Calculate the table support forces for an irregular polygon table.

table_support.f90

    program table_support
    ! code to accomapny the follwoing Physics.SE answer
    ! https://physics.stackexchange.com/a/459404/392

    implicit none

    ! Variables
    integer :: i, n
    real, allocatable :: x(:), y(:), F(:)
    real :: C_x, C_y, d, W
    real :: S_x,S_xx,S_y,S_yy,S_xy
    
    ! Body of program
    write (*,*) 'Table with n legs of irrgular shape.' 
    write (*,*) 'Find each leg support as a percent of the total weight of the table'    
    write (*,*) 'Enter the number of legs n='
    read (*,*) n
    
    allocate(x(n),y(n))
    
    write (*,*) 'Enter leg coordinates relative to the center of gravity'
    
    do i=1,n
        write(*,'(1x,a,i2,a)') 'Leg i=', i, ' coordinates (x,y):'
        read(*,*) x(i),y(i)
    end do
    
    S_x = sum(x)
    S_y = sum(y)
    S_xy = sum(x * y)
    S_xx = sum(x**2)
    S_yy = sum(y**2)
    
    d = (n*S_yy-S_x**2)*(n*S_xx-S_x**2)-(n*S_xy-S_x*S_y)**2
    
    C_x = (S_x*S_xy-S_xx*S_y)/d
    C_y = (S_x*S_yy-S_y*S_xy)/d
    
    allocate(F(n))
    
    do i=1,n
        F(i) = 1d0/n + (n*y(i)-S_y)*C_x + (S_x-n*x(i))*C_y
        write(*,'(1x,a,i2,a,g,a,g,a,g)') 'Leg i=', i, ' x=', x(i), ' y=', y(i), ' Force=', F(i)
    end do
    
    W = sum(F)
    
    write (*,'(1x,a,g)') 'Sum of forces is W=', W

    end program table_support