Процедурна генерація цифрового рельєфу за допомогою дискретних гідродинамічних моделей

• Date: 2025
• Main Authors: Жолтовський, Олексій, Станіславів, Олександр, Смалько, Олена
• Format: Article
• Language: English
• Published: Kamianets-Podilskyi National Ivan Ohiienko University 2025
• Online Access: http://mcm-tech.kpnu.edu.ua/article/view/332367
• Journal Title: Mathematical and computer modelling. Series: Technical sciences

This article investigates discrete hydrodynamic models for advanced procedural generation of digital terrains, aiming to synthesize dynamic and geomorphologically plausible landscapes. Our approach proposes a novel hybrid method. It combines procedural fractal noise with layered discrete hydrodynamic modeling, providing a robust and realistic synthesis pipeline that significantly surpasses conventional static techniques. Initially, fractal algorithms create a foundational base heightmap, establishing essential large-scale elevation variations. To enhance physics-based modeling plausibility, successive hydrodynamic simulations meticulously mimic water flow, erosion, sediment transport, and channel formation. Specifically, Euler's and shallow water equations model large-scale water dynamics and terrain evolution. For micro-scale refinement, Burgers' and Korteweg-de Vries equations are utilized for sedimentation processes, generating finer redistribution patterns and adding morphological complexity consistent with natural fluvial landscapes. A custom software application was developed to sequentially integrate these layers, enabling precise and iterative application of hydrodynamic effects. This ensures the generated topographical features are both accurate and aesthetically compelling. Simulations demonstrate the proposed method generates heightfields with realistic geomorphology, while maintaining high computational efficiency facilitated by optimized numerical methods. This makes it well-suited for diverse applications: computer graphics, game development, virtual reality, and geographical education. Integrating discrete physics-based hydrodynamics into procedural noise synthesis fundamentally elevates the realism, coherence, and structural consistency of synthetic terrains, offering a versatile and effective tool for complex environmental representation.