GeoSVG: An Interactive Geometry Authoring Tool

Existing Interactive Geometry Software Geometer’s SketchPad Cabri Geometry II –Can export file to TI calculator C.a.R. (open source, in Java) Kseg (open source, in C++) Cinderella (in Java) –Euclidean Geometry, hyperbolic geometry, elliptic geometry and projective geometry Euklides (in Java) –Can deal with conics (hyperbola, parabola, ellipse)

What can Interactive Geometry Software do Dynamic geometric object construction and manipulation –All mathematical relations are preserved while objects are being dragged by mouse or values are changing. –Parallelogram / Box-and-Whisker examples Transformation of geometric objects –Translate, Rotate, Dilate, and Reflect –Half Head.gsp Measurement –Area.gsp

What can Interactive Geometry Software do (cont.) Animation –Parametric Functions.gsp Calculation –A dynamic calculator Analytic Geometry –Plot function –Coordinate System View.gsp Calculus –Integration.gsp –Compute derivative

What can Interactive Geometry Software do(cont.) Locus –a totality of all points, satisfying the certain given conditions –Thought Experiment.gsp Iteration –Geometric iteration and numerical iteration –Integration.gsp –Fractal Gallery.gsp Script/Macro –A sequence of steps that can be defined as a new function –Sample Tools.gsp

Deficiency of Geometer’s SketchPad No separate view of authoring phase and manipulation phase –Students need to learn the software or may be deviated from the what a teacher has constructed. –SketchPad can export what is constructed as a Java applet, which is used in the manipulation phase. However, the applets only have a subset of the capability of the software.

Deficiency of Geometer’s SketchPad (cont.) No special object types to ease composing –Philosophy of SketchPad: Many or Few –This is an advantage, but also a disadvantage –Lots of hidden objects to help construct a manipulative –Example: Hard to copy a shape No Linux version Some other small deficiency –No user input –No function to handle a sequence of numbers –Not very good support for multiple coordinates systems –No ruler and Protractor

Deficiency of Geometer’s SketchPad (cont.) Big Deficiency: NOT web-oriented –A tool called JavaSketchPad can convert what Geometer’s SketchPad generates to Java applets. However: Some constructions such as iteration cannot be converted. User can only manipulate objects, but cannot construct new objects. The applet supports much fewer mathematical constructions than the desktop software. –Author needs to have the software installed in his/her machine. Then the author needs to know how to publish a web page online, and may also need to know how to embed an applet in a web page. This small obstacle may stop many teachers from using the software

GeoSVG Written in SVG and Javascript –SVG, which stands for Scalable Vector Graphics, is an application of XML that makes it possible to represent graphic information in a compact, portable form Inherent web-oriented –What GeoSVG generates automatically can be viewed and manipulated online –The whole GeoSVG authoring tool can be a web page User does NOT need to install software and compose web pages –We may set up a web site for GeoSVG users. File open, File edit, and File save are all online.

GeoSVG (cont.) Platform independent (Windows/Mac/Linux) Can also be developed into a standalone application using Batik –Batik gives developers a set of core modules which can be used together or individually to support specific SVG solutions. Examples of modules are the SVG Parser, the SVG Generator and the SVG DOM. Manipulatives can have the full power of the capacity of GeoSVG by exporting menu functions

Algorithms All the objects form an acyclic directed graph –Ancestors/Parents/Children Independent Points are the source of the graph A change of a top-level object invalidates all its descendents. All descendents need to recalculate its status. Geometric Reversibility: a change of a descendent affects its ancestor(s). –Selection of a segment is equivalent to selection of two end points.

Algorithms (cont.) Philosophy: Many or few? What objects should be atoms? Special objects to help ease composing –Pivot Point: ease the work to copy a shape –Angle Point: fixed angle and changeable distance. Help to create a axis. Useful Action Buttons: –Show/Hide: Show or Hide a group of objects –Movement: Animation –Presentation: Execute a sequence of action buttons –CircularEvents: Circular execution of a sequence of action buttons. Execute one per button click.

Algorithms (cont.) As a geometry software, there are lots of mathematical computation algorithms. –Translate –Rotation –Intersection –Parallel/Perpendicular –Determine if a point is on an object (line/circle/polygon) –And etc.

Difficulty in Developing GeoSVG GeoSVG is currently an online authoring tool, which cannot save files to local disk, and cannot utilize copy- and-paste provided by OS. –Current Solution: Under Windows IE, the data can be exported to an textarea. User needs to copy and save it. –Future Solution: next slide SVG-XHTML communication problem. – With all the existing Interactive Geometry Software, do I still need to develop a new one? –Applet is not a problem. Once it’s loaded, it’s also fast.

Batik SVG Toolkit Batik is a Java(tm) technology based toolkit for applications or applets that want to use images in the Scalable Vector Graphics (SVG) format for various purposes, such as viewing, generation or manipulation. Examples of modules are an SVG parser, an SVG generator and an SVG DOM implementations. Batik contains a Swing component that can add SVG viewing capability to all Java technology applications or applets. With Batik, a desktop software of GeoSVG can be developed.

What is GeoSVG capable of now Create basic shape: point, line, circle, polygon Measurement: length, slope, distance, angle, area, perimeter, circumference, coordinates Calculation: sorting a sequence of values, max, min, Q1, Q3, mean, count Ruler, Protractor, and Simple Grids Simple animation Action Buttons / User Input / Plain Text Show/Hide Object, and Set Object(s) Manipulable Save what is constructed as a string Export menu functions: Manipulatives have all the capability of the authoring environment.

Future Work Learn more advanced SVG topics Learn more XML technology and browser plugin technology Optimize several algorithms Implement more functions for analytic geometry Implement algorithms for locus, script, and iteration. Integrate Batik with GeoSVG