How many normals are needed to have a smooth surface?

Question

I'm trying to draw a smooth cloth surface and I have a per-pixel shader. I expect to have a smooth surface but it's not the case. I think the problem comes from my normals.

The image show the surface drawn with multiple triangles. The surface is lit; the white zone are specular reflection.

Here is the way I calculate normals

ofVec3f v0(ps[i].pos.x, ps[i].pos.y, ps[i].pos.z);          
ofVec3f v3(ps[i+cols+1].pos.x, ps[i+cols+1].pos.y, ps[i+cols+1].pos.z);         
ofVec3f v1(ps[i+1].pos.x, ps[i+1].pos.y, ps[i+1].pos.z);
ofVec3f v2(ps[i+cols].pos.x, ps[i+cols].pos.y, ps[i+cols].pos.z);

    ofVec3f n0 = (v1-v0).cross(v3-v0);
    n0.normalize();
    ofVec3f n2 = (v0-v2).cross(v3-v2);      
    n2.normalize();
    ofVec3f n3 = (v0-v3).cross(v1-v3);      
    n3.normalize();
    ofVec3f n1 = -(v0-v1).cross(v3-v1);     
    n1.normalize();

Here is the code to draw my surface. It's a 64x64 array of double triangles

glBegin(GL_TRIANGLES);

for (int i=0; i<ps.size()-(cols+1); i++) { 
//  v0 - v1
//  | \  |
//  v2 - v3

// v0
glNormal3f(n0.x, n0.y, n0.z);
glVertex3f(ps[i].pos.x, ps[i].pos.y, ps[i].pos.z);

//v3
glNormal3f(n3.x, n3.y, n3.z);
glVertex3f(ps[i+cols+1].pos.x, ps[i+cols+1].pos.y, ps[i+cols+1].pos.z);


//v1
glNormal3f(n1.x, n1.y, n1.z);
glVertex3f(ps[i+1].pos.x, ps[i+1].pos.y, ps[i+1].pos.z);


//v0
glNormal3f(n0.x, n0.y, n0.z);
glVertex3f(ps[i].pos.x, ps[i].pos.y, ps[i].pos.z);

//v2
glNormal3f(n2.x, n2.y, n2.z);
glVertex3f(ps[i+cols].pos.x, ps[i+cols].pos.y, ps[i+cols].pos.z);

//v3
glNormal3f(n3.x, n3.y, n3.z);
glVertex3f(ps[i+cols+1].pos.x, ps[i+cols+1].pos.y, ps[i+cols+1].pos.z);

I don't know how many normals I need and where to put them: at each vertex, one by face ? four by vertex ? I still have a flat triangulated surface although I have a per pixel glsl shader

Thanks for help.

Answer 1

The way you are computing vertex normals only considers an individual quad and not its neighbours. Thus you get the discontinuities between the somewhat flat quads.

If you want smooth normals, the way to compute them is to consider the gradient of nearby vertices on your grid.

If you've got points on the form

a-b-c
| | |
d-e-f
| | |
g-h-i

then you want to use the gradient between b,h and d,f when computing your normal for the vertex e. Alternatively, you can compute face normals for each surrounding quad and normalize the average of them to be your vertex normal.

All in all, you need to consider the neighbourhood of your vertices in order to get smooth shading across them. No amount of per-pixel shading will help you if the interpolated quantities are essentially constant.

Answer 2

Smooth shading can be enabled with glShadeModel(GL_SMOOTH) which is, however, the default. Your screenshot does look like you have the flat shading set.