The slider moves the tangent, normal, and osculating plane of the seam and illustrates how the tangent developable envelopes the osculating planes. A tangent developable of a curve is the envelope of its osculating planes. The involute is the intersection of the tangent developable with the base plane. The surface is called the tangent developable. Snapshots 4, 5, and 6: Another view of the involute of the base is obtained by considering the surface swept out by the movement of the tangent along the seam. The intersection of the tangent line of the seam and the plane containing the base traces the involute of the base curve. We call the seam helical because, like the helix, its height above the base is proportional to the distance traversed along the base. Snapshots 1, 2, and 3: The slider unwraps the right cylinder based on the selected plane curve and along a helical seam of slope 1/2 inscribed in the cylinder.
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