How can I plot a triangle with its altitudes?

Question

Jack Bason 2018-4-30

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https://ww2.mathworks.cn/matlabcentral/answers/398265-how-can-i-plot-a-triangle-with-its-altitudes

编辑： John BG 2018-5-11

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

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John BG 2018-5-4

编辑：John BG 2018-5-11

Thanks Jan

.

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]

.

2. missing 2 altitudes

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

.

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

.

My answer catches such altitudes missed by Jan's answer

.

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

.

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

.

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

John BG 2018-5-5

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 2018-5-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/398265-how-can-i-plot-a-triangle-with-its-altitudes#answer_318647

编辑：Jan 2018-5-4

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.

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Answer 2

sloppydisk 2018-4-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/398265-how-can-i-plot-a-triangle-with-its-altitudes#answer_317975

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

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Jack Bason 2018-4-30

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.

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Answer 3

John BG 2018-5-1

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/398265-how-can-i-plot-a-triangle-with-its-altitudes#answer_318031

编辑：John BG 2018-5-1

test98765.m

Hi Jack Bason

this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>

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