Unit Progress Delay Remap

Description

Remap an explicit progress interval into a clamped unit interval; delay/end are finite ordered coordinates, not a scheduler.

Easing maps normalized progress to a dimensionless curve value. A slope differentiates that curve with respect to progress, while delay remapping and ping-pong phases change the input coordinate. To turn progress into position or time-dependent velocity, supply the application’s distance scale and duration separately.

Remap an explicit progress interval into a clamped unit interval; delay/end are finite ordered coordinates, not a scheduler.

When to use this tool

Use this tool to remap an explicit progress interval into a clamped unit interval; delay/end are finite ordered coordinates, not a scheduler.

How to use the tool and how it works

Enter t, delay, end using the input definitions below.
Run the operation. Resolve malformed-input errors before interpreting the result.
Read result.progress. Interpret signs, units, ordering and null values using the rules below.

Require end>delay, compute (t−delay)/(end−delay), and clamp the result to [0,1].^[1]

Input field	Meaning and units	Accepted input
t	Dimensionless normalized input from 0 through 1, except the explicitly described delay-remapping coordinate.	Finite number satisfying the stated comparisons.
delay	Lower start coordinate of the remapped interval, in the same units as t and end.	Finite number satisfying the stated comparisons.
end	Upper coordinate of the remapped interval, strictly greater than delay.	Finite number satisfying the stated comparisons.

Output field	Interpretation
result	Object containing the fields below.
result.progress	Input interval remapped and clamped to [0,1].

json

{
  "input": {
    "t": 0.5,
    "delay": 0.25,
    "end": 0.75
  },
  "output": {
    "result": {
      "progress": 0.5
    }
  }
}

Limitations and assumptions

t, delay and end must use the same progress/time coordinate; the operation does not wait, schedule or choose an easing curve.
Curves ordinarily require normalized input t from 0 through 1; ping-pong and delay-remapping operations instead accept their explicitly stated progress coordinates. Floating-point roundoff remains possible.
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

Choose the curve and parameter convention before combining operations. Use a scheduler or animation engine for playback, and apply the appropriate duration/distance factors when interpreting slopes physically.

References

Tool behavior and example: Unit Progress Delay Remap — tool.io

Similar or alternative tools

Unit Progress Ping Pong Phase
Map signed continuous progress to a triangular ping-pong phase with period two and explicit branch direction; turning points use the outgoing branch.
Unit Cubic In Out Easing Value
Evaluate Unit Cubic In Out Easing Value on the closed unit domain; deterministic numerical curve arithmetic without animation scheduling.