function p = poisson_kernel ( r, n, c, x, y ) %*****************************************************************************80 % %% POISSON_KERNEL evaluates the Poisson kernel. % % Discussion: % % P(X,Y) = ( R^2 - |X-C|^2 ) / ( R * A * |X-Y|^N ) % % where the N-dimensional ball has radius R and center C, % and A is the area of the unit sphere. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 22 November 2011 % % Author: % % John Burkardt % % Parameters: % % Input, real R, the radius of the ball. % % Input, integer N, the spatial dimension. % % Input, real C(N), the center of the ball. % % Input, real X(N), a point inside the ball. % % Input, real Y(N), a point on the surface of the ball. % % Output, real P, the Poisson kernel function P(X,Y). % xc_diff_norm = r8vec_diff_norm ( n, x, c ); xy_diff_norm = r8vec_diff_norm ( n, x, y ); area = sphere_unit_area_nd ( n ); t = ( r + xc_diff_norm ) * ( r - xc_diff_norm ); b = r * area * ( xy_diff_norm ) ^ n; p = t / b; return end