# Calculating normals

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I am using an indexed vertex buffer as a plane (10x10 sections). I can set the y-value for the vertex, but I don't know how to recalculate the normal for that vertex. I need some help with this.

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To calculate a normal for a single triangle you do the following.

x = cross(b - a, c - a)

where a, b, and c are points on the triangle and cross is the cross product of the two vectors.

Then to calculate a normal for a single point you simply sum up the normals for every face the point is part of then normalize it.

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I don't think I'm doing it correctly...... I have a plane that is subdivided into a 10x10 square grid. Each of the "squares" on the grid alternate the way the square is divided by the two triangles that make up the square (I hope I'm making sense). This will give me an alternating pattern accross the plane and will result in every other vertex being affected by 8 or 4 triangles. Here is the code so far:

			//calculate the normals
bool rev=false;
for (int py=1;py<10;py++){//these values will be for the interior vertexes only
for (int px=1;px<10;px++) {

D3DXVECTOR3 tmpv;
if (rev){
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px-1][py-1].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px][py-1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px-1][py-1].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px-1][py].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px-1][py].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px-1][py+1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px-1][py+1].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px][py+1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px][py+1].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px+1][py+1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px+1][py+1].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px+1][py].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px+1][py].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px+1][py-1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px+1][py-1].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px][py-1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
Range0[i].vert[px][py].n/=8.0f;
}
else {
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px-1][py].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px][py-1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px+1][py].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px][py-1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px-1][py].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px][py+1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
D3DXVec3Cross(&tmpv,&(Range0[i].vert[px+1][py].v-Range0[i].vert[px][py].v),&(Range0[i].vert[px][py+1].v-Range0[i].vert[px][py].v));
Range0[i].vert[px][py].n+=tmpv;
Range0[i].vert[px][py].n/=4.0f;
}

rev=!rev;

D3DXVec3Normalize(&Range0[i].vert[px][py].n,&Range0[i].vert[px][py].n);
}
}



The Range0 is just the reference for the data of each plane. I'm only using 1 plane at the moment. This loop only normalizes the inside 9x9 verts because I will be normalizing the edge ones using data from the surounding planes of the terrain. The "rev" variable simply tells it to cycle between 8 and 4.

It's not coming out right, so I must be doing something wrong.....

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You need to normalise the result of the cross product, probably? Otherwise it's scaled by the sine of the angle between them.

You also don't need to divide by a constant scalar before normalising a vector, since scaling before normalisation is a waste of time.

EDIT: Also check that you are consistent with the order of your vectors in the cross product, since a X b = -b X a. Always go round the vertices in a consistent order (clockwise or anticlockwise).

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Have a look at this thread for calculating heightmap normals (sounds like that's what you're looking for:)

http://www.gamedev.net/topic/163625-fast-way-to-calculate-heightmap-normals/

(look at the 2nd post)

That's the simplest way and the way it's most commonly done.

HappyCoder's way works too, but the results you get will be dependent on the triangulation - switch the way the triangles are oriented and you'll get different results.

Edited by phil_t

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As Paradigm Shifter pointed out, you need to make sure the vertices are consistently being wound the correct way. If you reverse the winding then the normal would be pointing the wrong way.

I would reccomend breaking up that normalizing code. It is hard to follow. I would create a seperate method for calculating normals to begin with.
void CalculateNormal(D3DXVECTOR3 *pOut, const D3DXVECTOR3 *pV1, const D3DXVECTOR3 *pV2, const D3DXVECTOR3 *pV3)
{
D3DXVec3Cross(pOut, &(*pV2 - *pV1), &(*pV3 - *pV1));
}

Then I would calculate the normals on each face and apply them to the vertices rather than having each vertex recalculate the normal of the adjacent faces.

So the steps.

Set all vertex normals to zero.
Loop through each face and calculate the normal, then add that normal to the normals of all vertices in that face.
Loop through all the vertices and normalize them.

You can normalize each face normal as you calculate them before adding them to the vertex normal. That will give each adjacent face equal weight in calculating the vertex normal. If you don't normalize them then faces with a larger surface area will have a greater influence on the calculated normal. Depending on what you want you can go either way. If the areas are roughly the same then it wont make much of a difference.

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I don't just have:

B

|

C---O---A

|

D

Every other one has 8 instead of 4. I think I have it working. The only probjem occurs when (for instance) A,B,C,&D are at the same elevation. It has to have more verts to show it correctly. That's not a problem because the terrain won't vary that much within that small an area.

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What if you use all 8 neighbouring verts to calculate the normal in all cases (i.e. ignore the underlying triangulation and pretend there are always 8 triangles meeting at each vertex). Does that improve things?

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That could cause problems if the two verts have a valley between them.

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