She said if her dad took over three decades to attain stardom, she should be given at least half the time to prove herself.
She said: "It's a tough life for star kids...for people they are stars; for us, they are the people that we know."
"As star children, we face the expectations, which is as much as that of the achievers who are the fathers or mothers who took so much time to achieve it. My father is a superstar now, but he took 31 years to reach here, at least give me 15 years," the 30-year-old, who is married to Chennai-based businessman Ashwin, told IANS.
Rajinikanth, who rose to meteoric heights from a bus conductor to Tamil cinema's superstar, enjoys a huge fan following.
Achievers' children can't afford to take their lineage for granted, Soundarya said.
"Be it in any business, when the achievers' children enter, the expectation and pressure on them are much more. Yes, we do have an access no doubt, but there is too much of pressure," she said.
"Kochadaiiyaan", a Rs.125-crore film, said to be India's first motion capture photo-realistic 3D animated movie, is expected to release worldwide May 1 on about 6,000 screens in six languages.
Bollywood diva Deepika Padukone plays the female lead opposite Rajinikanth in the film, which also features Jackie Shroff, R. Sarath Kumar, Shobana, Nasser, Aadi Pinisetty and Rukmini.
Shot predominantly in Ocher studios, owned by Soundarya, the film features no live locations. Everything was shot indoors.
Sharing the shooting experience with her dad, she vouched for his professionalism and punctuality.
She said: "My father is a thorough professional - what the script demands, what the director demands, he will do it. Even if the director is convinced with the shot and the actor of his seniority thinks he can do better, he will take that extra effort as an actor even if the director says it's okay."
"Time punctuality? My god! He is the most punctual person I have ever seen...the discipline he has on the floor is outstanding," she added.
Soundarya, who has a clear idea about what fans expect from her father on the screen, said "Kochadaiiyaan" has all the commercial elements that will excite viewers.
"We have done a lot of commercial elements that will excite my dad's fans. For me, my father doing Rudra Tandav excites me. The feedback I have received from my father's fans has been commendable.
"What the audience wants from my father is that they want to see him on the screen as commercial star because they are used to seeing him like that.
"My father's older movies, if you have seen, are performance-oriented roles. He reached a stage in his life where he became the mass hero where people wanted him to be just that - larger than life... Entertainment is what my father's fans want," she added.
The Tamil period-drama has been passed with a U-certificate by the Central Board of Film Certification.
Soundarya, however, lamented that animation is still not understood in India.
"In our country, animation is not understood yet. Animation is associated with cartoons and it is very tough for us as technicians. Animation is a process and the toughest part for me was to explain the process.
"Films like this take six to seven years to make. As soon as I finished shooting, everybody was like when can we see the film? But it's like you can only see the dots, it's like the capture point. People feel the film has been delayed, but it's not delayed. It's a time-consuming process," Soundarya added.
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