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Objective:

This guide explains using the Remap Field block to scale or translate an implicit body. While other blocks exist in nTop for these operations, this method provides a foundational understanding of how field remapping and coordinate systems work.

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Applies to:

  • Implicit modeling
  • Field remapping

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Procedure:

To gain a further understanding of fields and remapping in nTop, take a look at thisField-Driven Design White Paper by George Allen, an nTop Fellow. In general, Remap Field allows you to warp geometry by supplying functions or fields to specify a replacement position for every point in the model. Let’s start with a simple 2D analogy: We have a number line [0, 1, 2, 3]. If you multiply this number by 10, you get [0, 10, 20, 30]. Basically, you are stretching out these values. This is what happens with Remap Field, but we do it to 3D geometry across XYZ. Ex. 1 Let’s use the remap block to magnify a sphere.
  • Add a Sphere block
  • Add a Remap Field block
    • Input the Sphere into the Field input
    • X: X*10 (can also use a Multiply block)
    • Y: Y
    • Z: Z
We stretch all the X values but keep the same Y and Z values of the sphere. Multiplication scales the model while addition and subtraction translate the model. A gif showing how to use the Remap Field block to modify a Sphere In nTop, when you modify a field, you aren’t directly modifying a shape; you change the coordinate system used to define that shape. This is a key difference between explicit and implicit modeling:
  • Explicit geometry transforms actively (you move the object itself).
  • Implicit geometry transforms passively (you move the coordinate system, and the object moves relative to it).

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Understanding Remapping through Equations

If you want to plot a function in the form 
z = f(x, y)
, you can implicitize it by moving all the terms to one side. e.g. 
0 = z - f(x, y)
You want the expression opposite the zero to be negative where the part is solid. Ex. 2 The unit circle centered at the origin has the equation 
sqrt(x^2 + y^2) - r = 0
. We want to shift this circle by +1 unit along the x-axis, the new equation is 
`sqrt((x-1)^2 + y^2) - 1mm = 0mm `
. To move the circle +1 in the x-direction, we replaced x by x-1, not by x+1. An example of how to create a circle using the equation for a circle. The blue circle is the translated object. The same circle that was created in the previous image, but the center has been moved 1 mm to the right Example as shown using a primitive sphere block.
  • Input a Subtract block into the X input
    • Set Operand A: x
    • Operand B: 1
Two implicit spheres that are overlapping. The blue sphere is the original and the grey sphere has been moved 1 mm to the right using Remap Field. Ex. 3 We want to scale our unit circle by a factor of 3. The scaled-up circle has the equation 
sqrt((x/3)^2 + (y/3)^2) - 1mm = 0mm
. To scale the shape by a factor of 3, we scale its coordinates by a factor of 1/3. A small circle inside a larger circle that have been generated from equations Example as shown using a primitive sphere block.
  • Input a Divide block into the X input
    • Set Operand A: X
    • Operand B: 3
  • Input a Divide block into the Y input
    • Set Operand A: Y
    • Operand B: 3
  • Input a Divide block into the Z input
    • Set Operand A: Z
    • Operand B: 3
A small sphere that has been remapped using Remap Field. The result is a sphere that has been scaled by 3 in the x, y, and z directions. Are you still having issues? Contact the support team, and we’ll be happy to help!

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Download the Example file:

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Keywords:

block field translate map scale fields remap math how-to re coordinates equation remapping sdf magnify scales