Description
Calculate a parallelogram's signed left-positive height from two vectors.
Planar orientation and geometric projections depend on the direction of axes and vectors as well as length units. Signed area and height retain side information, while chord sagitta and cone slant angles use specific ideal shapes. Finite-precision formulas and degenerate boundary cases require explicit interpretation.
Calculate a parallelogram's signed left-positive height from two vectors.
When to use this tool
Use Parallelogram Signed Height From Cross Product when checking the stated oriented vector, ideal cone or circle convention.
How to use the tool and how it works
- Enter baseX, baseY, sideX, sideY. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leftPositiveHeight. Use the output convention below.
Require a nonzero planar base vector. Return (baseX*sideY-baseY*sideX)/hypot(baseX,baseY) as left-positive perpendicular height.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| baseX | Base X | Required. Finite number. |
| baseY | Base Y | Required. Finite number. |
| sideX | Side X | Required. Finite number. |
| sideY | Side Y | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leftPositiveHeight | Cross product divided by base length; positive left of oriented base in Cartesian axes. | Required. Finite number. |
{
"input": {
"baseX": 4,
"baseY": 0,
"sideX": 1,
"sideY": 3
},
"output": {
"leftPositiveHeight": 3
}
}Limitations and assumptions
- Positive side means left of the oriented base in a Cartesian frame; near-zero determinants receive no geometric tolerance.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use complete geometry and appropriate robust predicates or uncertainty analysis for near-degenerate inputs and physical design conclusions.
References
Similar or alternative tools
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