- Project Background:
The accurate drawing of surfaces and curves in three dimensions is
challenging but very helpful when students are learning the material
in third semester
calculus.
I am insufficiently skilled as an artist to faithfully depict
three-dimensional objects at the chalk board in freehand.
However, I can produce reasonably good
facsimiles
using software such
as
Mathematica
or
MATLAB.
Depictions of curves and surfaces made using even these types of
software lack several pedagogically desirable features: viewer
interactivity and flexibility of presentation.
- Project Description:
I would like to see developed student usable computer-aided
instruction modules geared toward helping faculty and
students draw, manipulate,
and modify surfaces and curves in two and three dimensional spaces.
Among the desirable features of the end result of the project are:
- Surfaces and curves should be able to be
drawn in cartesian, cylindrical, and spherical
coordinate systems.
- Orientation of the coordinate system and the viewpoint should be
viewer selectable with real time updating through controls in the user
interface.
- Ancillary features such as tangent vectors, unit tangent vectors,
lines, planes, velocity
and/or acceleration vectors, normal vectors, and principal unit normal
vectors should be drawn at the option of the viewer.
- Animations of curves and surfaces with viewer selectable viewpoint.
- Desired Student Qualifications:
Experience in web page design, programming in Java, use of computer
algebra systems, computer graphics, pedagogy, and
mathematical background equivalent
to
third semester
calculus.
This project could be a senior project for a mathematics or computer
science major.
Page maintained by: Bob Buchanan
Bob.Buchanan@millersville.edu
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