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This lesson explains how to take a “straight” geometric body and deform it to follow a specific path using a Curved Coordinate System. By the end of this tutorial, you will understand how to use the Remap Field block to map standard Cartesian space onto a custom vector field defined by a curve.

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1. The Core Concept: Spatial Remapping

In a standard 3D environment, every point is represented by (x, y, z). The Remap Field block allows us to “re-target” these coordinates. Instead of the body looking for its shape at (x, y, z), it looks for its shape at a new set of coordinates defined by a Vector Field. Below is an example of Translating the Body by adding an X value to the equation. Translation offset (a) Drag to see how coordinate logic affects position. 0 mm fnew(x) = fold(x) No translation applied. If we define a Vector Field where the “X” axis follows the length of a curve and the “Y” axis follows the distance away from that curve, the body will naturally “wrap” itself around that geometry. Follow Along: Remap Field Example

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2. Building the Curved Coordinate System

To bend the body, we must first build a new coordinate system using the Vector Field from Components block. This block requires three inputs representing the new X, Y, and Z axes.

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The X-Axis: Movement Along the Curve

The X-component defines where the body sits along the length of the curve.
  • Radiate Field from Plane: This generates a gradient representing distance. When combined with the curve’s arc length, it creates a field that increases as you move along the path of the curve.
Radiate Field from Plane.ntop
  • The Subtract Block (Translation): This is your “Slider” for positioning. By subtracting a value (Operand B) from the Radiate Field, you shift the body’s starting point.
    • Example: If you subtract 10mm, the body moves 10mm further along the curve.

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The Y-Axis: Distance from the Curve

The Y-component defines the thickness and the body’s perpendicular orientation relative to the curve.
  • Profile from Curve: This block generates a field where the value is 0 on the curve itself. It determines the “inside” and “outside” of the curve. This ensures your body is oriented correctly (e.g., standing upright on the curve rather than lying flat).

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The Z-Axis: Maintaining Height

  • z: By simply inputting “z”, we ensure the body maintains its original height and does not compress or stretch vertically.

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3. Executing the Remap

Once the Vector Field is constructed, we apply it using the Remap Field block:
InputDescription
FieldThe original, straight body (Body 1 or Body 2).
Vector FieldThe “Curved Coordinate System” we built above.
Fnew(x,y,z)=Fold(Vx,Vy,Vz)F_{new}(x, y, z) = F_{old}(V_x, V_y, V_z) Where V is the new coordinate logic derived from your curve. The result is a body that respects the curvature of the path while allowing for precise longitudinal translation via the subtraction operand.