BSplineSolid: Symbolic construction and visualization of rational trivariate solids in Mathematica

We present BSplineSolid, a symbolic and graphical command for constructing and visualizing rational trivariate B-spline and NURBS solids within Mathematica. Unlike existing built-in primitives, BSplineSolid supports rational weights, customizable knot vectors, and smooth directional closures. The framework is based on tensor-product spline structures, enabling symbolic manipulation and high-quality graphical rendering. Designed for educational and technical applications in computational geometry and CAD, BSplineSolid facilitates interactive modeling of volumetric spline solids with explicit access to control points, weights, and basis functions. This enhances conceptual understanding and promotes experimentation in advanced geometry or engineering courses. Moreover, the framework seamlessly integrates with Mathematica’s symbolic capabilities to support analytical derivations of geometric properties, export of mesh data, and visual inspection. BSplineSolid fills a gap in Mathematica’s geometric modeling toolset, offering a reproducible, transparent, and flexible method for exploring trivariate rational spline solids in engineering education, research prototyping, and design-oriented computation.