## 1 Introduction  
From a spatial perspective, geometric rationalization is a distinctly human construct; in nature, straight lines are rare. Traditional architecture often relies on orthogonal approaches, where spaces and paths are formed by intersecting static, perpendicular planes [1]. This geometric simplification facilitates the construction and fabrication of structural elements but can create a disconnect from natural biomimetic patterns, reducing the ergonomic and sensory richness of spatial environments. Considering motor and psychological factors is particularly significant during the early stages of human development, when play serves as a primary learning mechanism [2]. During these formative years, it is critical to encourage less linear, more organic movements that promote asynchronous and multidirectional body motions. Environments reflecting natural forms can enhance reflexes, motor coordination, and cognitive responses, contributing to holistic human development. Recent research underscores the importance of designing nature-based outdoor play and learning environments for children under three years old, showing that such spaces significantly impact their holistic development [3]. Incorporating natural elements and organic forms into these environments enhances sensory experiences, encourages exploration, and fosters physical, cognitive, and emotional growth [3]. This aligns with the increasing recognition that early childhood environments should mimic natural settings to support health and learning outcomes. In keeping with this understanding, there is a growing need to develop children's play equipment that is more closely connected to natural morphological patterns. By implementing designs that support motor development and enable early diagnosis of developmental issues, a more suitable environment for holistic child development can be achieved [4]. Creating such ergonomic geometries, especially those based on Gaussian curvature [5; 6], presents significant manufacturing challenges. Traditional methods often struggle to produce double-curved surfaces and complex organic shapes. Thermoforming has emerged as a key technique for fabricating such geometries, particularly for materials that require precise control over deformation processes [7]. This process involves heating a plastic sheet to a pliable temperature, forming it over a mold, and trimming it to produce a usable product, offering efficiency and the ability to create large parts with intricate details. Advanced modeling of the thermoforming process using thermo-visco-hyperelastic models has been explored to predict material behavior accurately during forming [7]. Factors such as temperature, pressure, and mold interaction significantly influence the thickness distribution and mechanical properties of the formed material [7; 8]. Moreover, advances in thermoforming fiber-reinforced thermoplastic composites have shown promise for creating lightweight, durable structures with complex shapes [9; 10]. These composites offer advantages such as recyclability, high strength-to-weight ratios, and reduced environmental impact. However, challenges remain in optimizing process parameters to avoid defects like wrinkling, thinning, and residual stresses [9; 11]. In the context of outdoor children's play areas, it is essential to consider manufacturability, durability, safety, and environmental impact. Solid surface materials stand out as promising candidates due to their thermoformability, non-porosity, antibacterial properties, and resistance to external agents. The material used in this case study is composed of approximately two-thirds natural minerals and a low percentage of high-resistance resins [12]. These properties make it ideal for creating complex geometries while meeting strict safety and hygiene standards. Previous studies have highlighted the importance of precise control in the thermoforming process to prevent defects and achieve the desired geometry [13]. [PERSON] et al.