800 pixels (w) x 600 pixels (h), computer ‘painting’ using my own ‘kinetic’ abstract computer program.
Date produced: 2nd May 2002

This abstract image only uses rectangles that are aligned either vertically or horizontally.

800 pixels (w) x 600 pixels (h), computer ‘painting’ using my own ‘kinetic’ abstract computer program,
and post-processed with my own image processing program for creating some special distortion mappings.
Date produced: 18th April 2002

This abstract image uses a special ‘re-mapping’, to modify the previous abstract image. The ‘projection’ or ‘re-mapping’, is a form of ‘Coaxal Orthographic Projection’.

I performed this re-mapping using my own computer program. I wrote a computer program to apply some different forms of ‘Coaxal-Orthographic projections’ to high quality digital images. I originally developed this re-mapping program because I felt that this type of re-mapping may give photographs a much stronger sense of being from a real world of wide, curved space. Coaxal-Orthographic projections can distort a flat rectangular image to a ‘kind of’ sphere (or a surface similar to an ‘opened sphere’). The entire top edge of the rectangular image ends up being remapped around a point that is horizontally located in the middle of the new image, but vertically located near the top of the new image. Likewise, the entire bottom edge of the rectangular starting image ends up being remapped around a point that is horizontally located in the middle of the new image, but vertically located near the bottom of the new image.

I was interested to see how my ‘Coaxal Orthographic Projection’ program remaps some of my kinetic abstract images. This particular image uses the true form of coaxal orthographic projection for both the ‘inner circle’ (a circle that sits between the 2 converging points that are aligned in the centre of the image) as well as the ‘outside region’ (everything outside that inner circle).

I wanted to present the original computer kinetic abstract image near the re-mapped image to give an idea of what the remapping has done.

This is the basic layout of ‘Coaxal Orthographic Projection’.

Start with a horizontal x-axis and a vertical y-axis.

There is firstly one ‘set’ of circles that always have their centres along the horizontal x-axis and that always have 2 points on their circles that pass through the same 2 convergence points on the vertical y-axis (that are equally spaced from the x-axis).

The second ‘set’ of circles always have their centres along the vertical y-axis and always intersect the circles of the first set at right angles. There are actually 2 ‘sets’ of circles in this second set; one set of circles that surrounds the convergence point above the x-axis, and the other set of second set circles surround the convergence point below the x-axis. But, the circles of both sets of the second set of circles always intersect the circles of the first set of circles at right angles.

It is an interesting layout. The two critical points are the two convergence points, equally distant from the x-axis on the vertical y-axis.

The circle in the first set of circles that just fits between the two convergence points I call the ‘inner circle’, for my Coaxal Orthographic Projection re-mappings. With my remapping program, I can set different types of coaxal mappings for both the inner circle and the outer region (the region outside the inner circle).

800 pixels (w) x 600 pixels (h), computer ‘painting’ using my own ‘kinetic’ abstract computer program,
and post-processed with my own image processing program for creating some special distortion mappings.
Date produced: 4th May 2002

This abstract image is the result of using my Coaxal Orthographic Projection computer program to modify a different starting abstract image. Here, the program projects ‘coaxally’ onto a sphere within the inner circle, and uses the colour from the left edge of the original abstract to ‘coaxally’ generate the circular bands of colour in the region outside the inner circle.