Free Space Boundary Splines With Adaptive Measurement Point Mapping

The patent applies local quality by dynamically adjusting the distribution of control points along the parametric curve based on local geometric characteristics. Control points are densified in regions with high curvature or complex boundary geometry while being sparse in regions with low curvature, thereby achieving high approximation quality only where necessary and reducing overall computational resource consumption.

The patent implements local quality by adaptively distributing control points according to local boundary complexity. By concentrating control points only in regions requiring high approximation accuracy (such as high-curvature areas) and using fewer control points in simple regions, the system achieves the desired approximation quality while minimizing memory consumption for storing control point data.

The patent resolves this contradiction by applying local quality through adaptive control point distribution. The system identifies regions of high geometric complexity (such as sharp corners or curved boundaries) and concentrates control points in those specific areas, while using fewer control points in regions with simple geometry. This ensures high approximation quality is maintained locally where needed while achieving overall computational efficiency.

The patent applies local quality by transitioning from uniform to non-uniform control point distribution based on local curvature characteristics. The system calculates curvature at different segments of the boundary and adjusts control point density accordingly, placing more control points in high-curvature regions and fewer in low-curvature regions. This adaptive approach maintains distribution simplicity in terms of algorithmic structure while dramatically improving approximation quality in varying curvature regions.