"accurate" and "precise" - they are synonymous but differ in what they emphasize.
accurate: be close and faithful to the object described or measured, free of error or defect.
precise: be exact, free of wide deviations, in measurement or description.
So "accurate" is more appropriate when there is a particular object involved.
"precise" is often better when describing general manners and ways or when emphasizing the exactitude in particular aspects.
For your "drawing ornaments" example, I would say using "accurate" makes it less clear and somewhat unnatural.
- The witness gave quite an accurate description of the criminal.
- Accuracy is the foremost goal in measurements.
- He was a person always precise in words in deeds.
- It is precisely in this regard the enterprise is considered a failure.