title: Why is most software dealing with Bézier curves focusing on the cubic ones, to the detriment of other curve orders?
body: <p>When you enter the Bézier curve feature of software like Microsoft Office, LibreOffice, and Blender, they let you create and juxtapose cubic, aka fourth-order, aka 4-control-point, Bézier curves. You click-and-drag creating the two points P0 and P3 and interpolate them, and the last two control points of the convex hull P1 and P2, that are not on the curve, are usually hidden or displayed as handles.</p>
  <ol>
  <li><p>Why this focus on cubic (4 points) over quadratic (3 points), quintic (5 points), and higher-order curves?</p>
  </li>
  <li><p>Why is it considered uninteresting to lower or elevate the curve order?</p>
  </li>
  <li><p>When you complicate your curve design you usually join cubic Bézier curves together: this is what happens when you click repeatedly to add points, or subdivide. Why is so little software allowing you to define all your N control points at once, and then interpolate those with a Nth-order Bézier curve? This would be a constraint-based approach in opposition to the traditional &quot;editing&quot; approach (not sure how to word it).</p>
  </li>
  </ol>