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interpolation of normal on low polygon useless

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I have created a tetrahedron using 4 vertices and 12 indices. I have then calculated the normals for each vertex and passed it to the shader to do ambient and diffuse lighting. The results are shown in the picture below and as you can see I get dark sections where I expected lit sections:

[attachment=9981:tetra bad shade.png]

I am assuming that this is because of interpolation of normals. As I say my approach to create this tetrahedron was to use only 4 vertices and let the indices do the rest. Should I actually define 4 faces (12 vertices) and define the normals for each face. I know this latter approach would work but my question is should the former approach also work, or should I reserve the low vertex count solution only for high polygon count objects?

My code for defining the vertices, indices and normal is below:

PrimitiveVertexStruct vertices[]=
{ D3DXVECTOR3(0.0f,1.0f,0.0f), WHITE_VECTOR, ZERO_VECTOR3 }, //1
{ D3DXVECTOR3(1.0f,-1.0f,0.0f), RED_VECTOR, ZERO_VECTOR3 }, //2
{ D3DXVECTOR3(-1.0f,-1.0f,0.0f),BLUE_VECTOR, ZERO_VECTOR3 }, //3
{ D3DXVECTOR3(0.0f,0.0f,2.0f), BLACK_VECTOR, ZERO_VECTOR3 }, //4
m_numTetraVertices = sizeof(vertices) / sizeof(PrimitiveVertexStruct);

DWORD indices[] =
0,1,3, //1,2,4
1,2,3, //2,3,4
2,0,3, //3,1,4
0,2,1 //1,3,2
//compute average normals
for(int i=0;i<m_numTetraVertices;i++) {
//indices of triangle
int i0=indices[i*3+0];
int i1=indices[i*3+1];
int i2=indices[i*3+2];
//vertices of triangle
D3DXVECTOR3 v0=vertices[i0].Pos;
D3DXVECTOR3 v1=vertices[i1].Pos;
D3DXVECTOR3 v2=vertices[i2].Pos;
//compute face normal
D3DXVECTOR3 e0=v1 - v0;
D3DXVECTOR3 e1=v2 - v0;
D3DXVECTOR3 normal;
D3DXVECTOR3 cross;
D3DXVec3Cross(&normal, &e0, &e1);
//add to any existing normals for that vertex
Edited by benp444

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For a low polygon object like that, you want to use face normals. So yeah, that means you'll want a separate vertex for each vertex on each face, with normals that don't vary across the 3 vertices of each face.

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If the angle between adjacent faces is more than a certain threshold, you really need to switch to using face normals. If you want a hard edge, use face normals. If you want a smooth edge, use averaged vertex normals.

Also, don't forget to re-normalise the normals after summing them together.

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When interpolating normals, you should re-normalise them for each pixel. Therefore adjust your pixelshader.

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Thanks, I was actually re-normalizing (in c++, not shader) I just didn't paste the code. Anyhow you have answered my question and I will now define the full faces for all my low polygon shapes.

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