﻿﻿﻿ math handbook calculator - Fractional Calculus Computer Algebra System software
+ + + =

﻿

# 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
3. Graphics objects
4. Drawing

## 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

 solar 3D 互动太阳系 solar system 编辑 edit 正弦函数 sin(x) 园锥 cone rose 玫瑰花 编辑 edit sea 可以升降的海水 编辑 edit

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

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
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.

### 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.

47. section3D
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. A plane deforming into a cylinder then back to a plane from the other direction.
85. bianchi-pinkall-animation 花环
86. bianchi-pinkall-animation-zoomed 花环
88. FlatTorus
89. sphere
90. Cylinder
91. Metaballs

<= Pre page Next =>

### Reference 参阅

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