🧣 Spline#

#bs.spline:help

Manipulate smooth curves created from control points.

../_images/spline.png

“Do not go where the path may lead, go instead where there is no path and leave a trail.”

—Ralph Waldo Emerson

🔧 Functions#

You can find below all functions available in this module.

Evaluate#

#bs.spline:evaluate_bezier

Evaluate a Bézier curve using 4 control points and a time parameter.

Inputs:

Storage bs:in spline.evaluate_bezier:

  • Arguments
    • points: The 4 control points, where each point is a coordinates list (e.g., 2D, 3D, …).
    • time: Position along the curve. Values must be between 0 and 1.
Outputs:

Storage bs:out spline.evaluate_bezier: Point at the evaluated time.

Example: Evaluate the point in the middle of a Bézier curve in 2D space (visualize the curve):

data modify storage bs:in spline.evaluate_bezier set value {points:[[0,0],[1,2],[2,-1],[3,1]],time:0.5}
function #bs.spline:evaluate_bezier
data get storage bs:out spline.evaluate_bezier
#bs.spline:evaluate_bspline

Evaluate a B-Spline curve using 4 control points and a time parameter.

Inputs:

Storage bs:in spline.evaluate_bspline:

  • Arguments
    • points: The 4 control points, where each point is a coordinates list (e.g., 2D, 3D, …).
    • time: Position along the curve. Values must be between 0 and 1.
Outputs:

Storage bs:out spline.evaluate_bspline: Point at the evaluated time.

Example: Evaluate the point in the middle of a B-Spline curve in 2D space (visualize the curve):

data modify storage bs:in spline.evaluate_bspline set value {points:[[0,0],[1,2],[2,-1],[3,1]],time:0.5}
function #bs.spline:evaluate_bspline
data get storage bs:out spline.evaluate_bspline
#bs.spline:evaluate_catmull_rom

Evaluate a Catmull-Rom curve using 4 control points and a time parameter.

Inputs:

Storage bs:in spline.evaluate_catmull_rom:

  • Arguments
    • points: The 4 control points, where each point is a coordinates list (e.g., 2D, 3D, …).
    • time: Position along the curve. Values must be between 0 and 1.
Outputs:

Storage bs:out spline.evaluate_catmull_rom: Point at the evaluated time.

Example: Evaluate the point in the middle of a Catmull-Rom curve in 2D space (visualize the curve):

data modify storage bs:in spline.evaluate_catmull_rom set value {points:[[0,0],[1,2],[2,-1],[3,1]],time:0.5}
function #bs.spline:evaluate_catmull_rom
data get storage bs:out spline.evaluate_catmull_rom
#bs.spline:evaluate_hermite

Evaluate a Hermite curve using 4 control points and a time parameter.

Inputs:

Storage bs:in spline.evaluate_hermite:

  • Arguments
    • points: The 4 control points, where each point is a coordinates list (e.g., 2D, 3D, …).
    • time: Position along the curve. Values must be between 0 and 1.
Outputs:

Storage bs:out spline.evaluate_hermite: Point at the evaluated time.

Example: Evaluate the point in the middle of a Hermite curve in 2D space (visualize the curve):

data modify storage bs:in spline.evaluate_hermite set value {points:[[0,0],[1,2],[2,-1],[3,1]],time:0.5}
function #bs.spline:evaluate_hermite
data get storage bs:out spline.evaluate_hermite

Credits: Aksiome

Sample#

#bs.spline:sample_bezier

Sample a Bézier curve using control points and a step parameter. Each segment is defined by 4 consecutive points, with the last point shared between adjacent segments.

Inputs:

Storage bs:in spline.sample_bezier:

  • Arguments
    • points: Control points for the curve, where each segment uses 4 points and shares the last point with the next.
    • step: Interval at which the curve is sampled. Smaller values generate more points.
Outputs:

Storage bs:out spline.sample_bezier: Sampled points along the curve.

Example: Sample 10 points along a Bézier curve in 2D space (visualize the curve):

data modify storage bs:in spline.sample_bezier set value {points:[[0,0],[1,2],[2,-1],[3,1]],step:0.1}
function #bs.spline:sample_bezier
data get storage bs:out spline.sample_bezier
#bs.spline:sample_bspline

Sample a B-Spline curve using control points and a step parameter. Each segment is defined by 4 consecutive points, with 3 points shared between adjacent segments.

Inputs:

Storage bs:in spline.sample_bspline:

  • Arguments
    • points: Control points for the curve, where each segment uses 4 points and shares 3 points with the next.
    • step: Interval at which the curve is sampled. Smaller values generate more points.
Outputs:

Storage bs:out spline.sample_bspline: Sampled points along the curve.

Example: Sample 10 points along a B-Spline curve in 2D space (visualize the curve):

data modify storage bs:in spline.sample_bspline set value {points:[[0,0],[1,2],[2,-1],[3,1]],step:0.1}
function #bs.spline:sample_bspline
data get storage bs:out spline.sample_bspline
#bs.spline:sample_catmull_rom

Sample a Catmull-Rom curve using control points and a step parameter. Each segment is defined by 4 consecutive points, with 3 points shared between adjacent segments.

Inputs:

Storage bs:in spline.sample_catmull_rom:

  • Arguments
    • points: Control points for the curve, where each segment uses 4 points and shares 3 points with the next.
    • step: Interval at which the curve is sampled. Smaller values generate more points.
Outputs:

Storage bs:out spline.sample_catmull_rom: Sampled points along the curve.

Example: Sample 10 points along a Catmull-Rom curve in 2D space (visualize the curve):

data modify storage bs:in spline.sample_catmull_rom set value {points:[[0,0],[1,2],[2,-1],[3,1]],step:0.1}
function #bs.spline:sample_catmull_rom
data get storage bs:out spline.sample_catmull_rom
#bs.spline:sample_hermite

Sample a Hermite curve using control points and a step parameter. Each segment is defined by 4 consecutive points, with 2 points shared between adjacent segments.

Inputs:

Storage bs:in spline.sample_hermite:

  • Arguments
    • points: Control points for the curve, where each segment uses 4 points and shares 2 points with the next.
    • step: Interval at which the curve is sampled. Smaller values generate more points.
Outputs:

Storage bs:out spline.sample_hermite: Sampled points along the curve.

Example: Sample 10 points along a Hermite curve in 2D space (visualize the curve):

data modify storage bs:in spline.sample_hermite set value {points:[[0,0],[1,2],[2,-1],[3,1]],step:0.1}
function #bs.spline:sample_hermite
data get storage bs:out spline.sample_hermite

Credits: Aksiome

Stream#

#bs.spline:stream_bezier

Stream a Bézier curve using control points and a step parameter. Each segment is defined by 4 consecutive points, with the last point shared between adjacent segments. This function processes each step over multiple ticks.

Inputs:

Storage bs:in spline.stream_bezier:

  • Arguments
    • points: Control points for the curve, where each segment uses 4 points and shares the last point with the next.
    • step: Interval at which the curve is sampled. Smaller values generate more points.
    • run: Command executed at each step of the curve sampling process. For each step, the following storage can be used:
      • bs:lambda spline.point: The evaluated point.

Example: Stream 10 points along a Bézier curve in 2D space and execute a command at each step (visualize the curve):

data modify storage bs:in spline.stream_bezier set value {points:[[0,0],[1,2],[2,-1],[3,1]],step:0.1,run:'tellraw @a {"storage":"bs:lambda","nbt":"spline.point"}'}
function #bs.spline:stream_bezier
#bs.spline:stream_bspline

Stream a B-Spline curve using control points and a step parameter. Each segment is defined by 4 consecutive points, with 3 points shared between adjacent segments. This function processes each step over multiple ticks.

Inputs:

Storage bs:in spline.stream_bspline:

  • Arguments
    • points: Control points for the curve, where each segment uses 4 points and shares 3 points with the next.
    • step: Interval at which the curve is sampled. Smaller values generate more points.
    • run: Command string executed at each step of the curve sampling process. For each step, the following storage can be used:
      • bs:lambda spline.point: The evaluated point.

Example: Stream 10 points along a B-Spline curve in 2D space and execute a command at each step (visualize the curve):

data modify storage bs:in spline.stream_bspline set value {points:[[0,0],[1,2],[2,-1],[3,1]],step:0.1,run:'tellraw @a {"storage":"bs:lambda","nbt":"spline.point"}'}
function #bs.spline:stream_bspline
#bs.spline:stream_catmull_rom

Stream a Catmull-Rom curve using control points and a step parameter. Each segment is defined by 4 consecutive points, with 3 points shared between adjacent segments. This function processes each step over multiple ticks.

Inputs:

Storage bs:in spline.stream_catmull_rom:

  • Arguments
    • points: Control points for the curve, where each segment uses 4 points and shares 3 points with the next.
    • step: Interval at which the curve is sampled. Smaller values generate more points.
    • run: Command string executed at each step of the curve sampling process. For each step, the following storage can be used:
      • bs:lambda spline.point: The evaluated point.

Example: Stream 10 points along a Catmull-Rom curve in 2D space and execute a command at each step (visualize the curve):

data modify storage bs:in spline.stream_catmull_rom set value {points:[[0,0],[1,2],[2,-1],[3,1]],step:0.1,run:'tellraw @a {"storage":"bs:lambda","nbt":"spline.point"}'}
function #bs.spline:stream_catmull_rom
#bs.spline:stream_hermite

Stream a Hermite curve using control points and a step parameter. Each segment is defined by 4 consecutive points, with 2 points shared between adjacent segments. This function processes each step over multiple ticks.

Inputs:

Storage bs:in spline.stream_hermite:

  • Arguments
    • points: Control points for the curve, where each segment uses 4 points and shares 2 points with the next.
    • step: Interval at which the curve is sampled. Smaller values generate more points.
    • run: Command string executed at each step of the curve sampling process. For each step, the following storage can be used:
      • bs:lambda spline.point: The evaluated point.

Example: Stream 10 points along a Hermite curve in 2D space and execute a command at each step (visualize the curve):

data modify storage bs:in spline.stream_hermite set value {points:[[0,0],[1,2],[2,-1],[3,1]],step:0.1,run:'tellraw @a {"storage":"bs:lambda","nbt":"spline.point"}'}
function #bs.spline:stream_hermite

Credits: Aksiome

🎓 About Splines#

Discover how these curves behave through these visual examples. For more in-depth insights into splines, watch this video.

Bézier

B-Spline

Catmull-Rom

Hermite

💬 Did it help you?

Feel free to leave your questions and feedback below!