Rhino has a command that could have been designed especially for paper modellers; Unroll Developable Surface... , or Unrollsrf in its command line/script form. This command takes a selected surface, checks it to make sure it can unroll it and then makes a copy of the surface on the construction plane as if it had been flattened out. The major limitation on this command is that the surface must be generated from straight lines between the ‘frame’ curves. In other words, it can only be curved in one direction. Compound, spheroid surfaces cannot be flattened out with this tool, so we must ensure the surfaces in the model conform to this restriction.

1.     First of all, lets see just how Unrollsrf works. In this first picture, two cylindrical surfaces have been unrolled. The selected (yellow) surface is from the thin tube. Notice that although the tubes are orientated at 90 degrees to each other, the unrolled surfaces have both been unrolled in the ‘Y’ direction on the construction plane. The first edge of both unrolled surfaces has been placed along the ‘X’ axis, with one corner on the origin (0,0)

2.     We cannot tell from this where the unroll operation started, or if the unrolled surface is inside facing up or down. If we punch a small hole in the cylinder and unroll it, we can see where the hole is on the unrolled surface. If we click the Direction button on the Analyse toolbar and select the cylinder the white arrows display the facing of the surface. The cursor will then show a green and red arrow to indicate the u and v directions of the surface as well as another white arrow which indicates the facing at that point on the surface. If the End snap is selected on the Osnap selection bar, the cursor will snap to the end points of the selected surface, and this will show us clearly where the unrolled surface will be aligned with the X axis (the red line from the 0,0 point on the construction plane.

3.     Now we know where the surface will be split, and along which direction the unroll operation will move, we can see the surface is unrolled so that its INSIDE surface is facing upwards. The following picture illustrates how this particular cylinder has been unrolled.

It is important to understand how this function operates. Sometimes Unrollsrf gives unexpected results, but usually this is caused by the End points of a surface being in a different location. This depends on many things, including the direction of curves used to loft or extrude surfaces, the order in which edge curves are selected, and any trimmed edges relating to the surface. Now we can look at unrolling some more complicated surfaces. Click here to go to Unroll Part 2.