Plot a curve with each points specifc distance away (Matlab) - matlab

Question

I am trying to draw a curve where each points are specific distance away from each other.
Now, blow shows pretty much what I wanted to do but I want sin like curve and not constant radius.
R = 50; %radius
Gap = 0.1; % gap between points
Curve = 180;
rad = 0;
n= pi*2*R*Curve/360/Gap; % n is length of arc
th = linspace( pi, rad ,n);
x = R*cos(th)+R;
y = R*sin(th)+100;
PathDB.Route1.x(1:1001,1)=0;
PathDB.Route1.y = (0:Gap:100)';
LengthY = length(PathDB.Route1.y);
PathDB.Route1.x(1001:1001+length(x)-1,1)=x ;
PathDB.Route1.y(LengthY:LengthY+length(y)-1) = y;
LengthX = length(PathDB.Route1.x);
LengthY = length(PathDB.Route1.y);
PathDB.Route1.x(LengthX:LengthX+1000,1)=PathDB.Route1.x(LengthX,1);
PathDB.Route1.y(LengthY:LengthY+1000,1)= (PathDB.Route1.y(LengthY,1):-Gap:0);
plot(PathDB.Route1.x, PathDB.Route1.y);
grid ;
axis equal
All I want to do is instead of perfect curve, I want to add sin like curve which are plotted by 0.1.
I'm sorry about my poor coding skills I hope you can understand and help me.
Any advice is appreciated!
Rui

Answer 1

If you want this to be robust, you'll probably need to use the Matlab Symbolic Toolbox. If you take a function f, and want to plot equidistant points along it's curve between a and b, you could do something like this (using sin(x) as the example function):
sym x;
f = sin(x);
g = diff(f); %derivative of f
b=5;
a=0;
%check syntax on this part
arc_length = int(sqrt(1+g^2)); %create function for arc_length
Sc = arc_length(b)-arc_length(a); %calculate total arc length
n = 30 %number of points to plot (not including b)
Sdist = Sc/n; %distance between points
xvals = zeros(1,(n+1)); %initialize array of x values, n+1 to include point at b
Next, we will want to iterate through the intervals to find equidistant points. To do this we take each S_ij where i represents the x value of the low end of the interval and j represents the high end. We start with i=a and stop when i=b. Using the inverse of our arc length equation we can solve for j. Sdist == S_ij => Sdist = arc_length(j) - arc_length(i) => Sdist+arc_length(i)=arc_length(j). Using this, we can compute: j = arc_length_inverse(Sdist+arc_length(i)). One way of implementing this would be as follows:
arc_length_inv = finverse(arc_length);
i=a
xvals(1)=i;
for ii=1:n
j = arc_length_inv(Sdist+arc_length(i)); %calculate high end
i = j %make high end new low end
xvals(ii+1)=i; %put new low end value in x array
end
With this array of x values, you can compute yvals=sin(xvals) and plot(xvals,yvals)
Some of this code probably needs tweaking but the math should be sound (the formula for arc length came from http://en.wikipedia.org/wiki/Arc_length). Mathematically, this should work for any function integrable on [a,b] and whose arc_length function has an inverse; that said, I do not know the capabilities of the int() and finverse() functions.
If you do not need robustness you can follow these steps for your specific function, doing the math by hand and entering the functions manually;