Algorithm 1. OCD4M

Require:

Camera sensor set ${\mathrm{S}=\{\mathrm{s}}_1{,\mathrm{s}}_2{,\dots ,\mathrm{s}}_{\mathrm{N}}\}$, target surface $\mathrm{A}:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=0$, Observation platform $\mathrm{B}:\mathrm{g}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=0$, Photography distance $\mathrm{D}$, sensing angle $\mathsf{\alpha }$

Ensure:

A is covered by the set of $\mathrm{C}\left(\mathrm{i}\right):\left(\mathrm{xyz}\right(\mathrm{s}\left(\mathrm{i}\right)), \mathrm{D}, \mathsf{\alpha },\overrightarrow{{\mathrm{d}}_{\mathrm{i}}})$, and the degree of overlap of adjacent $C\left(i\right)$ greater than 80%. (1) $\mathrm{A}\subseteq {\mathrm{C}}_{\mathrm{s}\left(1\right)}\cup {\mathrm{C}}_{\mathrm{s}\left(2\right)}\cup \dots \cup {\mathrm{C}}_{\mathrm{s}\left(\mathrm{N}\right)}$; (2) ${\mathrm{S}}_{{\mathrm{C}}_{\mathrm{s}\left(\mathrm{i}\right)}\cap {\mathrm{C}}_{\mathrm{s}\left(\mathrm{i}+1\right)}}\ge 0.8{\mathrm{S}}_{{\mathrm{C}}_{\mathrm{s}\left(\mathrm{i}\right)}}$; (3) ${\mathrm{xyz}(\mathrm{s}}_{\mathrm{i}})\subseteq \mathrm{B}$.

Process:

1: Compute the range of A. ${\mathrm{A}}_{\mathrm{Z}}{=\mathrm{A}}_{\mathrm{zmax}}{–\mathrm{A}}_{\mathrm{zmin}}{; \mathrm{A}}_{\mathrm{X}}{=\mathrm{A}}_{\mathrm{xmin}}{–\mathrm{A}}_{\mathrm{xmax}}$,

2: Compute the range of B. ${\mathrm{B}}_{\mathrm{Z}}{=\mathrm{B}}_{\mathrm{zmax}}{–\mathrm{B}}_{\mathrm{zmin}}{; \mathrm{B}}_{\mathrm{X}}{=\mathrm{B}}_{\mathrm{xmin}}{–\mathrm{B}}_{\mathrm{xmax}}$,

3: Compute the rang of Ci,

4: Whether to cover the Z direction of Mine Surface A

5: while ${\mathrm{C}}_{\mathrm{z}}{*\mathrm{K}<\mathrm{A}}_{\mathrm{Z}}$ do

6:    get the number of camera sensors at each point

7:    K++

8: End while

9: Judge the Length relationship of A and B

10: If (${\mathrm{B}}_{\mathrm{Xmin}}\le {\mathrm{A}}_{\mathrm{Xmin}}{ \mathrm{and} \mathrm{B}}_{\mathrm{Xmax}}\ge {\mathrm{A}}_{\mathrm{Xmax}}$) do

11:    normal case photography, compute the minimum of camera sensors by Formula (9):

12:    Compute the coordinate of each camera sensor according to the photography

13:    distance by Equation (11),

14:    ${\mathrm{y}=\mathrm{B}}_{\mathrm{ymax}}$, $z$

15: Else

16:    convergent photography (angle $\theta$);

17:    compute the range of camera sensor number by

18:    Equations (9)–(11),

19:    we can get K, N and ${(\mathrm{s}}_{\mathrm{i}}(\mathrm{x}, \mathrm{y}, \mathrm{z}))$

20: End If

21: Return number ($\mathrm{K}*\mathrm{N}$) and position of sensor ${(\mathrm{s}}_{\mathrm{i}}(\mathrm{x}, \mathrm{y}, \mathrm{z}))$