Description
Intersect two infinite planar perspective lines; signed parameters expose intersections behind either origin.
Studio measurements translate a design into lengths, areas, volumes, angles, proportions, and material quantities. Consistent units and an explicit geometric model make the calculation interpretable. Real materials, fabrication allowances, visual judgments, and installation conditions require information beyond a geometric term.
Intersect two infinite planar perspective lines; signed parameters expose intersections behind either origin.
When to use this tool
Use Perspective Vanishing Ray Intersection Parameter when you need a geometric or material-budget term for a supplied studio design before checking real material and installation conditions.
How to use the tool and how it works
- Enter firstOrigin, firstDirection, secondOrigin, secondDirection. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read firstParameter, secondParameter, point. Use the output convention below.
Intersect two planar parametric lines using cross products. Require four two-component origin/direction vectors and a nonzero direction determinant; return both line parameters and the point on the first line.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstOrigin | First Origin | Required. Array of Finite number.; maximum items 256. |
| firstDirection | First Direction | Required. Array of Finite number.; maximum items 256. |
| secondOrigin | Second Origin | Required. Array of Finite number.; maximum items 256. |
| secondDirection | Second Direction | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| firstParameter | Parameter on the first infinite line; may be negative. | Required. Finite number. |
| secondParameter | Parameter on the second infinite line; may be negative. | Required. Finite number. |
| point | Point | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"firstOrigin": [
0,
0
],
"firstDirection": [
1,
1
],
"secondOrigin": [
2,
0
],
"secondDirection": [
-1,
1
]
},
"output": {
"firstParameter": 1,
"secondParameter": 1,
"point": [
1,
1
]
}
}Limitations and assumptions
- Despite ray in the tool name, negative parameters are permitted, so the result can lie behind a ray origin. Parallel or coincident directions are rejected, and near-parallel intersections can be numerically sensitive.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use measured material allowances and a complete drawing or fabrication model when physical behavior matters. The supplied geometric term can be one input to that separate process.
References
Similar or alternative tools
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