Here’s a little matlab gui to play with a bilinar function in a square, visualizing its value and partial derivatives with respect to x and y. Save it into a file `bilinear_interactive.m`

.

```
function bilinear_interactive()
% BILINEAR_INTERACTIVE Create a little GUI to play with a bilinar function in
% a square, visualizing its value and partial derivatives with respect to x
% and y.
%
% bilinear_interactive()
%
clf;
[V,F] = create_regular_grid(50,50,0,0);
corner = [1 1 2 0];
bi = @(x,y,a,b,c,d) y.*(a+x.*(b-a)) + (1-y).*(c+x.*(d-c));
grad_bi_x = @(x,y,a,b,c,d) y.*((b-a)-(d-c))+(d-c);
grad_bi_y = @(x,y,a,b,c,d) x.*((b-a)-(d-c))+(a-c);
subplot(1,3,1);
tsh = trisurf(F,V(:,1),V(:,2), ...
bi(V(:,1),V(:,2),corner(1),corner(2),corner(3),corner(4)), ...
'EdgeColor','none','FaceColor','inter','FaceLighting','phong');
caxis([0 2]);
title('Bilinear function f','FontSize',20);
colormap(jet(15));
axis equal;
view(2);
subplot(1,3,2);
xsh = trisurf(F,V(:,1),V(:,2), ...
grad_bi_x(V(:,1),V(:,2),corner(1),corner(2),corner(3),corner(4)), ...
'EdgeColor','none','FaceColor','inter','FaceLighting','phong');
axis equal;
caxis([-2 2]);
title('df/dx','FontSize',20);
view(2);
subplot(1,3,3);
ysh = trisurf(F,V(:,1),V(:,2), ...
grad_bi_y(V(:,1),V(:,2),corner(1),corner(2),corner(3),corner(4)), ...
'EdgeColor','none','FaceColor','inter','FaceLighting','phong');
axis equal;
title('df/dy','FontSize',20);
caxis([-2 2]);
view(2);
set(gcf,'Position',[1 1 1440 830]);
pos = [ ...
[150-40 110+500 120 20];
[450-20 110+500 120 20];
[150-40 40+200 120 20];
[450-20 40+200 120 20];];
label = zeros(1,4);
for ind = 1:4
label(ind) = uicontrol('Style', 'text',...
'Position',pos(ind,:), ...
'FontSize',20, ...
'String',num2str(corner(ind)));
uicontrol('Style', 'slider',...
'Min',0,'Max',2, ...
'Value',corner(ind), ...
'Position',get(label(ind),'Position')-[0 20 0 0], ...
'Callback', @(src,evt) update(get(src,'Value'),ind));
end
function update(val,ind)
corner(ind) = val;
Z = bi(V(:,1),V(:,2),corner(1),corner(2),corner(3),corner(4));
set(label(ind),'String',num2str(val));
set(tsh,'Vertices',[V Z],'CData',Z);
Z = grad_bi_x(V(:,1),V(:,2),corner(1),corner(2),corner(3),corner(4));
set(xsh,'Vertices',[V Z],'CData',Z);
Z = grad_bi_y(V(:,1),V(:,2),corner(1),corner(2),corner(3),corner(4));
set(ysh,'Vertices',[V Z],'CData',Z);
drawnow;
end
end
```