C # programmer's Unity 3D note (10): Unity3D mathematical model of displacement and Rotation

C # programmer's Unity 3D note (10): Unity3D mathematical model of displacement and Rotation
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The core reason is that the concept of 3D mathematics in U3D is not flexible enough. So the system learns again-the third learning 3D mathematics.

 

This time, we hope to implement the following simple functions:

For example, in a small map, you want to dynamically draw the current position of the Player and the orientation of z: use three lines, the z axis is positive, 30 ° rotation, and-30 ° rotation.

The problem is: can be obtained, P1? Point P2 is unknown.

I tried for two hours and the results were unsatisfactory, less than frustrated.

 

You have to spend some time learning 3D mathematics:

1. Displacement-vector and point: the point and vector are consistent in mathematics. The concept of the point in real life is better understood. coordinate points are used to locate the South second ring and North second ring. [Points are marked with parentheses (3, 4, 5), or P for short]Vector: "commonly known as incremental", with a large and small direction, such as "one step forward. Turn left 90 degrees ". Go forward until you hit the wall and you stop. Before that, you cannot accurately obtain the coordinates of the points hitting the wall or the distance between you and the wall. . The vector is marked with <3, 4, 5> Angle brackets (V]In U3D, Vector3 objects are used to express vectors and points in a unified manner, which is also a very important reason for beginners to turn dizzy. One technique is to use position and Point in APIs, v3 certainly represents a point. All Vector and ction are vectors. Read the official API manual and write it clearly.

Make a game and list the Vector3 APIs you have used. analyze whether Vector3 is a vector (V) or a vertex (P)

Requirement	API	Vector (V) Point (P)	Remarks
Smooth displacement	Vector3 MoveTowards (Vector3 current, Vector3 target, float maxDistanceDelta );	P
Smooth displacement	Vector3 Slerp (Vector3 from, Vector3 to, float t)	P
New coordinate point	This. m_transform.position = pos;	P	Compliant with conventional thinking
Coordinates changed once	M_transform.Translate (new Vector3 (rx, 0,-m_Speed * Time. deltaTime ));	V	Can be considered as incremental
Direction	Vector3 relativePos = this. m_transform.position-m_Player.position;	V	Vector subtraction, hard to understand
Set new coordinate points	LineRenderer. SetPosition (0, this. gameObject. transform. position ); M_NavAgent.SetDestination (this. m_Player.transform.position );	P	Compliant with conventional thinking
New location	Pointer. transform. position = hitInfo. point + (transform. position-hitInfo. point) * 0.01f;	P, V	Force superposition?
Distance	Float dis = Vector3.Distance (v1, v2 ); Float f1 = (v1-v2). sqrmagn.pdf; Float f3 = (v1-v2). magn.pdf;	P, V	Distance can be clicked. Vector Subtraction is also possible.
Forward Scaling	Vector3 v3 = this. m_transform.forward * 200f;	V	Multiplication of V
Ray Detection	Ray r = new Ray (source, dest ); Physics. Raycast (r, out hit, 1000, m_ShootMask)	V, P	Source: P Dest: V
Add one force	Rigidbody. AddForce (0, 10, 0 );	V

 

Based on this game, we can figure out that four components (including Vector 3) are currently used for Displacement:

Displacement of commonly used four components and Vector3:

Components	Function	API description of the Unity Template	Whether Used
Transform component	Translate Function	How long does one move an object in a certain direction? [Default local coordinate system] Or move relative to an object	Yes
	Position attribute	Location of the world space coordinate transform	Yes
RigidBody component [FixedUpdate function]	Velocity attributes	Velocity vector of a rigid body The official Unity demo Done is very cool.	Yes
	AddForce Function	Add a force to the rigid body. As a result, the rigid body begins to move.	Yes
	MovePosition Function	Move a rigid body to position
NavMeshAgent component	SetDestination Function	Set automatic Path target point	Yes
CharacterController Components	Move Function	A more complex motion function, absolutely moving each time	Yes
	SimpleMove Function	Move a role at a certain speed
Vector3 Vector	Lerp Functions	Linear interpolation between two vectors. "Like spring, a target object following"
	Slerp Functions	The spherical interpolation is between two vectors. "Animated arc between sunrise and sunset"
	MoveToward Function	Current location moves to target Same as Vector3.Lerp, maxDistanceDelta Speed Limit
	SmoothDamp Function	Over time, a vector is gradually changed to the expected target.

 

 

 

Some of my vector-related questions:

How can we determine whether vector A and vector B are in the same direction? How can we determine the front, back, left, and right of vector A and vector B? How can we determine the angle between vector A and vector B? Does the subtraction of vectors seem more useful than the addition method? Vector. Forward and this. transform. Forward both express the local coordinate system. Why are the values different?

 

2 rotation-Quaternion, eulerAngles, Quaternion. Euler

 

Rotation is complex in 3D. In Unity 3D, Quaternion is generally used for rotation. rotation only involves the concept of vectors (vector direction ), do you have any significance for coordinate point or zero vector rotation?

According to the official statement of the Unity 3D API, there are only seven methods or operators that are commonly used and account for 99% of the probability. So far, I have not used so many methods or operators, I have used about four Quaterniong functions.

7 APIs for rotation:

Quaternion API	API description of the Unity Template	Whether Used
Quaternion. LookRotation	Create a rotation and follow the constraints of forward (Z axis) and the header along the upwards (Y axis. That is, create a rotation to make the Z axis orientation to the Y axis up. Commonly used is transform. LookAt.	Yes
Quaternion. Angle	Returns the angle between a and B.
Quaternion. Euler	Returns a rotation angle, which rotates z degrees around the z axis, x degrees around the x axis, and y degrees around the y axis (in this Order ).	Yes
Quaternion. Slerp	Spherical interpolation: interpolation between the from and (from) values.
Quaternion. FromToRotation	Create a rotation from fromDirection to toDirection.
Quaternion. identity	Returns the constant equation rotation (read-only ). This element is "non-rotating": the object is perfectly aligned with the world or its parent axis.	Yes
Quaternion. operator *	Rotate a rotation angle from another element or a vector from a rotation angle.	Yes

 

 

 

Some of my rotating problems:

1 what is the difference between Quaternion. LookRotation and Vector3.RotateTowards?

2 what is the difference between Quaternion. Angle and Vector3.Angle?

3 what is the difference between Quaternion. LookRotation and transform. LookAt?

[Official answer: you can replace it with transform. LookAt most of the time.

Quaternion. LookRotation]

4 how to implement two GameObject face to face, that is, the Z axis is relative?

 

 

 

After a week of review and verification, You can implement the following functions after studying 3D mathematics in the system:

 

 

 

Summary:

It is said that 80% and 90% Unity 3D programmers are self-taught. Most of them are reading books, practical videos, and source code analysis; students born from the cool class have the core course of 3D mathematics, which is estimated to take one semester and have homework. In order to catch up with the level of students in the course class, taking some time to complete the mathematical knowledge will reduce your detours. One sentence: "3D mathematical models are critical. "