Description
Evaluate Unit Smoothstep Slope on the closed unit domain; deterministic numerical curve arithmetic without animation scheduling.
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.
Evaluate Unit Smoothstep Slope on the closed unit domain; deterministic numerical curve arithmetic without animation scheduling.
When to use this tool
Use this tool to evaluate Unit Smoothstep Slope on the closed unit domain; deterministic numerical curve arithmetic without animation scheduling.
How to use the tool and how it works
- Enter t using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.value. Interpret signs, units, ordering and null values using the rules below.
Validate t in the closed interval [0,1] and compute 6t(1−t). The returned field value is the derivative with respect to t.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. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.value | Derivative with respect to normalized progress t; convert separately for physical time/distance. |
{
"input": {
"t": 0.25
},
"output": {
"result": {
"value": 1.125
}
}
}Limitations and assumptions
- Progress and curve values are dimensionless; a derivative is with respect to normalized progress, not physical time. No animation is scheduled.
- 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
Similar or alternative tools
- Unit Smootherstep Slope
Evaluate Unit Smootherstep Slope on the closed unit domain; deterministic numerical curve arithmetic without animation scheduling.
- Unit Smoothstep Value
Evaluate Unit Smoothstep Value on the closed unit domain; deterministic numerical curve arithmetic without animation scheduling.