This summer, I have been doing some amazing stuff for GeoGebra. First of all, I would like to thank two people: Miguel, my mentor, who guided me through all that really advanced mathematical stuff; and Heinz Kredel, JAS creator and developer, who answered all my questions and implemented my suggestions as quickly as I could write them.
This story is about a problem we found in JAS. It was really subtle, so I may need a brief introduction to the project I worked on: LocusEqu. That project retrieves the equation of “any” geometrical locus. If you don’t know what a locus is, Wolfram Math World defines it as “the set of all points (usually forming a curve or surface) satisfying some condition” . LocusEqu generates a few EquationExpression, and then, by using a EquationTranslator, it generates a GenPolynomial<BigRational> object.
For translating doubles, it calls the BigRational constructor whose only argument is a String. This is the code:
Can you spot the bug? Look at the 21st line. If s is “-0.5”, then n is new BigInteger(“-0”), and that’s what makes “-0.5” be parsed as 1/2.
My contributions for the first part of the first part of GSoC 2010 can be divided in two: general improvements and coding.
I made a few general improvements on GeoGebra:
- Refactored build.dir in ant build file. Previously, build.dir wasn’t in the root directory.
- A few ant tasks were added, such compile-grammar, compile-oe (outside Eclipse), run-easyb and run-easyb-outside-eclipse.
- SVN properties were set in order to work outside Eclipse. This way, .class files will be kept out of the repo without the intervention of any Eclipse plugin.
- Easyb, a BDD groovy-based framework, has been included in order to test GeoGebra. It is not RSpec, but I guess it’ll do.
First, I started creating a few EquationPoint classes, currently there are six EquationPoint children classes:
- EquationFreePoint represents an independent point.
- EquationSymbolicPoint represents a dependent point, EquationSpecialSymbolicPoint standing only for the locus point.
- EquationNormalPoint and EquationPointVectorPoint are only auxiliar elements.
Then, a few EquationElement classes were added, these stand for the different constructions:
EquationElement is an abstract class containing a few basic methods:
- forPoint: Given an EquationPoint, returns a String with the equation that means that the point is in the construction.
- isAlgebraic: returns true if the construction is algebraic, and false otherwise.
Both EquationGenericCircle and EquationGenericLine are abstractions of specific line and circle contructions, all of them algebraic. EquationGenericSegment is to segment what EquationGenericLine is to lines. Obviously, EquationGenericSegment is not algebraic.
All of these classes are used together by EquationScope.
A pause for a screenshot.
Click for enlarge.
A glimpse into the future.
What to do next?:
- Maybe Equation should be a proper class, not just a String.
- More equations.
- Working out the locus equation.
- Not using an algorithm twice.