论文标题
射线制造的瑟斯顿几何形状
Ray-marching Thurston geometries
论文作者
论文摘要
我们描述了使用射线图形产生八个瑟斯顿几何形状的准确的实时交互式空间视图的算法。我们为我们的算法提供了一个理论框架，与所涉及的几何形状无关。除了几何$ x $中的场景外，我们还考虑了商歧管和orbifolds $ x /γ$中的场景。我们将phong Lighting模型调整为非欧亚人几何形状。其中最困难的部分是光强度的计算，这与测量球的面积密度有关。我们还为每个几何形状提供了广泛的实用细节。
We describe algorithms that produce accurate real-time interactive in-space views of the eight Thurston geometries using ray-marching. We give a theoretical framework for our algorithms, independent of the geometry involved. In addition to scenes within a geometry $X$, we also consider scenes within quotient manifolds and orbifolds $X / Γ$. We adapt the Phong lighting model to non-euclidean geometries. The most difficult part of this is the calculation of light intensity, which relates to the area density of geodesic spheres. We also give extensive practical details for each geometry.
