CALCULATOR
Axis-Aligned Ellipse Point Residual Calculator
Axis-Aligned Ellipse Point Residual Calculator — change the supplied values to calculate axis-aligned ellipse point residual.
a,b are positive semi-axes; x,y,h,k,a,b share a coordinate unit. Residual is dimensionless: negative inside, zero on, positive outside; floating arithmetic is not an exact membership proof.
Accepted inputs: X: -100 to 100 units; Y: -100 to 100 units; H: -100 to 100 units; K: -100 to 100 units; Semi-axis a: 0.01 to 100 units; Semi-axis b: 0.01 to 100 units.
How the calculation works
R=((x-h)/a)²+((y-k)/b)²-1
Substitute a point into the normalized axis-aligned ellipse equation and subtract one.
Worked example
With x 3 units, y 0 units, h 0 units, k 0 units, semi-axis a 3 units, semi-axis b 2 units, axis-aligned ellipse point residual is 0 number.
Assumptions and limits
a,b are positive semi-axes; x,y,h,k,a,b share a coordinate unit. Residual is dimensionless: negative inside, zero on, positive outside; floating arithmetic is not an exact membership proof.