KX = -y(A)y(B) KY = y(B)(x(V)-x(A)) KZ = y(A)(x(B)-x(V)) KO = x(V)y(A)y(B) KX' = -y(A')y(B') KY' = y(B')(x(V')-x(A')) KZ' = y(A')(x(B')-x(V')) KO' = x(V')y(A')y(B') Plano alfa --> x*KX + y*KY + z*KZ + KO = 0 Plano beta --> x*KX' + y*KY' + z*KZ' + KO' = 0 PROYECCIÓN HORIZONTAL RECTA INTERSECCIÓN ELIMINAR Z x*KXKZ' + y*KYKZ' + z*KZKZ' + KOKZ' = 0 x*KX'KZ + y*KY'KZ + z*KZ'KZ + KO'KZ = 0 resetando Y CAMBIANDO EL SIGNO A y: x*((-y(A)y(B))y(A')(x(B')-x(V')) - (-y(A')y(B'))y(A)(x(B)-x(V))) - y*(y(B)(x(V)-x(A))y(A')(x(B')-x(V')) - y(B')(x(V')-x(A'))y(A)(x(B)-x(V))) + x(V)y(A)y(B)y(A')(x(B')-x(V')) - x(V')y(A')y(B')y(A)(x(B)-x(V)) = 0 PROYECCIÓN VERTICAL RECTA INTERSECCIÓN ELIMINAR Y x*KXKY' + y*KYKY' + z*KZKY' + KOKY' = 0 x*KX'KY + y*KY'KY + z*KZ'KY + KO'KY = 0 restando Y CAMBIANDO z POR y: x*((-y(A)y(B))y(B')(x(V')-x(A')) - (-y(A')y(B'))y(B)(x(V)-x(A))) + y*(y(A)(x(B)-x(V))y(B')(x(V')-x(A')) - y(A')(x(B')-x(V'))y(B)(x(V)-x(A))) + x(V)y(A)y(B)y(B')(x(V')-x(A')) - x(V')y(A')y(B')y(B)(x(V)-x(A)) = 0 NO UTILIZADO Traza horizontal alfa x*(-y(A)y(B)) - y*y(B)(x(V)-x(A)) + x(V)y(A)y(B) = 0 Traza vertical alfa x*(-y(A)y(B)) + y*y(A)(x(B)-x(V)) + x(V)y(A)y(B) = 0 Traza horizontal beta x*(-y(A')y(B')) - y*y(B')(x(V')-x(A')) + x(V')y(A')y(B') = 0 Traza vertical beta x*(-y(A')y(B')) + y*y(A')(x(B')-x(V')) + x(V')y(A')y(B') = 0