Bezier Lines and Matrix Transformations

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There are several ways to accomplish what you want to accomplish. You can certainly do what they're suggesting, but maybe another description of it will be easier.

Are you comfortable with vector math? Normals and the like? I think you can accomplish a simplified version of what you want without dropping into matrices by taking the perpendicular of the vectors between your bezier points and displacing the verts by this perpendicular in a given plane.

If you think of the points along your spline, then the lines between the points can be thought of as vectors. You can use a normal to that vector in order to display the original line. You can do it in a simplistic way, such as displacing the points along the normal but keeping the y-value the same (so all lines have the same height). Now every point on your line can be offset at the same point. Connect those points with lines and presto there are your three lines.

Given that you're using bezier lines, I'm going to guess you are comfortable with much of this :-)

Ken