1. While he was based on the sketches, Degas painted in his studio.

2. While he was walking on the street, he met a friend of his.

3. While he was driving, he sometimes smoked.

4. While he was chatting, he drank coffee from time to time.

(What about the sentences using 'while'? Are they all grammatical?)

1. is not correct. The term "based on" is not appropriate in this sentence.

But the other three are great.

Here are some correct uses of "based on."

The modern play, "West Side Story," is based on the Shakespeare play, "Romeo and Juliet."

Based on what I know about geography, I know that southern Vietnam is a tropical region.

I guessed that Mr. Pursley was right, based on his previous answers.