Research on Sanxingdui Cultural Relic Geometry Based on Polar Coordinate Method and Linear Interpolation

This paper focuses on the analysis of the unearthed bronze solar wheel and gold mask. For the bronze solar wheel: Firstly, a plane coordinate system is established to transform the three dimensional plane diagram into a two dimensional plane map. Then, polar coordinates are introduced, and linear interpolation is constructed to obtain the curve equation of cultural relics. Mathematical model of the bronze solar wheel needs to be established, and the general equation of the internal arc should be derived. With the center of the bronze solar wheel as the origin of XOY, according to the general equation of the circle and by substituting the disk data, the bronze sun wheel curve equation can be obtained. On the XOY plane rectangular coordinate frame, through introducing polar coordinates, the POINT command in CAD can determine the intersection coordinates of the five rays in the disk and the angle with the horizontal axis. Substituting these into the polar coordinate equation, the five - ray equation can be obtained. To obtain the general equations of the circular arc, polar coordinates need to be established. For the drawing of bronze solar wheel four, six, eight, and 12 ray patterns, it can be obtained by adjusting the angle θ between the ray and the horizontal axis X through CAD. **************** ACKNOWLEDGEMENTS**************** This work is supported by ministry of education industry-university cooperative education project (Grant No.: 231106441092432), the research and practice of integrating "curriculum thought and politics" into the whole process of graduation design of Mechanical engineering major: (Grant. No.: 30120300100-23-yb-jgkt03), research on the integration mechanism of "course-training-competition-creation-production" for innovation and entrepreneurship of mechanical engineering majors in applied local universities (Grant. No.: CXKT202405), Mechanical manufacturing equipment design school-level "gold class" construction project (Grant. No.: 30120324001).