We propose a novel method, based on the two-pass Z-buffer algorithm, to calculate shadows with sufficient precision and efficiency for rendering a daytime landscape with solar penumbrae. The special feature of the proposed method is that the shadows can be preserved with a precision superior to that of any visible surface. We use the optimal number of plural shadow buffers to do this; it gives a fairly satisfying trade-off between computation time and quality of shadows.

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3D applications using hardware depth buffers for visibility testing are confronted with multiple choices of buffer types, sizes and formats. Some of the options are not exposed through 3D API or may be used by the driver without application's knowledge. As a result, it becomes increasingly diffkult to select depth buffer optimal for desired balance between performance and precision.In this paper we provide comparative evaluation of depth precision for main depth buffer types with different size and format combinations. Results indicate that integer storage is preferred for some buffer types, while others achieve maximal depth resolution with floating-point format optimized for known scene parameters. We propose to give 3D applications full control of the depth buffer optimization by supporting multiple storage formats with the same buffer size and exposing them in 3D API.In the search for a unified depth buffer solution, we describe new type of the depth buffer and compare it with other options. Complementary floating-point Z buffer is a combination of a reversed-direction Z buffer and an optimal floating-point storage format. Non-linear mapping and storage format compensate each other's effect on the depth precision; as a result, depth errors become significantly less dependent on the eye-space distance, improving depth resolution by the orders of magnitude in comparison with standard Z buffer. Results show that complementary Z buffer is also superior to inverse W buffer at any storage size. At 16 and 24 bits/pixel, average depth errors of complementary Z buffer remain 2 times larger than for true W buffer utilizing expensive high-precision per-pixel division. However, it provides absolutely best precision at 32 bits/pixel, when errors are limited by floating-point per-vertex input.Results suggest that complementary floating-point Z buffer can be considered as a candidate for replacement of both screen Z and inverse W buffers, at the same time making hardware investment in the true W buffer support less attractive.

We propose a novel method, based on the two-pass zbuffer algorithm, to calculate shadows with sufficient precision and efficiency for rendering a daytime landscape with solar penumbrae. The feature of the proposed method is that the precision of the shadows can be preserved to be superior than that of any visible surface by using the appropriate number of plural shadow buffers; it gives a fairly satisfactory trade-off between computation time and quality of shadows. By using the shadow buffers, before calculating solar illuminance we can divide visible surfaces into three types of fragments, that is, bright regions, umbra regions, and the remaining penumbra regions. Thus, we can efficiently render a daytime landscape with sufficient precision of penumbrae because the algorithm can set the calculation points of solar illuminance variably, with their number depending on the type of region they belong to.

Water surface is an important element for rendering a realistic landscape image, particularly for visual environmental assessment. The incident light from the water surface to the viewpoint generally consists of two components, reflected and refracted light. The source of the latter is further subdivided into reflected light from the bottom of the water and scattered light in it. In order to render a realistic water surface, the calculation for each component of the light is a quite complex and time consuming task. We propose the fast rendering algorithms of the water surface for visual environmental assessment of outdoor scenes. The features are: (1) the reflected light from the water surface is rendered very quickly through the quasi-ray tracing techniques, which employ inversion and reflection mapping with consideration of the depth of objects mirrored on the water surface; (2) the refracted light coming through the water surface, which gives the color of water, is efficiently calculated by using a look-up table in which both characteristics of the light sources (both direct sunlight and skylight) and the effects of scattering and attenuation depending on turbidity are taken into account. In order to testify the proposed algorithms, some examples are given.