Plotting a plane in 3d:

Question

abhimanyu dubey 2020-4-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/518603-plotting-a-plane-in-3d

评论： abhimanyu dubey 2020-4-17

I'm trying to visualize the column space of a matrix before and after Row Reduction. Now the program is throwing error, when I've defined function handles seperately and then tried using them in fmesh function. Can anyone explain me why this is not working, or atleast point me in the right direction, where can I find this, and understand, where I'm going wrong here:

Your help is very much appreciated.

Thanks

%% MATRIX SPACES B4 AND AFTER ROW REDUCTION:
clear ; clc ; 
% Create the Matrix: (matrix M)
M = [3,2 ; 5,7 ; 9,1] ; 
% And it's Row Reduced Form:
Mr = rref(M) ; 
% Now let's see how Columns Space of the matrix M changes after it's
% converted into it's rref form:
figure(14) ; clf ; hold on ; 
% ===================== Why This Code is Not working =================
% % 
% % funx1 = @(s,t) M(1,1)  *s  + M( 1,2)*t ; 
% % funx2 = @(s,t) Mr(1,1) *s  + Mr(1,2)*t ; 
% % 
% % funy1 = @(s,t) M(2,1)  *s  + M( 2,2)*t ; 
% % funy2 = @(s,t) Mr(2,1) *s  + Mr(2,2)*t ;
% % 
% % funz1 = @(s,t)  M(3,1) *s +  M( 3,2)*t ; 
% % funz2 = @(s,t) Mr(3,1) *s +  Mr(3,2)*t ;
% h1 = fmesh( @(s,t)funx1 , @(s,t)funy1 , @(s,t)funz1  , repmat( [-1 1] , [1,3] )) ;
% h2 = fmesh( @(s,t)funx2 , @(s,t)funy2 , @(s,t)funz3  , repmat( [-1 1] , [1,3] )) ;
% ============================================================================
% Draw the planes spaned by M and Mr :
h1 = fmesh( @(s,t) M(1,1)  *s  + M( 1,2)*t  , ...
            @(s,t) M(2,1)  *s  + M( 2,2)*t  , ...
            @(s,t)  M(3,1) *s +  M( 3,2)*t  , ...
            [-0.25 , 0.25] ) ; 
        
h2 = fmesh( @(s,t) Mr(1,1)  *s  + Mr( 1,2)*t  , ...
            @(s,t) Mr(2,1)  *s  + Mr( 2,2)*t  , ...
            @(s,t) Mr(3,1) *s   + Mr( 3,2)*t  , ...
            [-1 , 1] ) ; 
        
 
% Adjusting colors for Visiblity:
set(h1 , 'facecolor' , '#77AC30' , 'LineStyle' , 'none' , 'FaceAlpha' , 0.9 ) ; % green
set(h2 , 'facecolor' , [0.4940 0.1840 0.5560] , 'LineStyle' , 'none' , 'FaceAlpha' , 0.9 ) ; % violet
% Draw Normalized Basis Vectors:
N = M / norm(M) ; 
% Vectors to Plot: v1 - vector 1:
v1 = [ N(:,1)'  ; [0 0 0] ] ; 
v2 = [ N(:,2)'  ; [0 0 0] ] ;
v3 = [ Mr(:,1)' ; [0 0 0] ] ;
v4 = [ Mr(:,2)' ; [0 0 0] ] ;
% Default Blue Color
plot3( v1(:,1) , v1(:,2) , v1(:,3) , 'color' , [0 0.4470 0.7410]      , 'linew' , 4 ) ; 
plot3( v2(:,1) , v2(:,2) , v2(:,3) , 'color' , [0 0.4470 0.7410]      , 'linew' , 4 ) ; 
% Yellow Color
plot3( v3(:,1) , v3(:,2) , v3(:,3) , 'color' , '#EDB120' , 'linew' , 4 ) ; 
plot3( v4(:,1) , v4(:,2) , v4(:,3) , 'color' , '#EDB120' , 'linew' , 4 ) ; 
xlabel('M_1') ; ylabel('M_2') ; zlabel('M_3') ; 
axis square ; grid on ; rotate3d on ; 
set(gca , 'fontsize' , 18 , 'fontweight' , 'bold') ;
title('\fontsize{25} Column Space of M And rref(M) :')
legend({'C(M)';'C(rref(M))'})

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Answer 1

Mehmed Saad 2020-4-17

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/518603-plotting-a-plane-in-3d#answer_426560

在 MATLAB Online 中打开

%% MATRIX SPACES B4 AND AFTER ROW REDUCTION:
clear ; clc ; 
% Create the Matrix: (matrix M)
M = [3,2 ; 5,7 ; 9,1] ; 
% And it's Row Reduced Form:
Mr = rref(M) ; 
% Now let's see how Columns Space of the matrix M changes after it's
% converted into it's rref form:
figure(14) ; clf ; hold on ; 
% ===================== Why This Code is Not working =================
% % 
funx1 = @(s,t) M(1,1)  *s  + M( 1,2)*t ; 
funx2 = @(s,t) Mr(1,1) *s  + Mr(1,2)*t ; 
funy1 = @(s,t) M(2,1)  *s  + M( 2,2)*t ; 
funy2 = @(s,t) Mr(2,1) *s  + Mr(2,2)*t ;
funz1 = @(s,t)  M(3,1) *s +  M( 3,2)*t ; 
funz3 = @(s,t) Mr(3,1) *s +  Mr(3,2)*t ;
h1 = fmesh( funx1 , funy1 , funz1  , repmat( [-1 1] , [1,2] )) ;
h2 = fmesh( funx2 , funy2 , funz3  , repmat( [-1 1] , [1,2] )) ;
% ============================================================================
% Draw the planes spaned by M and Mr :
h1 = fmesh( @(s,t) M(1,1)  *s  + M( 1,2)*t  , ...
            @(s,t) M(2,1)  *s  + M( 2,2)*t  , ...
            @(s,t)  M(3,1) *s +  M( 3,2)*t  , ...
            [-0.25 , 0.25] ) ; 
        
h2 = fmesh( @(s,t) Mr(1,1)  *s  + Mr( 1,2)*t  , ...
            @(s,t) Mr(2,1)  *s  + Mr( 2,2)*t  , ...
            @(s,t) Mr(3,1) *s   + Mr( 3,2)*t  , ...
            [-1 , 1] ) ; 
        
 
% Adjusting colors for Visiblity:
set(h1 , 'facecolor' , '#77AC30' , 'LineStyle' , 'none' , 'FaceAlpha' , 0.9 ) ; % green
set(h2 , 'facecolor' , [0.4940 0.1840 0.5560] , 'LineStyle' , 'none' , 'FaceAlpha' , 0.9 ) ; % violet
% Draw Normalized Basis Vectors:
N = M / norm(M) ; 
% Vectors to Plot: v1 - vector 1:
v1 = [ N(:,1)'  ; [0 0 0] ] ; 
v2 = [ N(:,2)'  ; [0 0 0] ] ;
v3 = [ Mr(:,1)' ; [0 0 0] ] ;
v4 = [ Mr(:,2)' ; [0 0 0] ] ;
% Default Blue Color
plot3( v1(:,1) , v1(:,2) , v1(:,3) , 'color' , [0 0.4470 0.7410]      , 'linew' , 4 ) ; 
plot3( v2(:,1) , v2(:,2) , v2(:,3) , 'color' , [0 0.4470 0.7410]      , 'linew' , 4 ) ; 
% Yellow Color
plot3( v3(:,1) , v3(:,2) , v3(:,3) , 'color' , '#EDB120' , 'linew' , 4 ) ; 
plot3( v4(:,1) , v4(:,2) , v4(:,3) , 'color' , '#EDB120' , 'linew' , 4 ) ; 
xlabel('M_1') ; ylabel('M_2') ; zlabel('M_3') ; 
axis square ; grid on ; rotate3d on ; 
set(gca , 'fontsize' , 18 , 'fontweight' , 'bold') ;
title('\fontsize{25} Column Space of M And rref(M) :')
legend({'C(M)';'C(rref(M))'})