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subroutine cross_3d ( x1, y1, z1, x2, y2, z2, x3, y3, z3 ) !*************************************************** !! CROSS_3D computes the cross product of two vectors in 3D. ! ! Definition: ! ! The cross product in 3D can be regarded as the determinant of the ! symbolic matrix: ! ! | i j k | ! det | x1 y1 z1 | ! | x2 y2 z2 | ! ! = ( y1 * z2 - z1 * y2 ) * i ! + ( z1 * x2 - x1 * z2 ) * j ! + ( x1 * y2 - y1 * x2 ) * k ! Modified: ! 19 April 1999 ! Author: ! John Burkardt ! Parameters: ! Input, real X1, Y1, Z1, X2, Y2, Z2, the coordinates of the vectors. ! Output, real X3, Y3, Z3, the cross product vector. implicit none real(8) x1 real(8) x2 real(8) x3 real(8) y1 real(8) y2 real(8) y3 real(8) z1 real(8) z2 real(8) z3 x3 = y1 * z2 - z1 * y2 y3 = z1 * x2 - x1 * z2 z3 = x1 * y2 - y1 * x2 end subroutine cross_3d