# Primitive Shape Fitting in Point Clouds Using the Bees Algorithm
## 6 Discussion
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & & \multicolumn{4}{c}{**Clean**} \\ \hline
**Shape** & **Algorithm** & **Min** & **First quartile** & **Median** & **Third quartile** & **Max** \\ \hline Sphere & Evolutionary algorithm & \(1.055\times 10^{-3}\) & \(8.898\times 10^{-3}\) & \(1.410\times 10^{-2}\) & \(2.135\times 10^{-2}\) & \(8.831\times 10^{-2}\) \\ Sphere & Bees algorithm & \(1.270\times 10^{-5}\) & \(1.594\times 10^{-4}\) & \(2.585\times 10^{-4}\) & \(4.132\times 10^{-4}\) & \(1.625\times 10^{-3}\) \\ Sphere & RANSAC & 0 & 0 & 0 & 0 & 0 \\ \hline Box & Evolutionary algorithm & \(8.170\times 10^{-3}\) & \(2.517\) & \(2.815\) & \(3.514\) & \(1.217\times 10^{1}\) \\ Box & Bees algorithm & \(7.828\times 10^{-2}\) & \(1.903\) & \(2.353\) & \(2.938\) & \(1.246\times 10^{1}\) \\ Box & RANSAC & \(1.490\times 10^{-8}\) & \(2.500\) & \(2.714\) & \(3.250\) & \(7.000\) \\ \hline Cylinder & Evolutionary algorithm & \(8.893\times 10^{-2}\) & \(1.954\) & \(4.441\) & \(8.938\) & \(1.071\times 10^{3}\) \\ Cylinder & Bees algorithm & \(2.069\times 10^{-1}\) & \(1.824\) & \(3.709\) & \(7.667\) & \(1.052\times 10^{3}\) \\ Cylinder & RANSAC & \(1.902\) & \(2.481\) & \(2.696\) & \(3.162\) & \(1.115\times 10^{2}\) \\ \hline \hline \multicolumn{6}{c}{**Single Error**} \\ \hline
**Shape** & **Algorithm** & **Min** & **First quartile** & **Median** & **Third quartile** & **Max** \\ \hline Sphere & Evolutionary algorithm & \(1.075\times 10^{-3}\) & \(9.255\times 10^{-3}\) & \(1.435\times 10^{-2}\) & \(2.205\times 10^{-2}\) & \(1.013\times 10^{-1}\) \\ Sphere & Bees algorithm & \(1.109\times 10^{-4}\) & \(1.022\times 10^{-3}\) & \(1.690\times 10^{-3}\) & \(2.885\times 10^{-3}\) & \(3.689\times 10^{-2}\) \\ Sphere & RANSAC & \(3.061\times 10^{-4}\) & \(3.462\times 10^{-3}\) & \(5.931\times 10^{-3}\) & \(9.289\times 10^{-3}\) & \(5.755\times 10^{-2}\) \\ \hline Box & Evolutionary algorithm & \(7.724\times 10^{-3}\) & \(2.496\) & \(2.802\) & \(3.517\) & \(1.212\times 10^{1}\) \\ Box & Bees algorithm & \(3.498\times 10^{-2}\) & \(1.872\) & \(2.348\) & \(2.938\) & \(1.167\times 10^{1}\) \\ Box & RANSAC & \(1.175\times 10^{-2}\) & \(2.230\) & \(2.511\) & \(2.955\) & \(7.106\) \\ \hline Cylinder & Evolutionary algorithm & \(8.816\times 10^{-2}\) & \(1.954\) & \(4.478\) & \(9.032\) & \(1.054\times 10^{3}\) \\ Cylinder & Bees algorithm & \(1.141\times 10^{-1}\) & \(1.813\) & \(3.758\) & \(7.711\) & \(1.140\times 10^{3}\) \\ Cylinder & RANSAC & \(6.959\times 10^{-2}\) & \(2.222\) & \(2.426\) & \(2.779\) & \(1.082\times 10^{3}\) \\ \hline \hline \multicolumn{6}{c}{**Double Error**} \\ \hline
**Shape** & **Algorithm** & **Min** & **First quartile** & **Median** & **Third quartile** & **Max** \\ \hline Sphere & Evolutionary algorithm & \(9.426\times 10^{-4}\) & \(9.769\times 10^{-3}\) & \(1.522\times 10^{-2}\) & \(2.319\times 10^{-2}\) & \(1.018\times 10^{-1}\) \\ Sphere & Bees algorithm & \(2.037\times 10^{-4}\) & \(1.838\times 10^{-3}\) & \(3.140\times 10^{-3}\) & \(5.610\times 10^{-3}\) & \(7.257\times 10^{-2}\) \\ Sphere & RANSAC & \(5.078\times 10^{-4}\) & \(6.800\times 10^{-3}\) & \(1.066\times 10^{-2}\) & \(1.776\times 10^{-2}\) & \(1.077\times 10^{-1}\) \\ \hline Box & Evolutionary algorithm & \(1.795\times 10^{-2}\) & \(2.482\) & \(2.768\) & \(3.471\) & \(1.210\times 10^{1}\) \\ Box & RANSAC & \(8.176\times 10^{-2}\) & \(1.899\) & \(2.351\) & \(2.991\) & \(1.200\times 10^{1}\) \\ Box & RANSAC & \(2.545\times 10^{-2}\) & \(2.081\) & \(2.425\) & \(2.843\) & \(7.272\) \\ \hline Cylinder & Evolutionary algorithm & \(8.970\times 10^{-2}\) & \(1.984\) & \(4.514\) & \(9.347\) & \(1.095\times 10^{3}\) \\ Cylinder & Bees algorithm & \(1.251\times 10^{-1}\) & \(1.880\) & \(3.884\) & \(8.076\) & \(1.170\times 10^{3}\) \\ Cylinder & RANSAC & \(1.562\times 10^{-1}\) & \(2.070\) & \(2.339\) & \(2.693\) & \(8.833\times 10^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Five-number summary of the primitive fitting results obtained by the evolutionary algorithm, bees algorithm and RANSAC on the three data sets.