A face is generated from a set of user-defined control points using an energy-minimizing curve model. The visualization displays the evolving contour as it deforms into a recognizable facial profile, with the underlying algorithm calculating signed distances from closed and unclosed curve segments. The implementation leverages D3.js v6 for rendering and NumJS for numerical operations, with the core `distPointClosed` and `distPointUnclosed` functions driving the shape's deformation.