How to draw tangent line at specified points in a curve

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Mrinal
Mrinal 2013-9-18
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
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Ngo Nguyen
Ngo Nguyen 2013-9-18
编辑：Ngo Nguyen 2013-9-18
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)

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回答（1 个）

Image Analyst
Image Analyst 2013-9-18
编辑：Image Analyst 2013-9-18
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.
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Mrinal
Mrinal 2013-9-18
编辑：Mrinal 2013-9-18
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

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