Ray-Marching Thurston Geometries
Ray-Marching Thurston Geometries
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DOI：
10.1080/10586458.2022.2030262
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发表时间：
2020-10
影响因子：
0.5
通讯作者：
Rémi Coulon;Elisabetta A. Matsumoto;Henry Segerman;Steve J. Trettel
中科院分区：
文献类型：
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作者：
Rémi Coulon;Elisabetta A. Matsumoto;Henry Segerman;Steve J. Trettel
翻译后摘要我们描述的算法，产生准确的实时交互式的空间视图的八个瑟斯顿几何形状，使用光线行进。我们给出了一个理论框架，我们的算法，独立的几何形状。除了几何X内的场景，我们还考虑商流形和orbifolds内的场景。我们将Phong照明模型适应于非欧几里德几何。其中最困难的部分是光强度的计算，这与测地线球体的面积密度有关。我们还为每个几何形状提供了广泛的实用细节。
Abstract 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 . 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.