## 3 Results
### Game \"Asteroid Shower\" with Virtual Reality
#### 3.1.2 Three-Dimensional Animation  
In the created VR game, the camera is driven in two ways: by a linear interpolator or by a spline curve. Linear interpolation moves the camera smoothly from one point to another by specifying a start and end position and the speed at which the camera moves through them. This interpolator is used for rectilinear movements and more straightforward camera transitions. Spline curves are applied when more complex motion is sought, while simultaneously applying a 3D transformation. The movement of the camera by applying Transform 3D with translational movement along the z-axis is shown in Figure 5 and by rotation along the y axis in Figure 6.  
Figure 7 shows an asteroid's explosion. It combines several basic techniques: modelling and texturing the asteroid; shredding by exploding and morphing; and light and sound effects that create a spectacular and realistic explosion that looks impactful in virtual reality. The camera is above the city and has been moved using spline curve and Transform 3D.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Step**} & \multicolumn{8}{c}{**Coordinate Values of the Vertices of a Regular Octagon**} \\ \cline{2-10}  & **C\({}_{1}\) (\(\mathbf{x}\) \(\mathbf{y}\))** & **C\({}_{2}\) (\(\mathbf{x}\) \(\mathbf{y}\))** & **C\({}_{3}\) (\(\mathbf{x}\) \(\mathbf{y}\))** & **C\({}_{4}\) (\(\mathbf{x}\) \(\mathbf{y}\))** & **C\({}_{5}\) (\(\mathbf{x}\) \(\mathbf{y}\))** & **C\({}_{6}\) (\(\mathbf{x}\) \(\mathbf{y}\))** & **C\({}_{7}\) (\(\mathbf{x}\) \(\mathbf{y}\))** & **C\({}_{6}\) (\(\mathbf{x}\) \(\mathbf{y}\))** \\ \hline
0.1 & \(-1.17;-0.4\) & \(-1.103;0.574\) & \(-0.4\) \(\pm\) 1.242 & 0.567; 1.167 & 1.17; 0.4 & 1.103; \(-0.574\) & 0.4 \(-1.242\) & \(-0.567;\)\(-1.167\) \\
0.2 & \(-1.17;-0.3\) & \(-1.036;0.648\) & \(-0.3\) \(\pm\) 1.242 & 0.634; 1.093 & 1.17; 0.3 & 1.036; \(-0.648\) & 0.3 \(-1.242\) & \(-0.634;\)\(-1.093\) \\
0.3 & \(-1.17;-0.2\) & \(-0.969;0.722\) & \(-0.2\) \(\pm\) 1.242 & 0.701; 1.019 & 1.17; 0.2 & 0.969; \(-0.722\) & 0.2 \(-1.242\) & \(-0.701;\)\(-1.019\) \\
0.4 & \(-1.17;-0.1\) & \(-0.901;0.796\) & \(-0.1\) \(\pm\) 1.242 & 0.768; 0.945 & 1.17; 0.1 & 0.901; \(-0.796\) & 0.1 \(-1.242\) & \(-0.768;\)\(-0.945\) \\
0.5 & \(-1.17;-0.0\) & \(-0.835;0.871\) & 0.0 \(\pm\) 1.242 & 0.835; 0.871 & 1.17; 0.0 & 0.835; \(-0.871\) & 0.0 \(-1.242\) & \(-0.835;\)\(-0.871\) \\
0.6 & \(-1.17;0.1\) & \(-0.768;0.945\) & 0.1 \(\pm\) 1.242 & 0.901; 0.796 & 1.17; \(-0.1\) & 0.768; \(-0.945\) & \(-0.1\) \(-1.242\) & \(-0.901;\)\(-0.796\) \\
0.7 & \(-1.17;0.2\) & \(-0.701;1.019\) & 0.2; 1.242 & 0.968; 0.722 & 1.17; \(-0.2\) & 0.701; \(-1.019\) & \(-0.2\); \(-1.242\) & \(-0.968;\)\(-0.722\) \\
0.8 & \(-1.17;0.3\) & \(-0.634;1.093\) & 0.3; 1.242 & 1.036; 0.648 & 1.17; \(-0.3\) & 0.634; \(-1.093\) & \(-0.3\); \(-1.242\) & \(-1.036;\)\(-0.648\) \\
0.9 & \(-1.17;0.4\) & \(-0.567;1.167\) & 0.4; 1.242 & 1.103; 0.574 & 1.17; \(-0.4\) & 0.567; \(-1.167\) & \(-0.4\); \(-1.242\) & \(-1.103;\)\(-0.574\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Coordinate values of the vertices of a regular octagon by applying the Bezier curve.  
Figure 5: Translational movement of the camera along the z-axis. (**A**) Positive value for z axis; (**B**) negative value for z axis.