Some alternative understandings about the basic concept of three-dimensional coordinate system

First, give some textbook ideas.

Concept 1: Left-handed and right-handed coordinate systems

Three-dimensional coordinate system is divided into two kinds, left-handed and right-handed coordinate. Here are the rules for the two coordinate systems (the square to the right of the x-axis is fixed in the figure, and the square upward of the y-axis):

Cases:

OpenGL is the right-hand coordinate system, the origin in the lower left corner, the right x-axis positive direction, up to the y-axis positive direction, the z-axis is the direction of the screen facing the human eye-the coordinate system of the high school math textbook is this coordinate system.

iOS Uikit is the left-hand coordinate system, the origin in the upper left corner, the right x-axis positive direction, downward for the y-axis positive direction, the z-axis is the direction of the screen facing the human eye

Concept 2: Rotational positive direction

In the left-handed coordinate system, after determining a rotating axis, the left hand holds the fist, the thumb points to the positive direction of the rotating axis, and the four fingers bend in the direction of rotation. Correspondingly, the right-hand coordinate system is judged by the right hand.

This is useful to determine the rotation of the square backwards, in the calculation of the formula it is easy to know whether to use a positive or negative angle.

I understand.

For these two concepts, I think it is very annoying, not intuitive enough, need to take the shot to carry out the gestures. In daily life, we judge the direction of the left and right do not need to take a shot to gestures, if the understanding of these two concepts as we judge the direction of the same intuitive, not very good? Below I have done some of my own understanding, or is a kind of a clever mind.

Concepts of low and high axes

The three-dimensional coordinate system has three axes, the x-axis, the y-axis, and the z-axis, which define the left-to-right properties of these three axes from low to high.

In the X and y axes, the x axis is low, the Y axis is high, the y-axis and z-axis, the y-axis is the low axis, and the z axis is the high axis.

What is special is the x-axis and z-axis, which define the z-axis as the low axis and the x-axis as the high axis.

So, in fact: the adjacent two axes in x-->y-->z->x direction, with a low axis on the left and a high axis on the right

Judgement of left-handed and right-handed coordinate system

A person standing, with the foot as the origin, with the human body from the foot of the head for the high axis positive direction, in front of the human eye for the low axis positive direction (can be visually understood into the high axis on the low axis), if the third axis is in the right direction of the person, that is, the left hand coordinate system;

Cases:

The y-axis is on the x-axis, the z-axis is right, the right-hand coordinate, the z-axis is on the left and the left-hand coordinate system.

The z axis is on the y axis, the x-axis is in the right direction, the right-hand coordinate, the x-axis is on the left and the left-hand coordinate system.

The x-axis is on the z axis, the y-axis is on the right, the right-hand coordinate, the x-axis is on the left and the left-hand coordinate system.

Note: in the future to determine whether the left-handed coordinate system or the right coordinate system, choose two axes, distinguish between the high and low axis, and then according to the other on the left or right, you can determine whether the left-handed or the right coordinate system.

Determination of the positive direction of rotation

Rotates around an axis, and its rotation is in the positive direction of the lower-axis positive-direction vertex in the other two axes, pointing to the direction of the high-axis positive direction vertex, whether it is a left-handed or right-handed coordinate system.

? The same is true for 2D planar coordinate systems.

Note: very simple, no longer need to take the shot to gestures.

Some alternative understandings about the basic concept of three-dimensional coordinate system