Converting a curve into a surface based on mathematical graphics

(Conversion) This article will show several basic graphics generation algorithms, including: Circle surface, ball, cylindrical, cone, ring, circle, spiral ring, circle screw, five-pointed ring, pyramid, positive 8 area. use the script code of the custom syntax to generate a mathematical image. for related software, see: Mathematical graphics visualization tool. This software is free and open-source.

A previous article: Mathematical graphics converts a curve (curve) into a curved tube. After writing it, I realized that this script code for generating a curved tube is too complicated. if the input is a curve + tube radius, it can be changed to a sentence. I need to add a line after the code for generating the curve to convert it into a curved tube. pipe = radius [0.5], type [0]

After being parsed by the "pipe" script, I thought that the curve could be transformed into a curved surface through rotation, scaling, and translation. OK, and the following syntax is implemented:

 

(1) rotate any line in the space to generate a rotating Surface

Rotate = anchor [0, 0, 0], axis [0, 1, 0], angle [0, 2 * Pi]

(2) Move the vertex along any orientation and a cylindrical surface can be generated.
Translate = dir [0, 1, 0], DIS [0, 5]

(3) scale the vertices on the curve based on any point in the space
Scale = anchor [0, 0, 0], X [1, 0], Z [1, 0]

Finally, a dimension data is added from the curve to the surface, and the data size needs to be set: surface_slices = 72

The following shows the graphics and script code generated using these new statements:

 

Circular Surface

vertices = 360u = from 0 to (2*PI)r = 5.0x = r*sin(u)y = r*cos(u)scale = anchor[0, 0, 0], x[1, 0], y[1, 0]

 

Ball

For more information about the algorithm used to generate a sphere, see sphere of mathematical graphics.

vertices = 360u = from 0 to (PI)r = 2.0x = r*sin(u)y = r*cos(u)rotate = anchor[0, 0, 0], axis[0,1, 0], angle[0, 2*PI]

 

Cylindrical

For general cylindrical generation algorithm, see: cylindrical surface of mathematical graphics

vertices = 360u = from 0 to (2*PI)r = 2.0x = r*sin(u)z = r*cos(u)translate = dir[0, 1, 0], dis[0, 5]

 

Cone

For general cone generation algorithms, see the cone of mathematical graphics.

vertices = 360u = from 0 to (2*PI)r = 2.0x = r*sin(u)z = r*cos(u)translate = dir[0, 1, 0], dis[0, 5]scale = anchor[0, 0, 0], x[1, 0], z[1, 0]

 

Ring

For general ring generation algorithms, see the ring of mathematical graphics.

vertices = 360u = from 0 to (2*PI)r = 2.0x = r*sin(u) + 5y = r*cos(u)surface_slices = 72rotate = anchor[0, 0, 0], axis[0,1, 0], angle[0, 2*PI]

 

Tube

vertices = 360u = from 0 to (2*PI)r = 5.0x = r*sin(u)z = r*cos(u)pipe = radius[0.5], type[0]

 

Spiral Ring

For general algorithms for generating spiral rings, see spiral tubes in mathematical graphics.

vertices = 100u = from 0 to (2*PI)r = 1.0x = r*sin(u) + 5y = r*cos(u)surface_slices = 200rotate = anchor[0, 0, 0], axis[0, 1, 0], angle[0, 8*PI]translate = dir[0, 1, 0], dis[0, 9]

 

Spiral

vertices = 100u = from 0 to (2*PI)r = 1.0x = r*sin(u) + 5y = r*cos(u)surface_slices = 200scale = anchor[0, 0, 0], x[1, 0], y[1, 0]rotate = anchor[0, 0, 0], axis[0, 1, 0], angle[0, 8*PI]translate = dir[0, 1, 0], dis[0,6]

 

Wujiaohuan

vertices =6u = from 0 to (2*PI)r = 2.0x = r*sin(u) + 5y = r*cos(u)surface_slices = 6rotate = anchor[0, 0, 0], axis[0,1, 0], angle[0, 2*PI]

 

Pyramid

vertices =5u = from 0 to (2*PI)r = 2.0x = r*sin(u)z = r*cos(u)surface_slices = 3translate = dir[0, 1, 0], dis[0, 2]scale = anchor[0, 0, 0], x[1, 0], z[1, 0]

 

Positive 8 face

vertices =3u = from 0 to (PI)r = 2.0x = r*sin(u)y = r*cos(u)surface_slices = 5rotate = anchor[0, 0, 0], axis[0,1, 0], angle[0, 2*PI]