Given a line on a plane, a direction along that line, and a point on the plane, find a point on the plane a distance d from the first point in the direction of the line and the direction.
Derive the formula for a plane given the formula for a line, the location of a point on that line, a direction along that line, and a distance f from the point along the line in the direction, such that the point a distance f from the other point is on the plane, and the plane is parallel to the line.
Restating.
Derive the formula for a plane C given the formula for a line Vl, a point on Vl, Vp, a direction along Vl, vr, and a distance df, such that a point Cc df from Vp in the vr direction on Vl is on C and C is perpendicular to Vl.
The formula for a plane is an array whose first element records the plane's type, which is followed by the elements required to define a plane of that type, with the three types being 1) invariant y, 2) variable y invariant x, and 3) variable y variable x.
In order to derive the formula for C we need the formula for Vl, which is also an array whose first element records the line type, and whose subsequent elements record the specification for a line of that type, with the types being 1) invariant x invariant y, 2) variable x invariant y, and 3) variable x variable y.
If the line type is 1, Cc.x = Vl.x, Cc.y = Vl.y, and Cc.z = Vp.z + vr * df, C.zxslope = 0, C.zb = Cc.z, C.zyslope = 0.
