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

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

图2 旋转图

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
   

   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，紫色立方体为原点(0,0,0),顺时针旋转30°后的立方体。
图1 俯视图

图2 旋转图

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。