I will present my attempt to apply the Hrushovski construction to ordered fields. I will introduce my result on the green points construction, which axiomatizes the real field with dense logarithmic spirals. I will focus on my recent progress on the raising to powers construction, an expansion of RCF by "power functions" on the unit circle, whose axiomatization consists of the Schanuel property and the EC-property. If time permits, I will verify the EC-property for the corresponding expansion of the real field.