Area Allocator

The texture atlas in my Vulkan sprite renderer relies on an AreaAllocator class to keep track of areas allocated to the individual atlas textures. I have implemented such a class before, when I was working on EVE Online. This time around I’m building it from the ground up with unit tests, trying to do it in a proper test driven development style.

Allocating

The AreaAllocator keeps a list of free areas that it pulls from when Allocate is called. The areas are rectangular, and the allocator starts out with one area, representing the whole texture atlas.

When allocating, the requested area is not likely to fit the allocation perfectly so the allocator looks for an area that is equal to or larger than the requested area. If an area is found, it is removed from the free list, the requested area cut from it and the remaining pieces added back to the free list.

Simple allocation

Here’s the source for the Allocate method:

Area* AreaAllocator::Allocate(int width, int height)
{
    Area *oldArea = getFreeArea(width, height);

    if(!oldArea) {
        collapseFreeAreas();
        oldArea = getFreeArea(width, height);
    }

    if(!oldArea) {
        return nullptr;
    }

    auto newArea = new Area {oldArea->x, oldArea->y, width, height};
    m_allocatedAreas.emplace_front(newArea);

    if(oldArea->width > width) {
        // Add an area to the right of newly allocated area
        m_freeAreas.emplace_back(new Area {oldArea->x + width, oldArea->y, oldArea->width - width, height});
    }
    if(oldArea->height > height) {
        // Add an area below the newly allocated area
        m_freeAreas.emplace_back(new Area {oldArea->x, oldArea->y + height, width, oldArea->height - height});
    }
    if(oldArea->width > width && oldArea->height > height) {
        // Add an area diagonally to the right and below the newly allocated area
        m_freeAreas.emplace_back(new Area {oldArea->x + width, oldArea->y + height, oldArea->width - width, oldArea->height - height});
    }
    return newArea;
}

When an area is freed it is simply added to the list:

void AreaAllocator::Free(Area *area)
{
    m_allocatedAreas.remove(area);
    m_freeAreas.emplace_back(area);
}

Note that keeping track of allocated areas isn’t strictly necessary, but it is useful for testing purposes. I could also use that to validate that an area being freed really was allocated.

Collapsing free areas

What happens if an area isn’t found? We may have plenty of space available even though no single area is large enough to accommodate the request. If no free area large enough is found, the allocator tries to collapse adjacent areas to produce larger areas and tries again.

void AreaAllocator::collapseFreeAreas()
{
    if( m_freeAreas.size() < 2 )
    {
        return;
    }

    int collapsed = 0;
    do {
        collapsed = 0;
        AreaList collapsedAreas;
        while(!m_freeAreas.empty()) {
            auto first = m_freeAreas.front();
            m_freeAreas.pop_front();
            while(!m_freeAreas.empty()) {
                auto other = m_freeAreas.FindAdjacent(*first);
                if(other != m_freeAreas.end()) {
                    first->CombineWith(**other);
                    delete *other;
                    m_freeAreas.erase(other);
                    ++collapsed;
                } else {
                    break;
                }
            }
            collapsedAreas.emplace_back(first);
        }
        m_freeAreas = collapsedAreas;
    } while(collapsed > 0);
}

The FindAdjacent method lives on the AreaList class, that extends a std::list. It simply iterates over all the areas, checking to see if they are adjacent to the given area:

AreaList::const_iterator AreaList::FindAdjacent(const Area &area)
{
    for(auto it = cbegin(); it != cend(); ++it) {
        if(area.IsAdjacent(**it)) {
            return it;
        }
    }
    return cend();
}

If an adjacent area is found, it’s combined with that area and the entry for that area is removed from the free areas list. This process is repeated until no adjacent areas are found.

For completeness sake, the source for IsAdjacent looks like this:

bool Area::IsAdjacent(const Area &other) const
{
    if (x == other.x && width == other.width && y + height == other.y) {
        // Other is immediately below
        return true;
    }

    if (x == other.x && width == other.width && other.y + other.height == y) {
        // Other is immediately above
        return true;
    }

    if(y == other.y && height == other.height && x + width == other.x) {
        // Other is immediately to the right
        return true;
    }

    if(y == other.y && height == other.height && other.x + other.width == x) {
        // Other is immediately to the left
        return true;
    }

    return false;
}

Simple and stupid

When looking for an area to allocate, I simply iterate over the list, looking for an area that is large enough:

AreaList::const_iterator AreaList::FindArea(int width, int height)
{
    auto foundIt = cend();

    for(auto it = cbegin(); it != cend(); ++it) {
        if((*it)->width >= width && (*it)->height >= height) {
            foundIt = it;
            break;
        }
    }

    return foundIt;
}

This simple approach works for my purposes for now. My samples so far load their textures up front, so there isn’t any churn on free areas, and I’m not doing anything on a scale where the texture atlas space is at a premium.

I know from experience, though, that at some point this simple approach won’t cut it. At the very least, we should try to find an exact fit and prefer that over the current greedy approach of taking the first area that is large enough.

Other considerations include trying to avoid thin (or tall) slivers that are unlikely to be usable later, and avoiding fragmentation.

On the other hand, I want to avoid premature and speculative optimizations. Also, with the TDD approach, I found that sticking to the process of writing a test first, then implementing the minimal code needed to make the test pass resulted in quite simple and elegant code. Sure, it doesn’t necessarily give me the most efficient solution, but later on, when that matters, I can revisit the area allocator. I will then add tests that check for those efficiency requirements before changing the allocation code itself.

[ c++  tdd  ]
Written on November 4, 2018