Description
Extract cubic Bezier subinterval control points, reparameterized to the unit interval; equal endpoints produce a point-valued cubic, no extrapolation.
A planar Bézier curve is defined by an ordered control polygon: three points for a quadratic or four for a cubic. Its parameter t runs from 0 to 1 and generally does not measure arc length. Derivative vectors, curve positions, control points and polynomial coefficients are different representations of the same parameterized geometry.
Extract cubic Bezier subinterval control points, reparameterized to the unit interval; equal endpoints produce a point-valued cubic, no extrapolation.
When to use this tool
Use this tool to extract cubic Bezier subinterval control points, reparameterized to the unit interval; equal endpoints produce a point-valued cubic, no extrapolation.
How to use the tool and how it works
- Enter points, start, end using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.points. Interpret signs, units, ordering and null values using the rules below.
Require 0≤start≤end≤1. Split the cubic at end, take its left part, then split that part at start/end and keep the right. If end is zero, return four copies of the first point.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| points | Ordered planar control points: three for a quadratic, four for a cubic. Basis-conversion tools use the representation stated above. | Dense list of at most 128 rows of at most 128 finite numbers; the operation’s shape constraints also apply. |
| start | Inclusive original cubic parameter start in [0,1]. | Finite number satisfying the stated comparisons. |
| end | Inclusive original cubic parameter end in [start,1]. | Finite number satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.points | Resulting ordered planar Bézier control polygon. |
{
"input": {
"points": [
[
0,
0
],
[
1,
0
],
[
2,
0
],
[
3,
0
]
],
"start": 0.25,
"end": 0.75
},
"output": {
"result": {
"points": [
[
0.75,
0
],
[
1.25,
0
],
[
1.75,
0
],
[
2.25,
0
]
]
}
}
}Limitations and assumptions
- The resulting cubic reparameterizes the selected original interval to [0,1]. Equal interval endpoints produce a point-valued cubic; extrapolation is rejected.
- Each geometric control point has two finite coordinates within ±1,000,000,000. t and interval endpoints are dimensionless in [0,1]. Calculations use floating arithmetic and do not perform curve fitting or robust topology analysis.
- Every declared top-level input is required and unknown fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and within the absolute safe-integer magnitude; exact larger integers use decimal text. Source positions are zero-based UTF-16 offsets and span ends are exclusive unless a different convention is explicitly stated.
Alternative or Complementary methods
Keep control polygons and constant-first power coefficients clearly labeled. Use separate arc-length integration or adaptive sampling when physical spacing or geometric approximation error matters.
References
Similar or alternative tools
- Cubic Bezier Split Control Points
Split at explicit t into two complete control polygons with duplicated join endpoint, preserving curve geometry.
- Bezier Control Point Order Reversal
Reverse a planar quadratic/cubic control polygon to represent the same Bezier curve under t -> 1-t, not a spatial mirror.