Experiments on isoptics by dynamic coloring

Please see http://www.nebrija.es/~pvelez/ACA2019/dana-picard.pdf for an overview.

This piece code uses CindyJS for visualizing and Giac for computing some preliminary calculations.

Usage

Start the file isoptics.html in your browser and enter one of the following functions:

• x^2+2-y
• x^2-x*y+1
• 3-x*y

Then drag the point C and learn the isoptic angles ACB where A and B are tangent points to the input curves. Angles above 90 degrees are colored with blue, above 90 degrees with red. Black points correspond to 90 degrees, therefore the orhoptic curve of the given input will be shown as a black curve. White points have no meanings to be selected for point C.

A black screen is shown if the formula cannot be interpreted correctly and therefore there is no way to completely calculate the initial equations in Giac.

A gray screen is shown if there is some internal error during the main computation process inside CindyJS.

Another experiment is available that provides only the investigation of ellipses.

Yet another experiment is for the quartic y=x^4 available.

Authors

• Thierry Dana-Picard ndp@jct.ac.il
• Zoltán Kovács zoltan@geogebra.org

Acknowledgments

• Aaron Montag and the CindyJS Develoment Team for CindyJS and WebGL
• Bernard Parisse for Giac
• The GeoGebra Team for providing a JavaScript version of Giac
• The MathJax Team for math typesetting

Known bugs

• The software tool cannot decide if the input or its opposite function should be used.
• Some formulas give the wrong output, including the following ones:
  • x^2+y^2-5, x^2+2*y^2-5 (circle, ellipse: the wrong tangent point is computed, a sign problem occurs)
• If there is no way to compute the roots symbolically, no numerical approach is forced.

Technical details

This project currently uses http://dev.geogebra.org/maven2/fr/ujf-grenoble/giac-gwt/68505/.