10.10.4.3. Camera

If a mutable has attribute type as camera, it’s a camera. A simple pinhole camera model is used.

Required attributes of a camera:

Name	Type
camera_parameters	dict

camera_parameters is a dictionary with 6 required keys with the types specified below.

Name	Type
screen_width	int
screen_height	int
focal_length	numeric
horizontal_aperture	numeric
near_clip	numeric
far_clip	numeric

10.10.4.3.1. Pinhole model

3D objects are projected onto a 2D plane, like this

Looking from a top view, towards the negative Y-axis, we have this

In the picture, f which is the distance from the camera to the projection plane, is focal_length; hA which is the distance from the left edge (upper end) to the right edge (lower end), is horizontal_aperture.

near_clip and far_clip define 2 planes perpendicular to the line of vision between which you can see things.

10.10.4.3.2. Assumptions in frame of reference and convertion from/to other common representations

If no transform operator is applied on the camera, the Y-axis points upwards and X-axis points to the right. The camera looks towards negative direction of the Z-axis.

There are many standards out there for the pinhole camera. To avoid confusion, we define a value called the \(pinholeRatio\) such that \(pinholeRatio=\frac{2∗focalLength∗aspectRatio}{horizontalAperture}\)

If you are familiar with OpenGL/Direct3D, \(fovy\) is used more often.

\[pinholeRatio=\frac{1}{\tan(fovy/2)}\]

If you are familiar with the intrinsic matrix or the Objectron standard, \(fx, fy, cx, cy\) are used.

\[\begin{split}fx = \frac{screenWidth \cdot pinholeRatio}{2 \cdot aspectRatio}\\ fy = \frac{screenHeight \cdot pinholeRatio}{2}\\ cx = screenWidth / 2\\ cy = screenHeight / 2\end{split}\]

Here, \(aspectRatio = screenWidth/screenHeight\)