Description
Number equally spaced perimeter holes on a supplied simple orthogonal outline, sample a phase and verify every Euclidean pair distance; material safety and physical usability remain caller-reviewed.
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.
Number equally spaced perimeter holes on a supplied simple orthogonal outline, sample a phase and verify every Euclidean pair distance; material safety and physical usability remain caller-reviewed.
When to use this tool
Use this generator to create reproducible lacing card hole layout 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 outline, holeCount, phaseTurns, minimumSpacing 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 holes, perimeter, phaseTurns, minimumPairDistance, boundingRectangleArea. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Validate a simple closed axis-aligned outline, select a phase, and place equally spaced perimeter-arclength holes. Measure every Euclidean hole pair and reject the chosen phase if minimumSpacing fails; return perimeter and bounding-rectangle area.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| outline | Outline | Required. Array of Array of Finite number.; minimum items 2; maximum items 2.; minimum items 4; maximum items 16. |
| holeCount | Hole Count | Required. Safe integer; minimum 3; maximum 64. |
| phaseTurns | Phase Turns | Required. Array of Finite number; minimum 0; strictly below 1.; minimum items 1; maximum items 16. |
| minimumSpacing | Minimum Spacing | Required. Finite number; strictly above 0. |
| 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 |
|---|---|---|
| holes | Holes | Required. Array of Object; no unknown keys.; minimum items 3; maximum items 64. |
| holes[].number | Number | Required. Safe integer; minimum 1; maximum 64. |
| holes[].point | Point | Required. Array of Finite number.; minimum items 2; maximum items 2. |
| holes[].arclength | Arclength | Required. Finite number; minimum 0. |
| perimeter | Perimeter | Required. Finite number; strictly above 0. |
| phaseTurns | Phase Turns | Required. Finite number; minimum 0; strictly below 1. |
| minimumPairDistance | Minimum Pair Distance | Required. Finite number; strictly above 0. |
| boundingRectangleArea | Bounding Rectangle Area | Required. Finite number; strictly above 0. |
| randomness | Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional numeric 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.
{
"input": {
"outline": [
[
0,
0
],
[
4,
0
],
[
4,
2
],
[
0,
2
]
],
"holeCount": 4,
"phaseTurns": [
0
],
"minimumSpacing": 2,
"seed": 42
},
"output": {
"holes": [
{
"number": 1,
"point": [
0,
0
],
"arclength": 0
},
{
"number": 2,
"point": [
3,
0
],
"arclength": 3
},
{
"number": 3,
"point": [
4,
2
],
"arclength": 6
},
{
"number": 4,
"point": [
1,
2
],
"arclength": 9
}
],
"perimeter": 12,
"phaseTurns": 0,
"minimumPairDistance": 2.23606797749979,
"boundingRectangleArea": 8,
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Equal arclength does not ensure equal straight-line spacing near corners. Other phases are not searched after a spacing failure. The area is the bounding rectangle's area, not necessarily the outline's area or a material-strength assessment.
- A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
- 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
Similar or alternative tools
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