function [dvda]=interp_dvda(a0,b0,c0)
load('V_dV_ani.mat','aa','bb','cc','dv_a')
ha = aa(2)-aa(1);
hb = bb(2)-bb(1);
hc = cc(2)-cc(1);
ja=min(floor((a0-aa(1))/ha)+1,size(aa,2)-1);
jb=min(floor((b0-bb(1))/hb)+1,size(bb,2)-1);
jc=min(floor((c0-cc(1))/hc)+1,size(cc,2)-1);
ja=max(ja,1);jb=max(jb,1);jc=max(jc,1);
N=zeros(1,8);
nz=size(a0,1);ny=size(a0,2);nx=size(a0,3);
dvda=zeros(size(a0));
for iz=1:nz
    for iy=1:ny
        for ix=1:nx
            a=a0(iz,iy,ix);
            b=b0(iz,iy,ix);
            c=c0(iz,iy,ix);
            a00=aa(ja(iz,iy,ix));
            b00=bb(jb(iz,iy,ix));
            c00=cc(jc(iz,iy,ix));
            N(1)=(ha+a00-a)*(hb+b00-b)*(hc+c00-c)/(ha*hb*hc);
            N(2)=(a-a00)*(hb+b00-b)*(hc+c00-c)/(ha*hb*hc);
            N(3)=(ha+a00-a)*(b-b00)*(hc+c00-c)/(ha*hb*hc);
            N(4)=(a-a00)*(b-b00)*(hc+c00-c)/(ha*hb*hc);
            N(5)=(ha+a00-a)*(hb+b00-b)*(c-c00)/(ha*hb*hc);
            N(6)=(a-a00)*(hb+b00-b)*(c-c00)/(ha*hb*hc);
            N(7)=(ha+a00-a)*(b-b00)*(c-c00)/(ha*hb*hc);
            N(8)=(a-a00)*(b-b00)*(c-c00)/(ha*hb*hc);
            R=compR(dv_a,ja(iz,iy,ix),jb(iz,iy,ix),jc(iz,iy,ix));
            dvda(iz,iy,ix)=N*R;
        end
    end
end
end
function R=compR(c,aj,bj,cj)
R=zeros(8,1);
R(1)=c(aj,bj,cj);
R(2)=c(aj+1,bj,cj);
R(3)=c(aj,bj+1,cj);
R(4)=c(aj+1,bj+1,cj);
R(5)=c(aj,bj,cj+1);
R(6)=c(aj+1,bj,cj+1);
R(7)=c(aj,bj+1,cj+1);
R(8)=c(aj+1,bj+1,cj+1);
end