UnityLearn – AI for Beginners – The Mathematics of AI – Pt. 01 – Cartesian Coordinates

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March 6, 2020

AI for Beginners

The Mathematics of AI

Cartesian Coordinates


Artificial Intelligence for Beginners

Unity Learn Course – AI for Beginners

Cartesian Coordinates

Cartesian Plane

Cartesian coordinates:
used to determine locations in space for any number of dimensions
generally used for 2D and 3D space in games (x, y) and (x, y, z)

2 Main Projection Types: Orthographic and Perspective

Orthographic:
3D space represented by a cube or rectangular prism

Perspective:
3D space that looks like a rectangular pyramid with its top cut off

The Camera size in Unity when using the Orthographic perspective dictates how far the camera sees for the smaller dimension of the aspect ratio. It is the number of units in both the positive and negative direction away from the origin the camera sees, so the smaller dimension of the aspect ratio is double that of the Size value given to the camera. The larger dimension in the aspect ratio is then the ratio multiplied by that Size value.

For example, if the orthographic perspective Camera Size is 100, and you select the aspect ratio of 16:10 for your view, the overall height seen is 200 units (+100 to -100 on the y-axis) and the overall width seen is 320 units (+160 to -160 on the x-axis). The size directly correlates with the y-axis since it is the smaller of the dimensions in the aspect ratio, and then the range for x is determined by multiplying that size (100) with the aspect ratio (16:10 or 16/10).

The viewing volume for this orthographic view is a rectangular prism (completely straight on viewing angle). They expound upon this to show movement on the z-axis does not particularly do anything in a 2D game built around the x-axis and y-axis. Placement can matter however as objects do need to be in front of the camera, and objects can be placed in front of or behind other objects.

SUMMARY

  • Unity Camera Size and Aspect Ratio together exactly determine the number of units for the dimensions of place shown on the camera at a time (especially for Orthographic perspective).
  • Orthographic view uses a rectangular prism viewing space, where a Perspective viewing space uses a rectangular pyramid shape.
  • Cartesian planes and coordinates can be used for any number of dimensions (not restricted to just 2D and 3D)