YOUR MATLAB ASSIGNMENT 4

Transcription

1 YOUR MATLAB ASSIGNMENT 4 Contents GOAL: USING MATLAB TO SKETCH THE GRAPHS OF A PARAMETERIZED SURFACES IN SPACE USE THE FOLLOWING STEPS: HERE IS AN ACTUAL EXAMPLE OF A CLOSED SURFACE DRAWN PARAMETERICALLY WITH MATLAB CREATE TWO DATA VECTORS u and v DEFINE 3 ANONYMOUS FUNCTIONS OF u and v THE UPPER CONE CUT OFF AT THE BOTTOM CREATE RECTANGULAR GRID DRAW CUT-OFF UPPER CONE AT THE BOTTOM DEFINE THE FLAT CIRCULAR COVER SURFACE (CALLED AN ANNULUS) DRAW AN ANNULUS IN SAME WINDOW USING THE DOMAIN AS THE UPPER CUT OFF CONE CREATE TWO DATA VECTORS s and t for the cylinder x^2+y^2 = 1 DEFINE THE CYLINDER DRAW THE CYCLINDER IN THE SAME WINDOW AS THE TWO OTHER SURFACES DRESSING UP YOUR PLOT YOUR MATLAB PROBLEM (DUE NEXT FRIDAY, NOT THIS FRIDAY!) GOAL: USING MATLAB TO SKETCH THE GRAPHS OF A PARAMETERIZED SURFACES IN SPACE Sketch the graph of the parameterized surface S with parameterization given by USE THE FOLLOWING STEPS: create three anonymous functions of two variables u and v with handles f and g and h respectively. For example in w -(1./2)*sin(u+2*v), we have w as the handle is the anonymous function of two variables u and v. create two data vectors u and v using linspace or the colon : constructor (make sure you use the same # of points in each) create a rectangular grid [phi,theta] using meshgrid as in [phi,theta] = meshgrid(u,v) Plot the surface using surf as in surf(f(phi,theta), g(phi,theta), h(phi,theta)) Dress-up your plot by adding a title, labeling the x and y and z axes, etc. (SEE THE EXAMPLE BELOW) HERE IS AN ACTUAL EXAMPLE OF A CLOSED SURFACE DRAWN PARAMETERICALLY WITH MATLAB clear all; clc;

2 clf reset; CREATE TWO DATA VECTORS u and v u = linspace(1,2,20); v = linspace (0,2*pi,25); DEFINE 3 ANONYMOUS FUNCTIONS OF u and v THE UPPER CONE CUT OFF AT THE BOTTOM f =@(u,v)u.*cos(v); g =@(u,v)u.*sin(v); h =@(u,v)u; CREATE RECTANGULAR GRID [phi,theta] = meshgrid(u,v); DRAW CUT-OFF UPPER CONE AT THE BOTTOM surf(f(phi,theta),g(phi,theta),h(phi,theta)) hold on

3 DEFINE THE FLAT CIRCULAR COVER SURFACE (CALLED AN ANNULUS) f =@(u,v)u.*cos(v); g =@(u,v)u.*sin(v); h =@(u,v)2+0.*u; DRAW AN ANNULUS IN SAME WINDOW USING THE DOMAIN AS THE UPPER CUT OFF CONE surf(f(phi,theta),g(phi,theta),h(phi,theta))

4 CREATE TWO DATA VECTORS s and t for the cylinder x^2+y^2 = 1 s = linspace(1,2,25); t = linspace (0,2*pi,25); [phi,theta] = meshgrid(s,t); DEFINE THE CYLINDER X =@(u,v)cos(v); Y =@(u,v)sin(v); Z =@(u,v)u; DRAW THE CYCLINDER IN THE SAME WINDOW AS THE TWO OTHER SURFACES surf(x(phi,theta),y(phi,theta),z(phi,theta))

5 DRESSING UP YOUR PLOT light('position',[1 0 0],'Style','infinite'); colormap gray rotate3d on view([134,34]) axis equal square axis([ ,2]) set(gca,'xtick',[-2:1:2],'xminortick','on','fontname','times','fontweight','bold') set(gca,'ytick',[-2:1:2],'yminortick','on','fontname','times','fontweight','bold') set(gca,'ztick',[1:.5:2],'zminortick','on','fontname','times','fontweight','bold') title({'region occupied by z = sqrt(x^2 + y^2) and x^2 + y^2 = 1','for 1 <= z <= 2','by','Antony Foster'}) xlabel('x-axis','color','black','fontname','mathematica','fontweight','bold','fontsize',12) ylabel('y-axis','color','blue','fontname','mathematica','fontweight','bold','fontsize',12) zlabel('z-axis','color','red','fontname','mathematica','fontweight','bold','fontsize',12)

6 YOUR MATLAB PROBLEM (DUE NEXT FRIDAY, NOT THIS FRIDAY!) SKETCH THREE CLOSED 3-DIMENSIONAL OBJECTS IN THREE SEPARATE FIGURE WINDOW The first object you should sketch is a CLOSED RIGHT CICULAR CYLINDER with base radius R = 4 and height H = 5 tangent to both the xz and yz planes and the base of the cylinder is in the first octant. The second object you should sketch is a CLOSED RIGHT CIRCULAR LOWER CONE with base radius R = 3 and height H = 5. The circular base of your cone lies in the first octant and is tangent to both the x and y axes. The Third and last object (the easiest) you should sketch is a SPHERE of radius R = 3 together ITS SPHERICAL CAP with height H = 1 (the cap should be covering the Northpole of the sphere if we view it as the surface of the earth). Hint: All surfaces involve should be parameterized (most of the these parameterizations have been given to you in class. You should as a challenge to yourself figure out how to make matlab sketch a flat circular disc. Then position the disc at a point in space) If you need assistance (you should be able to do it on your own) the ARTINO STAFF can help you with ideas. Do not ask them to do your work for you.

7 GOOD LUCK! Published with MATLAB 7.6