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:

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


Comments

Post a Comment

Popular posts from this blog

World, View and Projection Matrix Internals

Image
This convention below is applicable to Direct3D and XNA matrices World Matrix Given a  position  and basis vectors  right ,  up  and  look  of an  object , a world matrix can be formed by the following arrangement: View Matrix Given a  position  and basis vectors  right ,  up  and  look  of a viewer, a view matrix can be formed by the following arrangement: Projection Matrix Given field of view  FOV ,  aspect ratio , near clip plane  Zn  and far clip plane  Zf , a perspective projection matrix can be formed by the following arrangment:
Read more

BASH: Reading Text File

BASH for C programmers: Read a text file word-by-word in BASH: #!/bin/bash for WORD in `cat filename` do echo $WORD done Read a text file line-by-line in BASH: #!/bin/bash while read LINE do echo $LINE done < filename Looping in BASH: i=0 while [ $i -lt 10 ] do echo $i # next i=$(($i+1)) done Update : another way to loop suggested in the comment.
Read more

GDC 2015 Links

Here are [growing] links to GDC 2015 slides/presentations: Update: GDC Vault for GDC 2015 is now up!  Programming Track Khronos Group ( Link ) Khronos OpenCL GDC Khronos Vulkan GDC Valve Vulkan Session GDC Live Stream of Vulkan Session (Youtube) The Future of High-Performance Graphics Virtual Reality VR Direct: How NVIDIA Technology is Improving the VR Experience ( pptx ,  pdf ) - Nathan Reed, Dean Beeler Advanced VR Rendering  - Alex Vlachos Far Cry 4 Fast Iteration for Far Cry 4 - Optimizing Key Parts of Dunia Pipeline  - Remi Quenin Rendering the World of Far Cry 4  - Stephen McAuley Adaptive Virtual Texture Rendering in Far Cry 4  - Ka Chen Mesh Cutting in Farming Simulator 15 - Gino van den Bergen Advanced Visual Effects in 2D Games - Viktor Lidholt Great Management of Technical Leads - Mike Acton Code Clinic: How to Write Code the Compiler Can Actually Optimize - Mike Acton Parallelizing the Naughty Dog Engine Using Fibers - Christian Gyrling
Read more