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| Author(s): |
Mateus Pereira Araujo
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São José do Rio Preto. 2022-01-28. |
| Institution: | Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto |
| Defense date: | 2022-01-18 |
| Advisor: | Luciana de Fátima Martins |
| Abstract | |
Let M be a surface in R³ and consider the orthogonal projection of its points on a plane along a direction v. This map is singular when v is a tangent direction to M and is important to classify the type of contact between M and lines parallel to v. The singular set of the orthogonal projection restricted to M is called contour generator and its projection is called apparent contour. We gather in this work results about orthogonal projections of regular and singular surfaces in R³ . We study the classification of its singularities and we relate the singularity classes to differential geometry of M, when M is a regular surface or a cuspidal edge. Koenderink’s Theorem is a result that relates the Gaussian curvature of M with the curvatures of the normal section of M along the direction v and of the apparent contour, when this is regular. We present the proof of this theorem and also study extensions of this result considering apparent contours with (2,3)-cusps. We also studied a version of this result when M is a singular surface, namely a cuspidal edge. (AU) | |
| FAPESP's process: | 19/19714-0 - Apparent contour of surfaces in R3 and extensions of Koenderink's formula |
| Grantee: | Mateus Pereira Araujo |
| Support Opportunities: | Scholarships in Brazil - Master |