1. A collision determination device comprising: a shape data storage unit that stores both voxel model data representing a shape of a first object by a voxel model and boundary representation model data representing a shape of a second object by a boundary representation model, the voxel model being defined by a coordinate system fixed to the first object, the boundary representation model being defined by a coordinate system fixed to the second object; a target cell designation unit that designates, among cells constituting the voxel model, a target cell to determine a collision; a determination test point generation unit that generates determination test points to determine a collision for the target cell; a spatial curve creation unit that creates a spatial curve as the trajectory curve of the determination test point by applying a relative rigid body motion of the first object with respect to the second object to each of the determination test points; a curve intersecting determination unit that determines whether or not each boundary element of the boundary representation model is intersecting the spatial curve; a distance computation unit that computes the closest distance from the spatial curve to a boundary surface of the boundary representation model, when a determination result provided by the curve intersecting determination unit shows that the spatial curve intersects no boundary element; and a collision determination unit that determines the possibility of collision between both objects based on both the determination result provided by the curve intersecting determination unit and the computation result provided by the distance computation unit.