3D Planes 1
In this page, I will be introducing the basics of 3D Planes in the launch of the Robot Kinematics series. More information on the topics disclosed in this series will be explained further, in more detail, within there own tutorial pages.
To start I want to compare the differences between the basic 2D Coordinate System, with that of the 3D.
With a 2D Cartesian system, as shown in the figure above, have what is conventionally labelled the X and the Y axes. Axis are a reference to fixed paths from the origin point, of which all positions relate two, and are perpendicular to each other.
The names of these paths are Dimensions. With this, the axis of which follow these dimensions can have positive and negative directions, relative to the origin.
In the case of a 2D System, there are two dimensions, where D represents dimensions and the number represents the quantity.
A plane is 2D 'surface' of which coordinates can be position upon and are formed between two perpendicular axes. In a typical 2D system, all coordinates are placed on the XY plane.
A Coordinate is a point in space within the system and is noted as steps from the origin. In the case of a 2D system, a coordinate is represented as (Steps in X, Steps in Y) and will be placed on the XY Plane.
Take the example of the coordinate (2,2), where X=2 and Y=2 relate to two steps in the positive X direction and two positive steps in the Y direction.
With a 3D system, a third dimension is added; this is conventionally labelled as the Z-Axis.
This axis is perpendicular to both the X and Y axes. In a 3 Dimensional system, coordinates can be labelled in terms of ( Steps in X, Steps in Y, Steps in Z ).
The animation below shows the addition of the Z-Axis in respect to the XY plane.