3D circle center through 3 points #1029
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johannes-wolf
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Jan 31, 2026
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Thank you! Some small things to fix. I have not yet tested it.
src/util.typ
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| if args.len() == 4 { break } | ||
| } | ||
| // If two points are the same we take the midpoint with the two other. | ||
| if a == b or b == c { return ligne-pt(a, c, 0.5) } else if a == c { return line-pt(a, b, 0.5) } |
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Typo: ligne-pt → line-pt – maybe we should change that to vector.lerp.
src/util.typ
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| let vw = vx * wx + vy * wy + vz * wz // <v, w> | ||
| let denom = 2 * (v2 * w2 - calc.pow(vw, 2)) // 2*norm of "v cross w" | ||
| // if the points are aligned, we fail with error message returning the coordinates of the points | ||
| assert( |
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Since Typst evaluates all arguments of assert, this should be a panic inside an if.
| + str(c.at(2)) | ||
| + ") ", | ||
| ) | ||
| let lambda = w2 * (v2 - vw) / denom |
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I use typstyle to format the code, linebreaks and indentation are automatic... I put this string back to one line.
src/util.typ
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| // If two points are the same we take the midpoint with the two other. | ||
| if a == b or b == c { return ligne-pt(a, c, 0.5) } else if a == c { return line-pt(a, b, 0.5) } | ||
| // we compute the vectors b-a and c-a and the norm of their cross product | ||
| let (vx, vy, vz) = (0, 1, 2).map(i => b.at(i) - a.at(i)) // v=b-a |
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You can use range(0, 2) instead of (0, 1, 2) – same for line 114 and 145.
…ssert, range(3) instead of (0,1,2)
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Re-wrote the function calculate-circle-center-3pt in src/utils.typ
Previously, this function took three 3D vectors as input but was essentially 2D, taking the z-coordinate from the first vector. Now the output is the center of the circle passing through the 3 point even if they have not the same z-coordinates.
Note : if two of the points are equal, there is no uniqueness of the circle center. Originally it returned the center passing through the 2 different points with x-coordinate 0, which seems arbitrary. Now it returns the midpoint between the two different points.
The function fails if the 3 points are aligned and different.
This is a first step towards making arc-through and circle-through work with 3D points with different z-coordinates.
All test passed.