MATLAB 动画仿真
1 利用MATLAB进行图形处理
matlab调用画图plot函数族，返回该函数的句柄，通过句柄可以修改图形的属性。
t = 0:20;
plot_handle = plot(t, sin(t));
// 修改图形属性
set(plot_handle, 'YData', cos(t));
plot_handle1 = plot(t,sin(t));
hold on;
plot_handle2 = plot(t, cos(t));
set(plot_handle2,'YData', cos(2*t));总结：fill命令来模拟倒立摆
查看plot函数的属性：
get(plot_handle)
AlignVertexCenters: ‘off’
Annotation: [1x1 matlab.graphics.eventdata.Annotation]
BeingDeleted: ‘off’
BusyAction: ‘queue’
ButtonDownFcn: ”
Children: []
Clipping: ‘on’
Color: [0 0.4470 0.7410]
CreateFcn: ”
DeleteFcn: ”
DisplayName: ”
HandleVisibility: ‘on’
HitTest: ‘on’
Interruptible: ‘on’
LineStyle: ‘-’
LineWidth: 0.5000
Marker: ‘none’
MarkerEdgeColor: ‘auto’
MarkerFaceColor: ‘none’
MarkerSize: 6
Parent: [1x1 Axes]
PickableParts: ‘visible’
Selected: ‘off’
SelectionHighlight: ‘on’
Tag: ”
Type: ‘line’
UIContextMenu: []
UserData: []
Visible: ‘on’
XData: [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20]
XDataMode: ‘manual’
XDataSource: ”
YData: [1x21 double]
YDataSource: ”
ZData: [1x0 double]
ZDataSource: ”
2 动画举例：倒立摆
对于倒立摆的数学建模参考建模方程
倒立摆的四个角：
杆的两端：
matlab画出图形：
利用drawBase画图形，画杆和板子（几座）的图形
function handle = drawBase(y, width, height, gap, handle, mode)
X = [y - width/2, y + width/2, y + width/2; y - width/2];
Y = [gap, gap, gap+height, gap+height];
if isempty(handle)
handle = fill(X,Y,'m','EraseMode', mode);
else
set(handle,'XData',X,'YData',Y);
endhandle既做输入也做输出
绘制杆的代码：
function handle = drawRod(y, theta, L, gap, height, handle, mode)
X = [y, y+L*sin(theta)];
Y = [gap+height, gap + height + L*cos(theta)];
if isempty(handle)
handle = plot(X, Y, 'g', 'EraseMode', mode);
else
set(handle,'XData',X,'YData',Y);
endEraseMode擦出模式：normal、non、或者background
function drawPendulum(u,L,gap,width,height)
% process inputs to function
y = u(1);
theta = u(2);
t = u(3);
% define persistent variables
persistent base_handle
persistent rod_handle
% first time function is called, initialize plot and persistent vars
if t==0,
figure(1), clf
track_width=3;
plot([-track_width,track_width],[0,0],'k'); % plot track
hold on
base_handle = drawBase(y, width, height, gap, [], 'normal');
rod_handle = drawRod(y, theta, L, gap, height, [], 'normal');
axis([-track_width, track_width, -L, 2*track_width-L]);
% at every other time step, redraw base and rod
else
drawBase(y, width, height, gap, base_handle);
drawRod(y, theta, L, gap, height, rod_handle);
end
end
%
%=======================================================================
% drawBase
% draw the base of the pendulum
% return handle if 3rd argument is empty, otherwise use 3rd arg as handle
%=======================================================================
%
function handle = drawBase(y, width, height, gap, handle, mode)
X = [y-width/2, y+width/2, y+width/2, y-width/2];
Y = [gap, gap, gap+height, gap+height];
if isempty(handle),
handle = fill(X,Y,'m', 'EraseMode', mode);
%handle = plot(X,Y,'m', 'EraseMode', mode);
else
set(handle,'XData',X,'YData',Y);
drawnow
end
end
%
%=======================================================================
% drawRod
% draw the pendulum rod
% return handle if 3rd argument is empty, otherwise use 3rd arg as handle
%=======================================================================
%
function handle = drawRod(y, theta, L, gap, height, handle, mode)
X = [y, y+L*sin(theta)];
Y = [gap+height, gap + height + L*cos(theta)];
if isempty(handle),
handle = plot(X, Y, 'g', 'EraseMode', mode);
else
set(handle,'XData',X,'YData',Y);
drawnow
end
end3 动画举例：绘制航天器
function drawSpacecraft(uu,pts)
% process inputs to function
pn = uu(1); % inertial North position
pe = uu(2); % inertial East position
pd = uu(3); % inertial Down position
u = uu(4); % body frame velocities
v = uu(5);
w = uu(6);
phi = uu(7); % roll angle
theta = uu(8); % pitch angle
psi = uu(9); % yaw angle
p = uu(10); % roll rate
q = uu(11); % pitch rate
r = uu(12); % yaw rate
t = uu(13); % time
% define persistent variables
persistent spacecraft_handle;
% first time function is called, initialize plot and persistent vars
if t<=0.1,
figure(1), clf
spacecraft_handle = drawSpacecraftBody(pts,pn,pe,pd,phi,theta,psi, [], 'normal');
title('Spacecraft')
xlabel('East')
ylabel('North')
zlabel('-Down')
view(32,47) % set the vieew angle for figure
axis([-10,10,-10,10,-10,10]);
hold on
% at every other time step, redraw base and rod
else
drawSpacecraftBody(pts,pn,pe,pd,phi,theta,psi, spacecraft_handle);
end
end
%=======================================================================
% drawSpacecraftBody
% return handle if 7th argument is empty, otherwise use 7th arg as handle
%=======================================================================
%
function handle = drawSpacecraftBody(NED,pn,pe,pd,phi,theta,psi, handle, mode)
NED = rotate(NED,phi,theta,psi); % rotate spacecraft by phi, theta, psi
NED = translate(NED,pn,pe,pd); % translate spacecraft
% transform vertices from NED to XYZ (for matlab rendering)
R = [...
0, 1, 0;...
1, 0, 0;...
0, 0, -1;...
];
XYZ = R*NED;
% plot spacecraft
if isempty(handle),
handle = plot3(XYZ(1,:),XYZ(2,:),XYZ(3,:),'EraseMode', mode);
else
set(handle,'XData',XYZ(1,:),'YData',XYZ(2,:),'ZData',XYZ(3,:));
drawnow
end
end
%%%%%%%%%%%%%%%%%%%%%%%
function XYZ=rotate(XYZ,phi,theta,psi)
% define rotation matrix
R_roll = [...
1, 0, 0;...
0, cos(phi), -sin(phi);...
0, sin(phi), cos(phi)];
R_pitch = [...
cos(theta), 0, sin(theta);...
0, 1, 0;...
-sin(theta), 0, cos(theta)];
R_yaw = [...
cos(psi), -sin(psi), 0;...
sin(psi), cos(psi), 0;...
0, 0, 1];
R = R_yaw*R_pitch*R_roll;
% rotate vertices
XYZ = R*XYZ;
end
% end rotateVert
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% translate vertices by pn, pe, pd
function XYZ = translate(XYZ,pn,pe,pd)
XYZ = XYZ + repmat([pn;pe;pd],1,size(XYZ,2));
end
% end translateXYZ
4 动画举例：使用顶点和面的航天器
function drawSpacecraft(uu,V,F,patchcolors)
% process inputs to function
pn = uu(1); % inertial North position
pe = uu(2); % inertial East position
pd = uu(3);
u = uu(4);
v = uu(5);
w = uu(6);
phi = uu(7); % roll angle
theta = uu(8); % pitch angle
psi = uu(9); % yaw angle
p = uu(10); % roll rate
q = uu(11); % pitch rate
r = uu(12); % yaw rate
t = uu(13); % time
% define persistent variables
persistent spacecraft_handle;
% first time function is called, initialize plot and persistent vars
if t==0,
figure(1), clf
spacecraft_handle = drawSpacecraftBody(V,F,patchcolors,...
pn,pe,pd,phi,theta,psi,...
[],'normal');
title('Spacecraft')
xlabel('East')
ylabel('North')
zlabel('-Down')
view(32,47) % set the vieew angle for figure
axis([-10,10,-10,10,-10,10]);
hold on
% at every other time step, redraw base and rod
else
drawSpacecraftBody(V,F,patchcolors,...
pn,pe,pd,phi,theta,psi,...
spacecraft_handle);
end
end
%=======================================================================
% drawSpacecraft
% return handle if 3rd argument is empty, otherwise use 3rd arg as handle
%=======================================================================
%
function handle = drawSpacecraftBody(V,F,patchcolors,...
pn,pe,pd,phi,theta,psi,...
handle,mode)
V = rotate(V', phi, theta, psi)'; % rotate spacecraft
V = translate(V', pn, pe, pd)'; % translate spacecraft
% transform vertices from NED to XYZ (for matlab rendering)
R = [...
0, 1, 0;...
1, 0, 0;...
0, 0, -1;...
];
V = V*R;
if isempty(handle),
handle = patch('Vertices', V, 'Faces', F,...
'FaceVertexCData',patchcolors,...
'FaceColor','flat',...
'EraseMode', mode);
else
set(handle,'Vertices',V,'Faces',F);
drawnow
end
end
%%%%%%%%%%%%%%%%%%%%%%%
function XYZ=rotate(XYZ,phi,theta,psi);
% define rotation matrix
R_roll = [...
1, 0, 0;...
0, cos(phi), -sin(phi);...
0, sin(phi), cos(phi)];
R_pitch = [...
cos(theta), 0, sin(theta);...
0, 1, 0;...
-sin(theta), 0, cos(theta)];
R_yaw = [...
cos(psi), -sin(psi), 0;...
sin(psi), cos(psi), 0;...
0, 0, 1];
R = R_yaw*R_pitch*R_roll;
% rotate vertices
XYZ = R*XYZ;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% translate vertices by pn, pe, pd
function XYZ = translate(XYZ,pn,pe,pd)
XYZ = XYZ + repmat([pn;pe;pd],1,size(XYZ,2));
end