I have a pretty basic understanding of coordinates and can comprehend the X and Y axis relatively well, but the Z axis is where I fall flat. Like what does it represent?? Its for 3D stuff I’m pretty sure but thats about all I know about it.
In: 1
You have the x-axis and the y-axis meeting at 0 on the paper. Now imagine that you erect a third axis from the paper, vertically. It’s the height.
You have the x-axis and the y-axis meeting at 0 on the paper. Now imagine that you erect a third axis from the paper, vertically. It’s the height.
Take a look at the room you are in now.
Imagine the y axis is a point in the middle of the floor going up to the ceiling.
The x axis is from the same stating point but going across the floor to the right wall.
The z axis starts from the same point as the two others and goes along the floor to the wall in front of you.
Hope this helps
Take a look at the room you are in now.
Imagine the y axis is a point in the middle of the floor going up to the ceiling.
The x axis is from the same stating point but going across the floor to the right wall.
The z axis starts from the same point as the two others and goes along the floor to the wall in front of you.
Hope this helps
You are correct, the z axis is for 3D stuff. It has two main uses:
1.
Describing 3D shapes precisely, in much the same way one describes 2D shapes on an XY coordinate grid. Think 3D modeling/CAD software that engineers use to design stuff, or the 3D design software that animators use to build the world and characters they film.
2.
Representing and visualizing functions with more input and output variables. Thus far you’ve used an XY coordinate plane to graph functions with 1 input and 1 output. f(x) = y. If you have some advanced physics experience, maybe you’ve even seen functions with 2 inputs and 2 outputs represented as a 2D vector field. f(x, y) = [Vx, Vy]
An XYZ coordinate space can graph functions with 1 input and 2 or 3 outputs. (as represented by a curve in 3D space: f(t) = [x(t), y(t), z(t)])
Or with 2 inputs and 1 output. (represented by a surface or line where the output is the height Z: F(x, y) = z)
Or with 3 inputs and 3 outputs. (represented by a 3D vector field, F(x, y, z) = [Vx, Vy, Vz])
Humans love to interpret things visually, so this helps in spotting patterns. Unfortunately, functions with higher order than these usually require more dimensions, which is something we can’t picture. So we get as much use out of the XYZ grid as we can.
You have the x-axis and the y-axis meeting at 0 on the paper. Now imagine that you erect a third axis from the paper, vertically. It’s the height.
You are correct, the z axis is for 3D stuff. It has two main uses:
1.
Describing 3D shapes precisely, in much the same way one describes 2D shapes on an XY coordinate grid. Think 3D modeling/CAD software that engineers use to design stuff, or the 3D design software that animators use to build the world and characters they film.
2.
Representing and visualizing functions with more input and output variables. Thus far you’ve used an XY coordinate plane to graph functions with 1 input and 1 output. f(x) = y. If you have some advanced physics experience, maybe you’ve even seen functions with 2 inputs and 2 outputs represented as a 2D vector field. f(x, y) = [Vx, Vy]
An XYZ coordinate space can graph functions with 1 input and 2 or 3 outputs. (as represented by a curve in 3D space: f(t) = [x(t), y(t), z(t)])
Or with 2 inputs and 1 output. (represented by a surface or line where the output is the height Z: F(x, y) = z)
Or with 3 inputs and 3 outputs. (represented by a 3D vector field, F(x, y, z) = [Vx, Vy, Vz])
Humans love to interpret things visually, so this helps in spotting patterns. Unfortunately, functions with higher order than these usually require more dimensions, which is something we can’t picture. So we get as much use out of the XYZ grid as we can.
A boat operates in X/Y. It can go north or south, and it can go east or west.
A helicopter operates in X/Y/Z. It can go north or south and east or west, just like a boat, but it can also go up or down.
Take a look at the room you are in now.
Imagine the y axis is a point in the middle of the floor going up to the ceiling.
The x axis is from the same stating point but going across the floor to the right wall.
The z axis starts from the same point as the two others and goes along the floor to the wall in front of you.
Hope this helps
You are correct, the z axis is for 3D stuff. It has two main uses:
1.
Describing 3D shapes precisely, in much the same way one describes 2D shapes on an XY coordinate grid. Think 3D modeling/CAD software that engineers use to design stuff, or the 3D design software that animators use to build the world and characters they film.
2.
Representing and visualizing functions with more input and output variables. Thus far you’ve used an XY coordinate plane to graph functions with 1 input and 1 output. f(x) = y. If you have some advanced physics experience, maybe you’ve even seen functions with 2 inputs and 2 outputs represented as a 2D vector field. f(x, y) = [Vx, Vy]
An XYZ coordinate space can graph functions with 1 input and 2 or 3 outputs. (as represented by a curve in 3D space: f(t) = [x(t), y(t), z(t)])
Or with 2 inputs and 1 output. (represented by a surface or line where the output is the height Z: F(x, y) = z)
Or with 3 inputs and 3 outputs. (represented by a 3D vector field, F(x, y, z) = [Vx, Vy, Vz])
Humans love to interpret things visually, so this helps in spotting patterns. Unfortunately, functions with higher order than these usually require more dimensions, which is something we can’t picture. So we get as much use out of the XYZ grid as we can.
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