Description
Audit supplied three-coordinate barycentric closed-triangle membership with an explicit nonnegative absolute tolerance; does not validate a triangle’s geometry.
Planar geometry operates on two-coordinate Cartesian points and explicit shape boundaries. A closed rectangle includes its edges, while a segment parameter locates a point along a supporting line. Signed cross products, areas and axis gaps preserve orientation or direction information that a magnitude alone would lose.
Audit supplied three-coordinate barycentric closed-triangle membership with an explicit nonnegative absolute tolerance; does not validate a triangle’s geometry.
When to use this tool
Use this tool to audit supplied three-coordinate barycentric closed-triangle membership with an explicit nonnegative absolute tolerance; does not validate a triangle’s geometry.
How to use the tool and how it works
- Enter weights, tolerance using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.sum, result.member. Interpret signs, units, ordering and null values using the rules below.
Require three weights and nonnegative tolerance. Return their sum and member = true only when |sum−1| ≤ tolerance and every weight lies in [−tolerance,1+tolerance].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| weights | Three dimensionless barycentric weights in the supplied vertex order. | Dense list of at most 128 finite numbers, subject to the stated integer/shape rules. |
| tolerance | Nonnegative absolute tolerance on the sum and component bounds of barycentric weights. | Finite number satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.sum | Sum of the supplied barycentric weights. |
| result.member | Whether the explicit sum and component bounds pass the tolerance checks. |
{
"input": {
"weights": [
0.5,
0.25,
0.25
],
"tolerance": 0
},
"output": {
"result": {
"sum": 1,
"member": true
}
}
}Limitations and assumptions
- This tests supplied weights, not the triangle’s geometric validity or how the weights were obtained.
- Point components and rectangle bounds are finite within ±1,000,000,000. Rectangles use [minX,minY,maxX,maxY] with ordered inclusive bounds. Floating arithmetic is used without an implicit robustness tolerance.
- 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 boundary and coordinate convention explicitly. Use robust geometric predicates or a topology-aware library when near-coincidence, holes, invalid polygons or geographic coordinates matter.
References
Similar or alternative tools
- Triangle Barycentric Point
Map three supplied barycentric weights summing to one to a planar triangle point; weights may be negative, no inside-triangle claim.
- Triangle Point Barycentric Coordinates
Invert planar barycentric coordinates on a nondegenerate supplied triangle; floating arithmetic and signed exterior weights are retained.