raffitz
3 years ago
7 changed files with 85 additions and 1 deletions
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# Helix with radius s, inner radius 2s |
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define @b (3 * s) / 2 |
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define @a @b / π |
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-5*s <= x <= 5*s |
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-5*s <= y <= 5*s |
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-s <= z <= 2*s |
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(ρ - 3*s)^2 + (z - @b - (@a * φ))^2 <= s^2 \ |
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∨ \ |
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(ρ - 3*s)^2 + (z - 3*s - @b - (@a * φ))^2 <= s^2 \ |
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∨ \ |
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(ρ - 3*s)^2 + (z + 3*s - @b - (@a * φ))^2 <= s^2 |
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# Rotating triangle torus |
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define @angle0 φ |
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define @angle1 φ + ⅓π |
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define @angle2 φ + 2 * ⅓π |
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define @angle3 φ + π |
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define @angle4 φ + π + ⅓π |
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define @angle5 φ + 2π - ⅓π |
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-5 * s < x < 5 * s |
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-5 * s < y < 5 * s |
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-s < z < s |
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(ρ - (3 * s) - s * (cos @angle0)) * (cos @angle1) + (z - s * (sin @angle0)) * (sin @angle1) < 0 |
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(ρ - (3 * s) - s * (cos @angle2)) * (cos @angle3) + (z - s * (sin @angle2)) * (sin @angle3) < 0 |
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(ρ - (3 * s) - s * (cos @angle4)) * (cos @angle5) + (z - s * (sin @angle4)) * (sin @angle5) < 0 |
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# Rotating triangle torus |
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define @angle0 2 * φ |
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define @angle1 2 * φ + ⅓π |
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define @angle2 2 * φ + 2 * ⅓π |
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define @angle3 2 * φ + π |
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define @angle4 2 * φ + π + ⅓π |
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define @angle5 2 * φ + 2π - ⅓π |
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-5 * s < x < 5 * s |
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-5 * s < y < 5 * s |
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- s < z < s |
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(ρ - (3 * s) - s * (cos @angle0)) * (cos @angle1) + (z - s * (sin @angle0)) * (sin @angle1) < 0 |
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(ρ - (3 * s) - s * (cos @angle2)) * (cos @angle3) + (z - s * (sin @angle2)) * (sin @angle3) < 0 |
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(ρ - (3 * s) - s * (cos @angle4)) * (cos @angle5) + (z - s * (sin @angle4)) * (sin @angle5) < 0 |
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# Rotating triangle torus |
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define @angle0 (1/3) * φ |
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define @angle1 (1/3) * φ + ⅓π |
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define @angle2 (1/3) * φ + 2 * ⅓π |
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define @angle3 (1/3) * φ + π |
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define @angle4 (1/3) * φ + π + ⅓π |
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define @angle5 (1/3) * φ + 2π - ⅓π |
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5 * s < x < 5 * s |
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5 * s < y < 5 * s |
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- s < z < s |
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(ρ - (3 * s) - s * (cos @angle0)) * (cos @angle1) + (z - s * (sin @angle0)) * (sin @angle1) < 0 |
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(ρ - (3 * s) - s * (cos @angle2)) * (cos @angle3) + (z - s * (sin @angle2)) * (sin @angle3) < 0 |
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(ρ - (3 * s) - s * (cos @angle4)) * (cos @angle5) + (z - s * (sin @angle4)) * (sin @angle5) < 0 |
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# Rotating triangle torus |
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define @angle0 (2/3) * φ |
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define @angle1 (2/3) * φ + ⅓π |
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define @angle2 (2/3) * φ + 2 * ⅓π |
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define @angle3 (2/3) * φ + π |
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define @angle4 (2/3) * φ + π + ⅓π |
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define @angle5 (2/3) * φ + 2π - ⅓π |
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-5 * s < x < 5 * s |
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-5 * s < y < 5 * s |
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-s < z < s |
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(ρ - (3 * s) - s * (cos @angle0)) * (cos @angle1) + (z - s * (sin @angle0)) * (sin @angle1) < 0 |
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(ρ - (3 * s) - s * (cos @angle2)) * (cos @angle3) + (z - s * (sin @angle2)) * (sin @angle3) < 0 |
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(ρ - (3 * s) - s * (cos @angle4)) * (cos @angle5) + (z - s * (sin @angle4)) * (sin @angle5) < 0 |
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