Fitting 3D Curves from a Series of Spatial Points

To create smooth three-dimensional curves through a series of spatial points, this implementation utilizes spline interpolation algorithms such as cubic splines or B-splines. The input consists of coordinate points in 3D space (x,y,z coordinates), which are processed to generate a continuous curve that passes through all input points. The algorithm typically involves calculating control points and polynomial coefficients for each segment between consecutive input points. The output includes a multi-segment spline curve representation, where each segment is defined by parametric equations that ensure C² continuity (continuous second derivatives) at connecting points. Additionally, the implementation generates n equally spaced points along the curve length using arc length parameterization techniques. This involves numerical integration to calculate cumulative arc lengths and interpolation to determine coordinates at specific length intervals. Key implementation steps include: initial point validation and sorting, knot vector generation for non-uniform point distributions, coefficient matrix solving using tridiagonal matrix algorithms for cubic splines, and adaptive sampling for accurate equidistant point calculation. The resulting equally spaced points are particularly useful for CAD applications, motion path planning, and visualization systems requiring uniform point distributions along complex 3D paths.