# Animated drawing

### Examples for demonstration

Here you have a list of curves and surfaces plotted with animation. You may either see them directly, or load them into the menu and play with them (i.e. change parameters and options).
1. A plane curve which is progressively drawn. (Cycloid)
Show it   Load its equations the menu
2. The Cycloid is the orbit of a point on a circle rolling along a straight line. Here you can see how this is done precisely, with multiple curve plotting.
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3. By the same principle, the astroid (cos^3(t),sin^3(t)) is the orbit of a point on a circle of radius 1/4 rolling inside a fixed circle of radius 1.
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4. We have also the astroid with 3 arcs.
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5. Zooming effect on the curve sin(1/x).
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6. A moving tangent along a plane parametric curve (cardioid).
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7. The moving tangent along the astroid has a special property: the segment of the tangent cut out by the coordinate axes is of constant length.
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8. How an ellipse is drawn by a point on a segment of fixed length with two extremities on the x and y axes respectively.
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9. An animation which illustrates the functions sin and cos as vertical and horizontal positions of a moving point on a circle.
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10. Rotating and growing trefoil.
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11. A space cubic curve. Most simple, but only its movement shows what it is about.
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12. A Lissajous figure with rotating phase.
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13. The above Lissajous figure is a projection of this space curve. (To see how the projection works, load this formula into the menu and set vertical viewing angle to 0.)
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14. Another space curve, a little bit more complicated: hyperbolic spiral.
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15. Paraboloïd z=ax2+by2. One sees the surface deform with the variations of a and b.
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16. Deformation of hyperboloid x2+y2+az2=1. Vertical.
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17. Deformation of hyperboloïde x2+ay2+z2=1. Horizontal.
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18. The Moebius band.
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19. Riemann surface of two sheets crossing each other.
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20. A surface with a singular line, which resembles the precedent one but does not cross.
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21. Deformation of one into the other, for the above two surfaces. Without rotation.
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22. As above but with rotation at the same time.
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23. A plane deforming into a cylinder then back to a plane from the other direction.
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If you have produced a particularly interesting plot, please let me know (with descriptions, formulas et options). I might include it into this demo page (of course with credit to you).

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• Description: plot zooming, deforming and rotating curves and surfaces. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
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