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I have come across some text where [tex]f(x,y)=c_1+c_2x+c_3y+c_4xy[/tex] is used to define the corner points

[tex]f_1=f(0,0)=c_1[/tex]

[tex]f_2=f(a,0)=c_1+c_2a[/tex]

[tex]f_3=f(a,b)=c_1+c_2a+c_3b+c_4ab[/tex]

[tex]f_4=f(0,b)=c_1+c_3b[/tex]

How are these equations determined? F_1 to F_4 starts at bottom left hand corner and rotates counter clockwise.

Thanks

Note: This was posted last week on MHB with no response.

The equation of a hyperbolic paraboloid to derive the corner points of rectangle