Spinal curvature progression in scoliosis patients is monitored from X-rays, and this serial exposure to harmful radiation increases the incidence of developing cancer. With the aim of reducing the invasiveness of follow-up, this study seeks to relate the three-dimensional external surface to the internal geometry, having assumed that that the physiological links between these are sufficiently regular across patients. A database was used of 194 quasi-simultaneous acquisitions of two X-rays and a 3D laser scan of the entire trunk. Data was processed to sets of datapoints representing the trunk surface and spinal curve. Functional data analyses were performed using generalized Fourier series using a Haar basis and functional minimum noise fractions. The resulting coefficients became inputs and outputs, respectively, to an array of support vector regression (SVR) machines. SVR parameters were set based on theoretical results, and cross-validation increased confidence in the system's performance. Predicted lateral and frontal views of the spinal curve from the back surface demonstrated average L2-errors of 6.13 and 4.38 millimetres, respectively, across the test set; these compared favourably with measurement error in data. This constitutes a first robust prediction of the 3D spinal curve from external data using learning techniques.