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PH36010 Numerical Methods

PH36010 Numerical Methods. Advanced Plotting and Animation. Advanced Plotting in MathCAD. Polar Plots 3D Plots Surface Contour Scatter Bar Vector Field Plots. Polar Plots #1. X-Y Plot wrapped around a circle. r=cos 2 ( q ). Polar Plots #2. r=e k q. Uses for Polar Plots.

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PH36010 Numerical Methods

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  1. PH36010 Numerical Methods Advanced Plotting and Animation

  2. Advanced Plotting in MathCAD • Polar Plots • 3D Plots • Surface • Contour • Scatter • Bar • Vector Field Plots

  3. Polar Plots #1 • X-Y Plot wrapped around a circle r=cos2(q)

  4. Polar Plots #2 • r=ekq

  5. Uses for Polar Plots • Rotating Machines • Stirling engine • Vibration • Arctic & Antarctic systems

  6. 3D surface plotsSimple #1 • Plot of data stored in array • Indices of array represent x-y plane • Value of matrix is z value • Define size of matrix & indices • Determine values for x & y • Fill matrix • Plot

  7. 3D surface plotsSimple #2 • Define size & indices • Define Range for x & y • 2D-Gaussian • Fill matrix

  8. 3D surface plotsSimple #3

  9. 3D surface plotsSimple #4 – Lighting

  10. Contour Plot- from 3d plot data • Format plot type -> Contour plot

  11. Simple 3D plotsLimitations • X & Y axes scaled in indices • Suited to continuous single valued functions • More advanced 3D plots available

  12. 3D Scatter plot • Plot of individual points • Supply with 3 vectors of equal length (X,Y,Z) • Points plotted: • X0,Y0,Z0 • X1,Y1,Z1 • …

  13. 3D scatter plotPhoton Scatter in 3D

  14. 3D surface plotsParametric Plot • Plot complex surfaces • From Resource Centre Guide to 3D plotting

  15. 3D parametric plotExample - 1002 for H X- & Y-Axes scaled in m

  16. Parametric PlotsHow to… #1 • Rubber sheet N x M • Wrap sheet around surface • XXa,b is x-coord of point a,b • YYa,b is y-coord of point a,b • ZZa,b is z-coord of point a,b • (XX,YY,ZZ) will plot surface

  17. Parametric PlotsExample 1 - Gaussian • Ranges defined as before • Fill XX & YY matrices • Fill ZZ matrix

  18. Parametric PlotsExample 1 - Gaussian • Note: • Axes scaled

  19. The SeriesVector()program D (increment) and i (loop count) are ‘local’ to function. Function builds Result vector Returned on last line of program

  20. Parametric PlotsPolar 3D #1 • Create r vector0-10 radii, 100 teps • Create q vector-180..180 deg, 30 steps • Fill X & Y vectors

  21. Paramteric PlotsPolar 3D #2 Define 100 function Fill Z matrix with 100 function NB Only depends on r

  22. 3D parametric plotExample - 1002 for H X- & Y-Axes scaled in m

  23. Plot of 2102 for H • X & Y matrices as before • Z now depends on r,q

  24. 3D parametric plotExample - 2102 for H

  25. Pretty Pictures From Resource Centre Plot multiple Surfaces

  26. Pretty Pictures #3 Planetary Orbit • 3 objects • Planet : (xe,ye,ze) • Star : (xs,ys,zs) • Orbit: (xp,yp,zp)

  27. Animation Principles • Make output depend on FRAME • Tools|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 Visualization

  28. AnimationHints and Tips • Fix scale of graphs • Watch out for: • Size of AVI files • Long calculation times • Can test by usingFRAME:= • Delete afterwards • Put indicator in movie

  29. Animation Example #1 Cannon Ball with drag

  30. Animation Example #2LCR at resonance

  31. Animation Example #3Heat Flow in Plate

  32. Animation Example #4Planetary Orbits

  33. 3D with lighting & shadows

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