Surfaces of Functions of two Variables z=f(x,y) - Visualization by Ray-Tracing and Mesh-Grid

Objects of images

All images show and/or use two-dimensional surfaces in a three-dimensional (x,y,z)-space. These surfaces represent mathematical functions of two (real) variables such as z = f(x,y). Thus, as an example, image A000 represents the function z = sin(x*y). The surfaces can be designed as opaque, transparent, mirroring light or refracting light (in this case the surface is considered as a part of the surface of a solid body made out of some light-transmissive material like glass). The scene can be enriched by up to four planes (more precisly: plane rectangles), designed either as mirrors or "chessboards" or as "wallpapers" using some image (also possibly generated by mathematical functions) as repeating patterns.

Software

The rendering of the images is performed by ray-tracing algorithms and mesh-grid algorithms, both partly developed or improved by the author and implemented into a software developed by the author, too.

Image quality

The original images are bitmap images (*.bmp, 24bit color depth) with sizes up to 8000 x 8000 pixels. In order to keep the memory costs of the website and hence the times for downloading the images as low as possible, these images were scaled down to a maximum size of 930 x 930 pixels and then were converted to JPEG images. Although the quality level of these JPEG images was choosen very high, the graphical quality of the original images has suffered in evidence under these two transformations. The representation of the images on the monitor’s screen will be optimal if its resolution is at least 1024 x 768 pixels. The browser’s window should be set to "maximum size" or, even better, to "full screen" (some browsers switch to this mode and back by pressing key F11).

Enlargements / Slideshow

A left mouse button click on the small "slide"-images (previews) of the gallery pages opens the corresponding "original" image of the website with a size of up to 930 x 744 pixels. When a page "Galery ..." is shown, a slideshow can be launched using the navigator button "slide- show ...". The slideshow will run automatically or can be controlled manually by mouse clicking. Using the web browser "Opera 10.63" (possibly also with other browsers) a slide show by use of the keyboard can be performed: To do this, you click on the first (top left) "slide"-image of a gallery page in order to enlarge this image and then navigate through the gallery by the keys <Ctrl> + <right arrow> or <Ctrl> + <left arrow>, respectively.

All images as well as the whole website are under the copyright of the author Hans Werner Kohl (HWK). Without permission of Hans Werner Kohl (HWK), no use of the images is permitted.