Wood is typically processed into long, thin products due to its growth patterns and structure, resulting in many parts being left unused. These overlooked components, like branches, can be repurposed for load-bearing structures. However, they necessitate a new parametric description because of differences in material and geometric behavior. Accurately transferring these geometries into the calculation model is essential. To achieve this, the surface is represented using non-uniform rational B-splines (NURBS) based on image data. The Scaled Boundary Isogeometric Analysis (SBIGA) method allows for direct structural analysis using these geometries. This approach merges concepts from the scaled boundary finite element method (SBFEM) with isogeometric analysis (IGA). In this technique, two-dimensional surfaces are scaled relative to a central point. Obtuse-angled polyhedrons can arise within a patch when applied to thin, elongated structures, leading to numerical conditioning issues. This work presents a generalized SBIGA approach that utilizes a scaling center line instead of a scaling center point. This modification enables the analysis of slender, curved structures without the need for additional structural partitioning, simplifying preprocessing and improving overall performance.