gibson:teaching:fall-2014:math445:lecture16-diary
====== Differences ====== This shows you the differences between two versions of the page.
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gibson:teaching:fall-2014:math445:lecture16-diary [2014/11/18 07:23] gibson |
gibson:teaching:fall-2014:math445:lecture16-diary [2014/11/18 07:25] (current) gibson [surf, surfc] |
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| * axis (equal, tight) | * axis (equal, tight) | ||
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| - | ====== meshgrid: ====== | + | ===== meshgrid: ===== |
| The ''meshgrid'' function is essential for Matlab's 3D graphics. Meshgrid creates 2D arrays of x,y data covering the x,y, plane, over which a function can be evaluated and graphed. Example: | The ''meshgrid'' function is essential for Matlab's 3D graphics. Meshgrid creates 2D arrays of x,y data covering the x,y, plane, over which a function can be evaluated and graphed. Example: | ||
| Line 48: | Line 48: | ||
| It is conventional to use capital letters (X,Y) for the matrix output of meshgrid from small letter (x,y) vector inputs. Observe how the output matrices X varies left to right, along the x axis, and Y varies up and down, along the y axis. Together they provide x,y, coordinates for a grid of points on the x,y plane in the region $-2 \leq x \leq 2$, $-3 \leq y \leq 3$. | It is conventional to use capital letters (X,Y) for the matrix output of meshgrid from small letter (x,y) vector inputs. Observe how the output matrices X varies left to right, along the x axis, and Y varies up and down, along the y axis. Together they provide x,y, coordinates for a grid of points on the x,y plane in the region $-2 \leq x \leq 2$, $-3 \leq y \leq 3$. | ||
| - | We can then evaluate a function %z = f(x,y)$ over that 2D array via elementwise matrix operations. For example, this Matlab code would evaluate %z = f(x,y) = x^2 + y^2$ | + | We can then evaluate a function $z = f(x,y)$ over that 2D array via elementwise matrix operations. For example, this Matlab code would evaluate $z = f(x,y) = x^2 + y^2$ |
| <code matlab> | <code matlab> | ||
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| The previous plots were all looking straight down at the (x,y) plane, with the value of z = f(x,y) encoded as a color. The ''surf'' function will plot z = f(x,y) in 3D, as a surface of height z over the (x,y) plane. | The previous plots were all looking straight down at the (x,y) plane, with the value of z = f(x,y) encoded as a color. The ''surf'' function will plot z = f(x,y) in 3D, as a surface of height z over the (x,y) plane. | ||
| + | <code matlab> | ||
| surf(X,Y,Z) % draw z=f(x,y) as a surface over x,y | surf(X,Y,Z) % draw z=f(x,y) as a surface over x,y | ||
| xlabel('x'); ylabel('y'); zlabel('z') | xlabel('x'); ylabel('y'); zlabel('z') | ||
| axis equal; axis tight | axis equal; axis tight | ||
| + | </code> | ||
| It's also possible to draw more complicated surfaces (surfaces that are not simple graphs of the form | It's also possible to draw more complicated surfaces (surfaces that are not simple graphs of the form | ||
| Line 116: | Line 118: | ||
| - | % quiver plot | ||
| - | % used to show vector fields | ||
| - | load y.asc | ||
| - | load x.asc | ||
| - | load vx.asc | ||
| - | load vy.asc | ||
| - | clf() | ||
| - | quiver(x,y,vx,vy); | ||
| - | axis equal | ||
| - | axis tight | ||
| - | xlabel('x'); ylabel('y'); | ||
| - | title('vector field vx,vy over plane x,y') | ||
| - | |||
| - | |||
| - | % subplots | ||
| - | % make an array of plots within a figure window | ||
| - | clf() | ||
| - | subplot(2,2,1) % 1st subplot in 2 x 2 array | ||
| - | quiver(x,y,vx,vy); | ||
| - | axis equal | ||
| - | axis tight | ||
| - | subplot(2,2,2) % 2nd subplot in 2 x 2 array | ||
| - | surfc(X,Y,Z,C); axis equal | ||
| - | subplot(2,2,3) % 2nd subplot in 2 x 2 array | ||
| - | surf(X,Y,Z,Z); axis equal | ||
| - | subplot(2,2,4) % 4th | ||
| - | x = linspace(0,pi,20); | ||
gibson/teaching/fall-2014/math445/lecture16-diary.1416324207.txt.gz · Last modified: 2014/11/18 07:23 by gibson
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