Techniques for designing and optimization of solid/cellular structures are described using a modeling process referred to as high-definition cellular level set in B-splines (HD-CLIBS). With this process, the entire design domain for the solid/cellular structure in question is subdivided into a set of connected volumetric cells in three dimensions. An implicit trivariate B-spline function is defined on each subdomain cell. With this parameterization scheme, constraints can be imposed on the relevant B-spline coefficients to naturally maintain geometric continuities at the connection faces between neighboring cells. The method offers several useful properties and powerful functionalities to build and modify a solid/cellular structure in the modeling process and to conduct topology optimization by directly adjusting the B-spline coefficients. The model construction can be carried out using a fast B-spline interpolation, and the topology optimization can involve a sequence of discrete B-spline convolutions.