Question

If I have a texture, is it then possible to generate a normal-map for this texture, so it can be used for bump-mapping?

Or how are normal maps usually made?

Answer 1

Yes. Well, sort of. Normal maps can be accurately made from height-maps. Generally, you can also put a regular texture through and get decent results as well. Keep in mind there are other methods of making a normal map, such as taking a high-resolution model, making it low resolution, then doing ray casting to see what the normal should be for the low-resolution model to simulate the higher one.

For height-map to normal-map, you can use the Sobel Operator. This operator can be run in the x-direction, telling you the x-component of the normal, and then the y-direction, telling you the y-component. You can calculate z with 1.0 / strength where strength is the emphasis or “deepness” of the normal map. Then, take that x, y, and z, throw them into a vector, normalize it, and you have your normal at that point. Encode it into the pixel and you’re done.

Here’s some older incomplete-code that demonstrates this:

// pretend types, something like this
struct pixel
{
    uint8_t red;
    uint8_t green;
    uint8_t blue;
};

struct vector3d; // a 3-vector with doubles
struct texture; // a 2d array of pixels

// determine intensity of pixel, from 0 - 1
const double intensity(const pixel& pPixel)
{
    const double r = static_cast<double>(pPixel.red);
    const double g = static_cast<double>(pPixel.green);
    const double b = static_cast<double>(pPixel.blue);

    const double average = (r + g + b) / 3.0;

    return average / 255.0;
}

const int clamp(int pX, int pMax)
{
    if (pX > pMax)
    {
        return pMax;
    }
    else if (pX < 0)
    {
        return 0;
    }
    else
    {
        return pX;
    }
}

// transform -1 - 1 to 0 - 255
const uint8_t map_component(double pX)
{
    return (pX + 1.0) * (255.0 / 2.0);
}

texture normal_from_height(const texture& pTexture, double pStrength = 2.0)
{
    // assume square texture, not necessarily true in real code
    texture result(pTexture.size(), pTexture.size());

    const int textureSize = static_cast<int>(pTexture.size());
    for (size_t row = 0; row < textureSize; ++row)
    {
        for (size_t column = 0; column < textureSize; ++column)
        {
            // surrounding pixels
            const pixel topLeft = pTexture(clamp(row - 1, textureSize), clamp(column - 1, textureSize));
            const pixel top = pTexture(clamp(row - 1, textureSize), clamp(column, textureSize));
            const pixel topRight = pTexture(clamp(row - 1, textureSize), clamp(column + 1, textureSize));
            const pixel right = pTexture(clamp(row, textureSize), clamp(column + 1, textureSize));
            const pixel bottomRight = pTexture(clamp(row + 1, textureSize), clamp(column + 1, textureSize));
            const pixel bottom = pTexture(clamp(row + 1, textureSize), clamp(column, textureSize));
            const pixel bottomLeft = pTexture(clamp(row + 1, textureSize), clamp(column - 1, textureSize));
            const pixel left = pTexture(clamp(row, textureSize), clamp(column - 1, textureSize));

            // their intensities
            const double tl = intensity(topLeft);
            const double t = intensity(top);
            const double tr = intensity(topRight);
            const double r = intensity(right);
            const double br = intensity(bottomRight);
            const double b = intensity(bottom);
            const double bl = intensity(bottomLeft);
            const double l = intensity(left);

            // sobel filter
            const double dX = (tr + 2.0 * r + br) - (tl + 2.0 * l + bl);
            const double dY = (bl + 2.0 * b + br) - (tl + 2.0 * t + tr);
            const double dZ = 1.0 / pStrength;

            math::vector3d v(dX, dY, dZ);
            v.normalize();

            // convert to rgb
            result(row, column) = pixel(map_component(v.x), map_component(v.y), map_component(v.z));
        }
    }

    return result;
}