content_image/303225.jpg content_image/303226.jpg content_image/303227.jpg
Lemma 4.4.2. Using the notation of figures 4.6 and 4.9, we have ∂ $_{∂s}$g ( s, r ) = h$_{2}$ − h$_{1}$ = r sin( θ$_{2}$ ) − r sin( θ$_{1}$ ) . 

Proof. We have 

<img src='content_image/303225.jpg'>

The situation is illustrated in figure 4.9 where we can see that the area being added as we go from s to s + Δ s is the shaded region on the right with height r − h$_{1}$ and, considering first-order terms only, uniform width Δ s so has area ( r − h$_{1}$ )Δ s . Similarly, we are subtracting the area ( r − h$_{2}$ )Δ s on the left. Therefore, we have 

<img src='content_image/303226.jpg'>

## 4.5 Reconstructing shapes from T-like data 

<img src='content_image/303227.jpg'>

