Given a curve (u(t),v( t)) in the domain of a surface, we have a curve
In the control panel for the demo, there are two sliders for constants. The c slider controls a constant for the surface while the d slider controls a constant used in UVCurve .
In this demonstration, we select a surface in space and a curve (u(t),v( t)) in the domain of a surface and then show its image on the surface and on the Gauss map. We also graph the Gaussian curvature K(t) of the surface at the point X(t) as a function of the parameter t .
The default curve is a circle of chosen radius centered at a point selected
in the parameter domain. What happens as the center is moved around in the
domain?
In this demonstration, we select a point
(u0,v0)
in the domain of a surface with the middle mouse button and then select a
unit vector
(cos(
You may make the tangent plane show up in the Screen by clicking on Tangent Plane? . Note that solidifying the surface may help to make its contact with the tangent plane more visible. The X' and N' window clearly displays the vectors Xu , Xv , X' , and N' in the tangent plane at X(u0,v 0) .
How do these vectors change as
The normal strip above the image of a curve Y(t) =(u(t),v( t)) in a mapping X(u,v) is defined in the following way:
This demonstration allows you to define a surface as usual but also allows you to choose a curve in the domain of the surface. Curve Parameters controls the curve display. Progressive? allows one to draw only a portion ofthe curve, this portion being controlled by the tapedeck. Strip? will draw the normal strip of the curve to the surface and its the progressive acts on this also. The tapedeck goes from 0 to 1 scaling between the minimum and the maximum of the curve domain.