The magnitude and direction
In this tutorial, you are going to learn the coordinate system in blender 3D view with its correlation with magnitude and direction.
What is magnitude and direction?
The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. Whereas vector is a geometric object that has magnitude (or length) and direction. It is frequently represented by line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B. it is simply what is needed to ‘carry’ the point A to the point B
What is coordinate system?
The simplest example of a coordinate system is the identification of points on a line with real numbers using the number line. In this system, an arbitrary point O (the origin) is chosen on a given line. The coordinate of a point P is defined as the signed distance from O to P, where the signed distance is the distance taken as positive or negative depending on which side of the line P lies. Each point is given a unique coordinate and each real number is the coordinate of a unique point.
Cartesian coordinate system
The prototypical example of a coordinate system is the Cartesian coordinate system. In the plane, two perpendicular lines are chosen and the coordinates of a point are taken to be the signed distances to the lines.
In three dimensions, three mutually orthogonal planes are chosen and the three coordinates of a point are the signed distances to each of the planes. This can be generalized to create n coordinates for any point in n-dimensional Euclidean space.
Depending on the direction and order of the coordinate axes, the three-dimensional system may be a right-handed or a left-handed system. This is one of many coordinate systems.
Application of coordinate system in real life
Take a look at the angle of your room, you will notice the coordinate system can be deduced. The x and y lies on the floor while the z lies on the wall indicating the height.
At this point, if you recall your graph book, you will remember that graph book deals with x and y only. And when dealing with x and y only, it is called 2D.
But as far as 3D is concern, z is added to the existing x and y. The z can be called depth, as well as height, and it is been represented with blue vector, while the x and the y are the length and breadth and it is been represented by red and green respectively.
Though different 3D applications as different orientation concerning the arrangement of the x, y, z, axis, but we are going to look at it deeply as far as blender software is concerned.
Blender coordinate system
In the above blender 3D view picture illustration,
The 3D view comprises of Global coordinate and Object coordinate
If you take a deep look, the global coordinate axis is always parallel to the axis on the grid floor. That is the red arrow (y-axis) is parallel red line on your grid floor. The green arrow (y-axis) is also parallel to the green line on your grid floor. Take a look at the difference between 1 and 2 in the picture, the different between them is orbit, but the global coordinate maintains it parallel behavior.
This is telling us in essence that your own position on earth doesn’t change the position of the earth (global)
The object coordinate has several options which includes View, Gimbal, Normal, Local and Global, which is called Transformation Orientation.
The object coordinate is viewed in the aspect that we human being cannot rotate the earth, but we can make rotations to some objects on the earth.
Another analogy is that lets assumed that in your room, you have objects like chair and table, your room can represent the Global at that point in time while the chair and the table are your Object at that point in time. You cannot rotate or move your room (Global), but you can rotate and move your chair and table (Object). On that basis, both your room and your table and chair have their different coordinate system.
Comparing and contrasting the objects in the above picture, the Global transformation, Local Transformation and the View transformation, the 3 cubes were rotated but with different Transformation Orientation as indicated.
In the Global coordinate (Global transformation), the xyz axis maintains the illustration in the picture of the angle in a room, in which the x and y lies on the floor, not minding the object rotation transformation.
In the Local coordinate (Local transformation), the axis is rotated with the object thereby making a normal with the faces of the cube.
In the View coordinate (View transformation), the z- axis is lost, while the x and y axis is forming the right angle at view, as illustrated.
Note: What you are aiming at while modelling or while animating will dictate the choice of Transformation Orientation you will use.