# Pointwise coloring the plane or a region or curve

Is there a way to color the plane or a region or a curve (e.g., a locus) pointwise?

The only way I know is to create a curve that essentially covers the plane (e.g., a tight spiral, r = theta/300), then to place a point on that curve with the point dynamically colored; now animate the point slowly while its trace is on, preferably with small point size for greater precision.

The troubles with the above workaround are: (1) it is very slow; (2) I know of no way to save the coloration in GeoGebra [though I can save and export the image to e.g. "Paint", or via a printscreen]; (3) it seems imperfect in the sense that if I re-start the animation + tracing, there appears an artificial fuzzy boundary between my original colored animation and the new one [I suppose this is expected if I change the speed or point-size, but it even appears with no change in those parameters].

Is there a way to save such a trace image in GeoGebra? [Another application when this would be desirable is when one wants to see the envelope of a line dependent upon some varying parameter.] Perhaps I can save the image via "Paint" or printscreen, then reload that image into GeoGebra, but I'm not sure how to accurately place the image (translucently) onto my pre-existing GeoGebra construction. One example of one goal: Suppose the traced coloration produces an apparent ellipse (or other curve) whose equation I don't know; I could at least get an approximation to the ellipse by placing 5 independent points onto the colored trace image, etc.

What about creating a slider for the angle, say `ang` and define the spiral as r=theta/300 for theta=0 to ang?

This way, animating the slider, you get the pointwise animated graph of the spiral.

The equivalent for functions exists in ggb, and it's command SlowPlot() https://wiki.geogebra.org/e...

Move the slider in the attached file

For envelopes, maybe Locus command https://wiki.geogebra.org/e... or LocusEquation command https://wiki.geogebra.org/e... can be useful, too.

Two more troubles with my workaround: (4) Sometimes the coloration of the plane produces false moire pattern artifacts; (5) frequently, a slight change while working after the trace was constructed causes the trace [which perhaps took hours to create] to disappear.

original de Rafael Losada Liste hace unos diez años

https://www.geogebra.org/m/...

también hay procedimientos rápidos e inmediatos para zonas definidas por curvas mediante el uso de inecuaciones

si pone algún simple ejemplo concreto y es posible se lo daré relleno para explicar el proceso o para saber si la solicitud es inviable

1) Export the image using "Export Image"

2) Insert it back into GeoGebra

3) Set its corners to Corner(1), Corner(2), Corner(4)

https://wiki.geogebra.org/e...

https://wiki.geogebra.org/e...

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