Techniques for generating tissue support structure are presented. A curved minimal surface shape is determined as a template for generating a tissue support structure. The determined curved minimal surface shape is numerically or functionally defined to create data representing the shape. The data is exported to a rapid prototyping system to generate a plurality of tissue support structures having a curved minimal surface. The tissue support structure can have a pore sub-section and a non-pore sub-section divided by a non-intersecting two-sided surface. A number of characteristics of the tissue support structure can be modulated including porosity and mechanical strength.