Ruled Surface
A ruled surface is the surface generated by interpolating linearly between corresponding points of two curve entities. The u coordinate is the normalized parameter at which both curves are evaluated, and the v coordinate is the linear parameter between the two points. The curves are not defined in the local coordinate system of the part, so the resulting point must be transformed by the local coordinate system of the surface.
Data Format:
e1[3] Unit vector, in the u direction
e2[3] Unit vector, in the v direction
e3[3] Normal to the plane
origin[3] Origin of the ruled surface
curve_1 First generating curve
curve_2 Second generating curve
e2[3] Unit vector, in the v direction
e3[3] Normal to the plane
origin[3] Origin of the ruled surface
curve_1 First generating curve
curve_2 Second generating curve
Parameterization:
(x', y', z') is the point in local coordinates.
(x', y', z') = (1 - v) * C1(u) + v * C2(u)
(x, y, z) = x' * e1 + y' * e2 + z' * e3 + origin
(x', y', z') = (1 - v) * C1(u) + v * C2(u)
(x, y, z) = x' * e1 + y' * e2 + z' * e3 + origin