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Release Notes

Version 1/sqrt(tau) = 0.78615138, 6 June 2003

A major update of the asurf program. It has now can give almost perfect results for most types of singularities. Specifically

Version (1+sqrt(5))/2-1 = 1/tau = tau-1 = 0.61803399 May Day 2003

a focal surface
Interim release hence the irational version number.

Major new features:

The mapping, intersect, and icurve programs have not been adapted to run under JavaView. These allow such things as Parabolic lines, Ridges, Symmetry Sets and focal surfaces to be calculated.

The algebraic surface program has also been improved to make a better job around singular points.

Major missing features: (yet to come)

No load/save for definitions.
I'd like to add better interactive control for the parameters in the equations.
Still some bugs in teselating algebraic surfaces and the boundaries are still not correct.
The communication protocol is still not standardised, some are using CGI type encoding, others are using an XML format which all programs are migrating to.
The server programs could all do with a clean up and actually get round to freeing some memory!
No documentation apart from this for new programs.
The icuve program currently only produces integral curves, computing vector fields and wavefronts yet to come.

A few more specifics on the changes

The mapping, intersect and icurve programs all perform some operation on another geometry.
Furthermore each program can read part of the defining equation for the function from another geometry. For example the it is posible to write a generic project onto surface mapping, which can take parameterised surface and any set of points in parameter sace and project them onto the surface. i.e.
    Generic project onto surface mapping + definition of surface = mapping to project onto the surface
This feature makes it easy to implement many standard local differential geometry functions:
    Parabolic Lines, Ridge, Principal Directions, Focal Surfaces, Symmetry Sets etc.

There have been two major improvments to the algebraic surface program:
  1. The routine to produce the polygons once all the points on the surface have been found has been completely changed. It now calculates facets for the surface at the bottom (smallest size = fine) level of recursion, these facets are then joined together higher up the recursion tree to produced the polygons used in the final surface (ie. at corse resolution). This is the technically correct way to do it rather than the add-hoc algorithms used previously. Thankfully this did not entail the expected increase in compilation time.
  2. Convergence routines are now used to find the singular points, and the turning points. This means that far more acurate positions of singular points are found. (Warning still not converging to normal turning points, so surfaces are a little thiner than they should be).
Sarti's octic with 144 double pointsAs well as these a bit more mathematics has been used to work out if a singularity should lie in a box. Second derivatives are now examined in more detail. In particular the determinant of the second derivative matrix is now examined. The sign of this gives the diference between two lines crossing on a face (x^2-y^2=0) or an isolated point on the face (x^2+y^2=0) and similar fun in 3D. This has helped reduce the number of false positive singurlarity points found.

The upshot of all these improvments is that singularities are much sharper as the picture of Sarti's octic with 144 double points shows.

To Do

Long term stuff to do.

Copyright Richard Morris 2003

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Web page, applet and Algebraic Surface program by Richard Morris
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