How can I calculate the normal of a cone face in openGL 4.5?

Question

I'm new at openGL 4.5 and I currently working with lights and it's all okay when I calculate vertex normals during the geometry drawing, but now I have to calculate face's normal for a cone and I have no idea on how to do it. I'm drawing it with GL_TRIANGLE_STRIP. We can see the current snippet below:

    float coneAngle = (float) Math.atan(radius / height);

    coneCos = (float) Math.cos(coneAngle);
    coneSin = (float) Math.sin(coneAngle);

    // circleResolution * heightResolution * 3

    for(int i = 0; i <= circleResolution; i++)
    {
        for(int j = 0; j <= heightResolution; j++)
        {
            angle = 2 * ((float) Math.PI) * (i / (float) circleResolution);

            cos = ((float) Math.cos(angle));
            sin = ((float) Math.sin(angle));

            x = radius * cos;
            z = radius * sin;

            // Cone Bottom
            vertices.add(x);
            vertices.add(0.0f);
            vertices.add(z);                

            // Cone Bottom Normal
            vertices.add(coneCos * cos);
            vertices.add(coneSin);
            vertices.add(coneCos * sin);

            // Cone Top
            vertices.add(0f);
            vertices.add(height);
            vertices.add(0f);               

            // Cone Top Normal
            vertices.add(0f);
            vertices.add(0f);
            vertices.add(0f);
        }
    }

    // Center of Bottom Circle - Vertices
    vertices.add(0.0f);
    vertices.add(0.0f);
    vertices.add(0.0f);

    // Center of Bottom Circle - Normal
    vertices.add(0.0f);
    vertices.add(-1.0f);
    vertices.add(0.0f);

    // CircleResolution - Bottom Circle - TRIANGLE_FAN
    for (int j = 0; j <= circleResolution; j++)
    {
        angle = (2 * ((float) Math.PI)) * ( j / (float) circleResolution );

        x = (float) Math.cos(angle);
        z = (float) Math.sin(angle);

        vertices.add(radius * x);
        vertices.add(0.0f);
        vertices.add(radius * z);

        // Normal
        vertices.add(0.0f);
        vertices.add(-1.0f);
        vertices.add(0.0f);
    }

Polygon That Approximates a Cone

Answer 1

The normal vector to a line or (vetor) can be achiefed by a 90° rotation of a vector along the line.

A vector along the flank of the cone is (radius, -height). The normal vector is (-(-height), radius).

In your case the normal vector attribute of the flank of the cone, for the bottom ("Cone Bottom Normal") and top ("Cone Top Normal") vertices is:

// lenght of the flank of the cone
float flank_len = Math.sqrt(radius*radius + height*height); 

// unit vector along the flank of the cone
float cone_x = radius / flank_len; 
float cone_y = -height / flank_len;

.....

// Cone Bottom Normal
vertices.add(-cone_y * cos);
vertices.add( cone_x );
vertices.add(-cone_y * sin);

.....

// Cone Top Normal
vertices.add(-cone_y * cos);
vertices.add( cone_x );
vertices.add(-cone_y * sin);