# 3D Visualization in Digital Medicine Using XR Technology
## 3 Results
### Zooming in 3D Environment
#### 3.4.2 The SerialZoom Solution  
In our implementation, the user can select any point of the displayed 3D serial section using a laser pointer within the VR world. The selected point will be the center of the zoom. In order for the magnification to be functional, we wrote the appropriate conversion equations between the individual magnification levels of the medical sample. Equations (3)-(6) are implemented pixel-to-pixel between individual magnification levels.  
In SerialZoom, the resolution of the displayed 3-dimensional sample does not change but shows the doctor a smaller region of the original complete medical image. In order to be able to do this, we need the exact coordinate where the user zoomed in on the displayed sample in virtual reality.  
\[X_{so}=X_{0}*R_{w} \tag{3}\]  
\[Y_{so}=Y_{0}*\ R_{h} \tag{4}\]  
The equations used during the user's first zoom are (3) and (4). In this case, the magnification coordinates must be recalculated from the displayed sample with a lower resolution to the whole slide image. However, after the first zoom is performed by the user, Equations (5) and (6) are needed so that we can maintain sufficient accuracy through several zoom steps.  
\[X_{so}=\left[\left(\sum_{j=1}^{n}\frac{X_{n-j}-s}{k^{j}}\right)+X_{0}\right]*R _{w} \tag{5}\]  
\[Y_{so}=\left[\left(\sum_{j=1}^{n}\frac{Y_{n-j}-m}{k^{j}}\right)+Y_{0}\right]* \ R_{h} \tag{6}\]  
The following notations were used in the equations:  
* \(X_{so}\): The x coordinate of the zoom point converted to the original whole slide image resolution.
* \(Y_{so}\): The y coordinate of the zoom point converted to the original whole slide image resolution.
* \(X\): An array storing the x-coordinates of zooms performed by the user. These coordinates refer to the displayed lower-resolution samples.
* \(Y\): An array storing the y-coordinates of zooms performed by the user. These coordinates refer to the displayed, lower-resolution samples.  
Figure 7: (**a**) The result of the use of SlideZoom functionality virtual reality, without modification on the 3D model. (**b**) The result of the use of SlideZoom functionality in virtual reality with modification on the 3D model.  
* \(n\): The number of zooms performed by the user.
* \(k\): Magnitude of zoom performed.
* \(X_{0}\): The x coordinate on which the user first performed the zoom.
* \(Y_{0}\): The y coordinate on which the user first performed the zoom.
* \(m\): Half of the height of the displayed sample in pixels.
* \(s\): Half of the width of the displayed sample in pixels.
* \(R_{w}\): The ratio of the width of the original native resolution medical sample to the displayed sample. How it is calculated: The width of the native resolution sample divided by the width of the displayed sample.
* \(R_{h}\): The ratio of the height of the original native resolution medical sample to the displayed sample. How it is calculated: The height of the native resolution sample divided by the height of the displayed sample.  
The practical application of the equation provides the following result:  
Red circles in Figure 8 mark the area, where the user has used the SerialZoom functionality. The zooming results shown in the image follow one after the other, so the user must first perform a 10\(\times\) magnification (which results image Figure 8b), then with the next magnification performed, the user can see a 20\(\times\) magnification image compared to the originally displayed sample (this can be seen on image Figure 8c). In the case of SerialZoom, an important limitation is the size of the medical serial section. If the serial section consists of a large number of samples, the loading time may increase, which may affect the user experience.