Traditional tools to visualize geodesics in curved spacetimes of General Relativity, such as black holes or collisions of neutron stars, have been specialized for certain spacetimes or limited to certain kinds of numerical data. Utilizing a fiber bundle data model and the Vish visualization shell, the author presents an approach that is independent of the underlying numerical data. It allows the combination of several visualization modules, and opens the possibility of applying the computation and visualization of integral lines more readily to other scientific domains. After introducing the necessary mathematical background and concepts, the author describes the Vish visualization shell and the main algorithms written in C++ using template meta programming. Finally, he presents five applications stemming from Computational Fluid Dynamics, General Relativity and Magnet Resonance Imaging. Detailed descriptions and source code examples in the book provide a programming introduction for scientists to the open Vish visualization shell presuming an intermediate skill in C++ and OpenGL programming.