The present disclosure relates to systems, methods, and non-transitory computer readable media for removing an anchor point from a Bezier spline while preserving the shape of the Bezier spline. For example, the disclosed systems can replace adjacent input segments of an initial Bezier spline that are connected at an anchor point with a new contiguous segment that does not include an anchor point and that spans the portion of the spline covered by the adjacent segments. The disclosed systems can utilize an objective function to determine tangent vectors that indicate locations of control points for generating the new segment to replace the adjacent segments. In addition, the disclosed systems can generate a modified Bezier spline that includes the new segment in place of the adjacent segments of the initial Bezier spline.