How to draw tangent line at specified points in a curve

I am having a an array of points x,y and respective angles at those specified points. I want to plot a tangent line at those points, i am unable to figure out how to proceed.

http://postimg.org/image/s2y1pqqaj/

As shown in command window 1st column contains x points , 2nd column contains y points and 3rd column the respective tangent angle. Figure 1 is plot between x and y points. Thanking you.

Regards,

Mrinal

[Ngo Nguyen]

If you have the coordinates M(x,y) , so you can find the slope m:

m= -(x - x0) / (y - y0) , (x0,y0) is the center of the circle

After that, you can plot the tangent line at M y = m*(x - x0) + y0 plot(x,y)

Answer 1

[Image Analyst]

You have to figure out the slope at each point, then decide where the endpoints of the tangent line should be, then call line([x1, x2], [y1, y2], 'Color', 'b'). As a rough guess you can probably just say the slope at xn,yn is

slope = (y(n+1)-y(n-1)) / (x(n+1) - x(n-1));

or just get the slope from the tangent angle that you already have. Then the formula for the line is (from high school algebra)

y = slope * (x - x(n)) + y(n);

You just need to figure out how far away from x(n) do you want your endpoints of your tangent line segment. I believe you can just use xLeft = min(x) and xRight = max(x) if you just want the line to go everywhere and not see the endpoints lie inside the plot.

[Mrinal]

Thank you. It seems good but i am unable to implement it. As you told i need to use the slope at every point from tangent angle but unable to understand how to use it to draw tangent at points. Here is my code as i am using various functions, so it is not possible for me to upload the whole code but the function in which i am using this is below. Hope you can guide.

% Fill in parr a list of points and tangents to be used for display.

% @param parr (x,y) Array of points.

% @param tan Array of tangents.

% @param lengthStep Distance between points.

 function [x y tan] = GetPointListForDisplay(m_Length,r1,r2,count)

   global nn ca ce length; 

   GetLength = m_Length;
   length = GetLength;   
   ca = GetCurvatureAtDeltaLength(0.0);     
   ce = GetCurvatureAtDeltaLength(length);

   radius = 1.0 ./ max(abs(ca), abs(ce));

   nn = 3 + (180.0 * length/(2*pi*radius));  % Using modified formula of arc here
   lengthStep = length/nn; 
   currLen = -lengthStep;
   while (1) 
       currLen = currLen + lengthStep;
     if (currLen > m_Length)
           currLen = m_Length; 
       end

       [x,y] = GetPointAtDeltaLength(currLen);
       [tan] = GetTangentGridBearingAtDeltaLength(currLen); 

       z(count,1) = x;
       z(count,2)= y;
       z(count,3)= tan;

       figure(1);
       %plot(z(count,1).*sin(z(count,3)),z(count,2).*cos(z(count,3)),'b*');
       %plot(z(1,count).*cos(z(3,count)),z(2,count).*sin(z(3,count)),'b*');

       plot(z(count,1),z(count,2),'b*');

       %plot(z(1,count),z(2,count),'b*');
       hold on;
       %pause(0.1);
       count=count+1;
       axis equal;     
       if (currLen >= m_Length)
           z(count,1)= tan

           break;
       end
   end
 end