In Computer-Aided Design (CAD), parametric curves enable the creation of arbitrary yet controllable shapes. During sketching, designers often apply geometric constraints such as fixed points or tangency, leading to non-linear systems that are costly to solve in real time. This work presents a linear matrix formulation for enforcing directional tangency constraints without optimization algorithms. The method was implemented in Python and C++, and integrated into a commercial turbomachinery design tool to maintain blade-edge tangency constraints interactively.