If you look in the code example below for meshing in C++, you find the following info mapping the properties of the meshing parameters to the names used in the dialog:
m_relative_tolerance = 0.1; // Density
m_refine_angle = 0.0; // Maximum angle (radians)
m_grid_aspect_ratio = 0.0; // Maximum aspect radio
m_min_edge_length = 0.0001; // Minimum edge length
m_max_edge_length = 0.3; // Maximum edge length
m_tolerance = 0.0; // Maximum distance, edge to surface
m_grid_min_count = 0; // Minimum initial grid quads
m_bRefine = true; // Refine mesh
m_texture_range = 2; // Pack textures