C # Programmer's Consolidation of Unity 3D notes (10): 3D mathematical model of displacement and rotation of unity3d



Encountered a want to do the function, but can not achieve, the core reason is because the u3d 3D mathematical concept is not flexible thoroughly understand. So again system learning-the third time to learn 3D mathematics.

This time, the features you want to implement are simple:

As in the small map, you want to be able to dynamically draw the current position of the player, Z direction: With 3 lines, z-axis forward, 30° rotation, -30° rotation.

The question is: 0 points can be obtained, P1 points? The P2 point is unknown.

I tried for 2 hours, and it turned out to be less than disappointing.

Have to, take a little time to learn 3D math again:

1-bit shift – vectors and points:

• Points: points and vectors are mathematically consistent, the concept of real life midpoint is better understood, sit punctuation to locate – South two ring, North two ring. "dot (3,4,5) parentheses to mark, abbreviation P"
• Vector: "Commonly known as increment", there are size and direction, such as "forward 1 step walk." Left 90 degrees. "                                              Go ahead until you reach the wall and you stop-before you can get exactly the coordinates of the point you hit the wall or the distance between you and the wall . "Vector with <3,4,5> angle brackets, referred to as V"
• In the u3d, the unification uses the Vector3 object to express the vector and the point, this also causes the novice to be disoriented a very important reason; A skill, usually in the API with position, point, V3 is definitely a dot, all vectors, direction is a vector, read more official API manual, written very clearly.

Make a game, list out the API of Vector3 you used, analyze the use of Vector3 is vector (V) or point (P)

Demand	Api	Vector (V) Point (P)	Note
Smooth displacement	Vector3 Movetowards (Vector3 current, Vector3 target, float maxdistancedelta);	P
Smooth displacement	Vector3 Slerp (Vector3 from, Vector3 to, float t)	P
The new coordinate point	This.m_transform.position = pos;	P	Conform to conventional thinking
Change the coordinates of one time	M_transform. Translate (New Vector3 (Rx, 0,-m_speed * time.deltatime));	V	Can be considered an increment
Seeking direction	Vector3 relativepos = this.m_transform.position–m_player.position;	V	Vector subtraction, more difficult to understand
Set new coordinate points	Linerenderer.setposition (0,this.gameobject.transform.position); M_navagent.setdestination (this.m_Player.transform.position);	P	Conform to conventional thinking
The new location	Pointer.transform.position = Hitinfo.point + (transform.position–hitinfo.point) * 0.01F;	P, V	The superposition of force?
Ask for distance	float dis = vector3.distance (v1, v2); Float F1 = (v1–v2). Sqrmagnitude; float F3 = (v1–v2). magnitude;	P, V	Distance can be used. Vector subtraction can also
To scale forward	Vector3 v3 = This.m_transform.forward * 200F;	V	The multiplication of V
Radiographic Inspection	Ray R = new Ray (source, dest); Physics.raycast (R, out hit, M_shootmask)	V, P	Source:p Dest:v
Add a force	Rigidbody. Addforce (0, 10, 0);	V

According to this game, you can sort out the current 4 components (including Vector 3) will be shifted:

4 components and Vector3 commonly used in displacement:

Component	Function	API description for the Unity holy Scriptures	Whether Have used
Transform components	Translate function	How many distances to move an object in a direction "default local coordinate system" or moving relative to an object.	Yes
	Position property	Position of transform in world space coordinates	Yes
Rigidbody components [Fixedupdate Function]	Velocity Property	Velocity vectors for rigid bodies Unity official demo done used to be cool	Yes
	Addforce function	Add a force to the rigid body. As a result, the rigid body will begin to move.	Yes
	moveposition function	Moving rigid bodies to position
Navmeshagent components	setdestination function	Set Automatic path target point	Yes
Charactercontroller Component	Move function	A more complex motion function, with absolute motion every time.	Yes
	Simplemove function	Move a character at a certain speed
Vector3 Vector	Lerp function	The linear interpolation between the two vectors. "Like a spring that follows a target object"
	Slerp function	Spherical interpolation between two vectors "Animated arcs between sunrise and sunset"
	Movetoward function	Move the current location to the target Same as VECTOR3.LERP, Maxdistancedelta speed limit
	Smoothdamp function	Over time, gradually change a vector toward the desired target.

Some of my vector-related questions:

• How to tell if a vector and B vector are in the same direction?
• How to judge a vector and B vectors before, after, left, right?
• How to determine the angle between a vector and B vector?
• Does subtraction of vectors seem to be more useful than addition?
• Vector.forward and This.transform.Forward both express the local coordinate system, so why are the values different?

2 rotating –quaternion, eulerangles, Quaternion.euler

Rotation in the 3D is more complex, in unity 3D is generally used quaternion to rotate, rotation only involves the concept of vector (vector direction), think about the coordinate point or 0 vector rotation is meaningless?

And according to the Unity 3D API official say, only about 7 methods or operators are more commonly used, and accounted for 99% of the probability, I have not used so far so much, I used the quaterniong about 4 functions.

Rotate commonly used 7 APIs:

Quaternion API	API description for the Unity holy Scriptures	Whether Have used
Quaternion.lookrotation	Creates a rotation along the forward (z-axis) and the head along the upwards (Y-axis) constraint gaze. That is, create a rotation so that the z axis is facing up toward the Y axis. Commonly used is the transform. LookAt	Yes
Quaternion.angle	Returns the angle between A and B.
Quaternion.euler	Returns a rotation angle , rotates the Z-degree around the z-axis, rotates the X-degree around the x-axis, and rotates the Y-degree (in order of this) around the y-axis.	Yes
Quaternion.slerp	The spherical interpolation, interpolated from the T-value from.
Quaternion.fromtorotation	Create a rotation from fromdirection to todirection.
Quaternion.identity	Returns the identity rotation (read-only). This four-dollar number is for "No rotation": This object is completely aligned to the world or to the parent axis.	Yes
Quaternion.operator *	Rotates a rotation angle by another four-dollar number, or rotates a vector by a rotation angle	Yes

Some of my spin-related issues:

1 The difference between quaternion.lookrotation and vector3.rotatetowards?

2 The difference between Quaternion.angle and vector3.angle?

3 The difference between quaternion.lookrotation and Transform.lookat?

[Official answer: Most of the time you can use transform. LookAt instead

Quaternion.lookrotation]

4 How do I achieve 2 gameobject face-to-face, the z-axis relative?

Ax: After a week of review, repeated verification, sure enough in the system to learn 3D math, to achieve the function can be, as follows:

Reference blog:

A brief introduction to the coordinate system: C # Programmer's Consolidation of Unity 3D notes (eight): Introduction to Unity 3D coordinate system

Xuanhusung's Blog: http://www.xuanyusong.com/archives/1977

Summarize:

It is said that 80%, 90%unity 3D programmers are self-taught, most of them are reading books, actual combat video, source analysis, and the students will be born in mathematics this core class-estimated to occupy a semester, there will be homework. In order to catch up with the level of the students, spend some time, fill the math knowledge, will make oneself less go some detours. Bottom line: "3D math model is critical. “

C # Programmer's Consolidation of Unity 3D notes (10): 3D mathematical model of displacement and rotation of unity3d