An analytical approach for simulating aerial perspective effects on distant objects

Abstract

Aerial perspective effects are an integral part of a virtual application for outdoor simulation. These effects are modelled using the light transfer equation; borrowed from the field of physics. Typically, these applications make do with a watered-down version of the equation since the physically correct version requires heavy nested loops and complex optical depth estimation. The normal practice is to assume the atmosphere’s density as constant to allow the usage of distance between points as optical depth. However, this move causes failure in capturing the darkening effect of sky area approaching zenith, due to density fluctuations as the altitude increases. An analytical-based approach is proposed here to solve the above problem. A look-up table containing five-parameter coefficients of a chosen parametric luminance function was prepared in advance as a function of altitude, turbidity and Sun position. During the real-time visualization, a single rendering equation is used to determine each vertex’s display colour. Adding the initial colour value of the current vertex to its atmosphere-contributed colour value solves the equation. The atmosphere-contributed colour is obtained by an exponential interpolation of five separate colour values. Each value represents the colour of the intersected sky patch at each reference layer. The intersected sky patch is found by finding which sky patch coordinate solves the vector equation of a line passing through the camera’s point and the current vertex’s point. By referring to the lookup table, these five colour values are computed using the chosen parametric luminance function. This approach was implemented using the Cg Language as a vertex shader. Test results have shown that the proposed approach is able to produce visually correct daylight sky colour distributions at any altitude within the 30km range.