GPGPU Programming for Games and Science

Sample Applications 361

7.3.3.2 Fitting with Planes

Section 7.3.2 is about fitting samples (x

i

,y

i

,z

i

) with a plane z = Ax+By+

C.Thez-value is assumed to be dependent on the x-andy-values. The least

squares fitting uses errors measured in the z-direction. I refer to this as height

plane fitting to emphasize that errors are measured in the dependent variable

(the height of the graph). If the x-, y-, and z-values are independent variables,

we may measure the errors in the direction orthogonal to the postulated plane.

This is referred to as orthogonal plane fitting.

Because the variables are independent, orthogonal plane fitting may be

used in any dimension