给出这篇论文的逐字逐句翻译结果，公式另起一行居中的情况均严格遵守原文是否这样才可在翻译中进行另起一行...

Preparing document extraction

I’m assessing the PDF’s text, equations, captions, references, and layout so I can translate the complete paper while preserving paragraph structure and displaying formulas only when the source does.

Prepared document extraction

Refining formula handling

I’m narrowing equation regions carefully so translated prose isn’t duplicated. I’ll preserve source placement, keep centered formulas on separate lines, and retain surrounding mathematical notation as accurately as possible.

Refined formula handling

Created Chinese PDF translation with repaired equations and layout checks

Summarized and searched Isogeometric Analysis implementation details

Translated, formatted, rendered, and validated the Chinese IGA document

Worked for 18m 45s