Description
For nonzero crossCoefficient, return saddleX = -yCoefficient/crossCoefficient, saddleY = -xCoefficient/crossCoefficient, saddleValue = constant - xCoefficient·yCoefficient/crossCoefficient, and sign(targetLevel - saddleValue).
A bilinear cell combines constant, two linear, and one mixed coordinate term. Corner contrasts, stationary points, and edge intersections use normalized coordinates unless spans are supplied.
For nonzero crossCoefficient, return saddleX = -yCoefficient/crossCoefficient, saddleY = -xCoefficient/crossCoefficient, saddleValue = constant - xCoefficient·yCoefficient/crossCoefficient, and sign(targetLevel - saddleValue).
When to use this tool
Use Bilinear Level Set Saddle Sign when you need one explicit bilinear coefficient, sensitivity, or level-set term.
How to use the tool and how it works
- Enter constant, xCoefficient, yCoefficient, crossCoefficient, targetLevel. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read saddleX, saddleY, saddleValue, targetSide. Use the output convention below.
For nonzero crossCoefficient, return saddleX = -yCoefficient/crossCoefficient, saddleY = -xCoefficient/crossCoefficient, saddleValue = constant - xCoefficient·yCoefficient/crossCoefficient, and sign(targetLevel - saddleValue).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| constant | Constant | Required. Finite number. |
| xCoefficient | X Coefficient | Required. Finite number. |
| yCoefficient | Y Coefficient | Required. Finite number. |
| crossCoefficient | Cross Coefficient | Required. Finite number. |
| targetLevel | Target Level | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| saddleX | Saddle X | Required. Finite number. |
| saddleY | Saddle Y | Required. Finite number. |
| saddleValue | Saddle Value | Required. Finite number. |
| targetSide | Target Side | Required. Safe integer. |
{
"input": {
"constant": 1,
"xCoefficient": 2,
"yCoefficient": 3,
"crossCoefficient": 2,
"targetLevel": 0
},
"output": {
"saddleX": -1.5,
"saddleY": -1,
"saddleValue": -2,
"targetSide": 1
}
}Limitations and assumptions
- This uses the supplied bilinear polynomial in normalized coordinates; no cell bounds or contour connectivity decision is enforced.
- 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 a complete cell model and a documented contour or interpolation policy when reconstructing a surface.
References
Similar or alternative tools
- Bilinear Saddle Stationary Coordinate
Mark insideUnitCell inclusively.
- Bilinear Cross Term Corner Contrast
Return f11 - f10 - f01 + f00 as crossCoefficient in normalized cell coordinates.