Lesson Plan 12

Building a Virtual World

Lesson Title	Building a Virtual World
Duration	3 classes (4.5 hours)
Synopsis	Students are given the tools they need to lay out a virtual space and place 3-dimensional elements in it, to create their own virtual environment.
Description of Class	The issues one needs to consider when creating a virtual world are discussed. Examples of landscape plans are shown and discussed as a formalized view of the everyday physical world. A simple virtual world composed of rectangles, cylinders, and cones is shown in perspective view.  This is then viewed from the top, and recast as a plan drawing on a 2-d Cartesian grid.  2-d coordinates are introduced. The idea of specifying a polyhedron as a sequence of points is introduced via the specific example of doing so with quadrilaterals in the plane.  The other objects are similarly defined. A mathematical description of this set of simple objects is described.  This gives rise in a natural way to a computer file format which can serve as a description of the 3-d geometry making up a VR world.
Primary Educational Objective	Experience with the connection between 3-d physical objects and a mathematical description of their geometry
Additional Concepts and Skills	Demonstrate an understanding of trig functions as circular functions Apply trig functions to solve physical problems Demonstrate understanding of the construction of the coordinate plane Use basic geometric ideas in the context of the Euclidean Plane Describe the effect of rigid motions on figures in the coordinate plane Interpret and draw two-dimensional objects and find their area and perimeter Use a variety of computational models (e.g. mental arithmetic, paper and pencil, technological tools) Translate among tabular, symbolic, and graphical representations of functions Represent and analyze relationships using written and verbal expressions, tables, equations, and graphs
Assessment	Classroom participation and homework assignment.
Classroom Activities	Students work as a group to design and specify a virtual world by creating a plan drawing and transforming that into a mathematical formalization
Homework Assignments
Lecture Materials	Lecture materials are available as a Power Point presentation
Reference Materials	TBD
Prerequisites (this course)	Corel Imagecp Use of the DAFFIE viewer
Related Topics	Mathematics – 2D Cartesian coordinate systems 3-d Geometry
Technology Requirements	Corel DVD Wall system DAFFIE software, including imagecp VR World generation software
Comments