Area of Triangle

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developer
developer 2011-9-1
Hello, Is there any function to find the area of any triangle using 3D points in cartesian system, where i have the vertices of the triangle in 3d coordinate?
Thanks

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Grzegorz Knor
Grzegorz Knor 2011-9-1
According to Wikipedia:
http://en.wikipedia.org/wiki/Triangle#Using_coordinates
x = rand(3,1);
y = rand(3,1);
z = rand(3,1);
fill3(x,y,z,'r')
x = x(:)';
y = y(:)';
z = z(:)';
ons = [1 1 1];
A = 0.5*sqrt(det([x;y;ons])^2 + det([y;z;ons])^2 + det([z;x;ons])^2)
Grzegorz

更多回答（1 个）

Sean de Wolski
Sean de Wolski 2011-9-1
Yes, use Heron's numerically stable algorithm. Here's a function I wrote to do it with the output of the isosurface function:
function [A]= areaIsosurface(F,V)
%Function to calculate the area of an isosurface generated by MATLAB's
% built-in isosurface().
%SCd 07/12/2010
%
%This function uses Heron's numerically stable formula available here:
%>>web('http://en.wikipedia.org/wiki/Heron''s_formula','-new');
%
%Input Arguments:
% [F,V] = isosurface(...);
% F: calculation above
% V: calculation above
%
%Output Arguments:
% A: surface area of the triangulated isosurface.
%
%Calculate side lengths:
sides = zeros(size(F,1),3); %Preallocate
sides(:,1) = sqrt(... %a
(V(F(:,1),1)-V(F(:,2),1)).^2+...
(V(F(:,1),2)-V(F(:,2),2)).^2+...
(V(F(:,1),3)-V(F(:,2),3)).^2);
sides(:,2) = sqrt(... %b
(V(F(:,2),1)-V(F(:,3),1)).^2+...
(V(F(:,2),2)-V(F(:,3),2)).^2+...
(V(F(:,2),3)-V(F(:,3),3)).^2);
sides(:,3) = sqrt(... %c
(V(F(:,1),1)-V(F(:,3),1)).^2+...
(V(F(:,1),2)-V(F(:,3),2)).^2+...
(V(F(:,1),3)-V(F(:,3),3)).^2);
%Sort so: sides(:,1)>=sides(:,2)>=sides(:,3).
sides = sort(sides,2,'descend');
%Calculate Area!
A = sum(sqrt(...
(sides(:,1)+(sides(:,2)+sides(:,3))).*...
(sides(:,3)-(sides(:,1)-sides(:,2))).*...
(sides(:,3)+(sides(:,1)-sides(:,2))).*...
(sides(:,1)+(sides(:,2)-sides(:,3)))))/4;
end

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