Vectorization for Fast, Analytic, and Differentiable Visibility

In Computer Graphics, the two main approaches to rendering and visibility involve ray tracing and rasterization. However, a limitation of both approaches is that they essentially use point sampling. This is the source of noise and aliasing, and also leads to significant difficulties for differentiable rendering. In this work, we present a new rendering method, which we call vectorization, that computes 2D point-to-region integrals analytically, thus eliminating point sampling in the 2D integration domain such as for pixel footprints and area lights. Our vectorization revisits the concept of beam tracing, and handles the hidden surface removal problem robustly and accurately. That is, for each intersecting triangle inserted into the viewport of a beam in an arbitrary order, we are able to maintain all the visible regions formed by intersections and occlusions, thanks to our Visibility Bounding Volume Hierarchy structure. As a result, our vectorization produces perfectly anti-aliased visibility, accurate and analytic shading and shadows, and most important, fast and noise-free gradients with Automatic Differentiation or Finite Differences that directly enables differentiable rendering without any changes to our rendering pipeline. Our results are inherently high-quality and noise-free, and our gradients are one to two orders of magnitude faster than those computed with existing differentiable rendering methods.

Efficient spatial-spectral computation of local planar gravimetric terrain corrections from high-resolution digital elevation models

SUMMARY Computation of gravimetric terrain corrections (TCs) is a numerical challenge, especially when using very high-resolution (say, ∼30 m or less) digital elevation models (DEMs). TC computations can use spatial or/and spectral techniques: Spatial domain methods are more exact but can be very time-consuming; the discrete/fast Fourier transform (D/FFT) implementation of a binomial expansion is efficient, but fails to achieve a convergent solution for terrain slopes >45°. We show that this condition must be satisfied for each and every computation-roving point pair in the whole integration domain, not just at or near the computation points. A combination of spatial and spectral methods has been advocated by some through dividing the integration domain into inner and outer zones, where the TC is computed from the superposition of analytical mass-prism integration and the D/FFT. However, there remain two unresolved issues with this combined approach: (1) deciding upon a radius that best separates the inner and outer zones and (2) analytical mass-prism integration in the inner zone remains time-consuming, particularly for high-resolution DEMs. This paper provides a solution by proposing: (1) three methods to define the radius separating the inner and outer zones and (2) a numerical solution for near-zone TC computations based on the trapezoidal and Simpson's rules that is sufficiently accurate w.r.t. the exact analytical solution, but which can reduce the computation time by almost 50 per cent.

The Perception of Employee Effect and Brand in Industry and Services

Employee brand effect is a process that values the management of human resources in organizations and contributes to a real and concrete diagnosis of the relational environment inside organizations by promoting internal marketing in people management. This process results from the increase of actions in the domain of interpersonal relationships, which result from the informality of social exchanges in the organization. The present study covered 30 Portuguese organizations from the center region of Portugal in the services and industry areas that responded to a questionnaire survey measuring the process. The results show that in the industry sector there is a greater variation in the employee branding process through mentoring and helping relationships and also a greater variation in the organizational integration domain through the dynamics of interpersonal relationships, which consequently leads to the perception that employee branding effect is more positive in industry employees.

Disentangling Complexity in Bayesian Automatic Adaptive Quadrature

The paper describes a Bayesian automatic adaptive quadrature (BAAQ) solution for numerical integration which is simultaneously robust, reliable, and efficient. Detailed discussion is provided of three main factors which contribute to the enhancement of these features: (1) refinement of the m-panel automatic adaptive scheme through the use of integration-domain-length-scale-adapted quadrature sums; (2) fast early problem complexity assessment – enables the non-transitive choice among three execution paths: (i) immediate termination (exceptional cases); (ii) pessimistic – involves time and resource consuming Bayesian inference resulting in radical reformulation of the problem to be solved; (iii) optimistic – asks exclusively for subrange subdivision by bisection; (3) use of the weaker accuracy target from the two possible ones (the input accuracy specifications and the intrinsic integrand properties respectively) – results in maximum possible solution accuracy under minimum possible computing time.