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Example of Math Graphics 数学函数图

2.5. Surface 3D

Content
  1. Classication by plot function 按制图函数分类:
  2. Classication by appliaction 按应用分类:
    1. Astronomy, chemistry, etc.
    2. plane curve 2D
    3. surface 2D
    4. space curve 3D
    5. surface 3D
      1. surface in 3D with plot3D
      2. contour in 3D with contour3D
      3. wireframe in 3D with wirefram3D
      4. complex function in 3D with complex3D
      5. a line in 3D with parametric3D
      6. a column in 3D with parametric3D
    6. surface 4D = hypersurface
    7. animation

    surface3D(x)

  1. surface3D

    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( )

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

    Animation

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

  8. Metaballs

    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. All 3D graphes are interactive, zoom by mouse wheel, and animation by clicking the spin checkbox.
  9. plot3D( )

    plot3D plot with 1 parameter and 1,2,3 variables

  10. surface in 3D space by Internet Brower plot3DIE(sin(x))
  11. surface in 3D with plot3D(sin(x))
  12. contour in 3D with contour3D(x*y)
  13. wireframe in 3D with wireframe3D(x*y)
  14. a line in 3D space with parametric3D(x*x)
    More examples in space curve in 3D
  15. a column in 3D space with parametric3D(x*x+y*y-1)
  16. implicit3D graphically solve the 3-dimensional equation
    implicit3D(x*y*z-1=0)
    More examples in Surface in 3D

  17. complex function in 3D with complex3D(sqrt(x)) for 20 graphes in one plot.
    More examples in complex function

    parametric3D or wireframe3D

    with 1 parameter for equation f(x,y,z)=0

  18. parametric3D(x*x-y*y-1)
  19. parametric3D(y-sin(x))

    with 3 parameters and 2 variables x and y or u and v

  20. parametric3D(x,y,x*y)
  21. paremetric3D( cos(x)*cos(y),cos(x)*sin(y),sin(x) ) 2参数x y立体图
  22. Twisted torus: parameter x and y
  23. Cross cap: parameter u and v
  24. wireframe3D(x,y,x*y)
  25. wireframe3D( cos(x)*cos(y),cos(x)*sin(y),sin(x) ) 2参数立体图

    with 3 parameters and 3 variables x and y and n or u and v and tau

  26. helicoid

    implicit3D

    Here are some particularly nice examples by plot function
  27. implicit3D( )

    You may find here some examples of algebraic surfaces plotted with 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
  28. x2+y2-z2=0 Quadratic cone.
  29. x2+y2+z2+2x y z=1 Cubic with 4 singular points.
  30. x4+y4+z4+5x y z=0 A quartic surface with 4 branches touching at the origine.
  31. x3+y3+z3=(x+y+z) a cubic surface with rotation.
  32. x2 y2+y2 z2+z2 x2=(x2+y2+z2-0.75) a quartic surface.
  33. Schwarz Primitive Surface cos(x)+cos(y)+cos(z) = 0
  34. Proper spherical harmonics in 3D
  35. harmonic
  36. heart
  37. sinc(x,y) in 3D graph
  38. sin(x*y) in 3D graph
  39. sin(omega * x*y) in 3D graph
  40. tori
  41. x3D
  42. complex
  43. Complex-Logarithm
  44. step function
  45. torus
  46. Umbilic torus

    It plots animation by clicking the spin checkbox.

    project3D 投影图3D for 4 graphes spin different directions

    The project3D(x) combines 4 graphes into one plot,
    surface: f(x,y,z)=0 or z=f(x,y)
    1. cut in from x-axis, spin around x-axis. 2. cut in from y-axis, spin around y-axis.
    3. cross section, cut off from x-axis, spin around x-axis. 4. cross section, cut off from y-axis, spin around y-axis.

  47. project3D
  48. x*x
  49. sin(x)
  50. cos(x)
  51. sin(x)-x
  52. x-sin(x)
  53. x**2+y**2=1
  54. (x-2)**2-(y-2)**2

    implicit3D 隐函数图3D for equation f(x,y,z,t)=0

    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.
  55. x*x-y*y-z*z-t-1 =0
  56. 4*x^2 * (x^2 + y^2 + z^2 + z) + y^2 * (y^2 + z^2 - 1 - t) Lemniscate
    More examples in Surface in 4D

    spin3D 旋转图3D for 4 graphes spin different directions

    The spin3D( ) plots spin of implicit function for equation f(x,y)=0, 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. surface of equation f(x,y,z)=0, spin around z-axis. 2. spin around y-axis.
    3. spin around x-axis. 4. positive value of a curve spins to make stereo.
  57. spin3D
  58. x*x
  59. sin(x)
  60. cos(x)
  61. sin(x)-x
  62. x-sin(x)
  63. x**2+y**2=1
  64. (x-2)**2-(y-2)**2

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

  65. 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.

  66. Bessel function of the second kind

  67. Hankel function of the first kind

  68. Hankel function of the second kind

  69. Jacobi elliptic sine

  70. Jacobi elliptic cosine

  71. Jacobi delta amplitude function

  72. Gamma function

  73. Riemann zeta function

    More examples in complex function

    Animation

    It plots animation by clicking the spin checkbox.

    the 4-dimensional object (x,y,z,t) in 3D space

  74. the 4-dimensional object (x,y,z,t) in 3D space, manually change the t value by a slider
    implicit3D(x*y*z-t)
    More examples in Quadratic hypersurfaces in 4D

    Animation

  75. Paraboloïd z=ax2+by2. One sees the surface deform with the variations of a and b.
  76. Deformation of hyperboloid x2+y2+az2=1. Vertical.
  77. Deformation of hyperboloïde x2+ay2+z2=1. Horizontal.
  78. The Moebius band.
  79. Riemann surface of two sheets crossing each other.
  80. A surface with a singular line, which resembles the precedent one but does not cross.
  81. Deformation of one into the other, for the above two surfaces. Without rotation.
  82. As above but with rotation at the same time.
  83. A plane deforming into a cylinder then back to a plane from the other direction.
  84. bianchi-pinkall-animation 花环
  85. bianchi-pinkall-animation-zoomed 花环
  86. radar 雷达
  87. FlatTorus
  88. sphere
  89. Cylinder
  90. Metaballs

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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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