Conformal mapping is a mathematical technique from complex analysis that transforms a complex geometric domain into a simpler one while preserving local angles and shapes, enabling analytical or numerical solutions to otherwise intractable boundary value problems. In the context of pedestrian crowd flow modeled as a continuum fluid, conformal mapping is used to convert irregular or complex physical spaces, such as corridors with obstacles or non-rectangular room geometries, into canonical domains where the governing partial differential equations can be solved more tractably. Its importance lies in reducing computational complexity and enabling closed-form or semi-analytical solutions for crowd dynamics, with key variants including Schwarz-Christoffel transformations for polygonal domains and numerical conformal mapping methods for arbitrary boundary shapes.
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