LineCollection, need to draw separate points

Hi list, I have inherited a piece of code. It uses

    > LineCollection and works allright, except lines are plotted
    > and I want to see the points, not the interpolated line. Is
    > this a contradiction in itself, or might it be possible? I
    > see 'solid', 'dotted', 'dashed' and 'dashdot' as linestyle
    > options, but don't see 'points' among them.

    > The reason LineCollection is used, is that each point needs
    > to have a particular color; the plot has a third dimension
    > so as to say.

You can probably use "scatter" for this -- it allows you to create and
x,y plot of polygonal markers with different colors. But these are
intensities mapped to a color. If you need to specify the exact color
of the markers, use a PolygonCollection.