Example applications of the mathematics of Ellipsoids ...
Hip Roof with flared Rafters and Eaves
Graphing and Lofting Ovoids and Ellipsoids

Ellipsoid Calculator
Hip Roof ... Flared Rafters and Eaves
((x – h)/a)2 + (y/b)2 + ((z – c)/c)2 = 1
Semi-axis on x-axis ... a =
Semi-axis on y-axis ... b =
Semi-axis on z-axis ... c =
Offset Centroid on x-axis ... h =
Plan Angle ... θ =
Common Run Dimension ... y =

Quadratic Form of Equation
z = c – √(–AD² + BD + C)
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A =
B =
C =

Hip Rafter Ellipse

Level Axis ... 2d =
Plumb Axis ... 2c' =

Critical Points

Flare Height at D = 0 ... z =
Minumum z =
at minumum z ... D =
at minumum z ... x =
Hip Run Dimension ... D =
Rise at D ... z =
Slope at D ... m =
Ellipsoid Calculator
Plumb and Level Section Planes
(x/a)2 + (y/b)2 + (z/c)2 = 1
Semi-axis on x-axis ... a =
Semi-axis on y-axis ... b =
Semi-axis on z-axis ... c =
Offset Section Plane =
Axis normal to Section Plane ...




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Ovoid Level Section Calculator
Six Specified Points
(x/a)2 + (y/(bekx))2 + (z/c)2 = 1
Semi-axis on x-axis ... a =
Semi-axis on y-axis ... b =
Semi-axis on z-axis ... c =
Specify ± x =
Specify ± y =
Offset Section Plane on z-axis =
k =
Level Section Plane Formula
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Joe Bartok