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Ur�en� druhu plochy

SV�T GEOMETRIE

Anal�za obecn�ho tvaru

Obecn� tvar

Ax² + By² + Cz² + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Kz + L = 0

Anal�za obecn�ho tvaru

1. D = E = F = 0 : Dopln�n� na �tverec a porovn�n� se standardn�m tvarem rovnic.

Kulov� plocha	x² + y² + z² = R²
Elipsoid	x²/a² + y²/b² + z²/c² = 1
Eliptick� v�lcov� plocha	x²/a² + y²/b² = 1
Hyperbolick� v�lcov� plocha	x²/a² - y²/b² = +-1
Eliptick� paraboloid	x²/a² + y²/b² = z
Hyperbolick� paraboloid	x²/a² - y²/b² = z
Eliptick� ku�el	x²/a² + y²/b² - z²/c² = 0
Eliptick� hyperboloid jednod�ln�	x²/a² + y²/b² - z²/c² = 1
Eliptick� hyperboloid dvoud�ln�	x²/a² + y²/b² - z²/c² = -1

2. N�kter� s konstant D, E, F nerovn� se 0 : spektr�ln� metody, transformace sou�adnic.

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