$\bf{R}$ Err ($^\circ$)   Time (s)   $\bf{t}$ Err ($\%$)   $\bf{R}$ Err ($^\circ$)   Time (s)
  Olsson [@olsson2008solving]             2.03e-1               **5.46e-1**               2.22       5.75e-1               5.76e-1                   1.88       **3.60e-1**           **2.53e-1**               2.08
  Wientapper [@wientapper2018universal]   2.00e-1               5.72e-1                   0.58       4.32e-1               3.49e-1                   0.55       3.61e-1               2.58e-1                   0.56
  Briales [@briales2017convex]            1.96e-1               5.61e-1                   2.16       **4.31e-1**           **3.37e-1**               1.88       **3.60e-1**           **2.53e-1**               2.03
  **Ours**                                **1.95e-1**           5.61e-1                   **0.33**   **4.31e-1**           **3.37e-1**               **0.30**   **3.60e-1**           **2.53e-1**               **0.30**
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Experiments with Synthetic Data
-------------------------------

Our synthetic data is generated as [@briales2017convex]. Specifically, each geometric element is determined by randomly sampling a point within a sphere of radius $10m$. For lines and planes, a random unit direction and normal are generated. We uniformly sample the Euler angles $\alpha ,\beta ,\gamma $ of the rotation matrix ( $\alpha ,\gamma  \in \left[ {0^\circ ,360^\circ } \right]$ and $\beta  \in \left[ {0^\circ ,180^\circ } \right]$). The translation elements are uniformly distributed within $\left[ -10m, 10m\right]$. We use ${\mathbf{\hat R}}$ and ${\mathbf{\hat t}}$ to represent the estimated rotation and translation and use ${{\mathbf{R}}_{gt}}$ and ${{\mathbf{t}}_{gt}}$ to represent the ground truth. The rotation error is evaluated by the angle of the axis-angle representation of ${\mathbf{R}}_{gt}^{ - 1}{\mathbf{R}}$, and the translation error by $\text{ }{{{\left\| {{\mathbf{t}}_{gt}}-\mathbf{\hat{t}} \right\|}_{2}}}/{\left\| {{\mathbf{t}}_{gt}} \right\|}\;$. We 