Creating Knots

Building a knot

  1. Select "Freehand→ Formula".
  2. Insert the parametric equations for your knot.
  3. For example, a (3,2) trefoil knot has the equations x=Cos(3*t)*(3+Cos(2*t)), y=Sin(3*t)*(3+Cos(2*t)), z=Sin(2*t). Note that this is the format that is necessary for Cinema 4D to read your formulae.
  4. Select "Subdivision Surface→Sweep”.
  5. Select "Freehand → circle". Set the radius of your sweep.
  6. In Object Manager, make "circle" and "Formula" children of "Sweep".
  7. Remember to save copies of your shapes before adding text.

Fixing the join

When you create a knot in Cinema 4D, sometimes the two caps of the knot will not fit correctly. If that happens, follow these steps:

  1. Select and delete the caps on the ends of your knot by selecting them in Object Manager and deleting them.
  2. (Optional) Select all of the polygons around one end of the knot and use the rotate tool to move the edges to be as close to each other as possible. If you choose to do this, be careful that the knot is not distorted too much.
  3. To fill in the gap between the two ends of the knot:
  4. Click the “Select → Select All”.
  5. Right click anywhere in the viewport (not on your object) and select “Close Polygon Holes”.
  6. Hover your cursor over the hole in the knot where the two caps do not align until the hole turns white. Then click. The hole should now be filled.
  7. To correct the places where the two ends of the knots overlap:
  8. Select “points” from the menu on the left. Then “Select All.”
  9. Go to “Mesh Commands Optimize”, but click the wheel to the right of “Optimize”. This will allow you to make your tolerance for your optimization. The greater the tolerance, the greater the distance between any two points that will be connected once the object is optimized. Then click OK. There is a bit of a balancing act between capturing enough points and capturing too many.
  10. Note that you need to do this step even if the tubes do not overlap. This is because you need to merge any overlapping points into one point.

Adding text

To add an equation or text to the knot, follow the instructions on how to put text along a spline and an extruded parametric curve.

Summer 2015Ryan McDonnell (’17)

Prof Elizabeth Denne

Washington & Lee University