Moving a body that a boolean made no longer hangs: a boolean between a cylinder and a tilted plane (an elliptical edge) froze the app at 100 % CPU, because its retries move both bodies and the result back
Moving a body transforms its intersection-curve edges, and truck-geometry 0.5.0 scales each curve's tolerance by the operator norm of the matrix. matext4cgmath 0.1.0 computes it from eigenvalues through a quartic whose Newton refinement loops while the residual is above a tolerance and never gives up. For a translation matrix all four eigenvalues are 1, and near that quadruple root the iteration can cycle forever (about one translation in eight of the boolean retries' shifts, by a scan of sizes 0.1-2000 mm). matext4cgmath is vendored with both Newton loops stopped after 100 steps (vendor/README.md, ATTRIBUTION.md). truck master no longer computes the norm in transform_by, so the vendored copy can go once a truck release after 0.5.0 is adopted. Tests: moving_a_body_with_an_intersection_curve_edge_ends (kernel) cuts a cylinder with a tilted box and moves the result by one of the shifts that hung (hangs on main). examples/regressions/oblique_cut_of_cylinder_hang.json is the variant of the oblique cut that hung the app; it hangs on main, and since the previous commit it passes without reaching the shifted retries, so it is replayed by the engine test as a scenario only. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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CypherNaugh_0xandClaude Opus 5.5 authored and bherbruck committed
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use crate::*;
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#[cfg_attr(doc, katexit::katexit)]
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/// Solve equation: $x^2 + ax + b = 0$.
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///
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/// # Examples
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///
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/// ```
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/// use matext4cgmath::solver;
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/// use num_complex::Complex;
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/// const EPS: f64 = 1.0e-10;
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///
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/// let res = solver::solve_quadratic(3.0, -4.0);
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/// // Real solutions are always sorted in order of solution size.
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/// assert!(Complex::norm(res[0] + 4.0) < EPS);
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/// assert!(Complex::norm(res[1] - 1.0) < EPS);
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/// ```
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pub fn solve_quadratic<F: BaseFloat>(a: F, b: F) -> [Complex<F>; 2] {
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let two = F::one() + F::one();
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let four = two + two;
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let det = a * a - four * b;
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match det >= F::zero() {
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true => {
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let h = F::sqrt(det);
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[
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Complex::new((-a - h) / two, F::zero()),
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Complex::new((-a + h) / two, F::zero()),
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]
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}
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false => {
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let h = F::sqrt(-det);
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[Complex::new(-a, h) / two, Complex::new(-a, -h) / two]
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}
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}
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}
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#[cfg_attr(doc, katexit::katexit)]
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/// Solve equation: $x^3 + px + q = 0$.
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///
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/// # Examples
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///
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/// ```
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/// use matext4cgmath::solver;
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/// use num_complex::Complex;
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/// const EPS: f64 = 1.0e-10;
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///
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/// let mut res = solver::pre_solve_cubic(-7.0, -6.0);
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/// // Even in the case of real solutions, the order in the array is not guaranteed.
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/// res.sort_by(|x, y| x.re.partial_cmp(&y.re).unwrap());
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/// let ans = [Complex::from(-2.0), Complex::from(-1.0), Complex::from(3.0)];
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/// res.iter().zip(ans).for_each(|(x, y)| {
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/// assert!(Complex::norm(x - y) < EPS);
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/// });
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/// ```
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pub fn pre_solve_cubic<F: BaseFloat>(p: F, q: F) -> [Complex<F>; 3] {
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let two = F::one() + F::one();
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let three = two + F::one();
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let sqrt3_2 = F::sqrt(three) / two;
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let omega = Complex::new(-F::one() / two, sqrt3_2);
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let omega2 = Complex::new(-F::one() / two, -sqrt3_2);
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let eps_2 = F::sqrt(F::epsilon());
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let p_3 = p / three;
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let q_2 = q / two;
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let alpha2 = q_2 * q_2 + p_3 * p_3 * p_3;
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let (x, y) = match alpha2 >= F::zero() {
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true => {
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let alpha = F::sqrt(alpha2);
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let tmpx = -q_2 - alpha;
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let tmpy = -q_2 + alpha;
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(
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Complex::new(
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F::signum(tmpx) * F::powf(F::abs(tmpx), F::one() / three),
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F::zero(),
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),
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Complex::new(
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F::signum(tmpy) * F::powf(F::abs(tmpy), F::one() / three),
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F::zero(),
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),
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)
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}
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false => {
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let alphai = F::sqrt(-alpha2);
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(
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Complex::powf(Complex::new(-q_2, alphai), F::one() / three),
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Complex::powf(Complex::new(-q_2, -alphai), F::one() / three),
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)
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}
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};
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let mut res = [x + y, omega * x + omega2 * y, omega2 * x + omega * y];
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// precision by Newton method
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res.iter_mut().for_each(|x| {
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let mut f = *x * *x * *x + *x * p + q;
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let mut f_prime = *x * *x * three + p;
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// SolveCraft: at most 100 steps. Near a double root (the eigenvalues of a
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// translation matrix) the iteration can cycle forever without meeting the tolerance.
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let mut steps = 0;
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while f.norm() > eps_2 * f_prime.norm() && steps < 100 {
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steps += 1;
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if f_prime.norm() < eps_2 {
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return;
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}
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*x -= f / f_prime;
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f = *x * *x * *x + *x * p + q;
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f_prime = *x * *x * three + p;
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}
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});
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res
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}
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#[cfg_attr(doc, katexit::katexit)]
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/// solve equation: $x^3 + ax^2 + bx + c = 0$.
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///
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/// # Examples
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///
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/// ```
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/// use matext4cgmath::solver;
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/// use num_complex::Complex;
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/// const EPS: f64 = 1.0e-10;
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///
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/// let mut res = solver::solve_cubic(-3.0, 0.0, 4.0);
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/// // Even in the case of real solutions, the order in the array is not guaranteed.
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/// res.sort_by(|x, y| x.re.partial_cmp(&y.re).unwrap());
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/// let ans = [Complex::from(-1.0), Complex::from(2.0), Complex::from(2.0)];
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/// res.iter().zip(ans).for_each(|(x, y)| {
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/// assert!(Complex::norm(x - y) < EPS);
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/// });
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/// ```
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pub fn solve_cubic<F: BaseFloat>(a: F, b: F, c: F) -> [Complex<F>; 3] {
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let two = F::one() + F::one();
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let three = two + F::one();
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let twenty_seven = three * three * three;
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let p = b - a * a / three;
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let q = c - a * b / three + two * a * a * a / twenty_seven;
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let mut res = pre_solve_cubic(p, q);
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res.iter_mut().for_each(|x| {
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*x -= a / three;
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});
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res
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}
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#[cfg_attr(doc, katexit::katexit)]
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/// solve equation: $x^4 + px^2 + qx + r = 0$.
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///
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/// # Examples
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///
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/// ```
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/// use matext4cgmath::solver;
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/// use num_complex::Complex;
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/// const EPS: f64 = 1e-7;
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///
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/// let mut res = solver::pre_solve_quartic(-5.0, 0.0, 4.0);
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/// // Even in the case of real solutions, the order in the array is not guaranteed.
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/// res.sort_by(|x, y| x.re.partial_cmp(&y.re).unwrap());
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/// let ans = [Complex::from(-2.0), Complex::from(-1.0), Complex::from(1.0), Complex::from(2.0)];
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/// res.iter().zip(ans).for_each(|(x, y)| {
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/// assert!(Complex::norm(x - y) < EPS);
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/// });
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/// ```
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pub fn pre_solve_quartic<F: BaseFloat>(p: F, q: F, r: F) -> [Complex<F>; 4] {
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let one = F::one();
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let two = one + one;
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let four = two + two;
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let eps_2 = F::sqrt(F::epsilon());
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let a = two * p;
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let b = p * p - four * r;
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let c = -q * q;
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let f = solve_cubic(a, b, c);
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let a = f[0].sqrt() / two;
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let b = f[1].sqrt() / two;
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let c = f[2].sqrt() / two;
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let mut res = (0..8)
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.map(|i| {
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let a = a * F::powi(-F::one(), i % 2);
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let b = b * F::powi(-F::one(), (i / 2) % 2);
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let c = c * F::powi(-F::one(), (i / 4) % 2);
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[-a - b - c, -a + b + c, a - b + c, a + b - c]
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})
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.map(|x| {
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let f = x
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.iter()
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.map(|t| (t * t * t * t + t * t * p + t * q + r).norm_sqr())
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.max_by(|x, y| x.partial_cmp(y).unwrap())
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.unwrap();
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(x, f)
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})
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.min_by(|x, y| x.1.partial_cmp(&y.1).unwrap())
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.unwrap()
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.0;
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// refinement by Newton method
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res.iter_mut().for_each(|x| {
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let mut f = *x * *x * *x * *x + *x * *x * p + *x * q + r;
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let mut f_prime = *x * *x * *x * four + *x * p * two + q;
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// SolveCraft: at most 100 steps. Near a double root (the eigenvalues of a
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// translation matrix) the iteration can cycle forever without meeting the tolerance.
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let mut steps = 0;
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while f.norm() > eps_2 * f_prime.norm() && steps < 100 {
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steps += 1;
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if f_prime.norm() < eps_2 {
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return;
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}
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*x -= f / f_prime;
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f_prime = *x * *x * *x * four + *x * p * two + q;
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f = *x * *x * *x * *x + *x * *x * p + *x * q + r;
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}
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});
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res
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}
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#[cfg_attr(doc, katexit::katexit)]
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/// solve equation: $x^4 + ax^3 + bx^2 + cx + d = 0$.
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///
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/// # Examples
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///
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/// ```
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/// use matext4cgmath::solver;
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/// use num_complex::Complex;
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/// const EPS: f64 = 1.0e-10;
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///
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/// let mut res = solver::solve_quartic(1.0, -7.0, -1.0, 6.0);
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/// // Even in the case of real solutions, the order in the array is not guaranteed.
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/// res.sort_by(|x, y| x.re.partial_cmp(&y.re).unwrap());
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/// let ans = [Complex::from(-3.0), Complex::from(-1.0), Complex::from(1.0), Complex::from(2.0)];
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/// res.iter().zip(ans).for_each(|(x, y)| {
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/// assert!(Complex::norm(x * x * x * x + x * x * x - 7.0 * x * x - x + 6.0) < EPS);
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/// assert!(Complex::norm(x - y) < EPS, "{x} {y}");
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/// });
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/// ```
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pub fn solve_quartic<F: BaseFloat>(a: F, b: F, c: F, d: F) -> [Complex<F>; 4] {
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let one = F::one();
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let two = one + one;
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let three = one + two;
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let four = two + two;
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let six = two * three;
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let eight = four + four;
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let a_4 = a / four;
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let p = b - six * a_4 * a_4;
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let q = c - two * b * a_4 + eight * a_4 * a_4 * a_4;
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let r = d - c * a_4 + b * a_4 * a_4 - three * a_4 * a_4 * a_4 * a_4;
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let mut res = pre_solve_quartic(p, q, r);
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res.iter_mut().for_each(|x| *x -= a_4);
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res
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}
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