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Example of Math Graphics 数学函数图 制图法

3. Surface in 3D

plot3DIE 制图3DIE

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

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

plot3DIE(x*y), 立体图IE,

Animation

  • bianchi-pinkall-animation
  • 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.

    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
    x2+y2-z2=0 Quadratic cone.
    x2+y2+z2+2x y z=1 Cubic with 4 singular points.
    x4+y4+z4+5x y z=0 A quartic surface with 4 branches touching at the origine.
    x3+y3+z3=(x+y+z) a cubic surface with rotation.
    x2 y2+y2 z2+z2 x2=(x2+y2+z2-0.75) a quartic surface.
    1. Paraboloïd z=ax2+by2. One sees the surface deform with the variations of a and b.
    2. Deformation of hyperboloid x2+y2+az2=1. Vertical.
    3. Deformation of hyperboloïde x2+ay2+z2=1. Horizontal.
    4. The Moebius band.
    5. Riemann surface of two sheets crossing each other.
    6. A surface with a singular line, which resembles the precedent one but does not cross.
    7. Deformation of one into the other, for the above two surfaces. Without rotation.
    8. As above but with rotation at the same time.
    9. A plane deforming into a cylinder then back to a plane from the other direction.

    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 plot3D( )

    Proper spherical harmonics in 3D

    harmonic

    heart

    helicoid

    sinc(x,y) in 3D graph

    sin(x*y) in 3D graph

    sin(omega * x*y) in 3D graph

    tori

    x3D

    Schwarz Primitive Surface cos(x)+cos(y)+cos(z) = 0

    complex

    Complex-Logarithm

    step function

    torus

    Animation

    It plots animation by clicking the spin checkbox.

    complex3D 复变函数图3D

    The complex3D( ) plots a function on the complex plane and space.

    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.

    Bessel function of the second kind

    Hankel function of the first kind

    Hankel function of the second kind

    Jacobi elliptic sine

    Jacobi elliptic cosine

    Jacobi delta amplitude function

    Gamma function

    Riemann zeta function

    complex function

    spin3D 旋转图3D

    The spin3D( ) plots spin of a function, implicit function, parametric function, a spacial curve, and its inverse in 3D graph.

    1. a plane in space. 2. a curve in space. 3. cross-section. 4. positive value of a curve spins to make stereo.

  • x^2+y^2=1

    implicit3D 隐函数图3D

    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.
  • x*x-y*y-z*z-t-1

    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

    d0.5ydx0.5=sin(x-1)⋅sin(y-1) == ? d0.5ydx0.5-cosh(y)-sinh(y)=0 == ? d1.6ydx1.6-∫y(x)(dx)0.8-y-exp(x)=0 == ? ∫y(x)(dx)0.5-y-exp(x)=0 == ? d0.5ydx0.5-exp(y)⋅x=0 == ? d0.5ydx0.5-exp(y)⋅y=0 == ? d0.5ydx0.5=cos(x)x⋅y == ? y⋅dy0.5dx0.5-√x-1=0 == ? d1.2ydx1.2-2d0.6ydx0.6+y-exp(x)=0 == ? d0.5ydx0.5=cos(y)⋅exp(x)⋅x == ? d1.6ydx1.6-2d0.8ydx0.8+y-exp(x)=0 == ? d0.5ydx0.5-exp(y)⋅√x=0 == ? d1.6ydx1.6-3d0.8ydx0.8+2y-exp(x)=0 == ? d0.5ydx0.5 +log(y-1)-exp(x)-x=0 == ? d0.5ydx0.5-exp(y)⋅sin(x)=0 == ? d0.5ydx0.5=y⋅sin(x)x == ? y(0.5)(x)-4exp(x)⋅y-exp(x)=0 == ? dy0.5dx0.5=1x-y == ? dydx-d0.5ydx0.5 - y - exp(x)=0 == ? dydx-exp(y-1)-x-x2=0 == ? d1.2ydx1.2-3dy0.6dx0.6+2y-exp(x)=0 == ? dydx-d0.5ydx0.5-y-1=0 == ? d0.5ydx0.5-cos(y)⋅sin(x)=0 == ? d1.6ydx1.6-d0.8ydx0.8-y-exp(4x)=0 == ? dydx-exp(y-1)-exp(x)=0 == ? dydx-2d0.5ydx0.5-y-exp(x)=0 == ? d1.6ydx1.6-d0.8ydx0.8-y-exp(x)=0 == ? d0.5ydx0.5-e4x-y=0 == ? y(0.5)(x)-exp(x)⋅y-exp(x)=0 == ? y(0.5)(x)-exp(x)⋅y-4exp(x)=0 == ? dydx-3d0.5ydx0.5+2y-exp(x)=0 == ? y⋅d0.5ydx0.5-√x-1=0 == ? y(1)(x)-exp(y-1)-x=0 == ? d1.6ydx1.6-d0.8ydx0.8-2y-exp(x)=0 == ? d1.6ydx1.6-d0.8ydx0.8-y-exp(4x)=0 == ? d0.5ydx0.5-log(y-1)-exp(x)+x=0 == ? dydx+asin(y-1)-cos(x)-x=0 == ? d1.6ydx1.6-3d0.8ydx0.8+2y-exp(x)=0 == ? dydx-√y-1-x-1=0 == ? dydx-exp(y-1)-exp(x)=0 == ? dydx +asinh(y-1)-cosh(x)-x =0 == ? (d12ydx12)2-3y⋅dy0.5dx0.5+2y2=0 == ? dy0.5dx0.5=cos(x)⋅cos(y-1) == ? d0.5ydx0.5+log(y-1)-exp(x)-x=0 == ? dy0.5dx0.5=sin(x-1)⋅exp(y-1) == ? y⋅d2ydx2-(dydx)2+1=0 == ? y(1)(x)-exp(y-1)-log(x)=0 == ? d2ydx2⋅exp(x)-exp(y-1)=0 == ? d1.6ydx1.6-2d0.8ydx0.8-y-exp(x)=0 == ? d1.6ydx1.6-2d0.8ydx0.8+y-exp(x)=0 == ? dydx-3d0.5ydx0.5+2y-exp(x)=0 == ? y(0.5)(x)-x⋅y-x=0 == ? y⋅dy3dx3-x3-3x2-3x-1=0 == ? y(1.8)(x)-2y(0.9)(x)+y-1=0 == ? y(0.5)(x)=1x⋅y-1 == ? y(2)(x)⋅y2-x2-2x-1=0 == ? (d0.5ydx0.5)2-5d0.5ydx0.5+6=0 == ? y(0.5)(x)-2exp(x)⋅y-4exp(x)=0 == ? d1.6ydx1.6-d0.8ydx0.8-y-exp(x)=0 == ? y0.5(x)=2y⋅exp(x) == ? y(0.5)(x)-exp(x)⋅y2=0 == ? d1.6ydx1.6-2d0.8ydx0.8+y-exp(x)=0 == ? y(1)(x)-y2-x⋅y=0 == ? y(1)(x)-y(0.5)(x)-y-1=0 == ? y(2)(x)-y2-x2=0 == ? y(2)(x)-y2-x2-2x⋅y=0 == ? y(0.5)(x)-∫y(x)(dx)0.5-y-exp(x)=0 == ? d0.5dx0.5y-2cos(y)⋅exp(x)=0 == ? d0.5dx0.5y-4sin(y)⋅exp(x)=0 == ? d0.5ydx0.5=sin(x2)⋅y == ? d0.5ydx0.5-sin(x)⋅sin(y)=0 == ? d0.5ydx0.5-sinh(x)⋅sinh(y)=0 == ? y(1)(x)=exp(x-y)-x == ? x⋅d0.5ydx0.5-y-2x=0 == ? d0.5ydx0.5=sinh(x-1)⋅sinh(y-1) == ? y(0.5)(x)-exp(-x)⋅y2=0 == ? d0.5ydx0.5=yx⋅sin(x) == ? dydx-sin(x-y)-1=0 == ? d2.5ydx2.5=y⋅d0.5ydx0.5 == ? d0.5ydx0.5=y⋅dydx == ? d2-iydx2-i-y+x=0 == ? d2ydx2=y3⋅x2 == ? y⋅d2ydx2-x2-3x-1=0 == ? y⋅d2ydx2-2x2-3x-1=0 == ? (y-x-1)⋅d2ydx2-3x-1=0 == ? y2⋅d2ydx2-x2-4x-4=0 == ? (y-x-1)⋅d2ydx2-x2-4x-4=0 == ? y⋅d2ydx2-2x2-2x-1=0 == ? y⋅d3ydx3-6x3-3x2-3x-1=0 == ? y(0)(x)⋅y(1)(x)⋅y(2)(x)=x2 == ? y(3)(x)⋅y(2)(x)=y(12)(x) == ? y(3)(x)=exp(x)⋅y(1)(x)⋅y(12)(x) == ? y(12)(x)⋅y(3)(x)=exp(x) == ? y(12)(x)⋅y(2)(x)=exp(x) == ? d0.5ydx0.5-2x⋅y-1=0 == ? y2⋅d0.5ydx0.5-x2-4x-4=0 == ? exp(y-1)⋅d0.5ydx0.5-x=0 == ? y⋅d2ydx2-(x-2)⋅(2x-4)=0 == ? y⋅d3ydx3-6x3-4x2-4x-1=0 == ? exp(y-1)⋅d2ydx2-exp(x)=0 == ? y2⋅d2ydx2-x2-1=0 == ? 1y2⋅d2ydx2-x2-1=0 == ? (y-x-1)⋅d3ydx3-(x-2)⋅(2x-4)⋅(3x-1)=0 == ? d0.5ydx0.5-2x2⋅y2-8x2=0 == ? d0.5ydx0.5-2x⋅y2-8x=0 == ? d0.5ydx0.5-y2-2y-2=0 == ? d0.5ydx0.5-log(y-1)⋅exp(x)=0 == ? y⋅d2ydx2-(dydx)2-1=0 == ? d2ydx2-asin(y-1)-sin(x)-x=0 == ? dydx⋅(x--y)-x--y-1=0 == ?

    
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