乘法 矩法最优化方法 抛物线法随机抽样法 最速下降法 置换法常数变异法 加权平均法 度量空间中点Middle point 中点Mid-point 中值Mid-value 最小的Minimal 最小点Minimal point 最小值Minimal value 最小值Minimum 最小方差估计 子式Minimum variance estimation Minor 子行列式次对角线减、负Minor determinant Minor diagonal Minus 负无穷大带分数Minus infinity Mixed fraction 混合偏导数 众数Mixed partial derivative Mode 模Moduli 模Modulo 模Modulus 复数的模矩Modulus of complex number Moment 矩函数Moment function Moment generating function Moment method of estimation Monodrome function Monogamy 矩母函数矩估计法单值函数一一对应单项式Monomial expression Monotone 单调单调收敛定理 单调递减单调递增单调序列单调数列单调减少单调函数单调增加单调减少函数 单调增加函数 单调性Monotone convergence theorem Monotone decreasing Monotone increasing Monotone sequence Monotone sequence of numbers Monotonic decreasing quantity Monotonic function Monotonic increasing quantity Monotonically decreasing function Monotonically increasing function Monotonicity 单值函数可去奇点可去奇点m 次样条函数 多维的Monotropic function Movable singular point Moving singularity m-splines Multidimensional Multidimensional normal distribution多维正态分布多值函数多项式Multiform function Multinomial 复合Multiple 多重特征值 多重积分多重极限重数Multiple eigenvalues Multiple integral Multiple limits Multiple numbers 重根Multiple root 多值函数矩阵乘法乘法定理特征值的重数 根的重数多值函数多元正态分布 多元样条函数 互不相容互逆的Multiple valued function Multiplication of matrices Multiplication theorem Multiplicity of eigenvalue Multiplicity of root Multivalued function Multivariate normal distribution Multivariate splines Mutually exclusive Mutually inverse 自然对数自然对数n 维正态分布 n 维概率分布 n 维空间Napierian logarithms Natural logarithm n-dimensional normal distribution n-dimensional probability distribution n-dimensional space Necessary and sufficient condition Necessary condition 充分必要条件 必要条件负的Negative 负相关Negative correlation Negative definite matrix Negative definite quadratic form Negative number 负定矩阵负定二次型 负数半负定二次型 负号Negative semidefinite quadratic form Negative sign 邻域Neighborhood 牛顿插值公式 n 重极限Newton’s interpolatio n formula n-fold limit 幂零矩阵不可数集不可微函数 不可数集非齐次的非齐次微分方程非齐次线性微分方程 非齐次线性方程 非线性的非线性方程 Nilpotent matrix Non-denumerable set Non-differentiable function Non-enumerable set Non-homogeneous Non-homogeneous differential equation Non-homogeneous linear differential equation Non-homogeneous linear equation Nonlinear Nonlinear equation非线性回归非线性回归分析非负定矩阵非奇异的非奇异线性变换非奇异矩阵非零向量正态分布法线Nonlinear regression Nonlinear regression analysis Nonnegative definite matrix NonsingularNonsingular linear transformation Nonsingular matrixNon-vanishing vectorNormal distributionNormal line标准正交基正态总体零因子Normal orthogonal basis Normal populationNull divisor零矩阵Null matrix零点Null point零解Null solution零向量Null vector排列数Number of permutationsNumerable可数的分子Numerator数值分析数值计算数值计算数值计算数值积分组合Numerical analysis Numerical calculation Numerical computation Numerical evaluation Numerical integration Combination观测值Observed value 钝角Obtuse angle钝角三角形事件的出现奇函数Obtuse triangle Occurrence of event Odd function奇数Odd number奇排列Odd permutationOdd-even奇偶奇偶性Odevity一维概率分布一一映射单侧One-dimensional probability distribution One-one mappingOne-sided单侧导数单侧极限一一对应一一映射单值函数开区间One-sided derivativeOne-sided limitOne-to-one correspondence One-to-one mappingOne-valued function Open interval开邻域Open neighborhoodOpen region开区域开集Open set 运算法则 最优解 Operational rule Optimal solution Optimize 最优化 最优解 Optimum solution Optimum value Order of a differential equation Order of a matrix Order of infinitesimal Order of infinity Ordinary differential Ordinary differential equation Origin 最优值微分方程的阶 矩阵的阶 无穷小的阶 无穷大的阶 常微分常微分方程 原点初始值 Original value 垂心Orthocenter 正交的 Orthogonal 正交基 Orthogonal basis Orthogonal transformation Orthogonal vectors Orthogonalization Orthonormal basis Oscillatory series Outer diameter 正交变换 正交向量 正交化标准正交基 振荡级数 外径外点Outer point 无顺序 Out-of-order 外径Outside diameter Pairwise independence Pairwise independence events Pairwise orthogonal Parabola 两两独立两两独立事件 两两正交 抛物线 抛物柱面 悖论Parabolic cylinder Paradox 平行Parallel 平行直线 平行四边形 参数Parallel straight lines Parallelogram Parameter 参数估计 总体参数 参数方程 参变量 Parameter estimation Parameter of population Parameter equation Parametric variable Parenthesis 圆括号 奇偶性 Parity 奇偶数字 部分相关 偏导数 Parity digit Part correlation Partial derivative偏微分Partial differential Partial differential equation Partial fraction expansion Partial sum 偏微分方程 部分分式展开 部分和 特解Particular solution Partitioned matrix Peak 分块矩阵 峰值百分数 Percentage 周长Perimeter 周期Period 循环小数 容许误差 排列Periodic decimal Permissible error Permutation 垂线Perpendicular 垂直Perpendicularity Piecewise 分段分段函数分段线性插值 分段多项式插值 枢轴元素 旋转Piecewise function Piecewise linear interpolation Piecewise polynomial interpolation Pivotal Pivoting 平面图形 平面Planar graph Plane 平面几何 极坐标 Plane geometry Plane polar coordinates Plumb-line 铅垂线 正无穷大 点估计 Plus infinity Point estimation Point of discontinuity Point of inflection Point of intersection Point of tangency Point slope form Poisson distribution Polar axis 间断点 拐点交点切点点斜式 泊松分布 极轴极坐标 Polar coordinates Polar radius 极半径 极点Pole 极坐标的极点 多边形 Pole of polar coordinates Polygon 多项式Polynomial 多项式插值函数 n 次多项式 总体Polynomial interpolating function Polynomial of degree n Population 总体中心矩 Population central moment总体分布总体均值总体矩Population distribution Population mean Population moment Population parameter Population variance Positive总体参数总体方差正的正定的Positive definite正定矩阵正定二次型正定对称矩阵正整数Positive definite matrixPositive definite quadratic form Positive definite symmetric matrix Positive integer正数Positive number半正定的半正定矩阵半正定二次型正平方根正项级数正定矩阵可能性Positive semi-definitePositive semi-definite matrix Positive semi-definite quadratic form Positive square rootPositive term seriesPositively definite matrix Possibility后验概率右乘Posterior probability Postmultiplication Postulate公设幂Power幂函数Power function幂数Power of a numberPower series幂级数幂级数展开原函数Power series expansion Primary function素数Prime number主对角线主子式Principal diagonal Principal minor微分算子的主部主值Principal part of a differential operator Principal value先验概率概率模型概率Prior probability Probabilistic model Probability依概率收敛概率分布概率论Probability convergence Probability distribution Probability theory Process of iteration Product event迭代法积事件乘积公式集的交Product formula Product of sets右导数Progressive derivativeProlate axis长轴反证法 归纳证明 真分数 真子集 真包含 连续性 命题Proof of contradiction Proof of induction Proper fraction Proper subset Proper include Property of continuity Proposition 伪码Pseudo code 纯虚数 二次的 二次曲线 二次型 二次函数二次齐次多项式 平方根 平方和 二次曲面 二次项 求积分 二次曲线 二次柱面 二次型 二次曲面 分位数 拟牛顿法 商Purely imaginary number Quadratic Quadratic curve Quadratic form Quadratic function Quadratic homogeneous polynomial Quadratic root Quadratic sum Quadratic surface Quadratic term Quadrature Quadric curve Quadric cylinder Quadric form Quadric surface Quantile Quasi-Newton method Quatient 弧度Radian 根号Radical 被开方数 开方Radicand Radication 半径Radius 小数点 随机的 随机事件 随机试验 随机变量 随机向量 随机性函数的值域 秩Radix point Random Random event Random experiment Random variable Random vector Randomness Range of function Rank 稀疏Rarefaction 比率Ratio 等比Ratio of equality Rational fraction Rational number 有理分式 有理数射线Ray瑞利分布实的Rayleigh distribution Real实轴Real axis实数Real number实二次型倒数Real quadratic form Reciprocal互逆矩阵矩形Reciprocal matrix Rectangle直角坐标直角坐标系递推公式接受域收敛区域拒绝域回归Rectangular coordinates Rectangular coordinate system Recurrence equationRegion of acceptance Region of convergence Region of rejection Regression回归分析回归方程相关系数等价关系相对导数相对误差剩余Regression analysis Regression equation Related coefficient Relation of equivalence Relative derivative Relative error Remainder可去间断点累次积分累次极限重根Removable discontinuity Repeated integral Repeated limits Repeated root Residual残差残差平方和弹性Residual sum of squares Resilience可逆的菱形Reversible Rhomb直角Right angle右连续性右导数直角三角形罗尔定理根Right continuous Right derivative Right triangle Rolle’s theouem Root开平方根均方根舍入误差行RootingRoot-mean-square Round off error Row行秩Row rank行向量鞍点Row vector Saddle样本Sample样本均值样本相关系数样本均值样本矩Sample averageSample correlation coefficient Sample meanSample momentSample point样本点样本容量样本空间样本标准差样本方差抽样Sample sizeSample spaceSample standard deviation Sample variance Sampling抽样检验斯密特正交化法正割Sampling inspection Schmidt’s orthogonalization Secant次对角线分段连续扇形Secondary diagonal Sectionally continuous Sector半轴Semi-axis 半圆Semi-circle半定二次型半正定型序列Semi-definite quadratic form Semi-positive definite form Sequence事件序列数列Sequence of events Sequence of numbers Series级数级数展开函数级数集合Series expansion Series of functions Set方程组Set of equationsSet union集的并符号差Signature显著水平有效数字相似矩阵相似三角形相似性Significance level Significant figure Similar matrices Similar triangles Similarity相似变换简单平均简分数Similarity transformation Simple averageSimple fractionSimple root单根联立方程正弦Simultaneous equations Sine奇异的Singular奇异矩阵正弦曲线Singular matrix Sinusoidal curve斜率Slope解向量空间Solution vector Space稀疏矩阵球形Sparse matrix Sphere球冠Spherical cap 球冠Spherical crownSpline样条样条函数迹Spline function Spur矩阵的迹平方Spur of matrix Square方阵Square matrixSquare root 平方根残差平方和标准差标准正态分布标准化随机变量初始值统计Square sum of residues Standard deviation Standard normal distribution Standardized random variable Starting valueStatistic统计假设最速下降算法步长Statistical hypothesis Steepest descent algorithm Step length随机的直线Stochastic Straight line严格单调严格单调递减严格单调递增子集Strictly monotoneStrictly monotone decreasing Strictly monotone increasing Subaggregate子块Subblock子行列式子矩阵子集Subdeterminant Submatrix Subset代换Substitution充分条件充分估计量充分统计量并集Sufficient condition Sufficient estimates Sufficient statisticsSum aggregateSum of squares of deviations Supremum离差平方和上确界补集SupplementarySymmetric对称对称矩阵系统误差坐标系Symmetric matrix System error System of coordinates方程组System of equations System of fundamental solutions System of linear equations System of nonlinear equations Tangent 基础解系线性方程组非线性方程组 正切切线Tangent line 曲线的切线方程 切线Tangential equation of a curve Tangential line 泰勒级数泰勒公式t 分布Taylor series Taylor’s formula t-distribution 逐项微分多项式的项级数的项假设检验检验统计量假设检验立方Term by term differentiation Term of a polynomial Term of a series Test of hypothesis Test statistics Testing of hypothesis Third power 三维空间全微分Third-dimensional space Total differential Total differentiation Total probability Totality 全微分全概率总体迹Trace 矩阵的迹变换Trace of a matrix Transform 变换Transformation 变换矩阵坐标变换转置Transformation matrix Transformation of coordinates Transpose 矩阵的转置转置矩阵横截面Transpose of a matrix Transposed matrix Transversal surface Triangle 三角形三角函数三角行列式三角矩阵截短误差二维空间二重极限两点分布双侧检验无偏的Triangle function Triangular determinant Triangular matrix Truncation error Two-dimensional space Two-limit Two-point distribution Two-sides test Unbiased 无偏估计无偏估计 Unbiased estimate Unbiased estimation无偏性Unbiasedness Underdeterminant Uniform distribution Uniformly minimum variance unbiased estimation Unilateral limit Union 子行列式均匀分布一致最小方差无偏估计 单侧极限并集合的并唯一解Union of sets Unique solution Unit circle 单位圆单位长度单位向量未知数Unit length Unit vector Unknown number Unsymmetrical Untrivial solution Upper bound 不对称的非零解上界上三角矩阵有效性Upper triangular matrix Validity 趋于零Vanishingly 变量Variable 方差Variance 方差分析变量Variance analysis Variant 簇Variety 向量Vector 向量范数向量积Vector norm Vector product Vector space 向量空间铅垂渐近线竖轴Vertical asymptote Vertical axis 弱收敛Weak convergence Weak law of large numbers Weight 弱大数定律权加权平均值加权平均值无偏性Weighted average Weighted mean Without bias 零一分布 Zero-one distribution。
Asymptote作图指南
3.4 外接圆 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5 直角标记 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Asymptote 作图指南
莫图 (gzmfig@)
symptote
2008 年 8 月 5 日
ii
内容提要:
本书向你介绍一个功能强大的作图语言: Asymptote. 设计 Asymptote 的灵感来自有名的 MetaPost. 但由于 Asymptote 的语法格式与 C/C++ 很接 近, 使得它更容易被接受, 而且易学易懂不容易忘记. 你可以轻而易举地用它作出达到出版要求 的非常精美的数学图形, 例如几何图、示意图、函数和数据曲线或曲面图等. Asymptote 具有极 大的可扩展性, 稍加学习就可以写出自己的模块来. Asymptote 能够与 LATEX 完美地结合. 可以把 Asymptote 代码直接嵌入到 LATEX 文件, 也可以 使用 Asymptote 制作出高质量的 EPS 图形, 然后插入到 LATEX 文件中. Asymptote 利用 LATEX 对图形中的文字和数学公式排版, 这保证你的文章中的插图和正文具有完全相同的风格. 就象 LATEX 是数学排版的标准工具一样, Asymptote 的作者们也正在试图把它做成科技作图的标准 工具! 本书就是关于 Asymptote 的介绍. 读完之后你将学会怎样绘制出非常“专业”的数学图形. 相 信从中学到大学, 从学生到教师, 都会有它的受益者的.
geometrydescriptor geometry 转换坐标系 -回复
geometrydescriptor geometry 转换坐标系-回复如何将Geometry对象的坐标系转换。
步骤1：理解坐标系转换的概念在进行坐标系转换之前，我们首先需要了解什么是坐标系转换。
坐标系是一种用于描述和表示地理空间位置的系统。
不同的坐标系采用不同的参考点和度量单位。
坐标系转换是将一个Geometry对象从一个坐标系转换到另一个坐标系。
这种转换通常是为了在不同的GIS应用程序之间共享地理数据，或者在不同的坐标系下进行地理空间分析。
步骤2：确定源和目标坐标系在进行坐标系转换之前，我们需要确定源Geometry对象的坐标系和目标坐标系。
源坐标系是Geometry对象当前所在的坐标系，而目标坐标系是我们希望将Geometry对象转换到的坐标系。
源和目标坐标系通常由坐标参考系统（CRS）或坐标参考标识（CRS ID）表示。
步骤3：获取源Geometry对象的CRS信息在进行坐标系转换之前，我们需要获取源Geometry对象的坐标参考系统（CRS）信息。
CRS信息通常包括坐标系的名称、坐标系的地理范围、坐标系的投影信息等。
根据不同的GIS应用程序，获取CRS信息的方法可能会有所不同。
一种常见的方法是使用Geometry对象的metadata属性来获取CRS信息。
步骤4：确定源坐标系和目标坐标系的转换关系确定源坐标系和目标坐标系的转换关系是进行坐标系转换的关键步骤。
不同的坐标系转换方法和工具可能会采用不同的转换关系。
常见的转换关系包括七参数转换、四参数转换、仿射转换等。
我们需要根据具体的坐标系转换要求来确定适合的转换关系。
步骤5：使用合适的工具进行坐标系转换根据源坐标系和目标坐标系的转换关系，我们可以选择合适的工具或库来进行坐标系转换。
常用的工具包括GDAL、Proj4、ArcGIS等。
以下是一些常见的坐标系转换工具的使用示例：- GDAL：Pythonimport gdal# 读取源Geometry对象src_geom = ogr.CreateGeometryFromWkt('POINT(10 20)')# 源坐标系和目标坐标系的CRS信息src_crs = osr.SpatialReference()src_crs.ImportFromEPSG(4326) # EPSG code for WGS84tar_crs = osr.SpatialReference()tar_crs.ImportFromEPSG(3857) # EPSG code for Web Mercator# 坐标系转换transform = osr.CoordinateTransformation(src_crs, tar_crs)src_geom.Transform(transform)# 输出转换后的Geometry对象print(src_geom.ExportToWkt())- Proj4：Pythonfrom pyproj import Proj, transform# 源坐标系和目标坐标系的proj4字符串src_crs = Proj('+proj=longlat +datum=WGS84 +no_defs')tar_crs = Proj('+proj=utm +zone=33 +datum=WGS84 +units=m +no_defs')# 源Geometry对象src_geom = shapely.geometry.Point(10, 20)# 坐标系转换x, y = transform(src_crs, tar_crs, src_geom.x, src_geom.y)# 输出转换后的Geometry对象print(shapely.geometry.Point(x, y))- ArcGIS：使用ArcPy模块提供的功能进行坐标系转换，具体代码可以根据ArcPy 的文档进行选择和调整。
FLAC3D中出错警告
B ERROR MESSAGESB.1FLAC3D-Specific Errors***A zone has undefined material modelOne or more zones in the model has not had a material model defined.This must bedone before cycling.***All zones have NULL fluid modelNo zones with activefluid material models are present.Either activate some zonesforfluid calculations or disablefluid calculations.***Attempted to create a degenerate triangleThe generation a surface item caused the creation of a degenerate triangle(i.e.onewith co-linear points).***Bad commandFLAC3D failed to recognize the command entered.***Bad format parameter i(string)The i th parameter on the command line was not in the format required by the com-mand syntax.***Bad I/O on filefileFLAC3D was unable to either read or write tofilefile.If writing,there may be noavailable disk space.If reading,thefile may be corrupt.***Bad keyword parameter i(string)Parameter i on the command line was not processed by FLAC3D.Check the commandsyntax.***Bad overlay codeAn illegal overlay code was specified in the MODEL command.Legal values areintegers between-1and2.***Bad RANGE keywordA range was specified with an illegal or unrecognized keyword.Check for spellingerrors and see the manual for the correct syntax.***Biot modulus fluid mode is offMay not access Biot modulus when Biot modulus mode is off.***Biot modulus fluid mode is onMay not accessfluid modulus fmodulus when Biot modulus mode is on.***Cable element not foundA reference was made to a cable element that does not match any element currentlyin memory.***Cable has zero lengthA cable was specified/found with a zero element length.***Cable stiffness parameters have not been setSome cable material properties were not specified prior to cycling.***Cannot allocate memoryFLAC3D could not allocate its reserved memory.Specify less reserved memory atthe command line***Cannot apply stress in global and local axes on same faceApply stresses using one axis system.***Cannot combine NULL and PLANE keywords on a contour plot itemIt is impossible to contour the interior regions of null zones.This combination ofkeywords is not allowed.***Cannot deactivate an external volumeAn external volume is always active and may not be deactivated.***Cannot destroy base viewThe view“Base/0”cannot be destroyed.***Cannot destroy current viewThe current view can not be destroyed.Make another view current and try again.***Cannot find ID numberAn ID number was specified that does not match any existing object of that type.***Cannot FIX and APPLY velocity in the same directionA FIX condition is implied on gridpoints under an APPLY velocity condition.***Cannot fix or apply velocities to a node that is slaved to an active zoneA cable node that is internal to an active zone may not have its motion restricted inany way.Only a“free”cable node can have its velocity constrained.***Cannot have applied velocities in global and local axes at same gridpoint Apply velocities using one axis system.***Cannot open filefileFLAC3D was unable to open thefile.If reading,thefile probably does not exist.Ifwriting,thefile may already exist in a protected state.***Cannot rename base viewThe view‘Base/0’cannot be renamed.***Cannot set group of an active volumeAn active volume has already chosen its internal zones.This choice can only bemodified if the volume is made inactive.***Command line overflowA fully-expanded command line has exceeded the maximum length of1024char-acters.***Configuration file errorThe configurationfile is a mirror image of the information stored in the hardwarekey.Thisfile is created thefirst time FLAC3D is executed.Thereafter,thisfile allowsthe user to create models and generate plots without the hardware key attached.Thehardware key will still be required to be attached to cycle.The configurationfiledetected has invalid information,attach your hardware key to regenerate it or replacethe configurationfile specified.***Creep mode not availableCreep extentions are not available in this version of the code.***Density needed for thermal runThe thermal option requires that density be specified in all active zones.***Density not definedThe dynamic option requires that density be specified in all active zones.***Device mode mode not compatible with current hardwareThe specified device mode was not detected as being available on the hardware ofthe current system.***Device mode mode not foundThe specified device mode is not one currently recognized by the screen device.***Display information not availableThe screen display information was not available.This error should never happen;if it does,contact Itasca.***DOS critical error:stringA critical error(disk access,etc)has occurred on the system.You will be promptedfor possible corrective actions.***Dynamic extension absent from gpDynamic extention information was not present in a gridpoint.There is probablyinsufficient memory available.***Dynamic mode not availableDynamic extentions are not available in this version of the code.***Error creating PCX fileAn error occurred while attempting to output a PCX-file image of the screen device.***Error initializing deviceAn error occurred while initializing a screen device.Check the mode setting.***Error initializing graphics systemAn error occurred while trying to initialize an output device.Check that the properdevice has been selected.***Error in syntax while specifying output historiesFLAC3D encountered an incorrect syntax while specifying histories to output.Checkthe correct syntax.***Error in system/temp memoryThis is an internal FLAC3D memory management error.If it occurs,contact Itasca.***Error opening history temp fileFLAC3D was unable to open a temporaryfile to store history traces.There is probablya problem with the disk drive.***Error reading history temp fileFLAC3D was unable to read the temporaryfile it stores history traces in.There isprobably a problem with the disk drive.***Error writing history temp fileFLAC3D was unable to write to the temporaryfile it stores history traces in.The diskdrive may be full.***Extra array index out of boundsAn attempt was made to index a gridpont or zone extra array past the number thathad been specified with the CONFIG command.***Face a,b already has interface elementsCannot double place interface elements from the same interface on the same zoneface.***Face with less than3nodesA face was specified with less than the minimum of three nodes while building awater table.***Failure to assign gridpointAn error occurred while generating internal gridpoints in a zone primitive.There isprobably no more memory available.***Failure to initialize interface logicThe interface logic is unavailable in this session.There is probably insufficientmemory available.***Failure to insert valueThe Table logic was unable to insert a value into a table.This error should neverappear.If it does,contact Itasca.***Fatal key error--contact ItascaAn error has occurred in the hardware logic detection system that makes it impossibleto continue executing the program.***Filefile not save fileAn attempt was made to restore afile that was not a FLAC3D savefile.***Font file name not foundA fontfile needed by the screen device was not found.Check for their existence inthe current directory.***Free surface already exists at that locationAn attempt was made to create a surface triangle in a location where a free(notbound to a volume)surface already exists.***GEN iterator error:stringThis is an internal error to the grid iterator.These errors should never happen.If itdoes,note the contents of string and notify Itasca.***General interface error-stringAn internal interface processing error.This error should never occur.If it does,contact Itasca.***Generic dynamic array processing errorThis error should never occur.Contact Itasca.***Generic linked list processing errorThis error should never occur.Contact Itasca.***Gravity not definedThe gravity vector must be defined prior to the definition of the water table.***Gridpoint already has applied velocities in another local axes system Use one axis system.***Gridpoint i does not existA reference was made to a gridpoint ID that does not match any currently in memory.***Group’string’does not existA reference was made to a group whose name does not match any currently inmemory.***History i does not existAn attempt was made to access a history ID that does not exist.***Illegal block plot typeThis error should never occur.If it does,contact Itasca.***Illegal contour typeThis error should never occur.If it does,contact Itasca.***Illegal error code iThis error should never occur.If it does,contact Itasca.***Illegal geometry in zone iZone i contains one or more internal tetrahedrons with zero or negative volume.Check zone geometry.***Implicit scheme failed to converge***Insufficient memory to restore stateThe savefile used more memory than is available to this session of FLAC3D.RestartFLAC3D and reserve more memory.***Insufficient number of vertices definedMore vertices need to be specified to fully describe the surface desired.***Intended device not availableThe device specified for output is not available on this version of FLAC3D.***Interface element already exists with those vertices.Cannot create two identical interface elements in the same interface.***Interface i not foundA reference was made to an interface that does not yet exist.***Interface node i already exists at that location.Cannot create two nodes on the same interface at the same location.***Interface node not foundNo interface nodes are present in that interface.***Invalid history ID numberAn illegal integer was specified as a history ID number.***Invalid input type(i)This error should never appear.If it does,contact Itasca.***Key for different code IDThe hardware lock detected is for a different program.***Key for newer version of codeThe hardware lock detected is for an older version of the program.Contact Itascato update the version.***Library error stringThis is an internal C runtime library error.In general,this will pertain to afloatingpoint error.***May only have one contour plotitem per viewThere may only be a single PlotItem of type Contour in a view’s PlotItem list.***May only ouput one history to a single tableWhen writing a history to a table,only one history trace and one table may bespecified.***May only specify i output historiesA maximum of i histories may be output simultaneously.***Memory overflowFLAC3D has run out of its reserved memory.Save the run,and restart with morememory if available.***MetaWindow Query Error Code i/iAn internal error from the graphics library driving the screen device.***Missing parameter iFLAC3D required another parameter at position i on the command line.***Mouse driver not foundA mouse driver was not found on the system.Check your computers initializationfiles.***Multiple volume constraint failureA gridpoint which was constrained to two or more volumes was unable to meet all ofits constraints.A probable cause is a surface geometry much smaller that the zonesizes near it.***Must specify a non-zero extrusion vectorAn extrusion vector must be specified for an extruded type of surface generation.***Must specify position to create new nodeIn order to create a new cable node,a position in space must be specified.***Must specify all three nodes of an interface element.The locations of all vertices of an interface element must be specified to create it.***Must specify an interface ID number.An interface ID number must be specified for most interface commands.***Must specify position to create new nodeIn order to create a new cable node,a position in space must be specified.***No convergence in30SVDCMP iterationsThis error should never occur.If it does,contact Itasca.***Node not foundA reference was made to a cable or surface node that does not match any currentlyin memory.***Non-convex faceWhile entering a water table,a polygon was entered that was not convex.***Non-planar faceWhile entering a water table,a polygon was entered that was not planar.***Not configured for creep calculationThe code must be configured(using the CONFIG command)for creep calculationbefore creep extentions can be used.***Not configured for dynamic calculationThe code must be configured(using the CONFIG command)for dynamic calculationbefore dynamic extentions can be used.***Not configured for fluid flow calculationThe code must be configured(using the CONFIG command)forfluid calculationbefore thermalfluid can be used.***Not configured for thermal calculationThe code must be configured(using the CONFIG command)for thermal calculationbefore thermal extentions can be used.***Not enough memory available for command processorThere must be enough memory left in the system(outside of the memory reserved forFLAC3D)to load command processor.If possible,reserve less memory at start-up.***Open surface at zone a face b edge cThe grid iterator was unable to build a closed list of faces and gridpoints for a newlyactivated volume.***PlotItem ID i not foundA reference was made to a plot-item ID number that does not exist in the currentview list.***Property bad,or does not correspond to modelAn attempt was made to specify a non-existent property,or one that does not corre-spond to a given model.***Recursive use of named rangesA name was given to a range that matches a name used by one of its elements.Thisrecursive relationship is not allowed,and the new range is not saved under that name.***Referenced non-existent auxiliary input(i)This error should never occur;if it does,contact Itasca.***Save file incompatible with present versionThe savefile is no longer compatible with the present version of the e theold version or re-run the problem.***hardware copy protection not detected...Press ESC to exit program or any other key to try again and continue.If unsuccessful,contact your local code agentThe hardware copy protection(i.e.,hardware lock,hostid)was not detected.Replaceit and try again.If FLAC3D is still unable to detect it,contact your local code agent.***SOLVE Error:No master processes activeAt least on process(mechanical,fluid,or thermal)must not be a slave to use theSOLVE command.***Table i does not existA reference was made to a table number that does not yet exist.***Table i not foundA reference was made to a table ID that does not match any currently in memory.***Thermal mode not availableThermal extentions are not available in this version of the code.***This model name does not existPlease refer to the manual to determine the available models and their names.***Time step too large for given propertiesCheck the properties.***Timestep rejected by moduleThis error should never occur.Contact Itasca.***Token length overflowA single token has exceeded the maximum length of80characters.***Unable to fix degenerate zone iWhile grid iterating,a zone has degenerated in a way that the iterator was unable tomodify.Increasing the number of zones in the region might help,as might adjustingthe sizefield tofit the surface geometry better.***Unable to find Gp i in surface listThe grid iterator was unable to build a closed list of faces and gridpoints for a newlyactivated volume.***Unable to initialize device stringUnable to initialize screen device string.***Unable to load fontfileUnable to load fontfilefile,which is needed by the graphics system.***ViewID name already existsAn attempt was made to create a new View with an ID that matches one alreadypresent.***ViewID i not foundA reference was made to a ViewID number that does not exist.***ViewID name not foundA reference was made to a ViewID name that does not exist.***Viscous damping too highReduce the damping value specified.***Volume i not foundA reference was made to a V olume ID number that does not currently exist.***Water density not definedThe water density must be defined prior to the definition of the water table.***Water table orthogonal to gravityA water table element was added that was parallel with the direction of the gravityvector.This is not allowed.***Zero gridpoint massAn active gridpoint shows zero inertial mass.Check the material properties beingused.***Zero gridpoint stiffnessAn active gridpoint shows zero accumulated stiffness.Check the material propertiesbeing used.B.2FISH Error Messages***Array index is not an integer***Array name is already used by an array***Bad syntaxCheck your spelling(including case),punctuation and assignments.***Bad type conversionThis usually means that a string or a pointer is being used in an arithmetic expressionwith a number.***Call number is invalidThe given FISHCALL number is not between0and50.***Cannot execute(string)...not a functionThe named symbol is not a defined function.***Cannot give value to left-hand sideThe intrinsic variable is“read only”—i.e.,it cannot be given a value.***Cannot interpret function or array argumentThe argument of an intrinsic or FLAC3D-specific function has a bad format—seemanual.***Cannot interpret(string)as a numberA built-in function expects a number as argument,but something else is present.***Cannot process...not a DEFined functionCheck your spelling(including case),punctuation and assignments.***Cannot raise negative number to real powerThe manipulation of complex numbers is not within the scope of the code.***CASE must be followed by integer between0and256Only constant integer values are allowed.***CASE or END CASE,but no preceding CASE OFStructure is CASEOF...CASE...<CASE>...ENDCASE with multipleCASE clauses.***CASE OF must be followed by somethingA valid expression with an integer result is expected.***Dimension should be positive integerArray dimensions should either be integers or FISH variables names that have integervalues at compile time.***Duplicate CASE numberCASE numbers must appear once only in a CASE section.***ELSE or END IF,but no preceding IFStructure is IF...THEN...<ELSE>...ENDIF with a single ELSE clause optional.Indenting your code will help you track this error.***Empty line after’=’***END COMMAND,but no preceding COMMANDStructure is COMMAND...ENDCOMMAND.Indenting your code will help you trackthis error.***END LOOP,but no preceding LOOPStructure is LOOP...ENDLOOP.Indenting your code will help you track this error. ***Expected=<>#<=or>=but missing***Extraneous materialThere are extraneous characters on the same line after a FISH statement.***FISH compilation errorFISH was unable to compile the function as entered,probably due to an erroneouscommand or a spelling error.***FISH execution errorFISH was unable to execute the function as entered.This could be caused bycommand errors,division by zero,or other such programming faux pas.***Fish-function name expected but not found***Function name has been defined before***Function name is already an array***Function name is inappropriate or conflicts with reserved word***Function string is being called recursivelyThe named function is trying to execute itself(e.g.,the function name is on theleft-hand side of an assignment).***Inappropriate equals signAn equals sign is in an inappropriate place.***Inappropriate keywordA FISH keyword is being used in an inappropriate place.***Inappropriate right parenthesisCheck your punctuation.***Incomplete string(missing quotation mark)Check your punctuation.***Integer between0&255must follow CASE***Internal FISH error..send data file to Itasca***Missing argument(s)Refer to Chapter4,FISH User’s Guide,for the arguments required.***Missing comma in loop rangeCheck format of LOOP statement—see definition in manual.***Missing END CASE statementThe function has ended,but with an incomplete CASE section.***Missing END IF statement(s)A function definition has been ended,but with an incomplete IF section.***Missing END LOOP statementThe function has ended,but with an incomplete LOOP.***Missing left-hand side to assignment***Missing loop range(s)***Missing material***Missing name***Missing right-hand side to assignment***Missing test symbol:=<>#<=or>=One,and only one,of the noted test symbols may be used in the expression. ***More than one equals sign***Name conflicts with existing symbol name***Name conflicts with keyword or intrinsic name***Name corresponds to an existing function***Name is already an array;cannot re-define***Nested SECTIONs not allowed***No corresponding IF statementAn ENDIF has been given without a preceding IF.***No END SECTION statementThe function has ended,but with an incomplete SECTION.***No function name***No preceding CASE OFCASE or ENDCASE has been encountered with no proceeding CASEOF.***No preceding LOOP statement***No SECTION has been definedAn ENDSECTION or EXIT SECTION has been encountered,but there is no precedingSECTION.***Non-existent table***Not a user-defined symbol***Not currently within a SECTIONInappropriate EXIT SECTION in datafile.***Number has bad format***Number of arguments conflicts with previous usage***Parentheses do not balanceCheck your punctuation.***Pointers can only be compared with=or#The general test symbols(<,>,etc.)are not available for pointers.***Premature end of line***Reached END,but with missing END CASEFISH has reached the END of your function and has detected a bad CASE construct.***Reached END,but with missing END IFFISH has reached the END of your function and has detected a bad IF construct.***Reached END but with missing END SECTIONFISH has reached the END of your function and has detected a bad SECTION construct.***Reached END,but with unclosed LOOPFISH has reached the END of your function and has detected a bad LOOP construct. ***Requested table or item does not exist***Square root of negative number***This is a Fish variable,not a functionThe given FISH symbol cannot be executed because it is not the name of a function.***Too many ELSE statementsOnly one ELSE may come between IF and ENDIF.***Trying to divide by zero***Unbalanced parentheses***Unbalanced quote marks***WHILE STEPPING&COMMAND cannot co-exist in a function***Wrong number of argumentsRefer to Chapter4,FISH User’s Guide,for the arguments required.。
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Abstract This document deals with the use of the package geometry.asy extension which makes the production of plane Euclidean geometry figures easier. The package geometry.asy extension defines some new types and routines for the Asymptote software. First we will give the list with a brief description of the new types. Secondly we will study each of them and give details on the associated routines and operators. Acknowledgements I would like to thank • Olivier Guibé for numerous discussions on some computer algebra questions, his encouragements and his always attentive listening; • John Bowman and Andy Hammerlindl without asymptote does not exist; • MB which has followed the development of this extension and has allowed to correct, improve and add some features.
TC
C TB B′ K A C′
TA A′ BA MA B
∗ Copyright
c 2007 Philippe Ivaldi.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Lesser General Public License (see the file LICENSE in the top-level source directory).
geometry.asy∗ Euclidean geometry with asymptote
Original French Version by Philippe Ivaldi English Translation by Olivier Guibé & Philippe Ivaldi
Compiled with asymptote version 2.14svn-r5318 on June 28, 2011
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Objects types list . . . . . . . . . . . . . . . . . . . 1.2 Internal running . . . . . . . . . . . . . . . . . . . 1.3 Index and external examples . . . . . . . . . . . . 1.4 Casting . . . . . . . . . . . . . . . . . . . . . . . . Coordinate system . . . . . . . . . . . . . . . . . . . . . 2.1 The type coordsys . . . . . . . . . . . . . . . . . . 2.2 How to define a coordinate system . . . . . . . . . 2.3 Changing an object pair on coordinate system . . . 2.4 Other routines . . . . . . . . . . . . . . . . . . . . Points and vectors . . . . . . . . . . . . . . . . . . . . . 3.1 The points . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Basic principles . . . . . . . . . . . . . . . . 3.1.2 Another routines . . . . . . . . . . . . . . . 3.2 Vectors . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Basic principles . . . . . . . . . . . . . . . . . . . . 3.4 Vector/point casting . . . . . . . . . . . . . . . . . 3.5 Another routines . . . . . . . . . . . . . . . . . . . Mass points . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Basic Principles . . . . . . . . . . . . . . . . . . . . 4.2 Another routines . . . . . . . . . . . . . . . . . . . Transformations (Part 1) . . . . . . . . . . . . . . . . . 5.1 Independent coordinate system mappings . . . . . 5.2 Dependent coordinate system transformations . . . Lines, half-lines and segments . . . . . . . . . . . . . . . 6.1 The type “line” . . . . . . . . . . . . . . . . . . . . 6.1.1 Lines defined by two points, basic routines . 6.1.2 Lines defined by equations . . . . . . . . . . 6.1.3 Lines and parallelism . . . . . . . . . . . . . 6.1.4 Lines and angles . . . . . . . . . . . . . . . 6.1.5 Lines and operators . . . . . . . . . . . . . 6.1.6 Another routines . . . . . . . . . . . . . . . 6.1.7 Line and marker . . . . . . . . . . . . . . . 6.2 The type “segment” . . . . . . . . . . . . . . . . . Affine Transformations (Part 2) . . . . . . . . . . . . . . Conics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 The type “conic” . . . . . . . . . . . . . . . . . . . 8.1.1 Description . . . . . . . . . . . . . . . . . . 8.1.2 Basic routines . . . . . . . . . . . . . . . . . 8.1.3 Operators . . . . . . . . . . . . . . . . . . . 8.1.4 Conics equations . . . . . . . . . . . . . . . 8.1.5 Conics and casting . . . . . . . . . . . . . . 8.2 Circles . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 basic routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 4 4 4 5 5 5 5 6 6 6 6 8 10 10 11 13 13 13 13 16 17 19 22 22 22 23 23 24 27 28 29 30 31 33 33 33 34 36 36 37 38 38