%Two-dimensional vector plotter & graphical sum - This program draws two
%vectors with lengths and angles specified by the user and then
%demonstrates the process of graphically adding those two vectors. It does
%this by displacing one of the vectors (without changing its length or
%direction) so that its tail is at the head of the other vector. The sum
%of the vectors is then drawn from the origin to the end of the displaced
%vector. The user specifies which of the two vectors is displaced.
clear all; %Clears old variables and data
%The following code gets user input for length and angle of two vectors
options.WindowStyle='normal'; %Allows user to manipulate windows while
%waiting for user input
prompt={'Length of First Vector','Angle (deg) of First Vector (V1)',...
'Length of Second Vector','Angle (deg) of Second Vector (V2)'};
%This specifies the text shown to the user in the dialog box requesting
%inputs
title1='Vector Lengths and Angles';%Title of user-interface dialog box
dims=[1,70];%Sets dimensions (height and width) of user-input dialog box
definput={'1','0','2','90'};%Default inputs for vector lengths and angles
params=inputdlg(prompt,title1,dims,definput,options);%Generates dialog box
vec1_length=str2num(char(params(1)));%Converts first user input from
%character string to number and assigns variable for length
%of vector 1
vec1_angle=(pi/180)*str2num(char(params(2)));%Converts second user
%input from character string to number, then converts that
%number from degrees to radians and assigns variable for
%direction of vector 1
vec2_length=str2num(char(params(3)));%Converts third user input from
%character string to number and assigns variable for length
%of vector 2
vec2_angle=(pi/180)*str2num(char(params(4)));%Converts fourth user
%input from character string to number, then converts that
%number from degrees to radians and assigns variable for
%direction of vector 2
% Finding the end points of the two vectors
vec1start = [0 0];%Sets start point of vector 1 as origin
vec1x=vec1_length*cos(vec1_angle);%Finds x-component of vector 1
vec1y=vec1_length*sin(vec1_angle);%Finds y-component of vector 2
vec1end = [vec1x vec1y];%Finds end point of vector 1
vec1 = vec1end-vec1start;%Generates 2-D vector 1 from start to end point
vec2start = [0 0];%Sets start point of vector 2 as origin
vec2x=vec2_length*cos(vec2_angle);%Finds x-component of vector 2
vec2y=vec2_length*sin(vec2_angle);%Finds y-component of vector 2
vec2end = [vec2x vec2y];%Finds end point of vector 2
vec2 = vec2end-vec2start;%Generates 2-D vector 2 from start to end point
%Setting the start and end points of vec3 (the sum of vec1 and vec2)
vec3start=[0,0];%Sets start point of vector 3 as origin
vec3=vec1+vec2;%Adds vector1 to vector 2
vec3end=[vec1x+vec2x vec1y+vec2y];%Finds end point of vector 3
vec3_length=sqrt(vec3(1)^2+vec3(2)^2);%Finds length of vector 3
% The "quiver" command draws vectors - quiver(x0,y0,xcomp,ycomp) draws
% an arrow starting at x0,y0 with horizontal component xcomp and
% vertical component ycomp
figure(1);%Initializes figure
quiver(vec1start(1),vec1start(2),vec1(1),vec1(2),0,'k');%Plots vector 1
hold on;%Allows additional objects to be drawn on same plot
quiver(vec2start(1),vec2start(2),vec2(1),vec2(2),0,'k');%Plots vector 2
grid on;%Draws grid lines on plot
%Finding the longest vector to set the plot limits
biggestvec=max([vec1_length,vec2_length,vec3_length]);%Finds biggest length
plotlim=ceil(1.2*biggestvec);%Makes value 20 percent bigger than max length
axis([-plotlim plotlim -plotlim plotlim]);%Sets plot axis limits
%Labels for vector 1 and vector 2 and initial title for graph
text(vec1end(1),vec1end(2), ' V1');%Labels end of vector 1
text(vec2end(1),vec2end(2), ' V2');%Labels end of vector 2
title(['Two Vectors to Add']);%Initial title of plot
%Gives the user a few seconds to look at the two vectors
pause(3);%Nothing happens for three seconds
%Gets user input for which of the two vectors will be displaced
prompt={'Displace Vector 1 or 2?'};
title1='Vector to Displace';
dims=[1,60];
definput={'1'};
params=inputdlg(prompt,title1,dims,definput,options);
vectomove=str2num(char(params(1)));
% Sets up movedvec to be displaced and statvec to remain stationary
% and sets starting point of displaced vector to be the end of the
% stationary vector
if vectomove==1;%If user selects vector 1 to move, "vec to move" equals 1
vecnomove=2;%In this case, "vec no move" equals 2
statvec=vec2;%Sets stationary vector as vector 2
statvecstart=vec2start;%Sets start of stationary vector
statvecend=vec2end;%Sets end of stationary vector
movedvec=vec1;%Stores vector 1 as "moved vec"
movedvecstart=vec1start;%Sets start of moved vector as start of vec1
movedvecend=vec1end;%Sets end of moved vector as end of vec1
vec4start=vec2end;%Sets start of displaced vector as end of vector 2
else
vecnomove=1;%If user selects vector 2 to move, "vec no move" equals 1
statvec=vec1;%In this case, stationary vector is vec 1
statvecstart=vec1start;%Sets start of stationary vector
statvecend=vec1end;%Sets end of stationary vector
movedvec=vec2;%Stores vector 2 as "moved vec"
movedvecstart=vec2start;%Sets start of moved vector as start of vec 2
movedvecend=vec2end;%Sets end of moved vector as end of vec 2
vec4start=vec1end;%Sets start of displaced vector as end of vector 1
end;
%Moves displaced vector (as dashed arrow) from start to end
% of stationary vector (while keeping the length and angle the same)
% Each dashed arrow is deleted before a new one is drawn.
title(['Displacing Vector V',num2str(vectomove)]);%Plot title during move
for i=1:19;%Displacement will occur in 19 steps (final version of displaced
%vector is drawn after this loop completes)
movedvecstart=movedvecstart+(1/20)*statvec;%Moves start of vector which
%is being displaced by one increment (1/20th of
%distance to final displaced position)
movedvecend=movedvecend+(1/20)*statvec;%Moves end of vector which is
%being displaced by one increment
H=quiver(movedvecstart(1),movedvecstart(2),movedvec(1),movedvec(2),0,...
'LineStyle','--','Color','k');%Draws vector being displaced (dashed)
pause(0.1);%Short delay between positions for dashed moving vector
delete(H);%Erases previous dashed moving vector
end;
%Draws displaced vector (not dashed) in final position
vec4end=vec3end;%Sets end of displaced vector
vec4=vec4end-vec4start;%Generates 2-D displaced vector as vector 4
quiver(vec4start(1),vec4start(2),vec4(1),vec4(2),0,'Color','k');%Draws
%displaced vector
pause(1)%Gives the user a second to see displaced vector in final position
title(['Drawing Vector from Start of V',num2str(vecnomove),' to End of Displaced V'...
num2str(vectomove)]);%Adds title during displacement
% Draws an arrow of increasing length (in 19 steps) between start of
% stationary vector and end of displaced vector
for j=1:19;%Vector grows from origin in 19 steps
vecgrow=(j/20)*vec3;%Sets length of growing vector
H=quiver(statvecstart(1),statvecstart(2),vecgrow(1),vecgrow(2),0,'Color','k');
%Draws growing vector
pause(0.1);%Short pause to show growing vector
delete(H);%Clears previous version of growing vector
end;
%Draws thick arrow and labels it V1 + V2
quiver(vec3start(1),vec3start(2),vec3(1),vec3(2),0,'Color','k','Linewidth',2);
text(vec3end(1),vec3end(2), ' V1+V2');
title(['Graphical Vector Addition with V',num2str(vectomove),' displaced']);