Linear Algebra Powers Interactive Diagramming Editor
Ivan Shubin, in developing his interactive diagramming editor Schemio, cleverly used matrix operations from linear algebra to solve a series of challenging problems. Initially, Schemio only supported simple shape creation and manipulation. However, when a hierarchical structure was introduced, coordinate transformations became complex. The author initially used a recursive approach but encountered issues with scaling and pivot points. Ultimately, Shubin leveraged matrices to represent transformations (translation, rotation, scaling), using matrix multiplication for coordinate conversion and ingeniously employing matrix inversion to solve the world-to-local coordinate conversion problem. Furthermore, matrix operations addressed the precise adjustment of an object's position and rotation when moving within the hierarchy, preventing unexpected jumps. Schemio's source code is open-source and available on GitHub.