/** * Sets the Quaternion as a rotation from the {@code from} direction to the {@code to} direction. * * <p><b>Attention:</b> this rotation is not uniquely defined. The selected axis is usually * orthogonal to {@code from} and {@code to}, minimizing the rotation angle. This method is robust * and can handle small or almost identical vectors. * * @see #fromAxisAngle(PVector, float) */ public void fromTo(PVector from, PVector to) { float fromSqNorm = MathUtils.squaredNorm(from); float toSqNorm = MathUtils.squaredNorm(to); // Identity Quaternion when one vector is null if ((fromSqNorm < 1E-10f) || (toSqNorm < 1E-10f)) { this.x = this.y = this.z = 0.0f; this.w = 1.0f; } else { PVector axis = from.cross(to); float axisSqNorm = MathUtils.squaredNorm(axis); // Aligned vectors, pick any axis, not aligned with from or to if (axisSqNorm < 1E-10f) axis = MathUtils.orthogonalVector(from); float angle = PApplet.asin(PApplet.sqrt(axisSqNorm / (fromSqNorm * toSqNorm))); if (from.dot(to) < 0.0) angle = PI - angle; fromAxisAngle(axis, angle); } }
/** * Constructs and initializes a Quaternion from the specified rotation {@link #axis() axis} (non * null) and {@link #angle() angle} (in radians). * * @param axis the PVector representing the axis * @param angle the angle in radians * @see #fromAxisAngle(PVector, float) */ public Quaternion(PVector axis, float angle) { fromAxisAngle(axis, angle); }