Display Objects

Display Objects and Gadgets

Mathwright32 Display Objects are used for input and output, and to display and manipulate mathematical objects. Logically, these are associated with a page, and are implemented as classes with multiple instances, inheritance, data encapsulation, and methods for interaction with mathematical objects. Display Gadgets may be scripted, so that the script is run when the user interacts with them. Display Objects are not scripted.

These objects each have "names" through which they are identified in Mathscript. Mathwright32 PageManager is responsible for creating and destroying these objects, and for channeling instructions to and from them in a rational way. For a given type of object there can be only one object with that name (except for labels). Thus one writes commands or programs in Mathscript that manipulate the data in those objects in various ways. Presently we have implemented the following 13 classes of Display Objects.

Graph2D Gadgets. These scriptable objects display graphs of functions or curves defined by user input, solutions of differential equations, filled polygons, pictures, sprites that can be translated, rotated, or transformed by any affine transformation under program control, animations, and a variety of Logo objects such as points, lines, polygons, polylines, and so on. These gadgets may be scripted to respond to a mouse-click, or even to the motion of a mouse over them.

Graph3D Objects. These display objects hold "scenes" that are populated by "actors". The actors are parametric and implicit surfaces, space curves or "tubes," arbitrary geometry created with OpenGL, and imported 3D models from 3D Studio or DirectX format. OpenGL is a powerful rendering language that will display your scenes and allow the user to interact with them in real time. Mathscript contains 57 primitive OpenGL commands, 47 constants and principal state variables in interactive form. This means that you (and your readers) may use OpenGL in essentially its original form (its syntax blends seamlessly with Mathscript syntax) to experiment with geometry and graphics interactively.
And since Mathscript is so tightly integrated with OpenGL, it can in fact be an excellent tool to learn and experiment with OpenGL itself. In its scripts, you will see the results of your graphics instructions immediately, however, without the need to compile them into C++. This is a great advantage for building simulations that must be fine-tuned over many incremental cycles.
But Mathscript is also a highly flexible language that allows you to create your own commands, to build your own object hierarchies, and to create the mathematical objects that will support your simulation. What distinguishes our 3D Graph Objects from other 3D Graphics environments is the fact that the "actors" in the scenes you create are dynamic. They may be moved individually either interactively (at the command line) or under the control of scripts that you write. They may be selected by the reader when she clicks on them, and may respond in appropriate ways with the full Euclidean group of motions. Further, the reader may navigate your scenes by flying through them in the first person, or by moving the entire scene itself. This makes possible a large variety of realistic experiments and simulations that it would be difficult to imagine supporting on a 2 dimensional canvas.

MathEdit Objects. These are designed to display mathematical expressions in an intuitive form, with raised exponents and true fractions to any order of nesting. In addition, the MathEdit windows serve as word processors, with a variety of uses. As an editor, it is used by authors to provide colorful on-line explanations of the Microworld lessons. These windows also display pictures and "snapshots" of any part of any screen. Students use them to create and save their reports or notes. In Mathwright32 Reader, students may create and save files for these objects, and recall them at any later time, thereby customizing the text without actually changing it. MathEdit windows also display matrices and can be used as an interface for the input of matrix or of algebraic expressions.

DataTable Objects. For the input and output of tables of numeric, string, or function data, the data windows provide small "spreadsheet" environments. The columns of these windows are Mathscript vectors, and so they may be used in any calculation on vectors. For example, they may produce scatter plots or bar charts in Graph2D windows at the click of the mouse. String columns may be used to build Lexicons, and so on. Also, these data tables are Microsoft Access Active Data Objects, and so may be queried with SQL queries, saved to disk and retrieved later.

TextBox Objects. These are the work horse objects of Mathwright32, used principally for multiline text input and output. With the Enter command, they allow the user to define programs, commands, and full scripts interactively.

TextLine Gadgets. These scriptable objects are single-line text fields. They are used mainly for input. Their scripts are run when the user presses Enter at the end of the line. Text does not scroll.

Command Line Objects. These multiline text fields are also mainly for input. The player may enter any of the predefined or user-defined commands of Mathscript and the command is executed when the user presses Enter at the end of the line. This is an excellent place to define functions and short commands, to set values for variables, and so on.

Program Listeners. These objects are associated with any scriptable gadget, or with a page, or with the document itself. Use these to compose scripts, define programs and commands, to test and debug scripts, or even to program in LISP. The scripts created here may be saved to files, or may be saved with the object to which they are attached.

Label Objects. These provide static text for the background page, such as instructions.

HotSpot Gadgets. When a page has wallpaper (a .gif, .jpg, or bitmap background) then it may have associated with it any number of invisible, non-overlapping rectangles. When the mouse is moved over a hotspot, the cursor changes to a "pointing finger". When the reader left-clicks the mouse on a hotspot, the script for the hotspot is run.

Button Gadgets. These are scripted gadgets that respond to the left mouse-click by running their scripts.

Slider Gadgets. These are input gadgets that allow the reader to input numbers in some interval, either in a continuous or discrete fashion. They may also be scripted, so that any motion of their thumb causes the script to be run.

CheckBox Gadgets. These are input and output gadgets for Boolean data (True or False). They may also be scripted so that their activation causes an arbitrary script to be run.

Display Object Menus