Dots and Dots of Threes

Standard sudoku rules apply: each row, column, and 3x3 box must contain all the digits from 1 to 9.

Digits in cells separated by a white dot have a difference of 3.

Digits in cells separated by a black dot are in a 1:3 ratio.

All possible black dots are given. It is not necessarily the case that all possible white dots are given.