Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design with connectivity filtering during shape synthesis, include: a three-dimensional modeling program configured to provide disconnection detection, shape synthesis, and/or connectivity filtering during shape and/or topology optimization. The three-dimensional modeling program can be an architecture, engineering and/or construction program (e.g., building information management program), a product design and/or manufacturing program (e.g., a CAM program), and/or a media and/or entertainment production program (e.g., an animation production program).