Distance from Perspective Projection
This calculator helps determine the distance from the camera (or viewer) to the projection plane in a perspective projection setup. It’s especially useful in computer graphics, 3D modeling, and virtual camera configurations, where field of view (FOV) and projection geometry are crucial. Simply enter the desired viewing angle and the width of the viewport to get the optimal distance.
Distance from Perspective Projection
Distance from Perspective Projection Formula
Where:
- $$L$$ = Distance from the viewer to the screen or projection plane
- $$D$$ = Width of the viewport or screen
- $$\alpha$$ = Field of View (FOV) angle in radians
This formula comes from trigonometric relationships in a right triangle where the tangent function relates the field of view angle to half the width of the screen and the projection distance.
This formula is often used in rendering and simulation environments to calculate the camera distance based on a given field of view and screen width. It assumes a symmetrical perspective projection and calculates the distance such that the specified FOV angle spans the entire width. For example, if you’re designing a camera in a 3D game or creating a projection matrix, you can use this to position the camera at the correct distance. Make sure the angle is in radians or convert it accordingly if it’s in degrees.