圍繞着中心點旋轉
代碼
-
新建一個腳本命名爲：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 -
新建另外一個腳本，輸入：
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
下面兩幅圖中綠色立方體爲原始立方體，紫色立方體爲繞立方體中心順時針旋轉30°後的立方體。
圖1 俯視圖
圖2 旋轉圖
圍繞原點旋轉
代碼
- 新建一個腳本命名爲：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- 新建另外一個腳本，輸入：
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
下面兩幅圖中綠色立方體爲原始立方體，紫色立方體爲原點(0,0,0),順時針旋轉30°後的立方體。
圖1 俯視圖
圖2 旋轉圖
區別
繞立方體中心旋轉時計算公式如下，其中R是旋轉矩陣
for i = 1:8
verts(1:3,i) = R*[x(i);y(i);z(i)]+CV;
end
繞原點旋轉時計算公式如下，其中R是旋轉矩陣
for i = 1:8
verts(1:3,i) = R*[x(i);y(i);z(i)]+R*CV;
end
其他方法
還可以使用MATLAB提供的multicuboid函數畫立方體，但是不太清楚如何實現平移、旋轉等變換。詳情請看資料multicuboid函數。