How to combine continual and discrete function?

Questions
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1

I’m building one strategy war game, and I want to create mathematics function for hits chance (y axis) based on distance (x axis). I defined manualy one discrete function with coordinate pairs that will serve as main function, then I need to add another (continual) function that will serve as an increase of hits chance.

Discrete Function:

cList = {{0, 100}, {1, 95}, {5, 80}, {10, 70}, {15, 40}, {20, 
   25}, {25, 15}, {30, 10}}
ListLinePlot[cList]

Continual Function:

Plot[Sin[2 x^2]*x/4 + Sin[0.3 x] + (8/30)*x, {x, 0, 30}]

I need combined function that I can use later in C++ programming language to calculate hits chance.
for example: if is target and shooting unit at distance 5, then I will use randomly choosen point on combined function from interval X [4.5, 5.5]

So, first question is: “How to combine those functions?” and second is “How to use that combined function in my C++ application?”

2

Well, I found solution. I was blinded with graphical reprezentation of functions. I forgot for a moment that I have same functions in Math library in C++ :slight_smile: But Wolfram helped a lot because I can see function and can do improvement by adding some changes in function definition, but I’m realy interested about my fisrst question.

Thanks.

3

The most conceptually simple answer must be to use programming instead of mathematics to add these two functions.
f:= Which[x<1, 100, x<2, 95, x<5, 80, …]
g:=Sin[2 x^2]*x/4 + Sin[0.3 x] + (8/30)*x
h:=f+g

In terms of C-implementation, and efficiency, there could be some nonobvious solutions. For instance, convert the discrete function to a continuous function by making it piecewise linear, and then maybe using abs to make it a single expression. Then they can all be added together.

But to be more practical, you probably want to approximate. A linear fit works well enough possibly but you can try other functions too, e.g.,

Fit[{{0, 100}, {1, 95}, {5, 80}, {10, 70}, {15, 40}, {20, 25}, {25, 
   15}, {30, 10}}, {1, x, Sin[(Pi/15) x]}, x]