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Example of Math Graphics 数学函数图

2.5. Surface 3D

Content

    3D surface

  1. graph 3D plotted with graph3D

    surface3D(x)

  2. surface3D
    Please refresh this webpage to show different graphics, click the "Parametric Surfaces" to enlarge, click the "equation" to show 200 equations for graphics.


  3. solar 3D 互动太阳系 solar system 编辑 edit


    正弦函数 sin(x)


    园锥 cone


  4. rose 玫瑰花 编辑 edit


    love u 我爱你 编辑 edit


    sea 可以升降的海水 编辑 edit

  5. solar 3D 互动太阳系
  6. galaxy 3D 互动星系
  7. bianchi-pinkall-animation
  8. bianchi-pinkall-animation zoomed
  9. Metaballs

    function3D 函数3D 立体图

    The function3D( ) plots a function in 3D space by Internet Browser IE
  10. function3D( ) - function3D(x*y) - function3D(x*x, sin(x)) two surfaces overlap

    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.

  11. plot3D( 2*sin(x)*sin(y) )

    spin3D( sin(x) )

    complex3D( sin(x) )

  12. implicit3D( cos(x)+cos(y)+cos(z)=0 )
    余弦

    wireframe3D( cos(x)*cos(y),cos(x)*sin(y),sin(x) )
    2参数立体图

    paremetric3D( cos(x)*cos(y),cos(x)*sin(y),sin(x) )
    2参数x y立体图

  13. plot3D( )

    plot3D plot with 1,2,3 variables

  14. Proper spherical harmonics in 3D
  15. harmonic
  16. heart
  17. sinc(x,y) in 3D graph
  18. sin(x*y) in 3D graph
  19. sin(omega * x*y) in 3D graph
  20. tori
  21. complex
  22. Complex-Logarithm
  23. step function
  24. torus
  25. 3 spheres
  26. 27 cubes
  27. x3D

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

  29. surface in 3D with plot3D(sin(x))
  30. contour in 3D with contour3D(x*y)
  31. wireframe in 3D with wireframe3D(x*y)
  32. a line in 3D space with parametric3D(x*x)
    More examples in space curve in 3D
  33. a column in 3D space with parametric3D(x*x+y*y-1)
  34. implicit3D graphically solve the 3-dimensional equation
    implicit3D(x*y*z-1=0)

    parametric3D

    1 equation f(x,y,z)=0

  35. parametric3D(x*x-y*y-1)
  36. parametric3D(y-sin(x))

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

  37. Umbilic torus
  38. parametric3D(x,y,x*y)
  39. paremetric3D( cos(x)*cos(y),cos(x)*sin(y),sin(x)*y ) 2参数x y立体图
  40. Twisted torus: parameter x and y
  41. Cross cap: parameter u and v
  42. Parametric Surfaces 25 parametric equations
  43. Parametric Surfaces 100 parametric equations

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

  44. helicoid
  45. parametric3D( sinh(u)*sin(v),sinh(u)*cos(v),10*n*v ) change n

    wireframe3D

  46. wireframe3D(x,y,x*y)
  47. wireframe3D( cos(x)*cos(y),cos(x)*sin(y),sin(x) ) 2参数立体图

    implicit3D

    Here are some particularly nice examples by plot function
  48. 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
  49. x2+y2-z2=0 Quadratic cone.
  50. x2+y2+z2+2x y z=1 Cubic with 4 singular points.
  51. x4+y4+z4+5x y z=0 A quartic surface with 4 branches touching at the origine.
  52. x3+y3+z3=(x+y+z) a cubic surface with rotation.
  53. x2 y2+y2 z2+z2 x2=(x2+y2+z2-0.75) a quartic surface.
  54. cos(x)+cos(y)+cos(z) = 0 Schwarz Primitive Surface

    It plots animation by clicking the spin checkbox.

    section3D for 4 graphes spin different directions

    The section3D(x) combines 4 graphes into one plot,
    surface: z=f(x,y) or f(x,y,z)=0
    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.

  55. section3D
  56. x*x
  57. sin(x)
  58. cos(x)
  59. sin(x)-x
  60. x-sin(x)
  61. x**2+y**2=1
  62. (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.
  63. x*x-y*y-z*z-t-1 =0
  64. 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 x-axis. 2. spin around y-axis.
    3. spin around z-axis. 4. positive value of a curve spins around z-axis to make stereo.
  65. spin3D
  66. x*x
  67. sin(x)
  68. cos(x)
  69. sin(x)-x
  70. x-sin(x)
  71. x**2+y**2=1
  72. (x-2)**2-(y-2)**2

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

  73. 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.

  74. Bessel function of the first kind
  75. Bessel function of the second kind
  76. Hankel function of the first kind
  77. Hankel function of the second kind
  78. Jacobi elliptic sine
  79. Jacobi elliptic cosine
  80. Jacobi delta amplitude function
  81. Gamma function
  82. Riemann zeta function

    More examples in complex function

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

  83. 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

    It plots animation by clicking the spin checkbox.
  84. Paraboloïd z=ax2+by2. One sees the surface deform with the variations of a and b.
  85. Deformation of hyperboloid x2+y2+az2=1. Vertical.
  86. Deformation of hyperboloïde x2+ay2+z2=1. Horizontal.
  87. The Moebius band.
  88. Riemann surface of two sheets crossing each other.
  89. A surface with a singular line, which resembles the precedent one but does not cross.
  90. Deformation of one into the other, for the above two surfaces. Without rotation.
  91. As above but with rotation at the same time.
  92. A plane deforming into a cylinder then back to a plane from the other direction.
  93. A plane deforming into a cylinder then back to a plane from the other direction.
  94. bianchi-pinkall-animation 花环
  95. bianchi-pinkall-animation-zoomed 花环
  96. radar 雷达
  97. FlatTorus
  98. sphere
  99. Cylinder
  100. Metaballs
  101. Lorenz Attractor

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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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