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How can I filter a magento product collection by expression of multiple attributes

I have added location attribute for my products and wanted to filter my products by distance to a location using products geocode. The following code does not work for me.

$productCollection->addExpressionAttributeToSelect('distance',"( 3959 * acos( cos( radians('.$center_lat.') ) * cos( radians( latitude ) ) * cos( radians( longitude) - radians('.$center_lng.') ) + sin( radians('.$center_lat.') ) * sin( radians( latitude ) ) ) )", array('latitude'=>'latitude', 'longitude'=>'longitude'));
$productCollection->getSelect()->having('distance<=?',10)
                              ->order('distance', Varien_Db_Select::SQL_ASC);

I tried using the two options there, neither worked. How to add dynamic field in magento collection

I finally solve the problem by join the eav/attribute_xxx table first. Here is the function to join the attribute.

protected function joinAttributeToSelect($select, $attrCode)
{
    $attribute = Mage::getSingleton('eav/config')->getAttribute('catalog_product', $attrCode);
    $attrId = $attribute->getAttributeId();
    $select->joinLeft(
        array($attrCode => $attribute->getBackendTable()),
        '(' . $attrCode . '.entity_id = e.entity_id) AND (' . $attrId . ' = ' . $attrCode . '.attribute_id)',
        array($attrCode => $attrCode . '.value')
    );
    return $select;
}

After that, I can do where condition as I want. In my case the following code works.

$dist = sprintf(
        "(%s*acos(cos(radians(%s))*cos(radians(latitude.value))*cos(radians(longitude.value)-radians(%s))+sin(radians(%s))*sin(radians(latitude.value))))",
        3959,
        (float)$center_lat,
        (float)$center_lng,
        (float)$center_lat
    );
$productCollection->getSelect()->where($dist.'<=?', (float)$radius)
                                          ->order($dist,asc);

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