This paper presents a novel approach for changing facial expressions in images. Its strength lies in its ability to map face images into a vector space in which users can easily control and generate novel facial expressions based on emotions. It relies on two main components. The first one learns how to map face images to a 3-dimensional vector space issued from a neural network trained for emotion classification. The second one is an image to image translator allowing to translate faces to faces with expressing different emotions, the emotions being represented as 3D points in the aforementioned vector space. The paper also shows that the proposed face embedding has several interesting properties: i) while being a continuous space it allows to represent discrete emotions efficiently and hence enables to use those discrete emotions as targeted facial expressions ii) this space is easy to sample and enables a fine-grained control on the generated emotions iii) the 3 orthogonal axes of this space may be mapped to arousal, valence and dominance-3 directions used by psychologists to describe emotions-which again is highly interesting to control the generation of facial expressions.