Module pair_section

Where two parametric surfaces meet, carried by nodes on both (ADR 0077).

Two B-spline surfaces have no implicit equation to read one in the other’s parameters, so their section is carried directly: a chain of PairNodes, each a point on both surfaces with its parameters on each, found to the last bits. Between two nodes the curve is defined, not interpolated: at local parameter s it is the point where both surfaces meet on the plane across the chord at P0 + s (P1 - P0), the unique solution of four equations in the four parameters near the chord – S1(a) = S2(b) and the plane – found by Newton from the nodes’ parameters. Derivatives follow from the same system.

Structs

PairNode

A point on both surfaces, with its parameters on each.

PairSection3

A stretch of the curve where two surfaces meet. The parameter runs over [0, nodes.len() - 1], one unit per chord.

Functions

solve4

Solve the 4x4 system m x = r by Gaussian elimination with partial pivoting; None when it is singular.