A framework for digital sunken relief generation based on 3D geometric models

Sunken relief is a special art form of sculpture whereby the depicted shapes are sunk into a given surface. This is traditionally created by laboriously carving materials such as stone. Sunken reliefs often utilize the engraved lines or strokes to strengthen the impressions of a 3D presence and to highlight the features which otherwise are unrevealed. In other types of reliefs, smooth surfaces and their shadows convey such information in a coherent manner. Existing methods for relief generation are focused on forming a smooth surface with a shallow depth which provides the presence of 3D figures. Such methods unfortunately do not help the art form of sunken reliefs as they omit the presence of feature lines. We propose a framework to produce sunken reliefs from a known 3D geometry, which transforms the 3D objects into three layers of input to incorporate the contour lines seamlessly with the smooth surfaces. The three input layers take the advantages of the geometric information and the visual cues to assist the relief generation. This framework alters existing techniques in line drawings and relief generation, and then combines them organically for this particular purpose

Holographic Tunneling Wave Function

The Hartle-Hawking wave function in cosmology can be viewed as a decaying wave function with anti-de Sitter (AdS) boundary conditions. We show that the growing wave function in AdS familiar from Euclidean AdS/CFT is equivalent, semiclassically and up to surface terms, to the tunneling wave function in cosmology. The cosmological measure in the tunneling state is given by the partition function of certain relevant deformations of CFTs on a locally AdS boundary. We compute the partition function of finite constant mass deformations of the O(N) vector model on the round three sphere and show this qualitatively reproduces the behaviour of the tunneling wave function in Einstein gravity coupled to a positive cosmological constant and a massive scalar. We find the amplitudes of inhomogeneities are not damped in the holographic tunneling state.Comment: 22 pages, 5 figures, Revisions according to the JHEP edito

Twistor Theory and Differential Equations

This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon arise from holomorphic vector bundles over T\CP^1. A different framework is provided for the dispersionless analogues of soliton equations, like dispersionless KP or $SU(\infty)$ Toda system in 2+1 dimensions. Their solutions correspond to deformations of (parts of) T\CP^1, and ultimately to Einstein--Weyl curved geometries generalising the flat Minkowski space. A number of exercises is included and the necessary facts about vector bundles over the Riemann sphere are summarised in the Appendix.Comment: 23 Pages, 9 Figure

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press

Precise localization for aerial inspection using augmented reality markers

The final publication is available at link.springer.comThis chapter is devoted to explaining a method for precise localization using augmented reality markers. This method can achieve precision of less of 5 mm in position at a distance of 0.7 m, using a visual mark of 17 mm × 17 mm, and it can be used by controller when the aerial robot is doing a manipulation task. The localization method is based on optimizing the alignment of deformable contours from textureless images working from the raw vertexes of the observed contour. The algorithm optimizes the alignment of the XOR area computed by means of computer graphics clipping techniques. The method can run at 25 frames per second.Peer ReviewedPostprint (author's final draft