17 Structures Simple Structures Structure Arrays Structures with

17. Structures Simple Structures Structure Arrays Structures with Array Fields Other Possibilities

Array vs. Cell Array n Simple array n n n Each component stores one value (e. g. , character, real, uint 8) All components have the same type Cell array n n ‘C’‘S’‘ ’‘ 1’‘ 1’‘ 2’ ‘C’‘S’ 1. 1 -7 12 8 1. 1 -1 12 Each cell can store something “bigger” than one value, e. g. , a vector, a matrix, a string The cells may store items of different types Insight Through Computing

Data are often related n n n A point in the plane has an x coordinate and a y coordinate. If a program manipulates lots of points, there will be lots of x’s and y’s. Anticipate clutter. Is there a way to “package” the two coordinate values? Insight Through Computing

Packaging affects thinking Our Reasoning Level: P and Q are points. Compute the midpoint M of the connecting line segment. Behind the scenes we do this: Mx = (Px + Qx)/2 My = (Py + Qy)/2 Insight Through Computing We’ve seen this before: functions are used to “package’’ calculations. This packaging (a type of abstraction) elevates the level of our reasoning and is critical for problem solving.

Simple example p 1 = struct(‘x’, 3, ’y’, 4); 3 x p 2 = struct(‘x’, -1, ’y’, 7); 4 y p 1 D = sqrt((p 1. x-p 2. x)^2 + (p 1. y-p 2. y)^2); D is distance between two points. p 1. x, p 1. y, p 2. x, p 2. y participating as variables—because they are. Insight Through Computing

Creating a structure (by direct assignment) p 1 = struct(‘x’, 3, ’y’, 4); p 1 is a structure. The structure has two fields. Their names are x and y. They are assigned the values 3 and 4. Insight Through Computing

How to visualize structure p 1 3 4 x y p 1 = struct(‘x’, 3, ’y’, 4); Insight Through Computing

Accessing the fields in a structure 3 4 x y p 1 A = p 1. x + p 1. y; Insight Through Computing Assigns the value 7 to A

Assigning to a field in a structure 3 4 x y p 1. x = p 1. y^2; Insight Through Computing Assigns the value 16 to p 1. x

A structure can have fields of different types A = struct(‘name’, ‘New York’, … ‘capital’, ‘Albany’, … ‘Pop’, 15. 5) n n Can have combinations of string fields and numeric fields Arguments are given in pairs: a field name, followed by the value Insight Through Computing

Legal/Illegal maneuvers Q = struct(‘x’, 5, ’y’, 6) R = Q % Legal. R is a copy of Q S = (Q+R)/2 % Illegal. Must access the % fields to do calculations P = struct(‘x’, 3, ’y’) % % Illegal. Args must be in pairs (field name followed by field value) P = struct(‘x’, 3, ’y’, []) % Legal. Use [] as P. y = 4 % place holder Insight Through Computing

Structures in functions function d = dist(P, Q) % P and Q are points (structure). % d is the distance between them. d = sqrt((P. x-Q. x)^2 +. . . (P. y-Q. y)^2); Insight Through Computing

Example “Make” Function e: l y st ke” d o Go a “ma to n use nctio t a fu hligh e’s hig ctur n u o str finiti de function P = Make. Point(x, y) % P is a point with P. x and P. y % assigned the values x and y. P = struct('x', x, 'y', y); Then in a script or some other function… a= 10; b= rand(1); Pt= Make. Point(a, b); % create a point struct % according to definition % in Make. Point function Insight Through Computing

Another function that has structure parameters function Draw. Line(P, Q, c) % P and Q are points (structure). % Draws a line segment connecting % P and Q. Color is specified by c. plot([P. x Q. x], [P. y Q. y], c) Insight Through Computing

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Pick Up Sticks s = 'rgbmcy'; for k=1: 100 P = Make. Point(randn(1), randn(1)); Q = Make. Point(randn(1), randn(1)); c = s(ceil(6*rand(1))); Draw. Line(P, Q, c) end Generates two random points and chooses one of six colors randomly. Insight Through Computing

Structure Arrays n n n P An array whose components are structures All the structures must be the same (have the same fields) in the array Example: an array of points (point structures). 5. 86 1. 5. 91. 4. 28 2. 5 1. 8 x y P(1) Insight Through Computing x y P(2) x y P(3) x y P(4)

An Array of Points . 50 . 86 x y P(1) = Make. Point(. 50, . 86) Insight Through Computing

An Array of Points -. 50 . 86 x y P(2) = Make. Point(-. 50, . 86) Insight Through Computing

An Array of Points -1. 0 0. 0 x y P(3) = Make. Point(-1. 0, 0. 0) Insight Through Computing

An Array of Points -. 5 -. 86 x y P(4) = Make. Point(-. 50, -. 86) Insight Through Computing

An Array of Points . 5 -. 86 x y P(5) = Make. Point(. 50, -. 86) Insight Through Computing

An Array of Points 1. 0 0. 0 x y P(6) = Make. Point(1. 0, 0. 0) Insight Through Computing

Function returning an array of points (point structures) function P = Circle. Points(n) theta = 2*pi/n; for k=1: n c = cos(theta*k); s = sin(theta*k); P(k) = Make. Point(c, s); end Insight Through Computing

Example: all possible triangles n n Place n points uniformly around the unit circle. Draw all possible unique triangles obtained by connecting these points 3 -at-a-time. Insight Through Computing

function Draw. Triangle(P, Q, R, c) % Draw c-colored triangle; % triangle vertices are points P, % Q, and R. fill([P. x Q. x R. x], . . . [P. y Q. y R. y], c) Insight Through Computing

The following triangles are the same: (1, 3, 6), (1, 6, 3), (3, 1, 6), (3, 6, 1), (6, 1, 3), (6, 3, 1) Insight Through Computing

Bad! i, j, and k should be different, and there should be no duplicates for i=1: n for j=1: n for k=1: n % Draw a triangle with vertices % P(i), P(j), and P(k) end end Insight Through Computing

All possible (i, j, k) combinations but avoid duplicates. Loop index values have this relationship i < j < k i j k 123 124 125 126 134 135 136 145 146 156 i = 1 Insight Through Computing 234 235 236 245 246 256 i = 2 345 346 356 456 i = 4 i = 3 for i=1: n-2 for j=i+1: n-1 for k=j+1: n disp([i j k]) end end

All possible (i, j, k) combinations but avoid duplicates. Loop index values have this relationship i < j < k for i=1: n-2 for j=i+1: n-1 for k=j+1: n % Draw triangle with % vertices P(i), P(j), P(k) end end Insight Through Computing

All possible (i, j, k) combinations but avoid duplicates. Loop index values have this relationship i < j < k for i=1: n-2 for j=i+1: n-1 for k=j+1: n % Draw triangle with % vertices P(i), P(j), P(k) end end Insight Through Computing

All possible triangles % Drawing on a black background for i=1: n-2 for j=i+1: n-1 for k=j+1: n Draw. Triangle( P(i), P(j), P(k), 'm') Draw. Points(P) pause Draw. Triangle(P(i), P(j), P(k), 'k') end end Insight Through Computing

All possible (i, j, k) combinations but avoid duplicates. Loop index values have this relationship i < j < k i j k 123 124 125 126 134 135 136 145 146 156 i = 1 Insight Through Computing 234 235 236 245 246 256 i = 2 345 346 356 456 i = 4 i = 3 for i=1: n-2 for j=i+1: n-1 for k=j+1: n disp([i j k]) end end

Still get the same result if all three loop indices end with n? A: Yes B: No i j k 123 124 125 126 134 135 136 145 146 156 i = 1 Insight Through Computing 234 235 236 245 246 256 i = 2 345 346 356 456 i = 4 i = 3 for i=1: n for j=i+1: n for k=j+1: n disp([i j k]) end end

What is the 7 th line of output? for i=1: 5 for j=i+1: 5 x = 10*i + j end A: 7 Insight Through Computing B: 21 C: 23 D: 25 E: other

Structures with array fields Let’s develop a structure that can be used to represent a colored disk. It has four fields: xc: x-coordinate of center yc: y-coordinate of center r: radius c: rgb color vector Examples: D 1 = struct(‘xc’, 1, ’yc’, 2, ’r’, 3, … ’c’, [1 0 1]); D 2 = struct(‘xc’, 4, ’yc’, 0, ’r’, 1, … ’c’, [. 2. 5. 3]); Insight Through Computing

Example: Averaging two disks D 2 D 1 Insight Through Computing

Example: Averaging two disks D 2 D 1 Insight Through Computing

Example: Averaging two disks D 2 D 1 Insight Through Computing D

Example: compute “average” of two disks % D 1 and D 2 are disk structures. % Average is: r = (D 1. r + D 2. r) /2; xc = (D 1. xc + D 2. xc)/2; yc = (D 1. yc + D 2. yc)/2; c = (D 1. c + D 2. c) /2; % The average is also a disk D = struct(‘xc’, xc, ’yc’yc, ’r’, r, ’c’, c) Insight Through Computing

How do you assign to g the green-color component of disk D? D= struct(‘xc’, 3. 5, ‘yc’, 2, . . . ‘r’, 1. 0, ‘c’, [. 4. 1. 5]) A: g = D. g; B: g = D. c. g; C: g = D. c. 2; D: g = D. c(2); Insight Through Computing E: other