Ray Tracing in Non-Euclidean Spaces

• Autor(a) principal: Silva, João Rodrigo de André e Alves
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.6/9901
• topic: Buraco de Minhoca; Buraco Negro; Espaço Não-Euclideano; Ray Casting; Ray Tracing; Renderização; Domínio/Área Científica::Engenharia e Tecnologia::Engenharia Eletrotécnica, Eletrónica e Informática

This dissertation describes a method for modeling, simulating and real-time rendering piecewise linear approximations of generic non-Euclidean 3D spaces. The 3D rendering pipeline most commonly used, where one multiplies each vertex coordinate by a 4x4 matrix to project it on the screen does not work for all cases where the space does not obey Euclid’s postulates (non-Euclidean space). Furthermore, while other non-Euclidean rendering tools only work for a limited type of spaces, our approach allows us to model, simulate, and render any isometrically embeddable non-Euclidean space and eventual objects lying therein. We envision at least two main applications for our approach. The first for helping mathematicians get a better understanding of what arbitrary spaces look like (e.g., hyperconical space, hyper-spherical space, and so forth). The second for assisting physicists to visualize and simulate the effects of bent space (e.g., black holes, wormholes, Alcubierre drive, and so forth) on light, and on physical objects