subroutine triangle_circumcenter_2d ( t, center ) !*****************************************************************************80 ! !! TRIANGLE_CIRCUMCENTER_2D computes the circumcenter of a triangle in 2D. ! ! Discussion: ! ! The circumcenter of a triangle is the center of the circumcircle, the ! circle that passes through the three vertices of the triangle. ! ! The circumcircle contains the triangle, but it is not necessarily the ! smallest triangle to do so. ! ! If all angles of the triangle are no greater than 90 degrees, then ! the center of the circumscribed circle will lie inside the triangle. ! Otherwise, the center will lie outside the circle. ! ! The circumcenter is the intersection of the perpendicular bisectors ! of the sides of the triangle. ! ! In geometry, the circumcenter of a triangle is often symbolized by "O". ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 09 February 2005 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, real ( kind = 8 ) T(2,3), the triangle vertices. ! ! Output, real ( kind = 8 ) CENTER(2), the circumcenter of the triangle. ! implicit none integer ( kind = 4 ), parameter :: dim_num = 2 real ( kind = 8 ) asq real ( kind = 8 ) bot real ( kind = 8 ) center(dim_num) real ( kind = 8 ) csq real ( kind = 8 ) t(dim_num,3) real ( kind = 8 ) top(dim_num) asq = ( t(1,2) - t(1,1) )**2 + ( t(2,2) - t(2,1) )**2 csq = ( t(1,3) - t(1,1) )**2 + ( t(2,3) - t(2,1) )**2 top(1) = ( t(2,2) - t(2,1) ) * csq - ( t(2,3) - t(2,1) ) * asq top(2) = ( t(1,2) - t(1,1) ) * csq - ( t(1,3) - t(1,1) ) * asq bot = ( t(2,2) - t(2,1) ) * ( t(1,3) - t(1,1) ) & - ( t(2,3) - t(2,1) ) * ( t(1,2) - t(1,1) ) center(1:2) = t(1:2,1) + 0.5D+00 * top(1:2) / bot return end