The paper discusses various aspects of the waved water surface and underwater bottom video representation simulation and also expands on the math models and algorithms of the following related tasks: waved water surface simulation; calculation of reflected and refracted rays directions in 3-D space; underwater caustics (extra illuminated areas) forming; refractive distortion of the bottom view account; reflected skylight addition.The 'Breeze' Microsoft Windows demo application realizes all described algorithms and enables real-time simulation of the underwater view. The paper also assesses the efficiency of the Intel Integrated Performance Primitives used in this application. Presented images illustrate all optical effects described in the paper.
Introduction
Despite certain achievements in the area of waved water surface video representation (see, for example, [1-6]), each work in this subject must be viewed as relevant. This article describes a physical model that was used in the development of the 'Breeze' Microsoft Windows demo application designed for modeling of underwater view video representation in real time. Unlike the algorithm described in [6], 'Breeze' application simulates more optical phenomena, namely light reflection, refraction and focusing by the waved water surface. The last one leads to forming of so-called caustics (intensively illuminated lines and shapes) on the bottom. Both algorithms have advantages and disadvantages, which will not be discussed in detail in the frames of this paper.
To increase the performance rate, we used the Intel? Integrated Performance Primitives (IPP) library [7]. Destination and capabilities of this software are briefly described in in section 5. As shown in that section, utilization of the IPP library enables to increase the performance rate by 3-5 times.
1. Algorithm
Video representation of the sea bottom, under the waved water, surface is built as a sequence of frames, each corresponding to the current time moment. The procedure of the building the frames is divided into the following steps.
1. Simulation of the waved surface, namely, calculation of the surface elevation z(x, y, t) and its declination angels (dz/dx and dz/dy) as functions of the horizontal plane coordinates x, y and time t. The simulated surface must have characteristics more or less close to the ones of the real water surface.
2. Calculation of reflected and refracted ray directions in each point of the surface (separately for the solar and view rays). This step is the most complicated and requires substantial computational resources.
3. Calculation of the number of refracted solar rays found for each bottom point to define illuminance in that particular point.
4. Calculation of coordinates where the view ray finds the bottom after refraction (those coordinates are necessary to build a distorted bottom view).
5. Calculation of the reflection coefficient in each surface point (to use together with the reflected ray direction to build the skylight reflection effect).
6. Frame forming, that is, reflected skylight and caustics effects adding to the bottom image (previously read graphical file) and its refraction distortion performing.
7. Perspective transforming of the frame.
Described procedure is repeated for each frame with the next value of t to simulate video representation of the sea bottom view. The following sections offer more details on these steps.
