How to load only the children categories that belong to the current product (magento)

Question

I want to show a list of categories a product belongs to, top categories and subcategories.

I figured out how to load the correct topcategories, but when I loop the subcats (children categories) it loads ALL subcats of that topcategory, not the categories that the product falls under.

Example:

Like you can see it loads a ton of subcategories, but only the ones with the red stripe are subcategories that the product falls under.

How can I make sure it only show those under their topcategories?

My code:

$currentCatIds = $_product->getCategoryIds();
  $categoryCollection = Mage::getResourceModel('catalog/category_collection')
 ->addAttributeToSelect('name')
 //  ->addFieldToFilter('level',2)
 ->addAttributeToSelect('url')
 ->addAttributeToFilter('entity_id', $currentCatIds)
 ->addIsActiveFilter();

  $out = "<ul>";
  foreach($categoryCollection as $cat){
      $out .= "<li>";
      $out .= "<b><a href='".$cat->getUrl()."'>".$cat->getName()."</a></b>";
      $out .="<ul class='sub'>";
      $children = Mage::getModel('catalog/category')
      // ->addAttributeToFilter('entity_id', $cat->getCategoryIds())
      ->load($cat->getId())
      ->getChildrenCategories();
          foreach($children as $child){
              $out .="<li><a href='".$child->getUrl()."'>".$child->getName()."</a></li>";
          }
          $out .="</ul>";
      $out .= "</li>";
  }
  $out .= "</ul>";
  echo $out;

Why are they shown below again? I only want the subcats under the topcategories, not subcats twice.

Answer 1

Try changing your category collection like below-

foreach($categoryCollection as $cat){
      $out .= "<li>";
      $out .= "<b><a href='".$cat->getUrl()."'>".$cat->getName()."</a></b>";
      $out .="<ul class='sub'>";
      $children = Mage::getModel('catalog/category')
      // ->addAttributeToFilter('entity_id', $cat->getCategoryIds())
      ->load($cat->getId())
      ->getChildrenCategories();
          foreach($children as $child){
              if(in_array($child->getId(), $product->getCategoryIds())){   // change $product->getCategoryIds() to your product category id array
                 $out .="<li><a href='".$child->getUrl()."'>".$child->getName()."</a></li>";
              }
          }
          $out .="</ul>";
      $out .= "</li>";
  }

Update to get parent level categories only change your category collection to below code

$categoryCollection = Mage::getResourceModel('catalog/category_collection')
 ->addAttributeToSelect('name')
 ->addAttributeToFilter('level', 2)//2 is actually the first level
 ->addAttributeToSelect('url')
 ->addAttributeToFilter('entity_id', $currentCatIds)
 ->addIsActiveFilter();