- #1
daudaudaudau
- 302
- 0
Hi!
I have to integrate on a triangular domain
[tex]
\int_T f(x,y,z)dxdydz
[/tex]
so I use simplex coordinates, i.e.
[tex]x=(1-\alpha-\beta)x_1+\alpha x_2+\beta x_3[/tex]
[tex]y=(1-\alpha-\beta)y_1+\alpha y_2+\beta y_3[/tex]
[tex]z=(1-\alpha-\beta)z_1+\alpha z_2+\beta z_3[/tex]
where [tex](x_i,y_i,z_i)[/tex] are the vertices of the triangle and [tex] 0\le\alpha\le1,\ 0\le\beta\le1-\alpha[/tex]
So what is the Jacobian? When I try to calculate it, the matrix is not square because I have two variables and three equations!
I have to integrate on a triangular domain
[tex]
\int_T f(x,y,z)dxdydz
[/tex]
so I use simplex coordinates, i.e.
[tex]x=(1-\alpha-\beta)x_1+\alpha x_2+\beta x_3[/tex]
[tex]y=(1-\alpha-\beta)y_1+\alpha y_2+\beta y_3[/tex]
[tex]z=(1-\alpha-\beta)z_1+\alpha z_2+\beta z_3[/tex]
where [tex](x_i,y_i,z_i)[/tex] are the vertices of the triangle and [tex] 0\le\alpha\le1,\ 0\le\beta\le1-\alpha[/tex]
So what is the Jacobian? When I try to calculate it, the matrix is not square because I have two variables and three equations!