How to create a TPMS from an equation

Objective:

Learn how to create a TPMS by using math equations. This example creates a Schwarz TPMS

Applies to:

  • TPMS
  • Math

Procedure:

1. Build the equation using math blocks

The equation for the Schwarz TPMS is cos(x)+cos(y)+cos(z). Equations in nTopology are built out by individual blocks. Some equations can quickly become complicated. Due to this, we recommend turning these workflows into Custom Blocks, so you only have to build it once.

    • Add 3 Cos blocks 
    • In the first Cos block, write in 'X/1 mm'. This gets rid of the units associated with X and allows it to work with Cos.

cos.jpg

    • Repeat this for the remaining Cos blocks using Y and Z instead of X.
    • Add an Add block
      • Insert Cos(X) and Cos(Y) into the Add block

cos1.jpg

    • Add another Add block
      • Insert the Add block with Cos(X) + Cos(Y)
      • Insert Cos(Z)

cos2.jpg

View the results of your equation. If you just see black, zoom out or use 'Z' to zoom to the object. The TPMS should be quite large.

cos6.jpg

2. Give your TPMS units

In order to use the TPMS in other operations, it needs units. Add units by multiplying the field by 1 mm.

    • Add a Multiply block
      • Insert the equation from Step 1 into Operand A
      • In Operand B, write 1 mm

cos3.jpg

3. Trim your TPMS down to size

Use the Boolean Intersect block to edit the size of the TPMS

    • Add a Boolean Intersect block
      • Insert the Multiply block from Step 2.
      • Insert a body that you want to intersect the TPMS with. In this example, we use a small Cube.

cos5.jpg

And that’s it! You’ve successfully created a TPMS using math blocks

Are you still having issues? Contact the support team, and we’ll be happy to help!

Download the Example file:

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Keywords:

 TPMS variable math build cos how-to x equation schwarz 
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