MINIMAL-ENERGY SPLINES .1. PLANE-CURVES WITH ANGLE CONSTRAINTS

This is the first in a series of papers on minimal‐energy splines. The paper is devoted to plane minimal‐energy splines with angle constraints. We first consider minimal‐energy spline segments, then general minimal‐energy spline curves. We formulate problems for minimal‐energy spline segments and curves, prove the existence of solutions, justify the Lagrange multiplier rules, and obtain some nice properties (e.g., the infinite smoothness). Finally, we report our computational experience on minimal‐energy splines. Copyright © 1990 John Wiley & Sons, Ltd