# Coordinate Frames¶

This section describes Camera, Grid/Matrix/Image, and Robot coordinate frames.

## Grid Pixel Center¶

Values on a grid $$a$$ are stored such that the grid cell stores the value at the coordinate $$i \times d\$$where $$d$$ is the spacing between sample points. This means $$a\left\lbrack i \right\rbrack = f\left( i \times d \right)$$. Thus if $$y = f\left( x \right)$$ shall be retrieved in “nearest” interpolation mode, $$x$$ is rounded to the nearest index $$i$$ and thus $$y = a\left\lbrack i \right\rbrack$$. In “linear” interpolation mode $$x$$ is mapped to the lower index $$i0$$ and thus $$y = \left( 1 - p \right) \times a\left\lbrack i0 \right\rbrack + p \times a\left\lbrack i0 + 1 \right\rbrack$$.

## Grid/Matrix/Image Coordinate Frame¶

In a 2-dimensional frame, the vector order is simple:

• 0: row

• 1: column

## Camera Coordinate Frame¶

Note: specifically a 3D point (x,y,z) in camera frame is represented as depicted in this diagram. If the 3D point is projected onto the image the coordinates are switched to image coordinates which follow the (row/col) order as shown in the following diagram.

The vector order is:

• 0: right

• 1: down

• 2: forward

## Robot Coordinate Frame¶

The robot coordinate frame is actually placed inside the robot. In the Carter robot the center of the frame is between the wheels.

The vector order is:

• 0: forward

• 1: left

• 2: up