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I am trying to draw a mathematical shape (prism) in 3D but having trouble creating the diagram so the 3D perspective looks good.

I essentially want a rectangle on top of a trapezium as the cross-section which I have here. I've tried putting in the internal lines but it just doesn't seem to come out right. How should the internal lines be drawn from a 3D perspective here and what I can do to improve the 3D-ness of the diagram?

enter image description here

2 Answers 2

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You have a parallel projection without perspective. It's often good for engineering purposes, but it looks wrong, because the distant end looks too tall and wide.

So, draw it with perspective. The easiest trick is to draw it like the trapezoid+rectangle faces were in parallel with the camera film. Artists call it "one point perspective":

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The parallel lines meet on the horizon in the vanishing point (V). I'm sure you have seen it numerous times before this - for example a railroad or highway seems to fade into the vanishing point on large flat terrain.

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The back face is like the front face, but scaled. The artist can by himself decide the place of the horizon and the vanishing point.

The vanishing point is not actually needed. Draw only the back face in a little smaller size than the front face and connect the corners.

enter image description here

The things become tricky if the front and back face are not in parallel with the camera film. Then everything must be constructed in the hard way if one expects a mathematically sound projection. Artists use shortcuts which can be learned from perspective drawing textbooks. You'll need 2-point perspective, because the front and back faces also need vanishing points.

3D programs can create it right automatically. Here the prism is extruded in Illustrator by using the legacy 3D extrude & bevel effect. The view is rotated and there's perspective:

enter image description here Also the shading of the surfaces is automatic and it's possible to change the direction of the light (=more options). You can use shading also in manually drawn versions for better 3D look.

Making it look like it's made of refractive and reflective glass or metal is really tricky. In drawing such cases the environment (light, surrounding items) gets as big role as the properties of the material and the projection geometry. How to draw glass or metal is beyond the scope of this answer.

Wireframe shading option gives the skeleton you wanted:

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The wireframe can be extracted by applying "Expand Appearance", releasing numerous clipping masks and ungrouping numerous groups. Finally there's a big bunch of free paths:

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Many of them are doubled, but they are all there.

Even the simplest 3D CAD programs can render it with the wireframe and partially transparent surfaces. Do not expect it will look like it's made of glass. But you'll get this in less than a minute:

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The viewing direction can be changed with no effort.

Free version of Fusion 360 knows some materials. Clear glass is included. There the same prism is rendered to this:

enter image description here

The light reflections look quite obscure, because they are produced by one of the available environments, which contains a few differently bright rectangles. The result is peculiar, because the environment itself is not shown.

Finally an easy to draw fake. In math it's rubbish but for illustration purposes it can be good enough:

enter image description here

A. Draw the front face

B. Select the left edge nodes with the node editing tool and move them upwards a little. Use the UP-arrow key to move all three nodes together. This trick is the worst one in pure math terms. A talented artist probably could guess the right looking geometric form better than this.

C. Make a duplicate. Scale it a little smaller proportionally (=hold Shift in Illustrator or Ctrl in Inkscape or use scale transformation)

D. Move the duplicate to a good place and connect the corners.

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  • Your images are cuter than mine :)
    – Rafael
    Commented Mar 1 at 8:37
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  1. You do not have perspective if you draw it in an isometric fashion. (Parallel lines)

enter image description here

  1. So in order to have any perspective, you need to define at least 1 vanishing point.

enter image description here


But let us forget the perspective concept. Let us focus on "Volume".

You can try adding shades to each face (Left example), or if what you mentioned about "internal lines" is my (Right example), add them in a different shade, so it looks transparent but solid, not wireframe.

enter image description here

For more tips please take a look:

What are some techniques to give drawings 3D appearance?

How can I make a shape look like it is made of glass?

Prototype Visualization: How can I learn to render glass convincingly?

Illustrator: How to create realistic reflective gold surface?

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