In quantum control, mathematical control theory as well as numerical optimization are employed in order to find optimal ways of manipulating quantum systems, which is particularly important in quantum-driven fields of research such as nuclear magnetic resonance spectroscopy. The results of said optimizations boast great robustness and stability, but their numerical nature makes them somewhat hard to reason about, which is eased by the geometric abstraction present in visualizations.

Several solutions for visualizing optimized NMR pulse sequences have been proposed in the past, one of which are three-dimensional Average Hamiltonian Theory (AHT) curves.

This thesis presents the real-time rendering of such AHT curves by sphere tracing a signed distance field representation of the curves‘ implicit geometry. It also suggests several performance optimization techniques: First, bounding volumes are used as a means to reduce SDF evaluation complexity as curves grow larger. Second, selective ray tracing of screen-spanning planes significantly accelerates ray convergence across large amounts of pixels.

For different visualization purposes, distinct shaders implement Phong and Fake IBL lighting models with axis-aligned cast shadows as well as a newly developed disc sector SDF for alternate curve geometry.

Real-time renderings of reasonably complex, real-world AHT curves are demonstrated using a curve construction algorithm built into the renderer.