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What is Remap Field?

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 and gives you a way to rescale existing fields to create new ones. Some common uses of the Remap Field are for mirroring, translating, scaling, arraying and the cylindrical and spherical remap which we will discuss in further detail in the future lessons.

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Examples

Let’s start with a simple 2D analogy: We have a number line [0, 1, 2, 3]. If you multiply these numbers by 10, you get [0, 10, 20, 30]. Basically, you are stretching out these values. This is what happens when we use Remap Field, but we do it in 3D space across XYZ. 

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Example 1

 Let’s use the Remap Field 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.
Note: Multiplication and division scale the model, while addition and subtraction translate the model.
When you add and multiply field values in nTop, you’re not directly modifying a shape; you’re modifying the coordinate system used to represent that shape.  One main difference between explicit and implicit modeling is that explicit geometry transforms actively (you move it where you want it), while implicits transform passively (you move the coordinate system, not the object). To apply a transformation to a shape, you have to apply the inverse transformation to its coordinate system. If your object is at the origin, and you move the origin to (-1, 0, 0), your object ends up at (1, 0, 0) relative to the updated coordinate system.

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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. 

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Example 2

The unit circle centered at the origin has the equation sqrt(x2 + y2) – r = 0 . We want to shift this circle by +1mm along the x-axis, so the new equation is sqrt((x-1)2 + y2) – 1mm = 0mm .
To move the circle +1mm in the x-direction, we replaced the x value 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
    • Operand A: x
    • Operand B: 1

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Example 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
    • Operand A: X
    • Operand B: 3
  • Input a Divide block into the Y input
    • Operand A: Y
    • Operand B: 3
  • Input a Divide block into the Z input
    • Operand A: Z
    • Operand B: 3