Problems passing options in specialized plot functions for Mathematica

Question

This should be quick to an expert, but I'm relatively new at defining functions with options. Here is a schematic of what I've tried, I'll explain after showing the code:

MyPlotFunction[params_, optionalparameter_List:{1,2,3}, opts:OptionsPattern[]]:=
    Plot [ stuff, {x,0,1},  Evaluate@FilterRules[{opts},Options@Plot]];

Options[MyPlotFunction] = {  PlotRange->{-5,5}, Frame->True, ... other plot options};

There are four slight subtleties:

1. I have an optional parameter in my function that needs to be a list of integers.
2. I want the ability to call the function with any option of Plot, especially using values other than the default values specified in the third line.
3. I want to have default values for some of the options.
4. I potentially want to put other options in the function, so it is not guaranteed that all of the options should be passed through to plot.

But what I have above doesn't work. The default options I set are ignored, yet they appear in the ??MyPlotFunction information for my function. I'll give examples if you guys can't spot the error yet.

Edit: Examples that doesn't work:

1. SimplePlot[t_,opts:OptionsPattern[{PlotRange->{-4,4},Frame->True}]]:= Plot[2x+t,{x,0,1},opts]; Fails, the default option is ignored.

2. SimplePlot[t_,opts:OptionPattern[]]:= Plot[2x+t],{x,0,1},opts]; Options[SimplePlot] = {PlotRange->{-4,4},Frame->True}; Fails, the default option is ignored.

3. SimplePlot[t_,opts__:{PlotRange->{-4,4},Frame->True}]:= Plot[2x+t,{x,0,1},opts]; Default options work with a bare call, but if one of these options or any other plot option is overridden the remaining defaults are lost.

Answer 1

OptionsPattern[] only catches the options that are passed in, so you need to explicitly include any non-default option settings, say by using something like:

FilterRules[{opts, Options[MyPlotFunction]}, Options@Plot]

Here's a simple example:

Options[MyPlotFunction] = {PlotRange -> {-5, 5}, Frame -> True};

MyPlotFunction[params_, optionalparameter_List: {1, 2, 3}, 
  opts : OptionsPattern[MyPlotFunction]] := 
 Plot[optionalparameter, {x, 0, 1}, 
  Evaluate@FilterRules[{opts, Options[MyPlotFunction]}, Options@Plot]]