Title: Procedural Multiscale Geometry Modeling using Implicit Functions Show Chinese title

Title: 基于隐函数的程序化多尺度几何建模

Abstract: Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is challenging but essential for computer graphics, engineering, and materials science. We present a framework inspired by hypertexture methods, using implicit functions and adaptive sphere tracing to synthesize multiscale structures on the fly without precomputation. This framework models volumetric materials with particulate, fibrous, porous, and laminar structures, allowing control over size, shape, density, distribution, and orientation. We enhance structural diversity by superimposing implicit periodic functions while improving computational efficiency. The framework also supports spatially varying particulate media, particle agglomeration, and piling on convex and concave structures, such as rock formations (mesoscale), without explicit simulation. We show its potential in the appearance modeling of volumetric materials and explore how spatially varying properties influence perceived macroscale appearance. Our framework enables seamless multiscale modeling, reconstructing procedural volumetric materials from image and signed distance field (SDF) synthetic exemplars using first-order and gradient-free optimization. Show Chinese abstract

Abstract: 材料在介观到微观尺度上表现出几何结构，影响宏观尺度的特性，如外观、机械强度和热行为。 捕捉和建模这些多尺度结构具有挑战性，但对计算机图形学、工程和材料科学至关重要。 我们提出了一种受超纹理方法启发的框架，使用隐函数和自适应球面追踪，在无需预计算的情况下实时合成多尺度结构。 该框架通过颗粒状、纤维状、多孔和层状结构对体积材料进行建模，允许控制尺寸、形状、密度、分布和方向。 我们通过叠加隐式周期函数来增强结构多样性，同时提高计算效率。 该框架还支持空间变化的颗粒介质、颗粒团聚以及在凸面和凹面结构（如岩石构造）上的堆积，而无需显式模拟。 我们展示了其在体积材料外观建模中的潜力，并探讨了空间变化的属性如何影响感知的宏观外观。 我们的框架实现了无缝的多尺度建模，通过一阶和无梯度优化从图像和带符号距离场（SDF）的合成示例中重建程序化体积材料。