It is hoped the public will be able to identify the man.
He is described as a hairy, chubby Indian, about 25 years old, with dark skin and a slight accent. He is about 1.67m tall, or about 5'6". On the night I question, the man was wearing a white netted baseball cap.
The vehicle the alleged rapist was driving has also been described. It was a light-coloured Toyota Vitz with black interior, in a messy condition. It had only one tail light working and had a white bag under the front passenger seat.
"This was a brutal, prolonged attack on a young woman and we're working very hard to make sure this person is brought to justice," Detective Sergeant Scott Armstrong said in a statement this afternoon.
"We have a solid description of the offender and his car and I'm urging people to cast their minds back and have a think about whether they recognise either of these pictures.
"We want to hear from anyone who recognises the person in the computer sketch, especially if they have any links to a Toyota Vitz like the one in the picture, either as the owner or as someone who has access to a vehicle like that.
"The cap is also distinctive and may well assist in identifying the person in the computer sketch."
Anyone with information should contact the Waitemata police Child Protection Team on 09 477 5003. Anonymous information can also be provided via Crimestoppers on 0800 555 111.