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Previous Lecture: Probability and random numbers 1-d array—vector
Today’s Lecture: More examples on vectors More MATLAB graphics Simulation
Announcement: P3 due 10/9 (Thurs) at 6pm P3: what is the result of rem(x,y) when x is negative?
February 26, 2009 Lecture 12 2
Example
Write a program fragment that calculates the
cumulative sums of a given vector v.
The cumulative sums should be stored in a
vector of the same length as v.
1, 3, 5, 0 v
1, 4, 9, 9 cumulative sums of v
February 26, 2009 Lecture 12 3 February 26, 2009 Lecture 12 5
Drawing a single line segment
a= 0; % x-coord of pt 1
b= 1; % y-coord of pt 1
c= 5; % x-coord of pt 2
d= 3; % y-coord of pt 2
plot([a c], [b d], ‘-*’)
x-values (a vector)
y-values (a vector)
Line/marker format
February 26, 2009 Lecture 12 6
Drawing a polygon (multiple line segments)
% Draw a rectangle with the lower-left
% corner at (a,b), width w, height h.
x= [a a+w a+w a a ]; % x data
y= [b b b+h b+h b ]; % y data
plot(x, y)
Fill in the missing vector values!
February 26, 2009 Lecture 12 11
Color is a 3-vector, sometimes called the RGB
values
Any color is a mix of red, green, and blue
Example:
c= [0.4 0.6 0]
Each component is a real value in [0,1]
[0 0 0] is black
[1 1 1] is white
February 26, 2009 Lecture 12 12
Let’s compute colors!
Show “all combinations” of red and blue
Assume some kind of granularity—discretize the color value range for red and blue Assume no contribution from green (set to 0)
Program development:
Compute the color first; worry about drawing later Decide on granularity, say, ∆=.
February 26, 2009 Lecture 12 14
% All combinations of R and B
gran= 0.25; %granularity For all red values
Set color vector
February 26, 2009 Lecture 12 21
Things to consider/try on the color computation problem
The granularity was the programmer’s choice
Choosing how to display the colors was a design
problem!
What if you want compute “all combinations” of
the R, G, and B values? How would the program
change?
Another design problem: how to show all color
combinations of the 3 -vector on a 2 -dimensional
plot?
February 26, 2009 Lecture 12 22
% given a<b, % given integer n> delta= (b-a)/n; for k= 1:n v(k)= a+k*delta; end
Yes
No
Do these two fragments produce the same vector?
A
B
% given a<b, % given integer n> v= linspace(a,b,n);
February 26, 2009 Lecture 12 23
Simulate twinkling stars
Get 10 user mouse clicks as locations of 10
stars—our constellation
Simulate twinkling
Loop through all the stars; each has equal likelihood of being bright or dark Repeat many times
% No. of stars and star radius N=10; r=.5; % Get mouse clicks, store coords In vectors x,y [x,y] = ginput(N); % Twinkle! for k= 1:50 % 50 rounds of twinkling
end
February 26, 2009 Lecture 12 45
−3 −3 −2 −1 0 1 2 3
−
−
0
1
2
3
Before
After
Second operation: normalize
Shrink (enlarge) the polygon so that the vertex furthest from the (0,0) is on the unit circle
February 26, 2009 Lecture 12 46
function [xNew,yNew] = Normalize(x,y) % Resize polygon defined by vectors x,y % such that distance of the vertex % furthest from origin is 1
d = max(sqrt(x.^2 + y.^2)); xNew = x/d; yNew = y/d;
Applied to a vector, max returns the largest value in the vector
Vectorized ops
February 26, 2009 Lecture 12 47
−1.5 −1 −0.5 0 0.5 1
−
−0.
−0.
−0.
−0.
0
1
Third operation: smooth
Obtain a new polygon by connecting the midpoints of the edges
February 26, 2009 Lecture 12 49
function [xNew,yNew] = Smooth(x,y) % Smooth polygon defined by vectors x,y % by connecting the midpoints of % adjacent edges
n = length(x); xNew = zeros(n,1); yNew = zeros(n,1);
for i=1:n Compute the midpt of ith edge. Store in xNew(i) and yNew(i) end
February 26, 2009 Lecture 12 50
xNew(1) = (x(1)+x(2))/ yNew(1) = (y(1)+y(2))/
(x 4 ,y 4 )
(x 1 ,y 1 )
(x 3 ,y 3 )
(x 2 ,y 2 )
(x 5 ,y 5 )
February 26, 2009 Lecture 12 54
xNew(5) = (x(5)+x(1))/ yNew(5) = (y(5)+y(1))/
(x 4 ,y 4 )
(x 1 ,y 1 )
(x 3 ,y 3 )
(x 2 ,y 2 )
(x 5 ,y 5 )
February 26, 2009 Lecture 12 55
for i=1:n
xNew(i) = (x(i) + x(i+1))/2;
yNew(i) = (y(i) + y(i+1))/2;
end
Will result in a subscript
out of bounds error when i is n.
Smooth
February 26, 2009 Lecture 12 58
Proposed Simulation
Create a polygon with randomly located vertices.
Repeat:
Centralize
Normalize
Smooth
February 26, 2009 Lecture 12 59
x= zeros(1,1); for k= 1: x= [x x]; end y= x(7);
Yes
No
No, but there’s
some other error
Is there a subscript out of bounds error?
A
B
C
