How can I add perspective to a CeTZ drawing?

Questions
,
1

I would like to reproduce the image below, including some perspective (a projection where distant elements are drawn smaller to create a sense of depth).

Is it possible with CeTZ? Maybe by properly setting the transformation matrix?

image
image436×300 18 KB

Thanks!

2

It sure is possible. You can use 3D coordinates inside functions like line.

You can choose your projection matrix with draw.set-transform . For example, for the Cabinet projection, with z-axis vertical, I use

draw.set-transform((
    (-calc.sqrt(1/8),1,0,0),
    (calc.sqrt(1/8),0,-1,0),
    (0,0,0,0),
    (0,0,0,1)
))```

What can't be done in my understanding is to render a 3D object (computing which face is hiding which part of the figure behind it). You have to decide what face must be drawn by hand.
3

Thanks, @gblot, for your answer. The cabinet projection is actually an oblique projection, but I’m interested in a perspective projection where distant elements are drawn smaller to create a sense of depth. I believe this should be possible using a transformation matrix, but I don’t know how to implement it in CeTZ.

I’ve edited the question to make it clearer.

4

I’m really not familiar enough with transformation matrices. I found this : Coding Labs :: World, View and Projection Transformation Matrices At the end, they give the matrix for a projection. Maybe you could give it a try.

If your question is more about which transformation matrix to apply, maybe you would have more chance in a 3D (render and gaming) community ?

EDIT :
I tried it and it works flawlessly :

#let perspective() = {
    let FOVx = 90deg // field of view
    let FOVy = 70deg
    let near = 0.1
    let far = 1000
    draw.set-transform((
        (1 / calc.tan(FOVx / 2), 0, 0, 0),
        (0, 1 / calc.tan(FOVy / 2), 0, 0),
        (0, 0, -(far + near) / (far - near), -2 * (near * far) / (far - near)),
        (0, 0, -1, 0),
    ))
}

you can then draw.rotate(x:45deg) for example or anything you want to look from the right angle.