Geometry

1) The multidimensional geometric structure analysis system is an educational tool aimed at bridging the gap between abstract mathematical theory and concrete architectural design. This system uses high-precision real-time rendering technology to parameterize and deconstruct complex architectural models, such as medieval fortifications, deep space orbital stations, and classical temples.

Unlike traditional static drawings, this system allows users to freely interact in three-dimensional space. When any building component is selected, the built-in mathematical engine will instantly calculate its surface area and volume, and use computer graphics algorithms to dynamically draw standard engineering three views (top view, front view, side view), achieving a "what you see is what you get" geometric cognitive experience.

2) Rendering Engine: Developed based on Three.js (WebGL), using ACES movie grade tone mapping and PBR physical material system (simulating stone roughness, metallic luster, and glass refraction).

Interactive algorithm: Raycasting algorithm is used to achieve sub-pixel level 3D spatial picking and accurately locate the geometric object clicked by the user.

Mathematical engine: For geometric bodies with different topological structures (spheres, prisms, cones, etc.), the backend extracts their geometric parameters (radius, height, bounding box) in real-time, and derives accurate values through analytical geometric formulas.

Dynamic drawing: Using HTML5 Canvas 2D API, real-time projection of 3D model data into 2D vector wireframes.