喆学(20)：Matlab学习之三维曲面图

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“喆学（20）：Matlab学习之三维曲面图”

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“Zhe Xue (20):

Matlab learning of three-dimensional surface map”

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一、思维导图(Mind Map)

二、平面网格数据的生成(Generation of Plane Grid Data)

在MATLAB中，平面网格数据通常指的是二维空间内定义的规则或不规则点集，这些点集能够表示平面上的几何形状、物理场的z轴分布、以及数据分布等。

In MATLAB, plane grid data usually refers to regular or irregular point sets defined in two-dimensional space. These point sets can represent geometric shapes on the plane, z-axis distribution of physical fields, and data distribution, etc.

(1)坐标矩阵(Coordinate Matrix)

在MATLAB中，平面网格数据常常通过坐标矩阵的形式来表示。具体地，矩阵的每一行都代表一个网格点的坐标。例如，矩阵X = [1, 2, 3; 4, 5, 6; 7, 8, 9]就展示了一个3×3的网格布局，意味着存在三个点，且每个点均包含三个坐标值。

In MATLAB, plane grid data is often represented in the form of a coordinate matrix. Specifically, each row of the matrix represents the coordinates of a grid point. For example, the matrix X = [1, 2, 3; 4, 5, 6; 7, 8, 9] shows a 3×3 grid layout, which means there are three points, and each point contains three coordinate values.

(2)网格生成(Mesh Generation)

1. meshgrid函数(meshgrid function)

meshgrid函数是生成二维网格的得力工具，它为二维空间数据的可视化和处理奠定了基础。当你需要在二维空间中绘制图形，例如作为三维曲面图的底面，或者进行二维插值任务时，meshgrid显得尤为实用。其基本语法为[X, Y] = meshgrid(x, y)，其中x和y是两个向量，分别代表X轴和Y轴上的点。该函数会返回两个矩阵X和Y：X的每一行都是x的副本，而Y的每一列都是y的副本。如此，X和Y便共同构成了一个网格，这个网格能够方便地应用于plot、mesh、surf等绘图函数中。

The meshgrid function is a powerful tool for generating two-dimensional grids, which lays the foundation for the visualization and processing of two-dimensional spatial data. Meshgrid is particularly useful when you need to draw graphics in two-dimensional space, such as as the bottom surface of a three-dimensional surface plot, or perform two-dimensional interpolation tasks. Its basic syntax is [X, Y] = meshgrid(x, y), where x and y are two vectors representing points on the X-axis and Y-axis respectively. The function returns two matrices X and Y: each row of X is a copy of x, and each column of Y is a copy of y. In this way, X and Y together form a grid, which can be easily applied to drawing functions such as plot, mesh, and surf.

2. linspace函数(linspace function)

MATLAB中的linspace函数能够在指定的区间内生成具有线性间隔的向量，它非常适合创建等间距的数值序列，并广泛应用于绘图、数值分析、算法实现等多种场合。具体使用语法为y = linspace(start, stop, num)。

The linspace function in MATLAB can generate vectors with linear intervals within a specified interval. It is very suitable for creating equally spaced numerical sequences and is widely used in various occasions such as drawing, numerical analysis, and algorithm implementation. The specific syntax is y = linspace(start, stop, num).

3. ndgrid函数(ndgrid function)

在MATLAB中，ndgrid函数用于生成多维网格，这在进行多维插值、数值积分或任何需要多维网格数据的操作时非常有用。ndgrid可以生成一个或多个维度的网格，并且可以很容易地与linspace或colon操作符结合使用。[X1, X2, …, Xn] = ndgrid(x1, x2, …, xn),例如，

In MATLAB, the ndgrid function is used to generate multidimensional grids, which is very useful when doing multidimensional interpolation, numerical integration, or any operation that requires multidimensional grid data. ndgrid can generate grids of one or more dimensions and can be easily combined with linspace or colon operators. [X1, X2, …, Xn] = ndgrid(x1, x2, …, xn), For example,

这将生成三个三维矩阵X、Y和Z，它们可以用于三维空间中的网格绘制或数值计算。

This will generate three three-dimensional matrices X, Y, and Z, which can be used for grid drawing or numerical calculations in three-dimensional space.

三、相关函数(Related functions)

(1) mesh函数和surf函数(mesh function and surf function)

mesh(x, y, z, c)为三维网格图，surf(x, y, z, c)为三维曲面图。一般 x，y， z 一般为同型矩阵，其中，x、y是网格坐标矩阵，z是网格点上的高度矩阵，c 用于指定在不同高度下的曲面颜色。c 省略时，颜色的设定正比于图形的高度。

mesh(x, y, z, c) is a 3D mesh graph, surf(x, y, z, c) is a 3D surface graph. Generally, x, y, and z are matrices of the same type, where x and y are grid coordinate matrices, z is the height matrix at the grid points, and c is used to specify the surface color at different heights. When c is omitted, the color setting is proportional to the height of the graph.

mesh(z, c)和surf(z, c)为mesh函数和surf函数的其他调用格式。当x、y省略时，z矩阵的第2维下标当作x轴坐标，z矩阵的第1维下标当作y轴坐标。

mesh(z, c) and surf(z, c) are other calling formats of mesh and surf functions. When x and y are omitted, the second dimension subscript of z matrix is regarded as the x-axis coordinate, and the first dimension subscript of z matrix is regarded as the y-axis coordinate.

(2)meshc, meshz, surfc, surfl函数(meshc, meshz, surfc, surfl functions)

meshc函数用于绘制三维网格线图，并在网格的轮廓上添加颜色编码的等高线。meshz函数用于在mesh函数绘制的网格图上，用不同颜色的网格线表示不同高度的Z值。surfc函数用于在三维曲面图上添加等高线。surfl函数用于在三维曲面图上添加等高线，并使用线条来连接等高线上的点。接下来我们通过一个列子来看看他们具体的区别。

The meshc function is used to draw a 3D mesh line graph and add color-coded contour lines to the outline of the mesh. The meshz function is used to use different colors of mesh lines to represent the Z values of different heights on the mesh graph drawn by the mesh function. The surfc function is used to add contour lines to a 3D surface graph. The surfl function is used to add contour lines to a 3D surface graph and use lines to connect the points on the contour lines. Next, let’s take a look at their specific differences through an example.

(3) sphere函数和cylinder函数(sphere function and cylinder function)

sphere函数用于绘制球体。它可以生成球体的表面网格，并允许用户指定球体的半径和分辨率。常见的代码为[Theta, Phi] = sphere(n);surf(Theta, Phi, r);其中，n为一个正整数，表示生成的网格的精细度。n越大，网格越精细。Theta和Phi分别代表球体的经纬度坐标。r为球体的半径，默认为1。

The sphere function is used to draw a sphere. It can generate a surface mesh of a sphere and allow the user to specify the radius and resolution of the sphere. The common code is [Theta, Phi] = sphere(n);surf(Theta, Phi, r); where n is a positive integer, indicating the fineness of the generated mesh. The larger n is, the finer the mesh is. Theta and Phi represent the latitude and longitude coordinates of the sphere, respectively. r is the radius of the sphere, which defaults to 1.

cylinder函数用于绘制圆柱体。它生成圆柱体的表面网格，允许用户指定圆柱体的高度和半径，以及网格的精细度。基本的代码为[X, Y, Z] = cylinder(n);surf(X, Y, Z)。其中，n：一个正整数，表示生成的网格的精细度。n越大，网格越精细。X、Y、Z：分别代表圆柱体表面的坐标点。

The cylinder function is used to draw a cylinder. It generates a surface mesh of the cylinder, allowing the user to specify the height and radius of the cylinder, as well as the fineness of the mesh. The basic code is [X, Y, Z] = cylinder(n);surf(X, Y, Z). Among them, n: a positive integer, indicating the fineness of the generated mesh. The larger n is, the finer the mesh. X, Y, Z: represent the coordinate points on the surface of the cylinder respectively.

(4) peaks函数(peaks function)

MATLAB中的peaks函数用于生成一个包含多个山峰形状的二维矩阵，这个矩阵通常用于测试和演示各种数值方法，比如插值、数值积分、数值微分、优化算法等。peaks函数生成的矩阵通常被称为”peaks”函数的图形或数据。与其他函数不同的是，peaks函数不需要输入参数，它默认生成一个大小为17×17的矩阵。

The peaks function in MATLAB is used to generate a two-dimensional matrix containing multiple peak shapes. This matrix is often used to test and demonstrate various numerical methods, such as interpolation, numerical integration, numerical differentiation, optimization algorithms, etc. The matrix generated by the peaks function is often referred to as the graph or data of the “peaks” function. Unlike other functions, the peaks function does not require input parameters and generates a matrix of size 17×17 by default.

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翻译：谷歌翻译

参考资料：百度、CSDN博客

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