Hi,

patch may not display a polygon.  Pls see the attached figure files.  Thanks,


The small example demonstrates a compatibility issue, or an error.

% CCW order, P0 is estimated from plane_1=@(x) [1 2 3 ]*x-06; 

P0=[6  4 -4
    0 -2 -4
    0 -6  6
    6 -6  3];
 

The P0 patch display, two triangles with one point intersection, is not a polygon and is incompatible with matlab, i.e., two triangles with line 1-3 intersection.   It does not matter if the intersection is line 1-3 or line 2-4, the output is a polygon.  

figure;   hold on;
for ii=1:size(P0,1), text(P0(ii,1), P0(ii,2), P0(ii,3), num2str(ii), 'fontsize', 20); end ;
patch(P0(:,1), P0(:,2), P0(:,3), 'r', 'facealpha', 0.1);  xlabel('x'); ylabel('y');
saveas(gcf, 'patch_P0.ofig');
%view([235 30]) 

A minor modification to P0(1,2) (y=3, instead y=4) change the display completely.  
   
figure;  
subplot(1,2,1); hold on;
for ii=1:size(P0,1), text(P0(ii,1), P0(ii,2), P0(ii,3), num2str(ii), 'fontsize', 20); end
patch(P0(:,1), P0(:,2), P0(:,3), 'r', 'facealpha', 0.1); hold on; xlabel('x'); ylabel('y');
subplot(1,2,2); hold on;
P0(1,2)=3;
for ii=1:size(P0,1), text(P0(ii,1), P0(ii,2), P0(ii,3), num2str(ii), 'fontsize', 20); end
patch(P0(:,1), P0(:,2), P0(:,3), 'r', 'facealpha', 0.1); hold on; xlabel('x'); ylabel('y'); title('Modified P0(1,2)')

saveas(gcf, 'patch_P0_update.ofig');