Create a triangular function

Hello.

I want to create a function in MatLab, which represents the image below.

Now, I can easily create a linear function for one of the lines and set the remaining to some constant, but I fail to do it for the combined two.

I was thinking about making a piecewise function or perhaps an inequality with the following restrictions:

I simply can't get it to work for both. If you have an idea, I'd love to hear it.

Answer 1

[Johannes Hougaard]

Hi Mikkel

I'm not quite sure whether I have understood how much of a mathematical function you would prefer for the graph to be.

But if it should just be a practical solution to the problem in a parametrical, piecewise way. I think this function (attached as m-file). Feel free to use it without any credits, copyright or whatever - and change everything you care to change :D

% Example data roughly taken from your question
x = 0:2500;
cutoff = 1250;
maxwidth = 1250;
minwidth = 100;

And here is the function in clear text (same as attached)

function y = triangularplot(x,maxwidth,minwidth,cutoff)
% TRIANGULARPLOT
%           Creates a triangular plot in response to MATLAB Central question 519827
% 
% I/O
%           y = triangularplot(x,maxwidth,minwidth,cutoff);
% 
% INPUT
%           x           = the x-data to use for the calculation
%           maxwidth    = the width at x = 0
%           minwidth    = the minimum width of the channel
%           cutoff      = the x value at which the width reaches the minimum
% 
% 2020-04-2020 Johannes Hougaard <[e-mail]>


% Preallocation of y
y = nan(size(x));

% Calculating the slope for the linear section of the graph
slope = (minwidth-maxwidth)/cutoff;

% Calculating the y-values for x <= cutoff
y(x <= cutoff) = maxwidth + x(x <= cutoff).*slope;

% Setting the y-values aboce cutoff as the minimum width
y(x > cutoff) = minwidth;

% Plotting the result
figure;
plot(x,y,'k-');
set(gca,'NextPlot','add');
plot(x,-y,'k-');
set(gca,'NextPlot','replace');
ylabel('Width (km)');

[Mikkel Christensen]

Thank you so much for this - that is quite cool.

I might have formulated my question poorly, but I think it is much simplere.

So, I need a function for the width of a glacier. I would like that function to represent the image above.

Basically a mathematical function

and similary for the other side of the triangle

I need it as one function if that make sense.

Should it be a peicewise function with the intervals ?

Would that work?

[Johannes Hougaard]

Ah - it relates to the value of 'y' not of 'x' - I misread that but I can't see how you would make conditions on the output rather than on your input.

e.g. what is is that or is that ?

Based on the description you give I have a hard time seeing how you would ever reach the 'constant' part of the image shown.

[Mikkel Christensen]

Yea, I see what you mean. It seems like I simple problem, but can't get it right.

For the constant part, I would let it be equal to | 100 m | from (1200:end).

[Johannes Hougaard]

But that is exactly what you get from the above function if you run it as.

y = triangularplot(0:2500,1250,100,1200);

I just still don't get which value you want at e.g. or

if you want the function I sent you to be simpler (just the input a) that would be fairly easy keeping most of the code and just changing the first few lines and hard-coding some stuff - but I'm still not quite sure what the math should be.

function y = triangularplot(x,a)
% TRIANGULARPLOT
%           Creates a triangular plot in response to MATLAB Central question 519827
% 
% I/O
%           y = triangularplot(x,maxwidth,minwidth,cutoff);
% 
% INPUT
%           x           = the x-data to use for the calculation
%           a           = the constant 'slope' of the initial part
% 
% 2020-04-2020 Johannes Hougaard <[e-mail]>


% Preallocation of y
maxwidth = 1250;
minwidth = 100;
y = nan(size(x));

cutoff = (maxwidth - minwidth)/a;


% Calculating the y-values for x <= cutoff
y(x <= cutoff) = maxwidth - a .* x(x <= cutoff);

% Setting the y-values aboce cutoff as the minimum width
y(x > cutoff) = minwidth;

% Plotting the result
figure;
plot(x,y,'k-');
set(gca,'NextPlot','add');
plot(x,-y,'k-');
set(gca,'NextPlot','replace');
ylabel('Width (km)');

could also be that you're simply looking for the built-in function 'sign' which could be multiplied to your a.

[Mikkel Christensen]

Ah, I was entering input in the wrong function and got something quite different ... : |

Well, that works then. Amazing!

Thank you so much