The remarkable functional versatility of proteins is made possible by the diverse array of three-dimensional folds that they adopt. The conventional representation of protein structure is a discrete coordinate model listing the positions of all atoms in the structure. While this representation is very useful for understanding intricate chemical details, it is not well suited to addressing more general questions about the nature of protein folds, their variability, and the relationships between them. To investigate such questions, we have developed a continuous representation of proteins based on the geometry of space curves. The description of a protein fold in terms of its underlying geometry has proved to be much more efficient than the coordinate representation, suggesting that sparse experimental data may be sufficient to restrain a curve model where a conventional coordinate model would be underdetermined. Many proteins are not amenable to high-resolution structural analysis, and for these challenging cases it is important to make the best use of the limited experimental information available. The talk will describe the application of the curve representation to diffraction techniques focusing in particular on low-resolution X-ray crystallography.