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

http://blog.csdn.net/janeky/article/details/17272625

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

Defined

• 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

Transformation

• 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));
4. Vector4 vy = rot. GetColumn (1);
5. Vector4 vz = rot. GetColumn (2);
7. 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.

Comparison

• 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