Function: surfarrows - plot a 3D surface (parametric or cartesian) with arrows from a vector field at points on the surface.
Calling sequence:
surfarrows(fld,surf,s=a1..b1,t=a2..b2);
Parameters:
fld - the vector field, either a 3-component list or vector expression in the parameters s and t (specifying the vectors in terms of those parameters) or a function of three variables whose values are 3-component lists or vectors (specifying the vector field in terms of the spatial coordinates , and ).
surf - the surface, either a 3-component list or vector expression in the parameters s and t (for a parametric representation of the surface) or a scalar expression in s and t (representing the coordinate while s and t are the and coordinates respectively).
s , t - names for the parameters.
a1 , b1 , a2 , b2 - endpoints for the parameter intervals. a1 and b1 must be constants, while a2 and b2 may depend on the first parameter s .
Optional arguments:
Description:
Examples:
> with(surfarro,surfarrows):
Surface is a sphere represented parametrically, vectors are tangent to meridians.
>
surf1:= [sin(t)*cos(s),sin(t)*sin(s),cos(t)];
F1:= diff(surf1,t);
surfarrows(F1, surf1, s = 0 .. 2*Pi, t = 0 .. Pi,
arrowcolour=blue, scalefactor=1/2,arrowthickness=3, scaling=constrained);
Surface is a hemisphere represented in Cartesian coordinates, vectors are normal to surface. Note that the interval depends on .
>
surf2:= sqrt(1-x^2-y^2);
F2:= [x,y,surf2];
surfarrows(F2,surf2, x = -1 .. 1, y = -0.999*sqrt(1-x^2) .. 0.999*sqrt(1-x^2),
scalefactor=1/3, style=patchcontour, scaling=constrained);
Parametric hemisphere, vector field is a function of , and coordinates (a dipole field in this case):
>
F3:= (x,y,z) -> [3*x*z, 3*y*z, 2*z^2-x^2-y^2];
surfarrows(F3,surf1, s = 0 .. 2*Pi, t = 0 .. Pi/2,
arrowcolour=blue, scalefactor = 1/4, arrowgrid=[10,5], scaling=constrained);
See also: arrow3d , curvarrows , plot3d
Maple Advisor Database
R. Israel, 1998