Four dimensional script in a efficient manner using variables Xrotation, Yrotation, and Zrotation

Question

Is there an efficient formula to map a four dimensional point in a three dimensional space using the variables Xrotation Z rotation and Yrotation as inputs?

I specifically need scratch language, but any other language will be suitable.

Answer 1

The four dimensional rotation you're probably talking about is called a quaternion. When talking about rotating around each axis in a 3D space, we call Euler angles. Wikipedia has page about these conversions, which includes this python source:

class Quaternion_toEulerianAngle():
    def __init__(self, x, y, z, w):
        self.x = x
        self.y = y
        self.z = z
        self.w = w

    def X(self):
        ysqr = self.y*self.y

        t0 = +2.0 * (self.w * self.x + self.y*self.z)
        t1 = +1.0 - 2.0 * (self.x*self.x + ysqr)
        X = math.degrees(math.atan2(t0, t1))

        return X

    def Y(self):
        ysqr = self.y*self.y

        t2 = +2.0 * (self.w*self.y - self.z*self.x)
        t2 =  1 if t2 > 1 else t2
        t2 = -1 if t2 < -1 else t2
        Y = math.degrees(math.asin(t2))

        return Y

    def Z(self):
        ysqr = self.y*self.y

        t3 = +2.0 * (self.w * self.z + self.x*self.y)
        t4 = +1.0 - 2.0 * (ysqr + self.z*self.z)
        Z = math.degrees(math.atan2(t3, t4))

        return Z