ColorFunction for ListPointPlot3D

Question

I am aware that this question has already been asked: Providing a color function for ListPointPlot3D. However, that question and its answers did not help. I had better luck with this other, similar question: ListPlot - coloring negative and positive points. My code is taken from the latter.

I have a largish set of points, of which this is a small sample (30):

data = {{41.9752, 51.0084, -0.14}, {46.3064, 55.7369, 0},
        {41.4526, 57.7858, 0}, {37.0897, 9.06416, 0},
        {44.0334, 55.3856, 1098.}, {44.5004, 50.5896, -3778.25},
        {44.6699, 53.0785, 0}, {32.7899, 7.67608, 0},
        {40.6237, 58.6538, 0}, {50.261, 63.6736, 0}, {46.7637, 51.6856, 0},
        {42.2847, 50.6747, 0}, {44.9239, 56.1008, 2619.29}, {32., 8.8501, 0},
        {46.951, 51.1587, -31.16}, {41.8275, 51.7466, -1318.44},
        {41.3532, 50.1727, -105.16}, {36.9869, 12.2926, 0},
        {46.7228, 50.8667, 0}, {37.7692, 12.9168, 0},
        {41.7265, 56.5381, -4748.22}, {45.4683, 51.9324, 5866.5},
        {46.9676, 55.7092, 3596.78}, {47.0195, 56.0355, -2888.82},
        {44.9408, 52.8141, 3537.41}, {40.5041, 52.5762, -785.58},
        {46.3697, 55.1177, 24437.9}, {46.5075, 52.7793, 6381.1},
        {42.1066, 52.3115, 0}, {43.7638, 52.579, -1678.97}}

I want the colour to depend on the third coordinate of each point. If it's above 0 it should be plotted as a green point, while if it's less than or equal to zero it should be blue. The code is:

ListPointPlot3D[data,
 ColorFunction -> 
 Piecewise[{{Green, #[[3]] >= 0}, {Blue, #[[3]] < 0}}] & /@ data,
 PlotRange -> {{7.25, 10.75}, {42, 45.5}, {-50000, 50000}}];

It almost works, meaning that I get just one error message, and the plot does appear, but all the points are the same colour (dark blue). The error message I get is

ListPointPlot3D::cfun: Value of option ColorFunction -> 
(here there is a blue box)
is not a valid color function, or a gradient ColorData entity

I am sorry if this is a really simple error that I can't see, but what am I doing wrong? Oh, I have MMA 10 on a Mac running Yosemite.

Many thanks

Answer 1

There appear to be two problems with my syntax:

1. the function definition is not enclosed in parentheses
2. I used the Map construct to apply the colour function to each element at the first level of the list data.

In addition, I did not use

ColorFunctionScaling -> False.

which is needed if discrete colours are desired rather than a smooth rainbow gradient.

J.M.'s hint helps understand the parentheses. The fact that the rule 'Operator Input Form' has higher precedence than the ampersand (&) means that the beginning of the function definition, i.e.

Piecewise[{{Green, #[[3]] >= 0}, {Blue, #[[3]] < 0}}],

is bound to ColorFunction before the & is recognised. Hence, the function definion is meaningless. Adding the parentheses ensures that the Function operator (&) is detected and applied first, making the rest an actual function.

The second error is less excusable. By using the Map construct I tried to override the internal workings of ListPointPlot3D (which I do not understand and am not familiar with) whereby the data list was already being fed by ListPointPlot3D to the ColorFunction I defined through the Rule (->). Clearly that wasn't going to work.

Interestingly, the Map operator (/@) has much higher precedence than either the Rule (->) or the Function (&) operators, so this would have probably thrown MMA for a loop.

Second interesting point is that now the error message is clear!