---
tag: g005
title: Bézier cubic spline
brief: Cubic B-spline with XYE destination and IJPQ offsets
author: thinkyhead

experimental: true
since: 1.1.0
group: motion

codes: [ G5 ]

videos:
  - aVwxzDHniEw

notes:
  - It is an error if an axis other than `X` or `Y` is specified.
  - The first control point is the current position of the head. `XY` is the destination (the last control point of the spline).
  - The next control-points are the current position plus `IJ` and the current position plus `PQ`.
  - "`I` and `J` can be omitted, which results in these offsets being zero. This produces a 3-point spline (try the [interactive demo](//www.geogebra.org/m/WPHQ9rUt)). However, `P` and `Q` are required (otherwise you just get a linear movement)."

parameters:
  -
    tag: X
    optional: false
    description: A destination coordinate on the X axis
    values:
      -
        tag: pos
        type: float
  -
    tag: Y
    optional: false
    description: A destination coordinate on the Y axis
    values:
      -
        tag: pos
        type: float
  -
    tag: E
    optional: true
    description: The length of filament to feed into the extruder between the start and end point
    values:
      -
        tag: pos
        type: float
  -
    tag: F
    optional: true
    description: The maximum feedrate of the move between the start and end point (in current units per second). This value applies to all subsequent moves.
    values:
      -
        tag: rate
        type: float
  -
    tag: I
    optional: false
    description: Offset from the `X` start point to first control point
    values:
      -
        tag: pos
        type: float
  -
    tag: J
    optional: false
    description: Offset from the `Y` start point to first control point
    values:
      -
        tag: pos
        type: float
  -
    tag: P
    optional: false
    description: Offset from the `X` end point to second control point
    values:
      -
        tag: pos
        type: float
  -
    tag: Q
    optional: false
    description: Offset from the `Y` end point to the second control point
    values:
      -
        tag: pos
        type: float
  -
    tag: S
    optional: true
    since: 2.0.8
    description: Set the Laser power for the move.
    values:
      -
        tag: power
        type: float

examples:
  -
    pre:
      - 'For example, to program a curvy "N" shape:'
    code:
      - G0 X0 Y0
      - G5 I0 J3 P0 Q-3 X1 Y1

  -
    pre:
      - 'A second curvy "N" that attaches smoothly to this one can now be made without specifying `I` and `J`:'
    code:
      - G5 P0 Q-3 X2 Y2
---
`G5` creates a cubic B-spline in the XY plane with the `X` and `Y` axes only. `P` and `Q` parameters are required. `I` and `J` are required for the first `G5` command in a series. For subsequent `G5` commands, either both `I` and `J` must be specified, or neither. If `I` and `J` are unspecified, the starting direction of the cubic will automatically match the ending direction of the previous cubic (as if `I` and `J` are the negation of the previous `P` and `Q`).

See [This interactive demo](//www.geogebra.org/m/WPHQ9rUt) to understand how Bézier control points work.