How to draw an arc on the plane where phi equals pi/3

Questions
,
1

Hello, friends. I’m trying to reproduce the image shown below, but I’m getting stuck at the arc-through function. I need to draw an arc on the plane where phi equals pi/3, but I’m unsure how to implement this. I would appreciate any advice you can provide. Thank you!

Additionally, I would like to know if I can redefine the direction of the axes, specifically: x = (angle: -60deg, radius: 1 cm), y = (angle: 0deg, radius: 1 cm), z = (angle: 90deg, radius: 1 cm)?

In CeTZ, is it possible to specify an arbitrary plane and draw graphics on that plane?

image
image666×627 36.8 KB


#set page(paper:"a4", flipped:true, margin:1cm)
#set align(center+horizon)

#import "@preview/cetz:0.4.2"
#cetz.canvas({
import cetz.draw:*
import calc:*

let sph(r, theta, phi)={
let x=r* sin(theta)* cos(phi)
let y=r* sin(theta)* sin(phi)
let z=r*cos(theta)
return (x,y,z)
}

scale(x:2,y:2,z:2)
ortho(x:300deg, y:0deg, z:250deg,{
let mark-style= ( mark:(end:(symbol:"curved-stealth", fill:black, scale:0.5) ) ) 
line((0,0,0), (4,0,0), name:"x",..mark-style, stroke:gray ) 
line((0,0,0), (0,4,0), name:"y",..mark-style, stroke:gray ) 
line((0,0,0), (0,0,4), name:"z",..mark-style, stroke:gray ) 
content((rel:(0.3,0,0), to: "x.end"), $x$) 
content((rel:(0,0.3,0), to: "y.end"), $y$) 
content((rel:(0,0,0.3), to: "z.end"), $z$) 

on-xy(z:0, arc((0,0),start:0deg, stop:90deg, radius:3.5, anchor:"origin")) 
on-xz(y:0, arc((0,0),start:0deg, stop:90deg, radius:3.5, anchor:"origin")) 
on-yz(x:0, arc((0,0),start:0deg, stop:90deg, radius:3.5, anchor:"origin")) 

let O=(0,0,0) 
let P= sph(3.5, pi/4, pi/3 ) 
line(O,P) 

// error comes from the following codes:
// let A=(0,0,3.5)
// let B=sph(3.5, pi/2, pi/3)
// arc-through(A, P, B)
})

})

The code above produces the image shown below.

image
image708×700 30.3 KB

2 
#set page(width:auto, height:auto, margin:1cm)
#set align(center+horizon)

#import "@preview/cetz:0.4.2"
#cetz.canvas({
import cetz.draw:*
import cetz.angle:*
import calc:*
set-style(stroke:(thickness:0.8pt))
let sph(r, theta, phi)={
let x=r* sin(theta)* cos(phi)
let y=r* sin(theta)* sin(phi)
let z=r*cos(theta)
return (x,y,z) }

scale(x:1.5,y:1.5,z:1.5)

ortho(x:300deg, y:0deg, z:250deg,{
let mark-style= ( mark:(end:(symbol:"stealth", fill:black, scale:0.6) ) ) 
line((0,0,0), (4,0,0), name:"x",..mark-style, stroke:(dash:"dashed")) 
line((0,0,0), (0,4,0), name:"y",..mark-style, stroke:(dash:"dashed") ) 
line((0,0,0), (0,0,4), name:"z",..mark-style, stroke:(dash:"dashed") ) 
content((rel:(0.3,0,0), to: "x.end"), $x$) 
content((rel:(0,0.3,0), to: "y.end"), $y$) 
content((rel:(0,0,0.3), to: "z.end"), $z$) 


on-xy(z:0, arc((0,0),start:0deg, stop:90deg, radius:3.5, anchor:"origin")) 
on-xz(y:0, arc((0,0),start:0deg, stop:90deg, radius:3.5, anchor:"origin")) 
on-yz(x:0, arc((0,0),start:0deg, stop:90deg, radius:3.5, anchor:"origin")) 

let (O, P)= ((0,0,0), sph(3.5, pi/4, pi/3 ) )
line(O,P,stroke:(dash:"dashed") , ..mark-style ) 
content((rel:(0, 0.5, 0.1), to: P), $P(r,theta,phi)$)

scope({
rotate(z:60deg);
on-xz(y:0, arc((0,0),start:0deg, stop:90deg, radius:3.5, anchor:"origin",)); }) 

let (PX,PY,PZ)=P
let (Px,Py,Pz,Pxy)=((PX,0,0),(0,PY,0),(0,0,PZ),(PX,PY,0)) 
line(Pz,P,Pxy,Px,stroke:(dash:"dashed") )
line(O,Pxy,Py,stroke:(dash:"dashed") )
angle((0,0,0),Px, Pxy, radius:PX, label: text(size:15pt,fill:teal)[$phi$], ..mark-style, stroke:(thickness:2pt, paint:teal)) ;
// angle((0,0,0),Pz, P, radius:1cm, label: text(fill:teal)[$theta$], ..mark-style, stroke:(thickness:2pt, paint:teal)); 

scope({
rotate(z:60deg);
on-xz(y:0, arc((0,0),start:90deg, stop:45deg, radius:1.5, anchor:"origin", ..mark-style, stroke:(thickness:2pt,paint:teal), name:"angle-theta"));
content(sph(0.8,pi/8,pi/3),text(size:15pt, fill:teal)[$theta$])
// Is there another method to draw the theta angle?

}) }) })
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