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--- gibson:teaching:spring-2016:math445:lecture:graphics3d [2016/03/29 08:47]
gibson
+++ gibson:teaching:spring-2016:math445:lecture:graphics3d [2016/03/29 09:02] (current)
gibson [Math 445 lecture 16: 3D graphics]
@@ Line 1: / Line 1: @@
-====== Math 445 lecture 16: 3D graphics ======
+====== Math 445 lecture 16: 2D, 3D graphics ======
+Some examples of plotting 2d functions $f(x,y)$ in Matlab.
 ----
@@ Line 59: / Line 60: @@
 </file>
+{{ :gibson:teaching:spring-2016:math445:lecture:twodplot.png?direct&400 |}}
+----
+==== quiver plots and the gradient===
+The function $f(x,y) = x e^{-x^2 - y^2}$ has gradient
+\begin{eqnarray*}
+\nabla f = \left( \begin{array}{c} \partial f/\partial x \\  \partial f/\partial y \end{array} \right) = \left( \begin{array}{c} (1-x^2) e^{-x^2 - y^2} \\ -2xy e^{-x^2 - y^2} \end{array} \right)
+\end{eqnarray*}
+Here's the Matlab code to make a contour plot of $f(x,y)$ with its gradient superimposed as a quiver plot.
+<file matlab plotgradient.m>
+% Plot f(x,y) = x e^(-x^2 - y^2) with contours and its gradient as arrows.
+x = linspace(-2, 2, 30);
+y = linspace(-2, 2, 30);
+[X,Y] = meshgrid(x,y);
+F = X .* exp(-X.^2 - Y.^2);  % evaluate f(x,y) on mesh
+contour(x,y,F);              % draw contour plot of f
+% let dfdy = y component of grad F = df/dy
+dfdx = (1-2*X.^2) .* exp(-X.^2 - Y.^2); % evaluate dfdx on mesh
+dfdy = -2*X.*Y .* exp(-X.^2 - Y.^2);    % evaluate dfdy on mesh
+hold on
+quiver(x,y,dfdx,dfdy);       % draw quiver plot
+xlabel('x')
+ylabel('y')
+title('f(x,y) = x e^{-x^2 - y^2} with \nabla f arrow plot')
+colorbar()
+</file>
+{{ :gibson:teaching:spring-2016:math445:lecture:quiver.png?direct&500 |}}

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