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Perform the following simulation in Mathlab and provide the code used:

Plot a 2D shape which resembles an airplane, and which starts by being centered at location (0,0) (i.e., the geometric center of the points which define the shape should be (0,0)).

The plane should continuously move within a square area which is limited between -15 to 15 horizontally and -15 to 15 vertically. The airplane should never exit this 30 × 30 square area. In other words, when the shape reaches those limits, it should bounce back so that it stays within the 30 × 30 box. The shape should be moving faster horizontally than vertically, with the nose and tail being, respectively, to the left and to the right (or to the right and to the left depending on which direction it moves).

At the same time, as the airplane approaches the vertical boundaries, it should slowly rotate about its center so that its nose is always in the front as it moves.

Also, as the airplane approaches the vertical boundaries, in addition to bouncing back within the 30 × 30 box, the shape should appear to be narrower (to give the impression of a 3D motion).

You may choose the speed with which the airplane moves, and the speed with which it rotates around its center yourselves. However, the airplane should not be moving just horizontally or just vertically. Also, it should not be moving with the same speed horizontally and vertically.

Explanation / Answer

function [h] = c130(varargin) %C130 draws a simple 3D airplane loosely modelled after a Lockheed C-130. % %% c130 Syntax % % c130 % c130(x,y,z) % c130(...,'roll',RollDegrees) % c130(...,'pitch',PitchDegrees) % c130(...,'yaw',YawDegrees) % c130(...,'color',AirplaneColor) % c130(...,'fuselage',FuseLageColor) % c130(...,'wing',WingColor) % c130(...,'tailwing',TailwingColor) % c130(...,'fin',FinColor) % c130(...,'prop',PropellerColor) % c130(...,'scale',SizeScaleFactor) % c130(...,'z',ZScaleFactor) % c130(...,'linestyle','LineStyle') % c130(...,'linecolor',LineColor) % h = c130(...) % %% c130 Description % % c130 draws a 3D airplane. % % c130(x,y,z) draws an airplane centered approximately at the location % given by x,y,z, where x, y, and z must be scalar values. % % c130(...,'roll',RollDegrees) specifies roll of the aircraft in degrees % relative to the approximate center of gravity of the aircraft. % % c130(...,'pitch',PitchDegrees) specifies pitch of the aircraft in % degrees. % % c130(...,'yaw',YawDegrees) specifies yaw of the aircraft in degrees in % the global coordinate system. The xyz2rpy function may help with % determining appropriate yaw values. % % c130(...,'color',AirplaneColor) specifies a color of all surfaces of % the plane. Color may be given by Matlab color name (e.g., 'red'), % Matlab color abbreviation (e.g., 'r'), or RGB value (e.g., [1 0 0]). % The 'color' option may be paired with options for specifying colors of % specific parts of the plane. For example, c130('color','b','wing',y) % creates a blue airplane with yellow wings. Default color is gray. % % c130(...,'fuselage',FuselageColor) specifies fuselage color. % % c130(...,'wing',WingColor) specifies wing color. % % c130(...,'tailwing',TailwingColor) specifies color of horizontal % stabilizer wings at the tail of the plane. % % c130(...,'fin',FinColor) specifies color of the vertical stabilizer fin % at the tail of the plane. % % c130(...,'prop',PropellerColor) specifies propeller color. % % c130(...,'scale',SizeScaleFactor) scales dimensions of the plane by % some scalar factor. By default, c130 draws an airplane with dimensions % which approximately match the dimensions C-130 airplane in meters. If you'd % like to draw a C-130 in dimensions of feet, try c130('scale',3.281). % % c130(...,'z',ZScaleFactor) scales only vertical dimensions by some % scalar value. This may be useful if you're animating an airplane in a % coordinate system where the vertical dimension is stretched to show % relief. If your axes are not equal, consider a ZScaleFactor given by % the ratio of (xlim(2)-xlim(1))/(zlim(2)-zlim(1)). % % c130(...,'linestyle','LineStyle') specifies style of the lines % connecting surface vertices. Default is '-', but can be set to any % valid linestyle, including 'none' to show a smooth surface. % % c130(...,'linecolor',LineColor) specifies edge color of lines % connecting surface verticies. Default line color is black. % % h = c130(...) returns handles of the 13 surface objects created by % c130. Handles correspond to the following: % % * h(1): main fuselage. % * h(2): nose. % * h(3): tail section of fuselage. % * h(4): top side of main wing. % * h(5): under side of main wing. % * h(6): top side of tail wing. % * h(7): under side of tail wing. % * h(8): right side of fin. % * h(9): left side of fin. % * h(10:13): propellers. % %% Author Info % Chad A. Greene of the University of Texas Institute for Geophysics (UTIG) % wrote this on Saturday, September 27, 2014. Feel free to visit Chad on % over at http://www.chadagreene.com. % % See also xyz2rpy %% Set Defaults: wingColor = .5*[1 1 1]; fusColor = .5*[1 1 1]; tailWingColor = .5*[1 1 1]; finColor = .5*[1 1 1]; propColor = .5*[1 1 1]; edgeColor = 'k'; linestyle = '-'; scale = 1; zscale = 1; setroll = false; setpitch = false; setyaw = false; %% Parse Inputs: if nargin>2 && isnumeric(varargin{1}) && isnumeric(varargin{2}) && isnumeric(varargin{3}) x = varargin{1}; y = varargin{2}; z = varargin{3}; assert(isscalar(x)==1,'c130 input x must be a scalar.') assert(isscalar(y)==1,'c130 input y must be a scalar.') assert(isscalar(z)==1,'c130 input z must be a scalar.') else x = 0; y = 0; z = 0; end tmp = strncmpi(varargin,'col',3); if any(tmp) wingColor = varargin{find(tmp)+1}; fusColor = varargin{find(tmp)+1}; tailWingColor = varargin{find(tmp)+1}; finColor = varargin{find(tmp)+1}; end tmp = strncmpi(varargin,'fus',3)|strcmpi(varargin,'body'); if any(tmp) fusColor = varargin{find(tmp)+1}; end tmp = strncmpi(varargin,'wing',4); if any(tmp) wingColor = varargin{find(tmp)+1}; end tmp = strncmpi(varargin,'tail',4); if any(tmp) tailWingColor = varargin{find(tmp)+1}; end tmp = strncmpi(varargin,'fin',3); if any(tmp) finColor = varargin{find(tmp)+1}; end tmp = strncmpi(varargin,'prop',4); if any(tmp) propColor = varargin{find(tmp)+1}; end tmp = strcmpi(varargin,'scale'); if any(tmp) scale = varargin{find(tmp)+1}; assert(isscalar(scale)==1,'It may seem redundant, but the scale must be a scalar.') end tmp = strncmpi(varargin,'z',1); if any(tmp) zscale = varargin{find(tmp)+1}; assert(isscalar(zscale)==1,'It may seem redundant, but the z scale must be a scalar.') end tmp = strncmpi(varargin,'lines',5); if any(tmp) linestyle = varargin{find(tmp)+1}; assert(isnumeric(linestyle)==0,'LineStyle cannot be numeric.') end tmp = strncmpi(varargin,'linecol',7)|strncmpi(varargin,'edgecol',3); if any(tmp) edgeColor = varargin{find(tmp)+1}; end tmp = strcmpi(varargin,'roll')|strcmpi(varargin,'biscuits'); if any(tmp) setroll = true; roll = varargin{find(tmp)+1}; assert(isscalar(roll)==1,'Roll must be a scalar value in degrees.') end tmp = strcmpi(varargin,'pitch'); if any(tmp) setpitch = true; pitch = varargin{find(tmp)+1}; assert(isscalar(pitch)==1,'Pitch must be a scalar value in degrees.') end tmp = strcmpi(varargin,'yaw')|strcmpi(varargin,'yall'); % to accommodate our southern friends if any(tmp) setyaw = true; yaw = varargin{find(tmp)+1}; assert(isscalar(yaw)==1,'Yaw must be a scalar value in degrees.') end %% Dimensions: wingspan = 40*scale; tailwingspan = 16*scale; tailLength = 12.5*scale; fusLength = 13*scale; fusRadius = 2.2*scale; wingWidth = 5*scale; % changing wingWidth will affect several dimensions % Center the dimensions: y = y+9*wingWidth/5; z = z+fusRadius; %% Determine if a figure is already open: initialHoldState = 0; SetView = isempty(get(gcf,'CurrentAxes')); if ~SetView if ishold initialHoldState = 1; % documents initial hold state to reset it later else cla % if hold is on initially, clear the axes and make a new plot SetView = true; end end %% Draw surfaces: % Fuselage: [xcf,zcf,ycf] = cylinder(fusRadius); h(1) = surface(xcf+x,y-ycf*fusLength,z+zcf*zscale,... 'facecolor',fusColor,'linestyle',linestyle,... 'edgecolor',edgeColor); if ~initialHoldState hold on end % Nose: [xcn,zcn,ycn] = cylinder(fusRadius.*([1 .95 .9 .8 .7 .5 .5 .5 .5]).*(cos(linspace(0,pi/2,9)).^.2)); zcn(6:end,:) = zcn(6:end,:)-fusRadius/5; ycn = -ycn.*.7*wingWidth; h(2) = surface(x+xcn,y-ycn,z+zcn*zscale,... 'facecolor',fusColor,'linestyle',linestyle,... 'edgecolor',edgeColor); % Tail x1 = xcf(1,:); x2 = .8*x1;% zeros(size(x1)); y1 = fusLength*ones(size(x1)); y2 = y1+tailLength; z1 = zcf(1,:); z2 = fusRadius*ones(size(z1)); h(3) = surface(x+[x1;x2],y-[y1;y2],z+[z1;z2]*zscale,... 'facecolor',fusColor,'linestyle',linestyle,... 'edgecolor',edgeColor); % Wings: xw1 = -linspace(-wingspan/2,wingspan/2,10); yw1 = 1.4*wingWidth + abs(xw1)/100; yw2 = zeros(size(xw1))+1.4*wingWidth + wingWidth/3; yw3 = yw1 + wingWidth-abs(xw1)/20; zw1 = .85*fusRadius*ones(size(xw1)); h(4) = surface(x+[.99*xw1;xw1;.97*xw1],y-[yw1;yw2;yw3],... z+[zw1;zw1+.15*fusRadius;zw1]*zscale,'facecolor',wingColor,... 'linestyle',linestyle,'edgecolor',edgeColor); h(5) = surface(x+[.99*xw1;xw1;.97*xw1],y-[yw1;yw2;yw3],... z+[zw1;zw1;zw1]*zscale,'facecolor',wingColor,... 'linestyle',linestyle,'edgecolor',edgeColor); % tail wing: xtw1 = -linspace(-tailwingspan/2,tailwingspan/2,5); xtw = [xtw1;xtw1;xtw1]; ytw1 = fusLength+.7*tailLength+ abs(xtw1)/10; ytw2 = zeros(size(xtw1))+ fusLength+.88*tailLength; ytw3 = ytw2+.12*tailLength-abs(xtw1)/10; ytw = [ytw1; ytw2;ytw3]; ztw1 = .9*fusRadius*ones(size(xtw1)); h(6) = surface(x+xtw,y-ytw,z+[ztw1;ztw1+.05*fusRadius;ztw1]*zscale,... 'facecolor',tailWingColor,'linestyle',linestyle,... 'edgecolor',edgeColor); h(7) = surface(x+xtw,y-ytw,z+[ztw1;ztw1;ztw1]*zscale,... 'facecolor',tailWingColor,'linestyle',linestyle,... 'edgecolor',edgeColor); % Fin: yts = fusLength+tailLength*[1 .88 .6]; yts = [yts;yts]; zts = fusRadius*[1 1 1]; zts(2,:)= zts+1.1*wingWidth*[1 1 0]; xts = [0 fusRadius/20 0;0 fusRadius/40 0]; h(8) = surface(x+xts,y-yts,z+zts*zscale,... 'facecolor',finColor,'linestyle',linestyle,... 'edgecolor',edgeColor); h(9) = surface(x-xts,y-yts,z+zts*zscale,... 'facecolor',finColor,'linestyle',linestyle,... 'edgecolor',edgeColor); % Propellers: xp = .4*wingWidth*sin(0:.2:2*pi); zp = .4*wingWidth*cos(0:.2:2*pi)+.4*wingWidth; yp = zeros(size(xp))-1.2*wingWidth; h(10) = patch(x+xp-2.16*wingWidth,y+yp,z+zp*zscale,propColor); h(11) = patch(x+xp+2.16*wingWidth,y+yp,z+zp*zscale,propColor); h(12) = patch(x+xp-1.2*wingWidth,y+yp,z+zp*zscale,propColor); h(13) = patch(x+xp+1.2*wingWidth,y+yp,z+zp*zscale,propColor); set(h(10:13),'facealpha',.2,'edgealpha',.5) %% Set Roll, Pitch, and Yaw: if setroll rotate(h,[0 1 0],roll,[x y z]); end if setpitch rotate(h,[1 0 0],pitch,[x y z]); end if setyaw rotate(h,[0 0 1],yaw,[x y z]); end %% Set view if SetView view([140 30]); axis tight equal lighting gouraud camlight else axis auto end %% Clean up: % Return axes to initial hold state if ~initialHoldState hold off end % Discard surface handles if they're unwanted: if nargout==0 clear h end end

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