/**
* Returns the exponential of the Quaternion.
*
* @see #log()
*/
public final Quaternion exp() {
float theta = PApplet.sqrt(this.x * this.x + this.y * this.y + this.z * this.z);
if (theta < 1E-6f) return new Quaternion(this.x, this.y, this.z, PApplet.cos(theta));
else {
float coef = PApplet.sin(theta) / theta;
return new Quaternion(this.x * coef, this.y * coef, this.z * coef, PApplet.cos(theta));
}
}
/**
* Returns a random unit Quaternion.
*
* <p>You can create a randomly directed unit vector using:
*
* <p>{@code PVector randomDir = new PVector(1.0f, 0.0f, 0.0f);} <br>
* {@code randomDir = Quaternion.multiply(Quaternion.randomQuaternion(), randomDir);}
*/
public static final Quaternion randomQuaternion() {
float seed = (float) Math.random();
float r1 = PApplet.sqrt(1.0f - seed);
float r2 = PApplet.sqrt(seed);
float t1 = 2.0f * PI * (float) Math.random();
float t2 = 2.0f * PI * (float) Math.random();
return new Quaternion(
PApplet.sin(t1) * r1, PApplet.cos(t1) * r1, PApplet.sin(t2) * r2, PApplet.cos(t2) * r2);
}
// A function to rotate a vector
public void rotateVector(PVector v, float theta) {
float m = v.mag();
float a = v.heading2D();
a += theta;
v.x = m * PApplet.cos(a);
v.y = m * PApplet.sin(a);
}
/**
* Sets the Quaternion as a rotation of {@link #axis() axis} and {@link #angle() angle} (in
* radians).
*
* <p>The {@code axis} does not need to be normalized. A null {@code axis} will result in an
* identity Quaternion.
*
* @param axis the PVector representing the axis
* @param angle the angle in radians
*/
public void fromAxisAngle(PVector axis, float angle) {
float norm = axis.mag();
if (norm < 1E-8f) {
// Null rotation
this.x = 0.0f;
this.y = 0.0f;
this.z = 0.0f;
this.w = 1.0f;
} else {
float sin_half_angle = PApplet.sin(angle / 2.0f);
this.x = sin_half_angle * axis.x / norm;
this.y = sin_half_angle * axis.y / norm;
this.z = sin_half_angle * axis.z / norm;
this.w = PApplet.cos(angle / 2.0f);
}
}
private final float cos(float a) {
return parent.cos(a);
}