Curving beams are a promising new method for bypassing obstacles in future millimeter-wave to sub-terahertz (sub-THz) networks but lack a general predictive model for their reflections from arbitrary surfaces. We show that, unfortunately, attempting to "mirror" the incident beam trajectory across the normal of the reflector, as in ray optics, fails in general. Thus, we introduce the first geometric framework capable of modeling the reflections of arbitrary convex sub-THz curving beams from general reflectors with experimental verification. Rather than "mirroring" the trajectory, we decompose the beam into a family of tangents and demonstrate that this process is equivalent to the Legendre transform. This approach allows us to accurately account for reflectors of any shape, size, and position while preserving the underlying physics of wave propagation. Our model is validated through finite element method simulations and over-the-air experiments, demonstrating millimeter-scale accuracy in predicting reflections. Our model provides a foundation for future curving beam communication and sensing systems, enabling the design of reflected curved links and curving radar paths.