MATLAB——patch绘制长方体(cuboid)+长方体平移+长方体旋转

待我称王封你为后i 2024-04-19 09:31 0阅读 0赞

### 文章目录 ###

*  围绕着中心点旋转
 *   *  代码
     *  效果
 *  围绕原点旋转
 *   *  代码
     *  效果
 *  区别
 *  其他方法

# 围绕着中心点旋转 #

## 代码 ##

1.  新建一个脚本命名为：drawCuboid.m
    
        function [CuboidHandle, verts, facs] = drawCuboid(varargin)
        % Draw Cuboid
        % Draw a Cuboid using 8 rectangular faces. Places Cuboid Into Current Figure
        %
        % Inputs (SL, CV, EA, colr, alph)
        % ----------------
        % SL    - [X;Y;Z] Length of Cuboid Side (SL - SideLength)
        % CV    - [X;Y;Z] Center of volume
        % EA    - [Yaw(Z-axis);Pitch(y-axis);Roll(x-axis)] Euler/Rotation angles [radians]
        % colr  - Color of cuboid; string (ex. 'r','b','g') or vector [R G B]
        % alph  - Alpha transparency value of cuboid
        %
        % Outputs (CuboidHandle, verts, facs)
        % ----------------
        % CuboidHandle  = Handle for Patch Object
        % verts         = 3x8 XYZ Vertices
        % facs          = 6x4 Order of faces
        %
        %% Number of inputs and assign defaults if not specified
        % Define Default Values
        SL = [1;1;1];   CV = [0;0;0];   EA = [0;0;0];   colr = [0.5 0.5 0.5];   alph = 0.5;
        switch nargin
            case 0
                % All Inputs Empty Using Default Values
            case 1
                SL = varargin{ 1};
            case 2
                SL = varargin{ 1};   CV = varargin{ 2};
            case 3
                SL = varargin{ 1};   CV = varargin{ 2};   EA = varargin{ 3};
            case 4
                SL = varargin{ 1};   CV = varargin{ 2};   EA = varargin{ 3};   colr = varargin{ 4};
            case 5
                SL = varargin{ 1};   CV = varargin{ 2};   EA = varargin{ 3};   colr = varargin{ 4};     alph = varargin{ 5};
            otherwise
                error('Invalid number of inputs')
        end
        %% Form ZYX Rotation Matrix
        % Calculate Sines and Cosines
        c1 = cos(EA(1));	s1 = sin(EA(1));
        c2 = cos(EA(2));	s2 = sin(EA(2));
        c3 = cos(EA(3));	s3 = sin(EA(3));
        % Calculate Matrix
        R = [c1*c2           -c2*s1          s2
             c3*s1+c1*s2*s3  c1*c3-s1*s2*s3  -c2*s3
             s1*s3-c1*c3*s2  c3*s1*s2+c1*s3  c2*c3]';
        %% Create Vertices
        x = 0.5*SL(1)*[-1 1 1 -1 -1 1 1 -1]';
        y = 0.5*SL(2)*[1 1 1 1 -1 -1 -1 -1]';
        z = 0.5*SL(3)*[-1 -1 1 1 1 1 -1 -1]';
        %% Create Faces
        facs = [1 2 3 4
                5 6 7 8
                4 3 6 5
                3 2 7 6
                2 1 8 7
                1 4 5 8];
        %% Rotate and Translate Vertices
        verts = zeros(3,8);
        for i = 1:8
            verts(1:3,i) = R*[x(i);y(i);z(i)]+CV;
        end
        %% Draw Patch Object
        CuboidHandle = patch('Faces',facs,'Vertices',verts','FaceColor',colr,'FaceAlpha',alph);
        end
2.  新建另外一个脚本，输入：
    
        drawCuboid([2;2;2],[2;2;2],[30/180*pi;0;0],'g',0.1)
        drawCuboid([2;2;2],[2;2;2],[0;0;0],'b',0.1)

## 效果 ##

下面两幅图中绿色立方体为原始立方体，紫色立方体为绕立方体中心顺时针旋转30°后的立方体。

图1 俯视图  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE2Nzc1Mjkz_size_16_color_FFFFFF_t_70]  
图2 旋转图  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE2Nzc1Mjkz_size_16_color_FFFFFF_t_70 1]

# 围绕原点旋转 #

## 代码 ##

1.  新建一个脚本命名为：drawCuboid.m
    
        function [CuboidHandle, verts, facs] = drawCuboid(varargin)
        % Draw Cuboid
        % Draw a Cuboid using 8 rectangular faces. Places Cuboid Into Current Figure
        %
        % Inputs (SL, CV, EA, colr, alph)
        % ----------------
        % SL    - [X;Y;Z] Length of Cuboid Side (SL - SideLength)
        % CV    - [X;Y;Z] Center of volume
        % EA    - [Yaw(Z-axis);Pitch(y-axis);Roll(x-axis)] Euler/Rotation angles [radians]
        % colr  - Color of cuboid; string (ex. 'r','b','g') or vector [R G B]
        % alph  - Alpha transparency value of cuboid
        %
        % Outputs (CuboidHandle, verts, facs)
        % ----------------
        % CuboidHandle  = Handle for Patch Object
        % verts         = 3x8 XYZ Vertices
        % facs          = 6x4 Order of faces
        %
        %% Number of inputs and assign defaults if not specified
        % Define Default Values
        SL = [1;1;1];   CV = [0;0;0];   EA = [0;0;0];   colr = [0.5 0.5 0.5];   alph = 0.5;
        switch nargin
            case 0
                % All Inputs Empty Using Default Values
            case 1
                SL = varargin{ 1};
            case 2
                SL = varargin{ 1};   CV = varargin{ 2};
            case 3
                SL = varargin{ 1};   CV = varargin{ 2};   EA = varargin{ 3};
            case 4
                SL = varargin{ 1};   CV = varargin{ 2};   EA = varargin{ 3};   colr = varargin{ 4};
            case 5
                SL = varargin{ 1};   CV = varargin{ 2};   EA = varargin{ 3};   colr = varargin{ 4};     alph = varargin{ 5};
            otherwise
                error('Invalid number of inputs')
        end
        %% Form ZYX Rotation Matrix
        % Calculate Sines and Cosines
        c1 = cos(EA(1));	s1 = sin(EA(1));
        c2 = cos(EA(2));	s2 = sin(EA(2));
        c3 = cos(EA(3));	s3 = sin(EA(3));
        % Calculate Matrix
        R = [c1*c2           -c2*s1          s2
             c3*s1+c1*s2*s3  c1*c3-s1*s2*s3  -c2*s3
             s1*s3-c1*c3*s2  c3*s1*s2+c1*s3  c2*c3]';
        %% Create Vertices
        x = 0.5*SL(1)*[-1 1 1 -1 -1 1 1 -1]';
        y = 0.5*SL(2)*[1 1 1 1 -1 -1 -1 -1]';
        z = 0.5*SL(3)*[-1 -1 1 1 1 1 -1 -1]';
        %% Create Faces
        facs = [1 2 3 4
                5 6 7 8
                4 3 6 5
                3 2 7 6
                2 1 8 7
                1 4 5 8];
        %% Rotate and Translate Vertices
        verts = zeros(3,8);
        for i = 1:8
            verts(1:3,i) = R*[x(i);y(i);z(i)]+R*CV;
        end
        %% Draw Patch Object
        CuboidHandle = patch('Faces',facs,'Vertices',verts','FaceColor',colr,'FaceAlpha',alph);
        end
    
    1.  新建另外一个脚本，输入：
    
        drawCuboid([2;2;2],[2;2;2],[30/180*pi;0;0],'g',0.1)
        drawCuboid([2;2;2],[2;2;2],[0;0;0],'b',0.1)

## 效果 ##

下面两幅图中绿色立方体为原始立方体，紫色立方体为原点(0,0,0),顺时针旋转30°后的立方体。  
图1 俯视图  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE2Nzc1Mjkz_size_16_color_FFFFFF_t_70 2]

图2 旋转图  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE2Nzc1Mjkz_size_16_color_FFFFFF_t_70 3]

# 区别 #

绕立方体中心旋转时计算公式如下，其中R是旋转矩阵

for i = 1:8
    	    verts(1:3,i) = R*[x(i);y(i);z(i)]+CV;
    	end

绕原点旋转时计算公式如下，其中R是旋转矩阵

for i = 1:8
    	    verts(1:3,i) = R*[x(i);y(i);z(i)]+R*CV;
    	end

# 其他方法 #

还可以使用MATLAB提供的[multicuboid函数][multicuboid]画立方体，但是不太清楚如何实现平移、旋转等变换。详情请看资料[multicuboid函数][multicuboid]。

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE2Nzc1Mjkz_size_16_color_FFFFFF_t_70]: https://image.dandelioncloud.cn/pgy_files/images/2024/04/18/d87076cbb84e4d9c835f7274a3905291.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE2Nzc1Mjkz_size_16_color_FFFFFF_t_70 1]: https://image.dandelioncloud.cn/pgy_files/images/2024/04/18/783b304e31764b10a3372e5f0cb368b5.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE2Nzc1Mjkz_size_16_color_FFFFFF_t_70 2]: https://image.dandelioncloud.cn/pgy_files/images/2024/04/18/a6eb169530dd445eae4ba51e5122de40.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzE2Nzc1Mjkz_size_16_color_FFFFFF_t_70 3]: https://image.dandelioncloud.cn/pgy_files/images/2024/04/18/147b85d098bf4e79bff90e1ac1bde088.png
[multicuboid]: https://blog.csdn.net/qq_16775293/article/details/100830966