| 1 |
function [excess]=excess_of_quad(V1,V2,V3,V4) |
| 2 |
% excess=excess_of_quad(V1,V2,V3,V4); |
| 3 |
% |
| 4 |
% where Vn are vectors |
| 5 |
|
| 6 |
plane1=plane_normal(V1,V2); |
| 7 |
plane2=plane_normal(V2,V3); |
| 8 |
plane3=plane_normal(V3,V4); |
| 9 |
plane4=plane_normal(V4,V1); |
| 10 |
|
| 11 |
angle12=pi-angle_between_vectors(plane2,plane1); |
| 12 |
angle23=pi-angle_between_vectors(plane3,plane2); |
| 13 |
angle34=pi-angle_between_vectors(plane4,plane3); |
| 14 |
angle41=pi-angle_between_vectors(plane1,plane4); |
| 15 |
|
| 16 |
excess=angle12+angle23+angle34+angle41-2*pi; |
| 17 |
|
| 18 |
%%% |
| 19 |
|
| 20 |
function [plane]=plane_normal(P1,P2); |
| 21 |
|
| 22 |
if ndims(P1)==4 |
| 23 |
plane(:,:,:,1)=P1(:,:,:,2).*P2(:,:,:,3)-P1(:,:,:,3).*P2(:,:,:,2); |
| 24 |
plane(:,:,:,2)=P1(:,:,:,3).*P2(:,:,:,1)-P1(:,:,:,1).*P2(:,:,:,3); |
| 25 |
plane(:,:,:,3)=P1(:,:,:,1).*P2(:,:,:,2)-P1(:,:,:,2).*P2(:,:,:,1); |
| 26 |
mag=sqrt(plane(:,:,:,1).^2 + plane(:,:,:,2).^2 + plane(:,:,:,3).^2); |
| 27 |
plane(:,:,:,1)=plane(:,:,:,1)./mag; |
| 28 |
plane(:,:,:,2)=plane(:,:,:,2)./mag; |
| 29 |
plane(:,:,:,3)=plane(:,:,:,3)./mag; |
| 30 |
elseif ndims(P1)==3 |
| 31 |
plane(:,:,1)=P1(:,:,2).*P2(:,:,3)-P1(:,:,3).*P2(:,:,2); |
| 32 |
plane(:,:,2)=P1(:,:,3).*P2(:,:,1)-P1(:,:,1).*P2(:,:,3); |
| 33 |
plane(:,:,3)=P1(:,:,1).*P2(:,:,2)-P1(:,:,2).*P2(:,:,1); |
| 34 |
mag=sqrt(plane(:,:,1).^2 + plane(:,:,2).^2 + plane(:,:,3).^2); |
| 35 |
plane(:,:,1)=plane(:,:,1)./mag; |
| 36 |
plane(:,:,2)=plane(:,:,2)./mag; |
| 37 |
plane(:,:,3)=plane(:,:,3)./mag; |
| 38 |
else |
| 39 |
error('Wrong ndims') |
| 40 |
end |
| 41 |
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