Radial-Axial Ring Rolling (RARR) is an industrial forging process for making strong, seamless metal rings. Conventionally, rings are made circular with constant cross-section. In this work we demonstrate a sensing and control strategy to create rings with variable radial wall thickness and variable curvature using standard RARR hardware. This has a number of potentially useful applications but also provides an understanding of how to control these properties for conventional RARR. The sensing uses a calibrated video camera to take a series of images of the ring top surface. Image processing is employed to measure and track the ring material in-situ. The complete state of the ring is represented by the ring thickness and curvature as a function of its volume fraction, which is computed by combining the measurements from the unoccluded areas with estimates of the ring shape elsewhere. Additionally, we present a marking technique for tracking of material as it rotates through the rolling machine, even after significant deformation of the ring has occurred. We show that rings with a wide range of variation in local thickness and curvature can be formed using conventional RARR hardware and a photogrammetric state measurement technique, combined with open-loop scheduling and feedback control of thickness and curvature. Rings with both variable thickness and non-circular shapes have been produced virtually using numerical simulations and in reality using modelling clay as a material to simulate metals at forging temperatures. We demonstrate that this technique extends the range of shapes achievable with standard RARR hardware.