Axes: Executable or Text Version

This program graphically depicts axes rotating in accordance with the only way to describe rotations using 3 independent angles, called the Euler Angles, after the prolific 18th century Swiss mathematician, Leonhard Euler.

Requested distance must be greater than 1. Press -r- to run again, or -s- to stop.
After entering the second angle, press -Enter- again to see the graphics.

Alt-F4 to exit the program if you seem to get stuck !!!!!!!!!!

3D Polygons: Executable or Text Version

Demo using the latest "C++"-like STRUCTURES in BBC BASIC for Windows, to illustrate moving 3-D polygons with 2 light sources - without having to use the awkward Direct3D API commands.

WAV File Demo: Executable or Text Version

This program enables you to construct a playable WAV Audio file from the 15 notes in two octaves of a Major scale -- but also to add 2 harmonics to the waveform, but on a dual Stereo waveform, with one channel double the frequency of the other. They don't even have to be integer harmonics, so you can produce some odd sounds.

From a mathematical perspective, the interest lies in the fact that you can subsequently view the actual dual Stereo waveforms you've made slide by on screen. During this phase, pressing any key will HALT the wave, and pressing any key again will cause it to re-commence.

For those not aware, since a WAV file is a stream of points on a waveform, sampled in this case at 44.1kHz, the notes in the full even-tempered 12-note standard chromatic scale are each set up as a sine wave with a frequency a multiple of the twelfth root of 2 apart. That is, the fifth note in the scale is the twelfth root of 2 raised to the power 5 times the frequency of the basic key-note, for example A=440Hz. The twelfth note is then the twelfth root of 2 raised to the power 12--or twice- the frequency of the basic note. The next A is therefore 880Hz.

Guitar Simulator: Executable or Text Version

A guitar fretboard appears on the screen, and you can either place single notes on the fretboard to make a playable chord, or choose to start off with a selected standard chord, which you can then alter. This chord can be saved, and further chords set up, and the chord sequence played as a MIDI file using the PC's internal set of instruments. Initially, it defaults to a steel-string acoustic guitar, but any of a further 120 instruments can be chosen thereafter to hear the chord progression.

3-D Rotating Cube in Full Perspective: Executable or Text Version

Solid 3-D Rotating Cube: Executable or Text Version

Based on the above AXES program, this program illustrates how / why the Euler Angle method works in practice.

Basically, it means you can control the orientation of an object in 3 dimensional rotations, with reference to the symmetry of the object itself. Although mathematically rather tricky, Euler Angles conform to the way we intuitively would rotate an object, say, held in the hand.

Use the keyboards' ARROW keys to change 2 of the angles, and the "<" and ">" keys to change the third one.
Press "F" or "B" to move towards or away from the Cube, and "U" and "D" to move up or down. These keys have an ACCUMULATIVE effect, so if you hold one down, the cube ACCELERATES.
Press the spacebar to halt the up/down or to/fro movement. Press "T" to toggle the display of parameters on/off.
Press the -Esc- key to stop the program, or Alt-F4 if the program gets stuck somehow.

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