This traditional furniture crafting process demands experience in woodworking and has historically been inaccessible to amateur users. Encouragingly, the continuing advancement and increasing availability of CAD programs and CNC machines have lowered the entry to the visual design and physical fabrication steps of the furniture crafting process. But, neither CAD programs nor CNC machines help users verify whether their visual design of the furniture fulfills all the necessary constraints, even though such verification often requires advanced woodworking knowledge not commonly held by everyday users. As a result, the verification step of the crafting process presents a serious challenge that prevents average users from expressing their creativity in furniture design.

This thesis explores ways to assist users with verifying their furniture designs and guide users towards visual designs that satisfy all the requisite constraints. We aim to develop algorithms that automate the difficult verification step, allowing users to focus on producing the visual design of their furniture rather than analyzing the validity of their design. This thesis introduces interactive design tools that integrate algorithms informed by woodworking techniques to enable users to create (1) stable furniture models assembled via decorative intrinsic joints and (2) curved furniture parts formed through flexible kerf patterns.