Abstract: Performance gains are realized by transforming less complex objects to the local space of a more complex object for collision detection against the more complex object. An inverse transformation stack may be used to efficiently enable transformation from world coordinate space to local coordinate space for collision detection. Avoiding the need to transform complex objects to world space for collision detection provides performance improvements by conserving processing resources and reducing the number of operations involved in collision detection. Advantages include: the ability to perform collision detection with animation objects, the ability to allow inheritance of motion in a complex hierarchy, and the ability to use instancing. Using the local coordinate space to perform collision detection with animated, instanced, hierarchical objects provides significant performance improvements over the world coordinates-based approach widely used in the past.