there's little math to it, other than it is based on the idea of a 2:1 isometric projection, an angle close to your original sprite, which means that a square in this projection resting in a horizontal plane will be twice as wide as it is high, and when measured against a vertical line (which represents the z axis btw), the angles for the x and y axes are of equal measure, in this case, a slope of 1/2 (see: 2:1 projection). For an object rotating around fixed point remaining equidistant form it, such as any body part rotating around the center of balance, the path of its rotation can be charted by a a regular circle. Because we are in 2:1 projection and the 'orbit' lies within a horizontal plane, the path is represented by an elispe which is twice as wide as it is high. the elipse is centered on the central point at a height equal to the percieved height of the body part. Blue in this particular case represents shoulders, green the hands, purple the head, and yellow both the waist and feet. important veritices, such as the shoulder and hip joints, hands and feet, are marked on the original sprite as well as the rotations.