We present Selective and Hierarchical Isopoint Clustering (SHIC) as a framework for interactive isosurface visualization. SHIC is an octree-based vertex hierarchy where each surface component in a cell is represented by a vertex (isopoint) with encoded connectivity. We describe a novel connectivity encoding scheme, called Connectivity Encoding Bitmap, and two topology-preserving isopoint clustering algorithms to build the vertex hierarchy. Our framework is able to cluster surface components with up to four intersection points on a cell edge. During rendering, an incremental isosurface extraction algorithm is used to construct the isosurface dynamically. Events associated with vertex tree modifications and active vertices changes are unified using timestamps. Our framework is efficient, space-saving, and suitable for rendering large isosurface objects with local modifications.