I have generated a picture using pointplot and display that creates a grid of colors based on the angle between vectors and (1,0) in R^2. Each angle is given a unique color via the HSV color space. I would like to provide a legend explaining the colour, something along the lines of

red (brown) green (blue) red
0                Pi                 2*Pi

and possibly

red       (brown)       green 
angle1                     angle2   

Is there an easy way to do this, or will I have to mess around with a custom pointplot/textplot solution?

I have a nice procedure that is as follows, that explores the behaviour of a mapping in R^2.

InversePoincare := proc (v) options operator, arrow; v*Norm(v, 2)/(1-Norm(v, 2)^2) end proc

SphereVectorPlot := proc (T, radius, radiusIncrements, angleIncrements, lengthParam)
local listOfPairs;
listOfPairs := {seq(seq([[radius*r*cos(2*angle*Pi/angleIncrements)/radiusIncrements, radius*r*sin(2*angle*Pi/angleIncrements)/radiusIncrements], T(InversePoincare(`<,>`(radius*r*cos(2*angle*Pi/angleIncrements)/radiusIncrements, radius*r*sin(2*angle*Pi/angleIncrements)/radiusIncrements)))-InversePoincare(`<,>`(radius*r*cos(2*angle*Pi/angleIncrements)/radiusIncrements, radius*r*sin(2*angle*Pi/angleIncrements)/radiusIncrements))], r = 0 .. radiusIncrements), angle = 0 .. angleIncrements)};
if lengthParam = false then
 return arrow(listOfPairs, scaling = constrained, shape = arrow)
else
 return arrow(listOfPairs, length = lengthParam, scaling = constrained, shape = arrow)
end if
end proc

Essentially, we plot vectors v at location u. Since the vectors v in general vary wildly in magnitude, I would like to visualize the magnitude change by using color and/or transparency, preferably the latter. Is it possible to do so, and if so, how?

I would like, for an arbitary point in R^2, to calculate the projection onto a curve, such as 1/x or 1/exp(x). Is there a "cheap" way to do so? If it makes it easier, I could mostly be interested in points strictly below the curve.

I'd like to plot the differences between terms in a sequence of vectors. Each difference term should start at the end of the last difference term, so that if I was to plot the actual term, the vector would meet at the end of the difference term. The sequence is limited in length and stored as a list.

Ex:

Suppose I have  . The difference terms would thus be . The first difference term would be plotted be plotted from <0,0>, the second starting at <1,1>, the third at <2,2>.

I can compute the difference terms, but I am not sure how to make the plot I desire. Is arrow(...) the answer, somehow?

Hello all,

Suppose I have a vector valued function f (dimensions of vectors is 2). I can use fieldplot to show me the function's behaviour over some window.

I'd like to do the same thing, but I want to compact the space down to the unit circle. Basically, given a vector <x,y>, I'd like to "fieldplot" f(<x,y>) but with each arrow f(<x,y>) appearing at <x,y>/(1 + Norm(<x,y>,2)) instead of <x,y>.

Is this possible?