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.

Applies to:

• Implicit modeling
• Field remapping

Procedure:

To gain a further understanding of fields and remapping in nTop, take a look at this Field-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. 

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).

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.

The blue circle is the translated object. 

Example as shown using a primitive sphere block. 

•  
  • Input a Subtract block into the X input
    • Set Operand A: x
    • Operand B: 1

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.

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

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

Download the Example file:

• Example file

More on this topic:

• How to use simulation results to create a Point Map or Field
• How to create a quadratic ramp