Obtaining normal of vertices of torus mesh

Question

I'm trying to create my own torus with smooth shading. However, the normal seems to be wrong. Here is my code.

GLfloat NoMat[]             =   {   0.0f,   0.0f,   0.0f,   1.0f    };
GLfloat MatAmbient[]        =   {   0.7f,   0.7f,   0.7f,   1.0f    };
GLfloat MatAmbientColor[]   =   {   0.21f,  0.13f,  0.05f,  1.0f    };
GLfloat MatDiffuse[]        =   {   0.71f,  0.43f,  0.18f,  1.0f    };
GLfloat Shine               =   100.0f; 
GLfloat NoShine             =   0.0f;

glMaterialfv(GL_FRONT, GL_AMBIENT, MatAmbientColor);
glMaterialfv(GL_FRONT, GL_DIFFUSE, MatDiffuse);
glEnable(GL_NORMALIZE);

glMaterialfv(GL_FRONT, GL_SPECULAR, MatAmbient);
glMaterialf(GL_FRONT, GL_SHININESS, Shine);

int i, j, k;
double s, t, x, y, z;

for (i = 0; i < nsides; i++) {
    glBegin(GL_QUAD_STRIP);
    for (j = 0; j <= rings + 1; j++) {
        for (k = 1; k >= 0; k--) { //for both negative and positive
            s = (i + k) % nsides + 0.5;
            t = j % rings;

            x = (totalRadius + centerRadius * cos(s*2*M_PI/nsides)) * cos(t*2*M_PI/rings);
            z = (totalRadius + centerRadius * cos(s*2*M_PI/nsides)) * sin(t*2*M_PI/rings);
            y = centerRadius * sin(s*2*M_PI/nsides);
            glVertex3f(x, y, z);
            glNormal3f(x, y, z);
        }
    }
    glEnd();
}

However, the lighting does not work properly, as it behaves like flat shading instead of smooth shading. I've did some googling, but apparantly it seems that I need to use differention. However, I'm not too sure how to do this. Anyone has any idea?

Answer 1

You're using the vertex positions for normals? This will work only (and only) for a unit radius sphere!

You need to calculate the normal. That is

The nice thing about a torus is, that you can evaluate this easily on paper, giving you an exact formula, instead of working with a numerical approximation.