1. New geometric intuitive expression: Through innovative mathematical symbols, figures or models, it provides a new way to explain and express geometric concepts and theorems. For example, animation, virtual reality, augmented reality and other technologies are used to make geometric concepts more intuitive and vivid.

2. Explore new geometric problems: discover new geometric problems, or re-examine traditional geometric problems and analyze and solve them from a new angle. For example, we can study non-Euclidean geometry, topological geometry and other fields, or explore practical problems from the perspective of geometric application.

3. Propose a new geometric theorem: through the research and analysis of geometric problems, propose a new geometric theorem or conclusion, and give a strict proof process. These theorems can be based on the generalization of traditional geometric theory, or they can be novel theorems that intersect with other disciplines.

4. Develop new geometric tools: put forward new geometric tools or methods to simplify the process of geometric reasoning and analysis. For example, software tools that can automatically prove geometry can be developed based on computer algorithms and geometric models.

It should be noted that the innovations of geometric intuitive papers are diverse and specific, depending on the author's research direction and interest. These are just some common innovation directions, and the specific innovation points need to be analyzed according to the contents of specific papers.