Skip to main content

plotting - ListPlot3D - How to make the Color depending on a second list


From a simulation (solid state physcis) i obtained a list1={{300,0,0},...} with x values=300,400,...,1500 and y-values=0,0.08,...,20 and z values. I plotted them using ListPlot3D.



I want to investigate the change in z value for fixed y, i.e. does z value change a lot for a given y in the range of all x values.


Therefore I want to make a coloring like this:



  1. If z' value of {x',y',z'} is equal to z value at {x=300,y',z} then it should be Gray

  2. If z' value of {x',y',z'} is lower than z value at {x=300,y',z}: going from Yellow to Red

  3. If z' value of {x',y',z'} is higher than z value at {x=300,y',z}: going from Green to Blue


How can I do that?


I tried the following:





  • Manipulation of list1 to get list2={0,0.3,...}, which has same amount of elements as points (x,y,z) in list1 and same ordering,




  • The values in list2 are 0.5 when point at same position in list1 satiesfies 1)




  • The values in list2 are < 0.5 when point at same position in list1 satiesfies 2)





  • The values in list2 are > 0.5 when point at same position in list1 satiesfies 3)




I tried to use a colorfunction:


colorf =  Blend[{{0, Blue}, {0.49, Green}, {0.5, Gray},{0.51, Yellow}, {1,Red}}, #] &;
ListPlot3D[list1,ColorFunction->colorf/@ list2]

I do get a coloring but not the correct one. I checked by exchanging all z values in list1 with values in list2 and made a density plot and colors are at different postions.


Is there any solution to make the color like I want to have it?



Answer




To be honest, I'm surprised that you can actually provide a list of colours to ColorFunction. Normally you would specify ColorFunction -> func, where func is a function. The arguments provided to func depend on the function used to create the plot. For ListPlot3D they are the three spacial coordinates. To create a suitable function in this case, you could interpolate the points in list1 and list2.


Consider for example


list1 = N@{##, Cos[#] Cos[#2]} & @@@ Tuples[Range[0, 2 Pi, Pi/15], 2];
list2 = N@(1/2 + (Cos[#] Cos[#2] - Cos[#2])/2) & @@@ Tuples[Range[0, 2 Pi, Pi/15], 2];

We construct a function by interpolating the values in list2. This function is then used as the second argument of your Blend function to create a ColorFunction


interp = Interpolation[Transpose[{list1[[All, ;; 2]], list2}]];
colorf = Function[{x, y}, Blend[{{0, Blue}, {0.49, Green}, {0.5, Gray}, {0.51, Yellow}, 
  {1, Red}}, interp[x, y]]];


Which produces something like


ListPlot3D[list1, ColorFunction -> colorf, ColorFunctionScaling -> False]

Mathematica graphics


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

How to remap graph properties?

Graph objects support both custom properties, which do not have special meanings, and standard properties, which may be used by some functions. When importing from formats such as GraphML, we usually get a result with custom properties. What is the simplest way to remap one property to another, e.g. to remap a custom property to a standard one so it can be used with various functions? Example: Let's get Zachary's karate club network with edge weights and vertex names from here: http://nexus.igraph.org/api/dataset_info?id=1&format=html g = Import[ "http://nexus.igraph.org/api/dataset?id=1&format=GraphML", {"ZIP", "karate.GraphML"}] I can remap "name" to VertexLabels and "weights" to EdgeWeight like this: sp[prop_][g_] := SetProperty[g, prop] g2 = g // sp[EdgeWeight -> (PropertyValue[{g, #}, "weight"] & /@ EdgeList[g])] // sp[VertexLabels -> (# -> PropertyValue[{g, #}, "name"]...
Post a Comment
Read more