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Example of Math Graphics 数学函数图 制图法

3. Surface in 3D

Content
  1. plane curve in 2D
  2. space curve in 3D
  3. surface in 3D
  4. surface in 4D = hypersurface

plot3DIE 制图3DIE 立体图IE

The plot3DIE( ) plots a function, parametric function in 3D graph.

Here are some particularly nice examples by plot function plot3DIE( )

  1. plot3DIE( )
  2. plot3DIE(x*y)
  3. plot3DIE(x*x, sin(x)) two surfaces overlap

    Animation

  4. solar in 3D 互动太阳系
  5. bianchi-pinkall-animation
  6. bianchi-pinkall-animation zoomed

    The following plot functions did not work on Microsoft IE and QQ browsers. Please use Google Chrome browser.

    plot3D(x*y), contour3D(x*y), wireframe3D(x*y), implicit3D(x*y*z), complex3D(x), parametric3D(t,t,t), parametric3Dxy(x,y,x*y), wireframe3Dxy(x,y,x*y), spin3D(x)
    立体图, 立体外形图, 立体线框图, 立体隐函数图, 复数图, 立体参数图t, 立体参数图xy, 立体线框图xy, 旋转图3D

    Notice that Microsoft Internet Explorer IE did not support svg, so IE cannot show following graph, please use other browrer.

    plot3D 制图3D

    The plot3D( ) plots a function, implicit function, parametric function in 3D graph. The figure can be rotated by clicking and dragging with a mouse or swiping on a touch device, as well as zoomed in or out with a mouse wheel or pinching on a touch device.

    Here are some particularly nice examples by plot function

  7. plot3D( )

    You may find here some examples of algebraic surfaces plotted with plot3D and implicit3D.

    If you click on a small image, you will have the menu of the plotter with the equation of the surfaces already loaded. Which will allow you to plot a bigger image of the surface, while playing with the parameters (colors, viewing angles, zoom, spin, etc). All 3D graphes are interactive, zoom by mouse wheel, and animation by clicking the spin checkbox.

    #DemoEquationDescription
  8. x2+y2-z2=0 Quadratic cone.
  9. x2+y2+z2+2x y z=1 Cubic with 4 singular points.
  10. x4+y4+z4+5x y z=0 A quartic surface with 4 branches touching at the origine.
  11. x3+y3+z3=(x+y+z) a cubic surface with rotation.
  12. x2 y2+y2 z2+z2 x2=(x2+y2+z2-0.75) a quartic surface.
  13. Paraboloïd z=ax2+by2. One sees the surface deform with the variations of a and b.
  14. Deformation of hyperboloid x2+y2+az2=1. Vertical.
  15. Deformation of hyperboloïde x2+ay2+z2=1. Horizontal.
  16. The Moebius band.
  17. Riemann surface of two sheets crossing each other.
  18. A surface with a singular line, which resembles the precedent one but does not cross.
  19. Deformation of one into the other, for the above two surfaces. Without rotation.
  20. As above but with rotation at the same time.
  21. A plane deforming into a cylinder then back to a plane from the other direction.
  22. Proper spherical harmonics in 3D
  23. harmonic
  24. heart
  25. helicoid
  26. sinc(x,y) in 3D graph
  27. sin(x*y) in 3D graph
  28. sin(omega * x*y) in 3D graph
  29. tori
  30. x3D
  31. Schwarz Primitive Surface cos(x)+cos(y)+cos(z) = 0
  32. complex
  33. Complex-Logarithm
  34. step function
  35. torus

    Animation

    It plots animation by clicking the spin checkbox.

  36. radar 雷达
  37. tori 花环

    implicit3D 隐函数图3D for equation plot

    The implicit3D( ) can plot a 4-dimensional (x,y,z,t) object in 3D space. You manually change the t value by slider. e.g.
  38. x*x-y*y-z*z-t-1 =0
    More examples in Surface in 4D

    spin3D 旋转图3D for 4 graphes in one plot

    The spin3D( ) plots spin of a function, implicit function, parametric function, a spacial curve, and its inverse in 3D graph. It combines 4 graphes ( surface in 3D, space curve, plane curve and a curve spins to make stereo ) into one plot:
    1. a surface in space. 2. a curve in space. 3. cross-section. 4. positive value of a curve spins to make stereo.
  39. spin3D
  40. x*x
  41. sin(x)
  42. cos(x)
  43. sin(x*x)
  44. cos(x*x)
  45. x^2+y^2=1
  46. x^2-y^2-1

    complex3D 复变函数图3D for 20 graphes in one plot

  47. complex3D( ) plots a function on the complex plane and space, for 20 graphes in one plot.

    In order to plot complex function, you should convert it to complex by tocomplex(x) before plot. Use complex(x) to set variable for complex variable in real value, and Use complex(0,x) to set variable for complex variable in imag value. Get real part by re() and imag part by im(). e.g. convert log(x) to re(log(complex(x))).

    Here are some particularly nice examples by plot function complex3D( ) that show real and imaginary parts of complex function including special functions on complex axes and plane.

  48. Bessel function of the second kind

  49. Hankel function of the first kind

  50. Hankel function of the second kind

  51. Jacobi elliptic sine

  52. Jacobi elliptic cosine

  53. Jacobi delta amplitude function

  54. Gamma function

  55. Riemann zeta function

    More examples in complex function

    Animation

    It plots animation by clicking the spin checkbox.

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Reference 参阅

  • example 例题
  • function graph 制图
  • graphics 制图法
  • animation 动画 
    See Also

    
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