QUADRIC SURFACES
CLICK HERE FOR SMALL
PRINTABLE REFERENCE
Quadric surfaces are the 3D version of conic sections. Equations for quadric
surfaces are second degree, in the form given below. Basic quadric surfaces are
shown.
xy trace in purple
xz trace in red
yz trace in blue
ELLIPSOID
SPHERE
all squared, all positive -- traces are ellipses
special case of eliipsoid: a = b = c -- traces are circles
ELLIPTIC PARABOLOID
two squared, one not - the axis of the paraboloid is the along the variable which is not squared -- traces are two parabolas, point at origin
HYPERBOLOID OF ONE SHEET
all squared, one negative - the axis of the hyperboloid is along the negative variable -- traces are two hyperbolas and an ellipse
HYPERBOLIC PARABOLOID
two squared, one not, one negative -- traces are two parabolas (axes of parabolas are along variable which is not squared) and a line
ELLIPTIC CONE
special case of hyperboloid of one sheet (= 0 instead of = 1) -- hyperbolic traces become intersecting lines, elliptic trace becomes point at origin
HYPERBOLOID OF TWO SHEETS
all squared, two negative, one positive - the axis of the hyperboloiod is along the positive variable -- traces are two hyperbolas