function [w] = morphweight(x,y,P,Q,a,b,p)
% w = morphweight(x,y,P,Q,a,b,p).  compute morphing weights of points
%    given column vectors x,y of the same length,
%    a 2D line segment with endpoints P, Q,
%    and parameters a,b,p,  compute the column vector w of weights
%    w(i) for each point (x(i),y(i)) according to the Beier-Neeley
%    weight function ((length^p) / (a + dist))^b, where length is
%    the length of the line segment PQ, and dist is the distance of
%    the point to the line segment

% use the algorithm presented in lecture:

x = x - P(1) ; y = y - P(2); Q = Q - P;
lensquared = Q' * Q; len = sqrt(lensquared);
dott = Q(1)*x + Q(2)*y;
behind = dott < 0;
infront = dott > lensquared;
between = ~behind & ~infront;

dist(behind) = sqrt(x(behind).^2 + y(behind).^2);
dist(infront) = sqrt((x(infront)-Q(1)).^2 + (y(infront)-Q(2)).^2);
dist(between) = abs(x(between) * Q(2) - y(between) * Q(1)) / len;

w = (len^p ./ (a+dist)).^b;