限制俯仰,偏航和滚 [英] Constrain pitch, yaw, & roll
问题描述
我将旋转表示为四元数,并试图限制音调,偏航和横滚轴。我试着这样做:
I've a rotation represented as a quaternion and am trying to constrain the pitch, yaw, & roll axes. I tried doing so thusly:
public struct Orientation
{
public Vector3 up, forward;
public Orientation(Vector3 up, Vector3 forward)
{
this.up = up;
this.forward = forward;
}
}
public static Orientation[] orientations = new Orientation[3]
{
new Orientation(Vector3.right, Vector3.up),
new Orientation(Vector3.up, Vector3.forward),
new Orientation(Vector3.forward, Vector3.right)
};
public enum Axis
{
Pitch,
Yaw,
Roll
};
private Vector3 ConstrainAxis(Vector3 vector, Axis axis, float from, float to)
{
Orientation orientation = orientations[(int)axis];
float theta = (to - from) * 0.5F;
Vector3 cons = Quaternion.AngleAxis(from + theta, orientation.up) * orientation.forward;
Vector3 proj = Vector3.ProjectOnPlane(vector, orientation.up);
return ConstrainVector(cons.normalized, proj.normalized, theta);
}
private Vector3 ConstrainVector(Vector3 from, Vector3 to, float angle)
{
float theta = Mathf.Abs(angle / Vector3.Angle(from, to));
if(theta < 1.0F)
{
return Vector3.Slerp(from, to, theta);
}
return to;
}
事实证明,这不过是过于复杂的约束方式欧拉角表示的各个组成部分,都面临着奇怪的抖动问题(与万向锁定有关吗?)。
Which turned out to be nothing more than an over-complicated way of constraining the individual components of an euler angle representation, of which both are subject to a strange jittering issue (gimbal lock related?).
约束这些轴的最佳方法是什么?
What is the best approach to constraining these axes?
推荐答案
对于关节约束,通常的做法是使用摆动扭曲参数化。
表示当前旋转为四元数的摆动扭曲,theare是很好的分解
http://www.alinenormoyle.com/weblog/?p=726
For joint constraints it is common practice to use "swing twist" parametrization. To represent current rotation as "swing twist" for quaternions, theare are good decomposition http://www.alinenormoyle.com/weblog/?p=726
可以限制摆动和扭曲四元数。
And constraint for "swing" and "twist" can be done with quaternions.
如果我们想将摆动限制为+ -30度,伪代码应为
if we want to constrain swing to +-30 degrees , pseudocode looks like
Quaternion swing;
const double maxMagnitude = sin( 0.5 * toRad(30) );
const double maxMagnitudeW = sqrt(1.0 - maxMagnitude*maxMagnitude );
if(swing.vec().normSqr() > maxMagnitude*maxMagnitude)
{
swing.vec() = swing.vec().normalized() * maxMagnitude;
swing.w() = maxMagnitudeW;
}
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