CHAPTER III: CONICS AND QUADRICS - OCW UPM
CHAPTER III: CONICS AND QUADRICS - OCW UPM
CHAPTER III: CONICS AND QUADRICS - OCW UPM
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AFFINE <strong>AND</strong> PROJECTIVE GEOMETRY, E. Rosado & S.L. Rueda<br />
Table of classification of quadrics with det A 00 = 0<br />
det A 00 = 0<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
rank(A) = 4<br />
Regular<br />
rank(A) = 3<br />
Cylinders<br />
rank(A) = 2<br />
Pair of planes<br />
rank(A) = 1<br />
{<br />
J > 0 Elliptic paraboloid<br />
⎧<br />
⎪⎨<br />
J < 0<br />
J > 0<br />
J < 0<br />
⎪⎩<br />
J = 0<br />
⎧<br />
J > 0<br />
⎪⎨ J < 0<br />
⎪⎩<br />
J = 0<br />
double plane<br />
Hyperbolic paraboloid<br />
Real elliptic cylinder<br />
Hyperbolic cylinder<br />
Parabolic cylinder<br />
Pair of imaginary planes (line)<br />
Pair of secant planes<br />
Pair of parallel planes<br />
{<br />
imaginary<br />
real
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