smooth shading of patches in 3D - partially correct

I am trying to render a nice 3d figure of a Voronoi cell by plotting the faces using the patch function and gouraud lighting to get smooth shading of the surfaces. The vertex normals are computed by a weighted average of the face (polygon) normals using the face areas as weights. It all looks relatively nice except that some faces do not have any light reflection. I cannot understand why I do not get the proper shading, and I would be very grateful any pointers to solve this.

Here is how it looks with the associated vertex normals drawn

and here is the code to produce it:

fig = figure();
ax = axes('Parent',fig);

p=patch('Faces',F,'Vertices',V); 
p.Parent = ax;
hold(ax,'on');
p.FaceColor = [0.95 0.95 0.95];  
p.VertexNormals = vnorm;

for n = 1:nqV      
    q=quiver3(V(n,1),V(n,2),V(n,3), vnorm(n,1), vnorm(n,2), vnorm(n,3) );

      q.Color = [0.8 0.3 0.3];
      q.LineWidth = 1.2;      
      q.MaxHeadSize = 2;
      q.Parent = ax;
      q.AutoScale = 'off';      
  end

   view([-128 11])
   axis equal

lighting gouraud

grid on

with matrices

F = [34    29    30    31    32    33    28     8     1     7
    17    16    15     3    13   NaN   NaN   NaN   NaN   NaN
    17    18    19     2    24    16   NaN   NaN   NaN   NaN
    13    17    18     5    11   NaN   NaN   NaN   NaN   NaN
     7     1    19    18     5   NaN   NaN   NaN   NaN   NaN
    16    24    25    14    15   NaN   NaN   NaN   NaN   NaN
    25    24     2    22   NaN   NaN   NaN   NaN   NaN   NaN
    26    28    33    27    23    14    25    22   NaN   NaN
    31    30     6    21   NaN   NaN   NaN   NaN   NaN   NaN
    21    31    32    27    23     4    20   NaN   NaN   NaN
    12    29    30     6     9   NaN   NaN   NaN   NaN   NaN
    20    21     6     9   NaN   NaN   NaN   NaN   NaN   NaN
    33    27    32   NaN   NaN   NaN   NaN   NaN   NaN   NaN
    22    26     8     1    19     2   NaN   NaN   NaN   NaN
    12    10     4    20     9   NaN   NaN   NaN   NaN   NaN
    28     8    26   NaN   NaN   NaN   NaN   NaN   NaN   NaN
    10     3    15    14    23     4   NaN   NaN   NaN   NaN
    34    11     5     7   NaN   NaN   NaN   NaN   NaN   NaN
    12    29    34    11    13     3    10   NaN   NaN   NaN];

V = [41.3411   42.6534   56.4570
   42.9971   42.6986   56.0056
   45.0957   42.6232   59.0728
   43.0092   39.8638   59.3526
   42.6463   44.4461   57.7151
   42.1427   40.7134   60.4942
   41.2465   44.0467   57.8011
   41.5264   41.3264   56.3131
   42.2348   40.7407   60.5345
   44.1656   41.6457   60.0810
   42.8749   44.4715   57.7761
   42.5611   41.2097   60.7129
   44.1996   44.2797   57.7430
   44.5492   41.5642   57.9694
   45.1375   42.5838   58.7361
   44.6270   43.5925   57.2962
   44.3424   44.0581   57.5101
   43.1233   43.3174   56.4938
   42.9432   42.7561   56.0245
   42.8686   39.8425   59.4215
   42.0284   39.7133   59.2071
   42.9318   42.5213   56.0112
   43.1946   39.8895   58.5593
   44.5263   43.4475   57.1530
   44.4736   41.7693   57.7335
   41.6762   41.2894   56.2694
   42.4125   39.7685   58.1382
   41.5866   41.0063   56.4636
   41.8281   41.6300   60.4530
   41.9439   40.8349   60.4245
   42.0070   39.7099   59.1804
   41.9873   39.7061   58.9383
   41.7631   40.2636   57.2521
   41.4068   43.5440   58.8224];

vnorm = [-0.9742    0.0570   -0.2185
    0.3383    0.0552   -0.9394
    0.4967    0.4317    0.7529
    0.6578   -0.6820    0.3196
   -0.1656    0.8073   -0.5664
   -0.2402   -0.6126    0.7530
   -0.9892    0.1186   -0.0857
   -0.9902   -0.1361   -0.0303
    0.2504   -0.6009    0.7591
    0.4696    0.2665    0.8417
    0.0978    0.7705    0.6299
    0.1726    0.5025    0.8472
    0.2059    0.7654    0.6097
    0.6904   -0.6060   -0.3951
    0.9321   -0.3617    0.0181
    0.8390    0.2851   -0.4635
    0.4482    0.7058   -0.5487
   -0.0528    0.6842   -0.7274
   -0.1447    0.5425   -0.8275
    0.2958   -0.7799    0.5516
    0.0018   -0.9486    0.3166
    0.4266   -0.4843   -0.7639
    0.6181   -0.7014   -0.3551
    0.7159   -0.0391   -0.6971
    0.5699   -0.4910   -0.6589
    0.3608   -0.5306   -0.7670
    0.3938   -0.6983   -0.5977
   -0.7569   -0.5513   -0.3510
   -0.6932    0.3597    0.6245
   -0.9805   -0.1564    0.1187
   -0.9669   -0.2384    0.0911
   -0.9626   -0.2614    0.0707
   -0.7447   -0.5696   -0.3478
   -0.6775    0.4064    0.6130];

Answer 1

[Mike Shives]

Also interested in this

Answer 2

[darova]

Changed the script a bit

clc,clear

run data
p = patch('Faces',F,'Vertices',V); 
set(p, 'FaceColor', [0.95 0.95 0.95])
grid on
hold on

q = quiver3(V(:,1),V(:,2),V(:,3), vnorm(:,1), vnorm(:,2), vnorm(:,3) );
hold off
set(q, 'Color', [0.8 0.3 0.3])
set(q, 'LineWidth', 1.2)
set(q, 'MaxHeadSize', 2)
set(q, 'AutoScale', 'off')

view([-128 11])
axis equal
lighting gouraud
light('Position',[0 -2 1])

It produces this:

[Filip]

Thanks for reviving this old problem. You removed the for-loop and changed the position of the light source? But this does not address the real problem; the cell should have smooth-looking shades around the corners (edges).

[darova]

You mean Linesmoothing?

Why don't like this image

[Filip]

I don't know what your are referring to. This is the desired result (Image from this ref, read it to understand the problem we are trying to solve here).

[darova]

I think it's a succes

clc,clear
run data
p = patch('Faces',F,'Vertices',V); 
set(p, 'FaceColor', [0.95 0.95 0.95])
% set(p, 'VertexNOrmals',vnorm);
set(p, 'BackFaceLighting', 'unlit')
grid on
hold on
q = quiver3(V(:,1),V(:,2),V(:,3), vnorm(:,1), vnorm(:,2), vnorm(:,3) );
hold off
set(q, 'Color', [0.8 0.3 0.3])
set(q, 'LineWidth', 1.2)
set(q, 'MaxHeadSize', 2)
set(q, 'AutoScale', 'off')
view([-128 11])
axis equal
% lighting gouraud
light('Position',[56 30 60])

[darova]

What we gonna about this?

Is this answer good?

[Filip]

I can't accept your answer as a solution as it does not solve the stated problem. If you do not agree, then argue why you think it does.

[darova]

Isn't that you wanted?

[Filip]

No. There is no smooth shading. I can't make myself more clearer than what I have already done.

Answer 3

[Mike Shives]

Filip.

I may not get the chance to look into it today, but I have a suspicion that if you manually specify the patch FaceNormals it might help. (I think the lighting may be relying on the VertexNormals.. which looks wrong.)