Random Cubic Hermite Curve Bank Generator

Description

Draw independent integer endpoint and tangent tuples and sample bounded Hermite curves, retaining unrounded values alongside delegated core values.

Procedural artwork expresses a visual idea through coordinates, repeated motifs, colors, or explicit placement constraints. A coordinate plan can be checked and reproduced before rendering, while physical material behavior and fabrication require separate information.

Draw independent integer endpoint and tangent tuples and sample bounded Hermite curves, retaining unrounded values alongside delegated core values.

When to use this tool

Use this generator to create reproducible cubic hermite curve bank cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply count, samplesPerCurve, p0Range, p1Range, m0Range, m1Range in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read curves, tangentConvention, corePrecision. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Draw integer endpoints and tangents, then sample cubic Hermite basis interpolation over normalized t from zero through one. Return direct arithmetic as value and the delegated calculator's rounded coreValue for each parameter sample.^[1]

Delegated operations used for this result: cubic hermite. Their calculation or parsing conventions apply to the corresponding result fields.^[2]

Input field	Meaning and units	Accepted input
count	Count	Required. Safe integer; minimum 1; maximum 32.
samplesPerCurve	Samples Per Curve	Required. Safe integer; minimum 2; maximum 65.
p0Range	P0 Range	Required. Object; no unknown keys.
p0Range.minimum	Minimum	Required. Safe integer.
p0Range.maximum	Maximum	Required. Safe integer.
p1Range	P1 Range	Required. Object; no unknown keys.
p1Range.minimum	Minimum	Required. Safe integer.
p1Range.maximum	Maximum	Required. Safe integer.
m0Range	M0 Range	Required. Object; no unknown keys.
m0Range.minimum	Minimum	Required. Safe integer.
m0Range.maximum	Maximum	Required. Safe integer.
m1Range	M1 Range	Required. Object; no unknown keys.
m1Range.minimum	Minimum	Required. Safe integer.
m1Range.maximum	Maximum	Required. Safe integer.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
curves	Curves	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 32.
curves[].p0	P0	Required. Finite number.
curves[].p1	P1	Required. Finite number.
curves[].m0	M0	Required. Finite number.
curves[].m1	M1	Required. Finite number.
curves[].samples	Samples	Required. Array of Object; no unknown keys.; minimum items 2; maximum items 65.
curves[].samples[].t	T	Required. Finite number; minimum 0; maximum 1.
curves[].samples[].value	Value	Required. Finite number.
curves[].samples[].coreValue	Core Value	Required. Finite number.
tangentConvention	Tangent Convention	Required. Text.
corePrecision	Core Precision	Required. Text.
randomness	Replay source and normalized 32-bit seed, or null seed for an advancing context source.	Required. Object; no unknown keys.
randomness.seed	Optional safe-integer replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "count": 2,
    "samplesPerCurve": 3,
    "p0Range": {
      "minimum": 0,
      "maximum": 4
    },
    "p1Range": {
      "minimum": 6,
      "maximum": 10
    },
    "m0Range": {
      "minimum": -4,
      "maximum": 4
    },
    "m1Range": {
      "minimum": -2,
      "maximum": 2
    },
    "seed": 42
  },
  "output": {
    "curves": [
      {
        "p0": 3,
        "p1": 8,
        "m0": 3,
        "m1": 1,
        "samples": [
          {
            "t": 0,
            "value": 3,
            "coreValue": 3
          },
          {
            "t": 0.5,
            "value": 5.75,
            "coreValue": 5.75
          },
          {
            "t": 1,
            "value": 8,
            "coreValue": 8
          }
        ]
      },
      {
        "p0": 0,
        "p1": 8,
        "m0": -2,
        "m1": 1,
        "samples": [
          {
            "t": 0,
            "value": 0,
            "coreValue": 0
          },
          {
            "t": 0.5,
            "value": 3.625,
            "coreValue": 3.625
          },
          {
            "t": 1,
            "value": 8,
            "coreValue": 8
          }
        ]
      }
    ],
    "tangentConvention": "Tangents are derivatives with respect to normalized t in [0,1]; curves may overshoot and need not be monotone.",
    "corePrecision": "coreValue inherits 12-significant-digit rounding; value preserves unrounded basis arithmetic.",
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Tangents are derivatives with respect to normalized t, not an external x coordinate. Curves can overshoot and need not be monotone. coreValue uses 12-significant-digit rounding while value retains direct floating-point arithmetic.
A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Cubic Hermite Curve Bank Generator — tool.io
Calculation or validation: interpolation/cubic-hermite — tool.io

Similar or alternative tools

Random Bead Loom Row Chart Generator
Construct an exact numeric-index bead chart from finite caller color stock under per-row repeat bounds, retaining compact matrix JSON and inventory conservation.
Random Bilinear Heightmap Tile Generator
Draw corner heights with optional consistent shared linear edges and delegate a bounded bilinear grid, returning both unrounded and inherited core values.