## Posts

Showing posts from 2016

### Radius of a Projected Sphere

It's useful to calculate sphere projection in clip space. One usage is to determine LOD of a model. As you might have known, sphere projection results in ellipse instead of sphere. In this post, a way to approximate radius of projected sphere is given.

Assume the sphere is in the center of the screen and we know the $$FOV$$ of the camera, sphere radius $$r$$ and distance from camera $$z$$. Looking at the diagram below:

The approximate projection of sphere radius in clip space is given by:

$$approx\_projected\_radius = \frac{y}{y_{max}} = \frac{r}{z \times \tan (\frac{FOV}{2})}$$