编辑更简单
一直到它我需要在 3D 空间中的 3 轴上旋转一个圆圈。我已经毫无问题地向下移动了 y 轴。然而，我与其他两个的工作只导致圆圈围绕中心点而不是旋转。我还需要能够在旋转后在这个圆的边缘找到一个点。这样我就可以将我的对象绘制在那些点或在那个点渲染效果。
到目前为止我所拥有的示例...上下文位于我的世界模组中，因为它可以轻松地以图形方式测试代码。http://puu.sh/38Z6x.jpg我使用 6 分来测试代码，但以后可以增加。
这是我到目前为止的代码-代码-它的github，所以它会在我同步我的代码时经常更改。所以不要依赖于我尝试过的东西，而是我正在使用的结构。上次同步我尝试选择球坐标系。
我也在寻找进行这些计算的性能提示。我将在我正在控制 1000 个移动物体的项目上运行其中的几个计算。
好的，看起来我已经开始工作了，我的轮换工作几乎 100%。我遇到的唯一问题是在设置行距后我无法围绕圆的边缘旋转。http://puu.sh/3ae63.jpg谢谢@Aggieboy 的帮助，非常棒
这是我的代码，虽然我认为它需要更多的工作，但它的东西。github 类将随着我对它们的更多工作而更新。但是，由于它是私有仓库，我无法将 github 文件链接到测试类。
/*
* This is the code used to test the rotation by generating a circle with the radius
* given
*/
double r = 3;
double s = (2 * Math.PI) / this.points.length;
Vector3 vec = new Vector3(this.xCoord + 0.5D, this.yCoord + 2D, this.zCoord + 0.5D);
boolean flip = false;
/*
* Rotation speed is set here though it could be control by anything. As well the
* rotation change is stored in a vector(x,y,z) and doesn't only have to be in the z axis
*/
this.rotation.z += 5;
for (int i = 0; i < points.length; i++)
{
Color color = flip ? Color.red : Color.blue;
Vector3 point = vec.clone().add(NetworkOrbit.getOrbitOffset(r, s * i, this.rotation));
points[i] = point.clone();
if (i != 0)
{
int a = i + 1 == this.points.length ? 0 : i - 1;
int b = i;
/*
* generatelaser creates a laser line from one point to another and is used for
* visual debug
*/
this.laser.generateLaser(this.worldObj, points[a], points[b], color, 10, 5);
}
flip = !flip;
}
this.laser.generateLaser(this.worldObj, points[this.points.length - 1], points[this.points.length - 2], flip ? Color.red : Color.blue, 10, 5);
//Markers to show me the center point and then a line to point 0
this.laser.generateLaser(this.worldObj, vec, vec.clone().add(new Vector3(0, -2, 0)), Color.darkGray, 10, 5);
this.laser.generateLaser(this.worldObj, points[0], vec, Color.darkGray, 10, 5);
Github 代码链接对格式感到抱歉，我似乎还不能发布超过 2 个链接 https://github.com/DarkGuardsman/Dark-Library/blob/master/src/minecraft/dark/library/ ...
...数学/四元数.java
...轨道/NetworkOrbit.java
这是我的简单四元数类。它使用了本教程中的许多语义：
public class Quaternion {
public double w, x, y, z;
public Quaternion(double angleRadian, double x, double y, double z){
double dAngle=angleRadian/2; //might as well divide by 2 here
this.w=Math.cos(dAngle);
this.x=x * Math.sin(dAngle);
this.y=y * Math.sin(dAngle);
this.z=z * Math.sin(dAngle);
}
public Quaternion(){
x=y=z=0; w=1;
}
public void norm(){
double magnitude = Math.sqrt(w*w + x*x + y*y + z*z);
w = w / magnitude;
x = x / magnitude;
y = y / magnitude;
z = z / magnitude;
}
public Quaternion conj(){
Quaternion ans = new Quaternion();
ans.set(this);
ans.conjLocal();
return ans;
}
public void conjLocal(){
x=-x;
y=-y;
z=-z;
}
public void set(Quaternion q){
w=q.w;
x=q.x;
y=q.y;
z=q.z;
}
public void set(double w, double x, double y, double z){
this.w=w;
this.x=x;
this.y=y;
this.z=z;
}
public Quaternion mult(Quaternion q){
Quaternion ans = new Quaternion();
ans.w = (this.w*q.w - this.x*q.x - this.y*q.y - this.z*q.z);
ans.x = (this.w*q.x + this.x*q.w + this.y*q.z - this.z*q.y);
ans.y = (this.w*q.y - this.x*q.z + this.y*q.w + this.z*q.x);
ans.z = (this.w*q.z + this.x*q.y - this.y*q.x + this.z*q.w);
return ans;
}
public void multLocal(Quaternion q){
Quaternion temp=this.mult(q);
this.set(temp);
}
public String toString(){ return "<"+w+", "+x+", "+y+", "+z+">"; }
}
v要通过四元数旋转向量q以获得结果向量v'，必须使用以下等式：
v' = q * v * q.conj()
这是一个围绕四元数旋转矢量（或位置坐标）的演示。
public class QuaternionExample {
public static void main(String[] args) {
/*
* Let's say we have a vector <1,0,0>, and we want to rotate it
* such that the result will be in the other unit axiis: <0,1,0>
* and <0,0,1>. Right hand rule applies for rotating about an axis!
* Convince yourself of the following through mental imagery:
* 1. For <0,1,0>, we want to rotate <1,0,0> by 90 degrees about the z axis
* 2. For <0,0,1>, we want to rotate <1,0,0> by 90 degrees about the -y axis (or -90 degrees also works)
*/
//the quaternion form of a 3d vector is simply <0,Vec3> or <0,x,y,z>
Quaternion x=new Quaternion();
x.set(0,1,0,0);
//1, we want <0,1,0>
Quaternion rot = new Quaternion(Math.PI/2,0,0,1);
System.out.println( rot.mult(x).mult(rot.conj()) );
//2, we want <0,0,1>
rot = new Quaternion(Math.PI/2,0,-1,0);
System.out.println( rot.mult(x).mult(rot.conj()) );
rot = new Quaternion(-Math.PI/2,0,1,0);
System.out.println( rot.mult(x).mult(rot.conj()) );
}
}
我想围绕原点旋转我的矢量（或位置坐标）。如果我想围绕不同的点旋转它（例如，对象的质心c），我需要先减去对象的质心，然后将其添加到结果中：
v' = q * (v-c) * q.conj() + c