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PH36010 Numerical Methods Advanced Plotting and Animation
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Advanced Plotting in MathCAD Polar PlotsPolar Plots 3D Plots3D Plots –Surface –Contour –Scatter –Bar Vector Field PlotsVector Field Plots
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Polar Plots #1 X-Y Plot wrapped around a circleX-Y Plot wrapped around a circle r=cos 2 ( )
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Polar Plots #2 r=e k r=e k
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Uses for Polar Plots Rotating MachinesRotating Machines –Stirling engine –Vibration Arctic & Antarctic systemsArctic & Antarctic systems
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3D surface plots Simple #1 Plot of data stored in arrayPlot of data stored in array Indices of array represent x-y planeIndices of array represent x-y plane Value of matrix is z valueValue of matrix is z value –Define size of matrix & indices –Determine values for x & y –Fill matrix –Plot
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3D surface plots Simple #2 Define size & indicesDefine size & indices Define Range for x & yDefine Range for x & y 2D-Gaussian2D-Gaussian Fill matrixFill matrix
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3D surface plots Simple #3
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3D surface plots Simple #4 – Lighting
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Contour Plot - from 3d plot data Format plot type -> Contour plotFormat plot type -> Contour plot
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Simple 3D plots Limitations X & Y axes scaled in indicesX & Y axes scaled in indices Suited to continuous single valued functionsSuited to continuous single valued functions More advanced 3D plots availableMore advanced 3D plots available
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3D Scatter plot Plot of individual pointsPlot of individual points Supply with 3 vectors of equal length (X,Y,Z)Supply with 3 vectors of equal length (X,Y,Z) Points plotted:Points plotted: –X 0,Y 0,Z 0 –X 1,Y 1,Z 1 –…–…–…–…
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3D scatter plot Photon Scatter in 3D
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3D surface plots Parametric Plot Plot complex surfacesPlot complex surfaces From Resource Centre Guide to 3D plottingFrom Resource Centre Guide to 3D plotting
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3D parametric plot Example - 100 2 for H X- & Y- Axes scaled in m
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Parametric Plots How to… #1 Rubber sheet N x MRubber sheet N x M Wrap sheet around surfaceWrap sheet around surface XX a,b is x-coord of point a,bXX a,b is x-coord of point a,b YY a,b is y-coord of point a,bYY a,b is y-coord of point a,b ZZ a,b is z-coord of point a,bZZ a,b is z-coord of point a,b (XX,YY,ZZ) will plot surface(XX,YY,ZZ) will plot surface
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Parametric Plots Example 1 - Gaussian Ranges defined as beforeRanges defined as before Fill XX & YY matricesFill XX & YY matrices Fill ZZ matrixFill ZZ matrix
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Parametric Plots Example 1 - Gaussian Note:Note: –Axes scaled
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A short diversion Simple Program #1 Often need to create a vector containing a range of valuesOften need to create a vector containing a range of values Create function to do this using MathCAD program stepsCreate function to do this using MathCAD program steps Use in graphics programsUse in graphics programs
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The SeriesVector() program (increment) and i (loop count) are ‘local’ to function. Function builds Result vector Returned on last line of program
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Testing the SeriesVector() function
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Parametric Plots Polar 3D #1 Create r vector 0-10 radii, 100 tepsCreate r vector 0-10 radii, 100 teps Create vector -180..180 deg, 30 stepsCreate vector -180..180 deg, 30 steps Fill X & Y vectorsFill X & Y vectors
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Paramteric Plots Polar 3D #2 Define 100 function Fill Z matrix with 100 function 100 function NB Only depends on r
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3D parametric plot Example - 100 2 for H X- & Y- Axes scaled in m
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Plot of 210 2 for H X & Y matrices as beforeX & Y matrices as before Z now depends on r,qZ now depends on r,q
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3D parametric plot Example - 210 2 for H
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Vector Field Plots #1 Arrows give strength & direction of field at each point of plot.Arrows give strength & direction of field at each point of plot. Constructed from either:Constructed from either: –Matrix of complex numbers –2 identical matrices of real numbers
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Vector Field Plots #2 From Resource Centre Example function to plotExample function to plot Gradient function of f(x,y)Gradient function of f(x,y)
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Vector Field Plot Surface Plot Vector Field Plot
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Pretty Pictures #1 From Resource Centre Chain of Tori Pyramid
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Pretty Pictures From Resource Centre Plot multiple Surfaces
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Pretty Pictures #3 Planetary Orbit 3 objects3 objects –Planet : (xe,ye,ze) –Star : (xs,ys,zs) –Orbit: (xp,yp,zp)
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Animation Principles Make output depend on FRAMEMake output depend on FRAME Tools|Animation|Record… to display dialogTools|Animation|Record… to display dialog –Fill in first & last frames –Drag cursor around area to animate –Select ‘Animate’ to go –View with AVI player –Save to disk Help|Quicksheets|Graphing and VisualizationHelp|Quicksheets|Graphing and Visualization
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Animation Hints and Tips Fix scale of graphsFix scale of graphs Watch out for:Watch out for: –Size of AVI files –Long calculation times Can test by using FRAME:=Can test by using FRAME:= –Delete afterwards Put indicator in moviePut indicator in movie
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Animation Example #1 Cannon Ball with drag
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Animation Example #2 LCR at resonance
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Animation Example #3 Heat Flow in Plate
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Animation Example #4 Planetary Orbits
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3D with lighting & shadows
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Ideas for projects Bouncing ballsBouncing balls –Gravity –Snooker Electron clouds around HElectron clouds around H Simulation of Ion ImplantationSimulation of Ion Implantation Heat flow by finite differenceHeat flow by finite difference
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