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How to draw gridlines on a curved surface?

2018-04-26 20:48:26

When you plot surfaces for parametric equations with Mathematica, by default, gridlines appear. So, where do these grid lines come from? Next, I will introduce the method of drawing gridlines.

Tools/Materials
1

computer

2

Mathematica

Methods/Steps
1

First, give a parametric equation for a surface and plot the surface: r[u_,v_]:={Sin[u],Cos[v],Sin[v] Cos[u]} This graph looks like an inflated pillow.

2

This article is an unauthorized grab from Experience

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In r[u,v], if v is given a definite value, then r[u,v] is a curve on the surface, called a U-curve, and the figure below is a U-curve drawn on the surface (blue line in the figure).

4

Use Table to draw more u curves: Table[r[u,v],{v,0,2 Pi,2 Pi/35}] Can you count the number of u curves in the graph?

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Similarly, it is possible to draw a single red v curve, which is the graph for a constant value of u: r[Pi/2+1,v]

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Use Table to plot several v curves: Table[r[u,v],{u,0,2 Pi,2 Pi/25}] and count the number of v curves.

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When we draw the top u curve and the top v curve together, we get grid lines, but the density of the grid lines is not the same.

8

Use Mesh and MeshStyle directly to control the style of the grid lines and compare it with the diagram above:... 26, Mesh - > {4}, MeshStyle - > {Red, Blue},...

Matters needing attention

Each point on the grid line can be concretely represented by u and v, which are the curved coordinates of the points on the surface. It follows that a surface in three dimensions is two dimensions.

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