How can I plot a triangle with its altitudes?

Hi I'd just like to know whats wrong with my coding i have as when i run this it does not plot the altitudes correctly.

x = [0,2,4,0];
y = [0,3,2,0];

%Altitude CF
% Gradient Forumla
% m = (y2-y1)/(x2-x1)
m3 = (y(2)-y(1))/(x(2)-x(1));
altitudem3=-1/m3;
% c = y-(m*x)
base3_c = y(1)-(m3*x(1));
altitude3_c = y(3)-(altitudem3*x(3));
% y=mx+c
% mx+base_c=altitudemx+altitude_c
% x=((altitude_c)-(base_c))/(m-altitudem)
xintersection=(altitude3_c-base3_c)/(m3-altitudem3);
yintersection=(altitudem3*xintersection)+altitude3_c;

%Altitude BE
m2 = (y(3)-y(1))/(x(3)-x(1));
altitudem2=-1/m2;
% c = y-(m*x)
base2_c = y(1)-(m2*x(1));
altitude2_c = y(2)-(altitudem2*x(2));
% y=mx+c
% mx+base_c=altitudemx+altitude_c
% x=((altitude_c)-(base_c))/(m-altitudem)
xintersection2=(altitude2_c-base2_c)/(m2-altitudem2);
yintersection2=(altitudem2*xintersection)+altitude2_c;

%Altitude AD
m = (y(3)-y(2))/(x(3)-x(2));
altitudem=-1/m;
% c = y-(m*x)
base_c = y(2)-(m*x(2));
altitude_c = y(1)-(altitudem*x(1));
% y=mx+c
% mx+base_c=altitudemx+altitude_c
% x=((altitude_c)-(base_c))/(m-altitudem)
xintersection3=(altitude_c-base_c)/(m-altitudem);
yintersection3=(altitudem*xintersection)+altitude_c;

hold on
plot(x,y);
plot([xintersection,x(3)],[yintersection,y(3)])
plot([xintersection2,x(2)],[yintersection2,y(2)])
plot([xintersection3,x(1)],[yintersection3,y(1)])

hold off

[John BG]

what you call 'altitude' is really a slope, right?

John BG

[e-mail]

[Jan]

The "altitude" is the line through a vertex, which is orthogonal to the opposite edge.

[John BG]

Thanks Jan

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I already supplied an answer satisfying the request of the question, the core point to solve being the calculation of such 'altutides' or normal segments to each triangle side.

The question originator added the request that in my opinion should be a new question to show the intersects of the altitudes, besides the intersects of the altitudes on each triangle side.

The answer you have supplied doesn't catch all altitudes for the following particular cases:

1. missing 1 altitude

x = [0,0,4]
y = [0,3,2]

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2. missing 2 altitudes

x = [0,0,4]
y = [0,4,0]

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the horizontal and vertical sides of the triangle should be coloured with the altitudes, but they aren't because this answer doesn't get these altitudes

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My answer catches such altitudes missed by Jan's answer

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x = [0,0,4]
y = [0,3,2]

.

x = [0,0,4]
y = [0,4,0]

.

.

John BG

<mailto:[e-mail] [e-mail]>

[John BG]

Also, none of the supplied answers so far, including mine, consider negative coordinates of the input points

x =[ -6 -5 -4] y =[ -10 4 10]

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Answer 1

[Jan]

If the question is: "I'd just like to know whats wrong with my coding", this is the answer:

x = [0,2,4,0];
y = [0,3,2,0];

% This is fine:  
m3 = (y(2)-y(1))/(x(2)-x(1));
altitudem3=-1/m3;
base3_c = y(1)-(m3*x(1));
altitude3_c = y(3)-(altitudem3*x(3));
xintersection=(altitude3_c-base3_c)/(m3-altitudem3);
yintersection=(altitudem3*xintersection)+altitude3_c;

m2 = (y(3)-y(1))/(x(3)-x(1));
altitudem2=-1/m2;
base2_c = y(1)-(m2*x(1));
altitude2_c = y(2)-(altitudem2*x(2));
xintersection2=(altitude2_c-base2_c)/(m2-altitudem2);
% yintersection2=(altitudem2*xintersection)+altitude2_c;
%                                         ^ Here is the problem  
% It must be xintersection2:
yintersection2=(altitudem2*xintersection2)+altitude2_c;

m = (y(3)-y(2))/(x(3)-x(2));
altitudem=-1/m;
base_c = y(2)-(m*x(2));
altitude_c = y(1)-(altitudem*x(1));
xintersection3=(altitude_c-base_c)/(m-altitudem);
yintersection3=(altitudem*xintersection)+altitude_c;
%                                     ^ Here is the problem  
% It must be xintersection3:
yintersection3=(altitudem*xintersection3)+altitude_c;

hold on
plot(x,y);
plot([xintersection,x(3)],[yintersection,y(3)])
plot([xintersection2,x(2)],[yintersection2,y(2)])
plot([xintersection3,x(1)],[yintersection3,y(1)])

This is a typical problem, when code is duplicated by copy&paste. Modifying all occurrences of the differences is tricky. A more reliable solution is to use a loop instead. See John BG's answer, which considers m==0 in addition. But a code as near as possible to your code:

x = [0,2,4,0];
y = [0,3,2,0];
hold on
plot(x,y);  

v = mod(1:5, 3) + 1;
for k = 1:3
  i1 = v(k);
  i2 = v(k+1);
  i3 = v(k+2);
  m                = (y(i2)-y(i1)) / (x(i2)-x(i1));
  altitudem        = -1/m;
  base_c           = y(i1) - m * x(i1);
  altitude_c       = y(i3) - altitudem * x(i3);
  xintersection(k) = (altitude_c - base_c) / (m - altitudem);
  yintersection(k) = (altitudem * xintersection(k)) + altitude_c;
  plot([xintersection(k), x(i3)], [yintersection(k), y(i3)])
end

Using loops instead of copy&past + modifications reduces the chance for typos.

Answer 2

[sloppydisk]

Please clarify what you are trying to do. What would you like to see as output?

[Jack Bason]

As an output I would like to see a plotted triangle with all 3 altitudes that intersect at one point. The coding needs to have the ability to change the co-ordinates and it still work.

Answer 3

[John BG]

Hi Jack Bason

this is John BG <mailto:[e-mail] [e-mail]>

I have rearranged your code to do what you asked for, please find attached copy of this script.

close all;clear all;clc
x=[0,2,4];y=[0,3,2];
x2=[x x x(1)];y2=[y y y(1)];
plot(x2,y2,'b')
hold on
x_intersect=zeros(1,3)
y_intersect=zeros(1,3)
for k=1:1:length(x)
      p1=[x2(k) y2(k)]
      p2=[x2(k+1) y2(k+1)]
      pref=[x2(k+2) y2(k+2)]

        % 1st segment slope: m offset: k0
        m1=(p2(2)-p1(2))/(p2(1)-p1(1))
        switch abs(m1)
            case Inf                         % vertical, 90.00 degree up
                  yint=pref(2)
                  xint=p1(1)              % = p2(1), xint
                  m2=0

            case 0                           % horizontal, completely flat, 0.00 degree
                  yint=p1(2)              % =p2(2)
                  xint=pref(1)            % = p2(1)
                  m2=0

            otherwise
                  k01=p1(2)-m1*p1(1)
                  m2=-1/m1                    % 2nd segment m k0
                  k02=pref(2)-m2*pref(1)
                  xint=(k01-k02)/(m2-m1)     % intersect point
                  yint=m1*xint+k01
                  x_intersect(k)=xint             % logging intersect point
                  yIntersect(k)=yint

        end

        plot([p1(1) p2(1)],[p1(2) p2(2)],'g*')
        plot(pref(1),pref(2),'y*')  
        plot(xint,yint,'g*')
        plot([xint pref(1)],[yint pref(2)],'r')
  end

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if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance for time and attention

John BG

<mailto:[e-mail] [e-mail]>