PROBLEM: Determine an equation for the surface of the object shown. The object has a square footprint. The two high corners are the same height, and the two low corners are the same height. The surface consists of straight lines that are parallel to the x - y plane. Lines continuously change slope as z decreases.

The coordinate system is given with the origin at the center of the surface. Both the x and z axes lie in the surface. Let the 'right hand' edge be x2 = 0.5, the 'left hand' edge be x1 = -0.5, the 'front' edge be z1 = 0.5, and the 'back' edge be z2 = -0.5. For the two high corners y = H and for the two low corners y = L.

Use the equation for a straight line:

1) y = intercept + slope * x

and the two point equation for determining the slope:

2) slope = (y2 - y1) / (x2 - x1).

Thus: y = (y2 - y1) x since (x2 - x1) = 1, intercept = 0

and y2 = (L - H) z since (z2 - z1) = 1, intercept = 0

similarly y1 = (H - L) z

Substituting in 1) y = (L - H)(H - L) z x

And y = -(H - L)2 z x

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