> ## Documentation Index
> Fetch the complete documentation index at: https://docs.ntop.com/llms.txt
> Use this file to discover all available pages before exploring further.

# How to use Remap Field to scale or translate an object

## 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.**](https://ntopology.box.com/s/moloniur010po3gwi3v4otsyb9lr7xtg)

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](https://files.learn.ntop.com/help-articles/implicit-modeling/1500004669302.png)

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.

![An example of how to create a circle using the equation for a circle.](https://files.learn.ntop.com/help-articles/implicit-modeling/1500005154201.png)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](https://files.learn.ntop.com/help-articles/implicit-modeling/1500005041662.png)

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.](https://files.learn.ntop.com/help-articles/implicit-modeling/1500004745822.png)

**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](https://files.learn.ntop.com/help-articles/implicit-modeling/1500005041722.png)

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.](https://files.learn.ntop.com/help-articles/implicit-modeling/1500004884001.png)

Are you still having issues? Contact the [support team](https://support.ntopology.com/hc/en-us/requests/new), and we'll be happy to help!

## Download the Example file:

* [Example file](https://files.learn.ntop.com/Support%20Article%20Example%20Files/Knowledge%20Base/Implicit%20Modeling/Remap%20Field%20to%20Scale%20or%20Translate%20Example.ntop)

## Keywords:

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