# tfg.rendering.camera.perspective.project

Projects a 3d point onto the 2d camera plane.

Projects a 3d point $$(x, y, z)$$ to a 2d point $$(x', y')$$ onto the image plane with

$$\begin{matrix} x' = \frac{f_x}{z}x + c_x, & y' = \frac{f_y}{z}y + c_y, \end{matrix}$$

where $$(f_x, f_y)$$ is the focal length and $$(c_x, c_y)$$ the principal point.

#### Note:

In the following, A1 to An are optional batch dimensions that must be broadcast compatible.

point_3d A tensor of shape [A1, ..., An, 3], where the last dimension represents a 3d point to project.
focal A tensor of shape [A1, ..., An, 2], where the last dimension represents a camera focal length.
principal_point A tensor of shape [A1, ..., An, 2], where the last dimension represents a camera principal point.
name A name for this op that defaults to "perspective_project".

A tensor of shape [A1, ..., An, 2], where the last dimension represents a 2d point.

ValueError If the shape of point_3d, focal, or principal_point is not supported.