geosvg an interactive geometry authoring tool l.
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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)

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existing interactive geometry software
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
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
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 cont5
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
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
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 cont8
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
  • 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
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
  • 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
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 cont13
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
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 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
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
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