To remain an attractive model, skeleton-based implicit surfaces have to allow the design and display of shapes at interactive rates. This paper focuses on surfaces whose skeletons are graphs of interconnected curves. We present subdivision-curve primitives that rely on convolution for generating bulge-free and crease-free implicit surfaces. These surfaces are efficiently yet correctly displayed using local meshes around each curve that locally overlap in blending regions. Subdivision-curve primitives offer a practical solution to the unwanted-blending problem that ensures C1 continuity everywhere. Moreover, they can be used to generate representations at different levels of detail, enabling the interactive display of at least a coarse version of the objects, whatever the performance of the workstation.