construct_bc.m

hodge decomposition for 2D vector fields.

function [B,C]=construct_BC(mv_x,mv_y,mv_u,mv_v) 
%% mv_x: horizontal coordinates of the grids 
%% mv_y: vertical coordinates of the grids 
%% mv_u: horizontal component of the input motion field 
%% mv_v: vertical component of the input motion field 
%% B: vector B 
%% C: vector C 
%% generate the Node Table 
mesh=mesh_points(mv_x,mv_y); 
%% generate the Grid Table 
triangle=triangle_definition(mv_x,mv_y);  

%% generate the Average Vector Table 
delta_x=mv_x(1,2)-mv_x(1,1); 
delta_y=mv_y(2,1)-mv_y(1,1); 
UV=triangle_uv(triangle,mesh,mv_x(1,1),mv_y(1,1),delta_x,delta_y,mv_u,mv_v); 
%% generate the Basis Gradient Table 
gradphi=phi_gradient(triangle,mesh); 
M=size(mesh,1); 
B=zeros(M,1); 
C=zeros(M,1); 
%% calculate the vectors B and C 
for i=1:M 
%% search for the neighboring triangles and neighboring nodes of a reference node i 
[neighbor_triangle neighbor_point]=get_neighbor(i,triangle); 
L=length(neighbor_triangle); 
for k=1:L 
t=neighbor_triangle(k); 
tri=triangle(t,:); 
order_in_triangle=find(tri==i); 
del_phi01=gradphi(t,order_in_triangle,1); 
del_phi02=gradphi(t,order_in_triangle,2); 
B(i)=B(i)+del_phi01*UV(t,1)+del_phi02*UV(t,2); 
C(i)=C(i)-del_phi01*UV(t,2)+del_phi02*UV(t,1); 
end; 
end; 
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