Diagonal Asterisk Kropki Sudoku

Sudoku with consecutive or double dots between neighbours. Both main diagonals must also contain each digit once. The nine shaded asterisk cells must contain every digit once.
Controls
Solve the sudoku. A white dot means neighbours differ by 1; a black dot means one is double the other. No dot means neither relation holds.
Logic · Numbers · Deduction · Grid
Brain training · PuzGo