Unity Hand Tour < four >3d rotation-four yuan, Euler angle and change matrix

Source: Internet
Author: User


Today we're going to talk about rotation in unity. There are three main ways of doing this. Transformation matrices, four-and Euler-angles.


    • Transformation matrices

You can perform arbitrary 3d transformations (panning, rotating, zooming, trimming) and perspective transformations using homogeneous coordinates. Generally less used. A matrix4x4 matrix class is available in unity

    • Four USD

The four-dollar number is the simplest super-plural. Complex numbers are composed of real numbers plus element I, where i^2 =-1. Similarly, four of dollars are composed of real numbers plus three elements I, J, K, and they are like the following relationship: i^2 = j^2 = k^2 = Ijk = 1, each four is a linear combination of 1, I, J, and K, that is, the four-tuple can generally be represented as a + bi + CJ + DK, its In A, B, C, D is a real number ". These concepts are hard to understand. Just remember that the quaternion in Unity has 4 components (X,Y,Z,W)

    • Euler angle

"A set of 3 independent angular parameters used to determine the position of a fixed-point rotating rigid body, consisting of the nutation angle θ, the precession angle (i.e., the precession angle) ψ and the rotation angle J"
In unity, Quaternion.eulerangles returns the angle of rotation, rotates the euler.z angle around the z axis, rotates euler.x degrees around the x axis, rotates euler.y degrees around the y axis


    • 1. Four meta-to-transform matrix
[CSharp]View Plaincopy
    1. quaternion q = quaternion.lookrotation (new Vector3 (0,0.5,1));
    2. matrix4x4 rot = new matrix4x4 ();
    3. Rot.    Settrs (new Vector3 (0,0,0), Q,new Vector3 (1,1,1));

    • 2. Transform matrix to four-dollar number
[CSharp]View Plaincopy
    1. matrix4x4 rot = new matrix4x4 ();
    2. Rot.    Settrs (new Vector3 (0,0,0), Q,new Vector3 (1,1,1));
    3. Vector4 vy = rot. GetColumn (1);
    4. Vector4 vz = rot. GetColumn (2);
    5. quaternion newq = quaternion.lookrotation (new Vector3 (VZ.X,VZ.Y,VZ.Z),new Vector3 (vy.x,vy.y,vy.z));

Common functions
function Toangleaxis (out angle:float, out Axis:vector3): void
Rotate the angle around the axis axis to create a rotation

static function Angle (A:quaternion, b:quaternion): float
Returns the angle between A and B.

var Eulerangles:vector3
Returns the Euler angle that represents the rotation. Represents the angle of rotation, rotates euler.z degrees around the z axis, rotates euler.x degrees around the x-axis, rotates euler.y degrees around the y-axis (in this order).

function Setfromtorotation (Fromdirection:vector3, Todirection:vector3): void
Rotate the fromdirection of the object to the Todirection

function Setlookrotation (View:vector3, Up:vector3 = vector3.up): void
Create a rotation to move the z axis toward the view Y axis up

static function Slerp (From:quaternion, To:quaternion, t:float): quaternion
From the from range to the to, the moving distance is T

static function Lerp (A:quaternion, B:quaternion, t:float): quaternion
Similar to Slerp, and faster than slerp. But if the rotation angle is far apart, it will look bad.


    • Transformation matrices

Can do a variety of complex transformations, but the learning curve is relatively large, using more memory, because the amount of data stored is larger.

    • Euler angle

Simple to understand, especially for art and planning colleagues. Operation speed and memory consumption are relatively small. There may be a universal lock problem (two axes of rotation coincident)

    • Four USD

Avoid the problem of universal lock. Not so straightforward to understand.
Have any questions welcome to explore [email protected]

Unity Hand Tour < four >3d rotation-four yuan, Euler angle and change matrix

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