Shape-changing displays enable real-time visualization and haptic exploration of 3D surfaces. However, many shape-changing displays are composed of individually actuated rigid bodies, which makes them both mechanically complex and unable to form smooth surfaces. In this work, we build a multi-stable curved line display inspired by physical splines. By using circular splines to initialize a discrete elastic rods simulator, we can model multiple stable shapes that fit specific boundary conditions. We then generate actuation instructions based on the circular spline initialization to drive the physical display. We demonstrate our display’s ability to create 16 shapes with 8 different boundary conditions. Our display is consistent in shape output, with an average standard deviation in height of 0.75 mm or 0.47% of the display’s maximum vertical range. We also show that our model is consistent with our display, with a mean RMSE of 6.68 mm or 3.85% of the display’s maximum vertical range for shapes we could stably simulate. We then demonstrate potential scalability by simulating a multi-segment version of the system and show the display’s ability to withstand loads during contour following in haptic exploration.