Coordinate Systems#
Overview#
This page defines the supported coordinate systems by combining:
- Origin location
- Axis direction
- Range formulas for
X_min,X_max,Y_min, andY_max
Note
If Columns or Rows are odd, the result of Columns / 2 and Rows / 2 is truncated.
Legend#
- Squares represent grid cells.
- Red circle represents the origin.
- X and Y arrows show the positive axis directions.
Coordinate System Matrix#
UpRight#
X increases to the right; Y increases upward.
| Origin | X_min | X_max | Y_min | Y_max |
|---|---|---|---|---|
| LowerLeft | 0 | Columns - 1 | 0 | Rows - 1 |
| UpperLeft | 0 | Columns - 1 | - Rows + 1 | 0 |
| LowerRight | - Columns + 1 | 0 | 0 | Rows - 1 |
| UpperRight | - Columns + 1 | 0 | - Rows + 1 | 0 |
| Center | Columns / 2 - Columns + 1 | Columns / 2 | Rows / 2 - Rows + 1 | Rows / 2 |
Origin at the lower-left corner. X increases to the right; Y increases upward.
Origin at the upper-left corner. X increases to the right; Y increases upward.
Origin at the lower-right corner. X increases to the right; Y increases upward.
Origin at the upper-right corner. X increases to the right; Y increases upward.
Origin at the center of the grid. X increases to the right; Y increases upward.
DownRight#
X increases to the right; Y increases downward.
| Origin | X_min | X_max | Y_min | Y_max |
|---|---|---|---|---|
| LowerLeft | 0 | Columns - 1 | - Rows + 1 | 0 |
| UpperLeft | 0 | Columns - 1 | 0 | Rows - 1 |
| LowerRight | - Columns + 1 | 0 | - Rows + 1 | 0 |
| UpperRight | - Columns + 1 | 0 | 0 | Rows - 1 |
| Center | Columns / 2 - Columns + 1 | Columns / 2 | - Rows / 2 | - Rows / 2 + Rows - 1 |
Origin at the lower-left corner. X increases to the right; Y increases downward.
Origin at the upper-left corner. X increases to the right; Y increases downward.
Origin at the lower-right corner. X increases to the right; Y increases downward.
Origin at the upper-right corner. X increases to the right; Y increases downward.
Origin at the center of the grid. X increases to the right; Y increases downward.
UpLeft#
X increases to the left; Y increases upward.
| Origin | X_min | X_max | Y_min | Y_max |
|---|---|---|---|---|
| LowerLeft | - Columns + 1 | 0 | 0 | Rows - 1 |
| UpperLeft | - Columns + 1 | 0 | - Rows + 1 | 0 |
| LowerRight | 0 | Columns - 1 | 0 | Rows - 1 |
| UpperRight | 0 | Columns - 1 | - Rows + 1 | 0 |
| Center | - Columns / 2 | - Columns / 2 + Columns - 1 | Rows / 2 - Rows + 1 | Rows / 2 |
Origin at the lower-left corner. X increases to the left; Y increases upward.
Origin at the upper-left corner. X increases to the left; Y increases upward.
Origin at the lower-right corner. X increases to the left; Y increases upward.
Origin at the upper-right corner. X increases to the left; Y increases upward.
Origin at the center of the grid. X increases to the left; Y increases upward.
DownLeft#
X increases to the left; Y increases downward.
| Origin | X_min | X_max | Y_min | Y_max |
|---|---|---|---|---|
| LowerLeft | - Columns + 1 | 0 | - Rows + 1 | 0 |
| UpperLeft | - Columns + 1 | 0 | 0 | Rows - 1 |
| LowerRight | 0 | Columns - 1 | - Rows + 1 | 0 |
| UpperRight | 0 | Columns - 1 | 0 | Rows - 1 |
| Center | - Columns / 2 | - Columns / 2 + Columns - 1 | - Rows / 2 | - Rows / 2 + Rows - 1 |
Origin at the lower-left corner. X increases to the left; Y increases downward.
Origin at the upper-left corner. X increases to the left; Y increases downward.
Origin at the lower-right corner. X increases to the left; Y increases downward.
Origin at the upper-right corner. X increases to the left; Y increases downward.
Origin at the center of the grid. X increases to the left; Y increases downward.