How to make three-dimensional ripples with geometric artboards

geometric drawing board as a common teaching aids, in addition to drawing plane graphics, in fact, can also make three-dimensional graphics. In mathematics, we all know that many of the graphs are done by the coordinate system, the coordinate system has two-dimensional also has three-dimensional, two-dimensional is usually used for planar graphics, three-dimensional used for three-dimensional graphics. Here's how to make three-dimensional ripples with geometric artboards?

Original: http://www.jihehuaban.com.cn/shiyongjiqiao/sanwei-bowen.html

Example of a three-dimensional ripple made from a geometry artboard:

Example of a three-dimensional ripple constructed in a geometry artboard

The specific production methods are as follows:

Step one after the three-dimensional coordinate system is built, first make the tool: flat grid, the effect as shown.

Example of making a planar mesh in a geometry artboard

The method of production is as follows:

Gives an independent parameter named Transverse stripe, which represents the number of lines in a segment.

Gives two public fixed-point segments (as a self-defined coordinate system) that are adjusted to approximate vertical states.

Example of two common fixed-point segments as defined coordinate systems

Calculate the ratio of the length of AD and AB, and then get a change from 0 to 1, using this amount as the basis for describing those segments, called the stripe Seed.

Step two calculates two quantities using the formula shown

Calculate an example with a formula

It can be seen that the last data gives a few discrete quantities, just a few equal points. is to divide 0 to 1 into the horizontal stripe number equal, these are the points. And you can see the 2nd number, is a decimal function, then the repetition from 0 to 1 continuous change, then we put these two quantities as coordinates in their own defined coordinate system (the method of intersection of parallel lines) So, this point about D point of the trajectory is the above line.

We can also draw the portrait, of course, if we want to be very horizontal and vertical number of bars, it is reversed, the trajectory can be traced, here the following method of processing.

Step three Xoy the grid tool with the three-dimensional coordinate system, and (by merging the endpoints to the point on the line), you get the effect as shown.

Examples of three-dimensional meshes obtained by merging

The coordinates of the moving point in the figure are (x, y), and then the moving point is shifted in the z direction, and the translated point is scaled by the following calculated values (the multiples of which can be adjusted to change the number of waves in the unit space) to get the moving points on the surface, and the points on the grid are tracked by D points. You can get the image on the first quadrant and then use the symmetric transform to make the image on the other quadrant.

The above is how to use the geometry of the three-dimensional corrugated board thinking, see the above steps, to make three-dimensional ripple have a certain understanding of it? If still at a loss, suggest that you follow the above ideas more practice several times, will certainly master. If you need courseware, please click on the Geometry artboard courseware .

How to make three-dimensional ripples with geometric artboards