How to add element to a list once and then the last element will get replaced in the following iterations?

Question

img= ExampleData[{"TestImage3D", "MRknee"}];    
Manipulate[
colors = {Black, Blue, Purple, Red, Brown, Gray, Green, Orange, Pink,
Cyan, Yellow, White};
w = List @@@ ColorConvert[colors, "RGB"].{0.2989, 0.5870, 0.1140};
opacities = {x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12};
co = Table[AppendTo[colors[[i]], opacities[[i]]], {i, 12}];
colorfn = Evaluate[Blend[{w, co}\[Transpose], #]] &;
Image3D[img, 
ColorFunction -> colorfn], {x1, 0, 1}, {x2, 0, 1}, {x3, 0, 1}, {x4, 
0, 1}, {x5, 0, 1}, {x6, 0, 1}, {x7, 0, 1}, {x8, 0, 1}, {x9, 0, 
1}, {x10, 0, 1}, {x11, 0, 1}, {x12, 0, 1}]

The above code snippet works fine. However, 'AppendTo' adds an element on each iteration. I want to append the opacity values to be appended to the color values only once (during the execution of the Manipulate for the first time) and from the next time onwards (for any change in the parameters x1, x2, ..) it will just replace the last the opacity value.

[

Table[AppendTo[colors[[i]], opacities[[i]]], {i, 12}]

results

{GrayLevel[0, 0], RGBColor[0, 0, 1, 0], RGBColor[0.5, 0, 0.5, 0], 
RGBColor[1, 0, 0, 0], RGBColor[0.6, 0.4, 0.2, 0], GrayLevel[0.5, 0],  
RGBColor[0, 1, 0, 0], RGBColor[1, 0.5, 0, 0], RGBColor[1, 0.5, 0.5, 0], 
RGBColor[0, 1, 1, 0], RGBColor[1, 1, 0, 0], GrayLevel[1, 0]}
(*when it is first called*)

Next iteration ...

{GrayLevel[0, 0, 0], RGBColor[0, 0, 1, 0, 0], RGBColor[0.5, 0, 0.5, 0, 0], 
RGBColor[1, 0, 0, 0, 0], RGBColor[0.6, 0.4, 0.2, 0, 0], GrayLevel[0.5, 0, 0],  
RGBColor[0, 1, 0, 0, 0], RGBColor[1, 0.5, 0, 0, 0], RGBColor[1, 0.5, 0.5, 0, 0], 
RGBColor[0, 1, 1, 0, 0], RGBColor[1, 1, 0, 0, 0], GrayLevel[1, 0, 0]}

and so on. ]

How can I modify the above code to serve the purpose?

Answer 1

The main problem is the use of AppendTo where Append would suffice. You could instead use:

co = MapThread[Append, {colors, opacities}];

Full code:

Okay, cleaner now

img = ExampleData[{"TestImage3D", "MRknee"}];

colors =
 {Black, Blue, Purple, Red, Brown, Gray, Green, Orange, Pink, Cyan, Yellow, White};

vars = Array[α, Length@colors];

w = List @@@ ColorConvert[colors, "RGB"].{0.2989, 0.5870, 0.1140};

makeColorFn[colors_, w_, vars_] :=
 {w, MapThread[Append, {colors, vars}]}\[Transpose] /. body_ :> (Blend[body, #] &)

With[{opa = vars},
  Manipulate[
    Image3D[img, ColorFunction -> makeColorFn[colors, w, opa]],
    Evaluate[Sequence @@ ({#, 0, 1} & /@ vars)]
  ]
]

In the code above With is used to address

• How are parameters evaluated for a Plot in Manipulate

---

An alternative to the way I used makeColorFn above is this:

myBlend[body_][n_] := Blend[body, n]

colorfn = myBlend[{w, MapThread[Append, {colors, vars}]}\[Transpose]];

With[{colorfn = colorfn}, 
  Manipulate[
    Image3D[img, ColorFunction -> colorfn], 
    Evaluate[Sequence @@ ({#, 0, 1} & /@ vars)]
  ]
]

The key here is to inject a color function in a form that is open to evaluation so that it "picks up" the values of α[x]. Function doesn't work here as its body is held. Compare:

Manipulate[Blend[x, #] &, {x, 0, 5}]

Manipulate[myBlend[x], {x, 0, 5}]

I still need With to get colorfn inside Manipulate before it is evaluated and the GUI is built, or the vars variables are not recognized and replaced correctly.