The construction of 3D interactive stories with variable storylines, user interactivity, and integration of personalized aspects poses challenges to the generation and simulation of dynamic story content. How to break down a narrative into computable units, provide sufficient independence when linking to its 3D presentational level, and simulating the story in an interactive 3D environment that guarantees a coherent conveying are prevailing topics of interest in the gaming and interactive narrative communities. Well known story structures in previous work make use of story units such as beats [Mateas and Stern 2003] and vignettes [Riedl and León 2008], but generated stories often lack in variability and rarely address the linking between the story structure and the 3D environment. In this work, we propose a story structure that enables us to explore temporal, thematic, and theatrical variations of an interactive story through the filtering of the story fragments (basic units of story) in an authored interactive 3D narrative. The narrative is represented as a branching story graph structure composed of story fragments (represented as nodes in the graph) and edges that logically link the fragments. A graph traversal algorithm we designed then filters and validates the story graph for logic and integrates user preferences such as the length of the story or the presence of a dramatic ending. Finally, and most importantly, the story fragments are presented in a coherent interactive 3D environment including character behaviors, character animation, and camera control.