Height Field with average normals - opengl

Question

I am creating height field and i want to create its normals (face/vertex), I am using Triangles to create a mesh. I already calculated GL quad Normals but confused here for Triangles instead of quads.
I searched the internet and found out that two types of normals exists like per face and per vertex but not found any my code related help.
Here is what i am doing right now to create heightfield.
int average_normal()
{
glPushMatrix();
GLfloat xdelta=xsize/xsteps;
GLfloat zdelta=zsize/zsteps;
glNormal3f(0,1,0);
for (int x=0; x<xsteps-1; x++)
for (int z=0; z<zsteps-1; z++)
{
glBegin(GL_TRIANGLES);
setMaterialHeight(map[x][z]);
glNormal3f(0, 0, 1);
glVertex3f(xdelta*x,map[x][z],zdelta*z);
setMaterialHeight(map[x+1][z]);
glNormal3f(0, 0, 1);
glVertex3f(xdelta*x+xdelta,map[x+1][z],zdelta*z);
setMaterialHeight(map[x][z+1]);
glNormal3f(0, 0, 1);
glVertex3f(xdelta*x,map[x][z+1],zdelta*z+zdelta);
glEnd();
glBegin(GL_TRIANGLES);
setMaterialHeight(map[x+1][z+1]);
glNormal3f(0, 0, 1);
glVertex3f(xdelta*x+xdelta,map[x+1][z+1],zdelta*z+zdelta);
setMaterialHeight(map[x][z+1]);
glNormal3f(0, 0, 1);
glVertex3f(xdelta*x,map[x][z+1],zdelta*z+zdelta);
setMaterialHeight(map[x+1][z]);
glNormal3f(0, 0, 1);
glVertex3f(xdelta*x+xdelta,map[x+1][z],zdelta*z);
glEnd();
}
glPopMatrix();
return true;
}
How can I calculate its normal?

Answer 1

The normal vector can be computed by the Cross product of 2 vectors. Create a function, which computes the cross product and sets the normal vector attribute:
void set_normal_from_cross_product(
float x1, float y1, float z1,
float x2, float y2, float z2)
{
float nx = y1*z2 - z1*y2;
float ny = z1*x2 - x1*z2;
float nz = x1*y2 - y1*x2;
float len = sqrt(nx*nx + ny*ny + nz*nz);
if (len != 0.0f)
glNormal3f(nx/len, ny/len, nz/len);
}
In a grid the normal vectors can be computed by the vectors between the adjacent vertices. Write function which computes the vectors between the adjacent vertices and invokes set_normal_from_cross_product:
void set_grid_normal(int x, int z)
{
int prev_x = x > 0 ? x - 1 : x;
int next_x = x < xsteps - 1 ? x + 1 : x;
int prev_z = z > 0 ? z - 1 : z;
int next_z = z < zsteps - 1 ? z + 1 : z;
set_normal_from_cross_product(
xdelta * 2, map[next_x][z]-map[prev_x][z], 0,
0, map[x][next_z]-map[x][prev_z], zdelta * 2);
}
Use the function to s et the normal vectors:
void set_attributes(int x, int z)
{
setMaterialHeight(map[x][z]);
set_grid_normal(x, z);
glVertex3f(xdelta*x,map[x][z],zdelta*z);
}
for (int x=0; x<xsteps-1; x++)
{
for (int z=0; z<zsteps-1; z++)
{
glBegin(GL_TRIANGLES);
set_attributes(x, z);
set_attributes(x+1, z);
set_attributes(x, z+1);
glEnd();
glBegin(GL_TRIANGLES);
set_attributes(x+1, z+1);
set_attributes(x, z+1);
set_attributes(x+1, z);
glEnd();
}
}