forked from 1b-agent/fieldcraft-upstream
mesh: node relaxation with UV surface slides and relaxation fields (#398)
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed
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//! Node relaxation: moving a few nodes of a finished mesh to fix its worst elements, the nodes on
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//! the geometry staying on it (`mesh.node.relax`).
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//!
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//! Each node to move carries a weight in `(0, 1]` (the strength, times a falloff that blends the
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//! edited zone into the mesh around it). A sweep visits the nodes in label order and tries, for
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//! each, two moves:
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//!
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//! 1. **Smart Laplacian.** The weighted step toward the centroid of the corner nodes it shares an
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//! element edge with, kept only when the worst element around the node does not get worse and
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//! no valid element becomes invalid; otherwise the step is halved (three times at most).
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//! L. Freitag, *On combining Laplacian and optimization-based mesh smoothing techniques*, AMD
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//! 220, 1997 (the quality-guarded Laplacian); S. Canann, J. Tristano, M. Staten, *An approach
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//! to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and
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//! quad-dominant meshes*, IMR 1998 (smart Laplacian: a move is accepted only if the local
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//! quality does not drop).
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//! 2. **Optimization.** A step up the gradient of the worst element's quality around the node
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//! (central differences), with a backtracking line search, kept only when the worst quality
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//! rises: the max–min formulation of L. Freitag, C. Ollivier-Gooch, *Tetrahedral mesh
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//! improvement using swapping and smoothing*, IJNME 40, 1997, and P. Knupp, *Achieving finite
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//! element mesh quality via optimization of the Jacobian matrix norm and associated
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//! quantities*, IJNME 48, 2000, restricted to the active (worst) element.
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//!
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//! An element's quality is its scaled Jacobian (a triangle's: its smallest angle over 60°), from
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//! [`crate::quality::element_quality`]; a solid is valid when its certified Jacobian check is,
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//! a shell when its normal keeps its side. So no move inverts an element, and none makes the
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//! worst element around a node worse.
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//!
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//! **Constraints** ([`Freedom`]): an interior node moves freely; a node on a geometry face moves
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//! in the face's parameters and is evaluated back on it ([`Constraints::slide_face`]); a node on a
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//! geometry edge slides along it ([`Constraints::slide_curve`]); a fixed node (a geometry vertex,
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//! or a skin node whose geometry is unknown) does not move. Mid-side nodes of quadratic elements
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//! follow their edge's corners, keeping their offset from the edge's midpoint (the curvature),
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//! and are put back on their face or edge.
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use std::collections::{BTreeMap, BTreeSet};
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use fieldcraft_model::{ElementKind, Model, RelaxationCell};
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use crate::quality::{self, Metric, Validity};
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use crate::{Error, Result};
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type P = [f64; 3];
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/// Most sweeps over the nodes.
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pub const MAX_ITERATIONS: usize = 100;
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/// Most nodes one relaxation moves.
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pub const MAX_NODES: usize = 200_000;
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/// Elements listed as the worst of the region.
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pub const WORST_LISTED: usize = 5;
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/// How a node may move.
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#[derive(Debug, Clone, Copy, PartialEq, Eq)]
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pub enum Freedom {
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/// Anywhere (an interior node).
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Free,
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/// Not at all.
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Fixed,
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/// On the face with this id (the caller's).
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Face(u32),
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/// Along the curve with this id (the caller's).
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Curve(u32),
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}
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/// Where nodes may go: the caller's faces and curves.
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pub trait Constraints {
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/// How `node` may move; `None` when the caller does not know the node's geometry: it then
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/// moves freely inside the mesh and is held on its skin.
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fn freedom(&self, node: u32) -> Option<Freedom>;
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/// `p` (on face `face`) moved by `d` in the face's parameters; `None` refuses the move.
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fn slide_face(&self, face: u32, p: P, d: P) -> Option<P>;
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/// `p` (on curve `curve`) moved by `d` along the curve; `None` refuses the move.
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fn slide_curve(&self, curve: u32, p: P, d: P) -> Option<P>;
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}
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/// No geometry: interior nodes move, every node on the skin is held.
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#[derive(Debug, Clone, Copy, Default)]
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pub struct NoGeometry;
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impl Constraints for NoGeometry {
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fn freedom(&self, _: u32) -> Option<Freedom> {
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None
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}
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fn slide_face(&self, _: u32, _: P, _: P) -> Option<P> {
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None
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}
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fn slide_curve(&self, _: u32, _: P, _: P) -> Option<P> {
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None
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}
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}
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/// How the weight falls from the centre of a sphere of influence to its radius.
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#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
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pub enum Falloff {
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/// `(1 − t²)²` of the relative distance `t`: 1 at the centre, 0 with a zero slope at the
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/// radius, so the edited zone blends into the mesh around it.
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#[default]
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Smooth,
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/// `1 − t`.
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Linear,
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/// The full strength everywhere inside.
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None,
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}
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impl Falloff {
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pub fn from_name(name: &str) -> Option<Falloff> {
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match name {
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"smooth" => Some(Falloff::Smooth),
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"linear" => Some(Falloff::Linear),
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"none" => Some(Falloff::None),
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_ => None,
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}
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}
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/// The weight at relative distance `t` in `[0, 1]`.
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pub fn weight(self, t: f64) -> f64 {
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let t = t.clamp(0.0, 1.0);
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match self {
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Falloff::Smooth => (1.0 - t * t).powi(2),
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Falloff::Linear => 1.0 - t,
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Falloff::None => 1.0,
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}
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}
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}
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/// The quality of the elements around the moved nodes.
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#[derive(Debug, Clone, PartialEq, Default)]
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pub struct RegionQuality {
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pub elements: usize,
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/// Smallest element quality (scaled Jacobian; a triangle's smallest angle over 60°).
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pub min_quality: f64,
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/// Largest ratio of an element's longest to its shortest edge.
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pub max_edge_ratio: f64,
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/// Elements whose Jacobian (or a shell's normal) is not valid.
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pub invalid: usize,
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/// The worst elements and their quality, worst first.
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pub worst: Vec<(u32, f64)>,
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}
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/// What [`relax`] did.
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#[derive(Debug, Clone, PartialEq, Default)]
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pub struct Relaxed {
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/// The new position of every node that moved (corners and the mid-side nodes following them).
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pub positions: BTreeMap<u32, P>,
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/// Corner nodes that moved.
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pub moved: usize,
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/// Largest distance a node moved.
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pub max_displacement: f64,
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pub before: RegionQuality,
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pub after: RegionQuality,
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/// Sweeps made (fewer than asked when a sweep moved nothing).
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pub iterations: usize,
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}
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/// The corner nodes of measured elements (solids and shells) inside the sphere, weighted by
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/// `strength` × the falloff; only nodes of `only` when given.
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pub fn sphere_weights(
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model: &Model,
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center: P,
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radius: f64,
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strength: f64,
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falloff: Falloff,
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only: Option<&BTreeSet<u32>>,
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) -> Result<BTreeMap<u32, f64>> {
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if !(radius > 0.0 && radius.is_finite()) || !center.iter().all(|c| c.is_finite()) {
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return Err(Error::Invalid("the sphere needs a finite centre and a positive radius".into()));
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}
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check_strength(strength)?;
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let mut out = BTreeMap::new();
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for n in corner_nodes(model) {
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if only.is_some_and(|o| !o.contains(&n)) {
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continue;
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}
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let Some(node) = model.node(n) else { continue };
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let t = dist(node.xyz, center) / radius;
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if t < 1.0 {
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let w = strength * falloff.weight(t);
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if w > 0.0 {
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out.insert(n, w);
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}
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}
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if out.len() > MAX_NODES {
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return Err(Error::Limit(format!("more than {MAX_NODES} nodes inside the sphere; give a smaller radius")));
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}
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}
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Ok(out)
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}
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/// The corner nodes among `nodes` (nodes of measured elements that are a corner of one), each
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/// weighted `strength`.
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pub fn uniform_weights(model: &Model, nodes: &BTreeSet<u32>, strength: f64) -> Result<BTreeMap<u32, f64>> {
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check_strength(strength)?;
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let corners = corner_nodes(model);
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let out: BTreeMap<u32, f64> = nodes.iter().filter(|n| corners.contains(n)).map(|&n| (n, strength)).collect();
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if out.len() > MAX_NODES {
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return Err(Error::Limit(format!("more than {MAX_NODES} nodes to relax")));
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}
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Ok(out)
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}
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fn check_strength(strength: f64) -> Result<()> {
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if strength > 0.0 && strength <= 1.0 { Ok(()) } else { Err(Error::Invalid(format!("strength must be in (0, 1], got {strength}"))) }
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}
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/// Corner nodes of the solid and shell elements.
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fn corner_nodes(model: &Model) -> BTreeSet<u32> {
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let mut out = BTreeSet::new();
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for e in model.elements().values().filter(|e| quality::is_measured(e.kind)) {
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out.extend(e.nodes.iter().take(e.kind.corner_count()).copied());
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}
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out
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}
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/// Nodes on the skin of the mesh: on a solid face no other solid shares, or on a shell.
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fn skin_nodes(model: &Model, near: &BTreeSet<u32>) -> BTreeSet<u32> {
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let mut faces: BTreeMap<Vec<u32>, (usize, Vec<u32>)> = BTreeMap::new();
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let mut skin = BTreeSet::new();
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for e in model.elements().values() {
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if !e.nodes.iter().any(|n| near.contains(n)) {
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continue;
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}
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match e.kind.dimension() {
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3 => {
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for f in e.kind.faces() {
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let nodes: Vec<u32> = f.iter().filter_map(|&i| e.nodes.get(i).copied()).collect();
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let mut key: Vec<u32> = nodes.iter().take(corner_len(f.len())).copied().collect();
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key.sort_unstable();
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faces.entry(key).or_insert((0, nodes)).0 += 1;
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}
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}
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2 => skin.extend(e.nodes.iter().copied()),
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_ => {}
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}
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}
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for (count, nodes) in faces.into_values() {
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if count == 1 {
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skin.extend(nodes);
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}
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}
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skin
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}
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/// Corners of a face with `n` nodes (3, 4 linear; 6, 8 quadratic).
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fn corner_len(n: usize) -> usize {
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match n {
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6 => 3,
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8 => 4,
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n => n,
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}
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}
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fn sub(a: P, b: P) -> P {
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[a[0] - b[0], a[1] - b[1], a[2] - b[2]]
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}
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fn add(a: P, b: P) -> P {
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[a[0] + b[0], a[1] + b[1], a[2] + b[2]]
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}
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fn scale(a: P, s: f64) -> P {
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[a[0] * s, a[1] * s, a[2] * s]
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}
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fn dot(a: P, b: P) -> f64 {
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a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
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}
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fn cross(a: P, b: P) -> P {
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[a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]]
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}
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fn dist(a: P, b: P) -> f64 {
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dot(sub(a, b), sub(a, b)).sqrt()
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}
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/// One element of the region.
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struct Elem {
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label: u32,
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kind: ElementKind,
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nodes: Vec<u32>,
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/// A shell's normal as it was: its side, which a move must keep.
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normal: Option<P>,
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}
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/// The shell normal from its corners (`None` for solids).
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fn shell_normal(kind: ElementKind, x: &[P]) -> Option<P> {
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if kind.dimension() != 2 {
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return None;
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}
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let c = |i: usize| x.get(i).copied().unwrap_or([0.0; 3]);
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Some(match kind.corner_count() {
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3 => cross(sub(c(1), c(0)), sub(c(2), c(0))),
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_ => cross(sub(c(2), c(0)), sub(c(3), c(1))),
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})
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}
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/// An element's quality and whether it is valid.
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fn measure(e: &Elem, x: &[P]) -> (f64, bool) {
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let Ok(q) = quality::element_quality(e.kind, x) else { return (-1.0, false) };
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let score = q.get(Metric::ScaledJacobian).or_else(|| q.get(Metric::MinAngle).map(|a| a / 60.0)).unwrap_or(-1.0);
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let valid = match (q.validity(), e.normal) {
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(Some(v), _) => v == Validity::Valid,
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(None, Some(n0)) => shell_normal(e.kind, x).is_some_and(|n| dot(n, n0) > 0.0) && q.size > 0.0,
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(None, None) => q.size > 0.0,
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};
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(score, valid)
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}
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/// Longest over shortest corner edge.
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fn edge_ratio(kind: ElementKind, x: &[P]) -> f64 {
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let (mut lo, mut hi) = (f64::INFINITY, 0.0f64);
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for e in kind.edges() {
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if let (Some(&a), Some(&b)) = (e.first().and_then(|&i| x.get(i)), e.get(1).and_then(|&i| x.get(i))) {
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let l = dist(a, b);
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lo = lo.min(l);
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hi = hi.max(l);
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}
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}
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if lo > 0.0 { hi / lo } else { f64::INFINITY }
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}
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/// The working state: positions, the region's elements and who depends on whom.
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struct State<'a> {
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pos: BTreeMap<u32, P>,
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elems: Vec<Elem>,
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/// Corner node → its elements (indices into `elems`).
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around: BTreeMap<u32, Vec<usize>>,
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/// Corner node → corner nodes it shares an element edge with.
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neighbours: BTreeMap<u32, BTreeSet<u32>>,
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/// Mid-side node → its edge's corners and its offset from their midpoint.
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mids: BTreeMap<u32, (u32, u32, P)>,
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/// Corner node → the mid-side nodes on its edges.
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mids_of: BTreeMap<u32, Vec<u32>>,
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skin: BTreeSet<u32>,
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geometry: &'a dyn Constraints,
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}
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impl State<'_> {
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fn at(&self, n: u32) -> P {
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self.pos.get(&n).copied().unwrap_or([0.0; 3])
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}
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fn coords(&self, e: &Elem) -> Vec<P> {
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e.nodes.iter().map(|&n| self.at(n)).collect()
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}
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/// How `n` may move: a skin node the caller left free is held.
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fn freedom(&self, n: u32) -> Freedom {
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match self.geometry.freedom(n) {
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Some(f) => f,
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None if self.skin.contains(&n) => Freedom::Fixed,
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None => Freedom::Free,
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}
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}
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/// `p` moved by `d` under `freedom`.
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fn moved(&self, freedom: Freedom, p: P, d: P) -> Option<P> {
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let q = match freedom {
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Freedom::Fixed => return None,
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Freedom::Free => add(p, d),
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Freedom::Face(f) => self.geometry.slide_face(f, p, d)?,
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Freedom::Curve(c) => self.geometry.slide_curve(c, p, d)?,
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};
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q.iter().all(|x| x.is_finite() && x.abs() <= fieldcraft_model::MAX_COORD).then_some(q)
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}
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/// The worst quality around `n` and the validity of each element there.
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fn local(&self, n: u32) -> (f64, Vec<bool>) {
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let mut worst = f64::INFINITY;
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let mut valid = Vec::new();
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for &i in self.around.get(&n).map(Vec::as_slice).unwrap_or(&[]) {
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let Some(e) = self.elems.get(i) else { continue };
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let (q, v) = measure(e, &self.coords(e));
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worst = worst.min(q);
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valid.push(v);
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}
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(worst, valid)
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}
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/// The worst element around `n`: its index and quality.
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fn worst_around(&self, n: u32) -> Option<(usize, f64)> {
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let mut best: Option<(usize, f64)> = None;
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for &i in self.around.get(&n)? {
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let Some(e) = self.elems.get(i) else { continue };
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let (q, _) = measure(e, &self.coords(e));
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if best.is_none_or(|(_, b)| q < b) {
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best = Some((i, q));
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}
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}
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best
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}
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/// Put `n` at `p` with its mid-side nodes following; returns what to restore.
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fn place(&mut self, n: u32, p: P) -> Vec<(u32, P)> {
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let mut undo = vec![(n, self.at(n))];
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self.pos.insert(n, p);
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for m in self.mids_of.get(&n).cloned().unwrap_or_default() {
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let Some(&(a, b, bulge)) = self.mids.get(&m) else { continue };
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let old = self.at(m);
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let guess = add(scale(add(self.at(a), self.at(b)), 0.5), bulge);
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let q = match self.freedom(m) {
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Freedom::Free => Some(guess),
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Freedom::Fixed => None,
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f => self.moved(f, old, sub(guess, old)),
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};
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if let Some(q) = q {
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undo.push((m, old));
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self.pos.insert(m, q);
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}
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}
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undo
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}
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|
||||
fn restore(&mut self, undo: Vec<(u32, P)>) {
|
||||
for (n, p) in undo.into_iter().rev() {
|
||||
self.pos.insert(n, p);
|
||||
}
|
||||
}
|
||||
|
||||
/// Try moving `n` by `d` (under its freedom): kept when no valid element around it becomes
|
||||
/// invalid and its worst quality does not drop (rises by more than `gain`).
|
||||
fn attempt(&mut self, n: u32, freedom: Freedom, d: P, before: &(f64, Vec<bool>), gain: f64) -> bool {
|
||||
let p = self.at(n);
|
||||
let Some(q) = self.moved(freedom, p, d) else { return false };
|
||||
if dist(p, q) == 0.0 {
|
||||
return false;
|
||||
}
|
||||
let undo = self.place(n, q);
|
||||
let (worst, valid) = self.local(n);
|
||||
let ok = worst >= before.0 + gain && before.1.iter().zip(&valid).all(|(was, is)| !was || *is);
|
||||
if !ok {
|
||||
self.restore(undo);
|
||||
}
|
||||
ok
|
||||
}
|
||||
|
||||
/// The mean length of the element edges at `n`.
|
||||
fn local_length(&self, n: u32) -> f64 {
|
||||
let p = self.at(n);
|
||||
let nb = self.neighbours.get(&n);
|
||||
let (sum, count) = nb.into_iter().flatten().fold((0.0, 0usize), |(s, c), &m| (s + dist(p, self.at(m)), c + 1));
|
||||
if count > 0 { sum / count as f64 } else { 0.0 }
|
||||
}
|
||||
|
||||
/// One relaxation of `n` with weight `w`; whether it moved.
|
||||
fn relax_node(&mut self, n: u32, w: f64) -> bool {
|
||||
let freedom = self.freedom(n);
|
||||
if freedom == Freedom::Fixed {
|
||||
return false;
|
||||
}
|
||||
let p = self.at(n);
|
||||
let mut moved = false;
|
||||
// 1. Smart Laplacian.
|
||||
let nb: Vec<u32> = self.neighbours.get(&n).map(|s| s.iter().copied().collect()).unwrap_or_default();
|
||||
if !nb.is_empty() {
|
||||
let centroid = scale(nb.iter().fold([0.0; 3], |s, &m| add(s, self.at(m))), 1.0 / nb.len() as f64);
|
||||
let before = self.local(n);
|
||||
let mut d = scale(sub(centroid, p), w);
|
||||
for _ in 0..4 {
|
||||
if self.attempt(n, freedom, d, &before, 0.0) {
|
||||
moved = true;
|
||||
break;
|
||||
}
|
||||
d = scale(d, 0.5);
|
||||
}
|
||||
}
|
||||
// 2. Optimization of the worst element around the node.
|
||||
let h = self.local_length(n);
|
||||
if !(h > 0.0) {
|
||||
return moved;
|
||||
}
|
||||
let Some((worst, q0)) = self.worst_around(n) else { return moved };
|
||||
let Some(e) = self.elems.get(worst) else { return moved };
|
||||
let slot = e.nodes.iter().position(|&m| m == n);
|
||||
let Some(slot) = slot else { return moved };
|
||||
let mut x = self.coords(e);
|
||||
let here = self.at(n);
|
||||
let eps = 1e-4 * h;
|
||||
let mut grad = [0.0; 3];
|
||||
for k in 0..3 {
|
||||
let mut f = [0.0; 2];
|
||||
for (j, sign) in [1.0, -1.0].into_iter().enumerate() {
|
||||
if let Some(c) = x.get_mut(slot) {
|
||||
c[k] = here[k] + sign * eps;
|
||||
}
|
||||
f[j] = measure(e, &x).0;
|
||||
}
|
||||
if let Some(c) = x.get_mut(slot) {
|
||||
c[k] = here[k];
|
||||
}
|
||||
grad[k] = (f[0] - f[1]) / (2.0 * eps);
|
||||
}
|
||||
let g = dot(grad, grad).sqrt();
|
||||
if !(g > 0.0 && g.is_finite()) || q0 >= 1.0 - 1e-9 {
|
||||
return moved;
|
||||
}
|
||||
let before = self.local(n);
|
||||
let mut step = 0.25 * w * h;
|
||||
for _ in 0..5 {
|
||||
if self.attempt(n, freedom, scale(grad, step / g), &before, 1e-9) {
|
||||
return true;
|
||||
}
|
||||
step *= 0.5;
|
||||
}
|
||||
moved
|
||||
}
|
||||
}
|
||||
|
||||
/// Quality over the region.
|
||||
fn region_quality(s: &State<'_>) -> RegionQuality {
|
||||
let mut r = RegionQuality { elements: s.elems.len(), min_quality: f64::INFINITY, max_edge_ratio: 0.0, invalid: 0, worst: Vec::new() };
|
||||
let mut all = Vec::with_capacity(s.elems.len());
|
||||
for e in &s.elems {
|
||||
let x = s.coords(e);
|
||||
let (q, valid) = measure(e, &x);
|
||||
r.min_quality = r.min_quality.min(q);
|
||||
r.max_edge_ratio = r.max_edge_ratio.max(edge_ratio(e.kind, &x));
|
||||
r.invalid += usize::from(!valid);
|
||||
all.push((e.label, q));
|
||||
}
|
||||
all.sort_by(|a, b| a.1.total_cmp(&b.1).then(a.0.cmp(&b.0)));
|
||||
all.truncate(WORST_LISTED);
|
||||
r.worst = all;
|
||||
if r.elements == 0 {
|
||||
r.min_quality = 0.0;
|
||||
}
|
||||
r
|
||||
}
|
||||
|
||||
/// Relax the nodes of `weights` (node → weight in `(0, 1]`) for `iterations` sweeps, nodes
|
||||
/// moving as `geometry` allows. The model is not changed: the result has the new positions.
|
||||
pub fn relax(model: &Model, weights: &BTreeMap<u32, f64>, iterations: usize, geometry: &dyn Constraints) -> Result<Relaxed> {
|
||||
if iterations == 0 || iterations > MAX_ITERATIONS {
|
||||
return Err(Error::Invalid(format!("iterations must be 1 to {MAX_ITERATIONS}, got {iterations}")));
|
||||
}
|
||||
if weights.len() > MAX_NODES {
|
||||
return Err(Error::Limit(format!("more than {MAX_NODES} nodes to relax")));
|
||||
}
|
||||
if let Some((n, w)) = weights.iter().find(|(_, w)| !(**w > 0.0 && **w <= 1.0)) {
|
||||
return Err(Error::Invalid(format!("node {n} has weight {w}; weights are in (0, 1]")));
|
||||
}
|
||||
let movers: BTreeSet<u32> = weights.keys().copied().collect();
|
||||
let mut state = State {
|
||||
pos: BTreeMap::new(),
|
||||
elems: Vec::new(),
|
||||
around: BTreeMap::new(),
|
||||
neighbours: BTreeMap::new(),
|
||||
mids: BTreeMap::new(),
|
||||
mids_of: BTreeMap::new(),
|
||||
skin: skin_nodes(model, &movers),
|
||||
geometry,
|
||||
};
|
||||
for (&label, e) in model.elements() {
|
||||
if !quality::is_measured(e.kind) || e.nodes.len() != e.kind.node_count() {
|
||||
continue;
|
||||
}
|
||||
let corners = e.kind.corner_count();
|
||||
if !e.nodes.iter().take(corners).any(|n| movers.contains(n)) {
|
||||
continue;
|
||||
}
|
||||
let mut x = Vec::with_capacity(e.nodes.len());
|
||||
for &n in &e.nodes {
|
||||
let p = model.node(n).map(|n| n.xyz).ok_or_else(|| Error::Invalid(format!("element {label} refers to missing node {n}")))?;
|
||||
state.pos.insert(n, p);
|
||||
x.push(p);
|
||||
}
|
||||
let index = state.elems.len();
|
||||
for &n in e.nodes.iter().take(corners) {
|
||||
if movers.contains(&n) {
|
||||
state.around.entry(n).or_default().push(index);
|
||||
}
|
||||
}
|
||||
for edge in e.kind.edges() {
|
||||
let (Some(&a), Some(&b)) = (edge.first().and_then(|&i| e.nodes.get(i)), edge.get(1).and_then(|&i| e.nodes.get(i))) else { continue };
|
||||
for (u, v) in [(a, b), (b, a)] {
|
||||
if movers.contains(&u) {
|
||||
state.neighbours.entry(u).or_default().insert(v);
|
||||
}
|
||||
}
|
||||
if let Some(&m) = edge.get(2).and_then(|&i| e.nodes.get(i)) {
|
||||
let (pa, pb, pm) = (x.get(edge[0]).copied(), x.get(edge[1]).copied(), x.get(edge[2]).copied());
|
||||
if let (Some(pa), Some(pb), Some(pm)) = (pa, pb, pm) {
|
||||
state.mids.entry(m).or_insert((a, b, sub(pm, scale(add(pa, pb), 0.5))));
|
||||
for c in [a, b] {
|
||||
let list = state.mids_of.entry(c).or_default();
|
||||
if !list.contains(&m) {
|
||||
list.push(m);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
state.elems.push(Elem { label, kind: e.kind, normal: shell_normal(e.kind, &x), nodes: e.nodes.clone() });
|
||||
}
|
||||
let original = state.pos.clone();
|
||||
let before = region_quality(&state);
|
||||
let mut done = 0;
|
||||
for _ in 0..iterations {
|
||||
done += 1;
|
||||
let mut any = false;
|
||||
for (&n, &w) in weights {
|
||||
if state.around.contains_key(&n) {
|
||||
any |= state.relax_node(n, w);
|
||||
}
|
||||
}
|
||||
if !any {
|
||||
break;
|
||||
}
|
||||
}
|
||||
let after = region_quality(&state);
|
||||
let mut out = Relaxed { before, after, iterations: done, ..Default::default() };
|
||||
for (n, p) in &state.pos {
|
||||
let Some(o) = original.get(n) else { continue };
|
||||
let d = dist(*o, *p);
|
||||
if d > 0.0 {
|
||||
out.max_displacement = out.max_displacement.max(d);
|
||||
out.moved += usize::from(movers.contains(n));
|
||||
out.positions.insert(*n, *p);
|
||||
}
|
||||
}
|
||||
Ok(out)
|
||||
}
|
||||
|
||||
// ---- Relaxation fields ----
|
||||
|
||||
/// The linear kind of a quadratic element's corners.
|
||||
fn linear(kind: ElementKind) -> Option<ElementKind> {
|
||||
Some(match kind {
|
||||
ElementKind::Tri3 | ElementKind::Tri6 => ElementKind::Tri3,
|
||||
ElementKind::Quad4 | ElementKind::Quad8 => ElementKind::Quad4,
|
||||
ElementKind::Tet4 | ElementKind::Tet10 => ElementKind::Tet4,
|
||||
ElementKind::Wedge6 => ElementKind::Wedge6,
|
||||
ElementKind::Hex8 | ElementKind::Hex20 => ElementKind::Hex8,
|
||||
_ => return None,
|
||||
})
|
||||
}
|
||||
|
||||
/// The relaxation as a field ([`fieldcraft_model::Relaxation`]'s cells): every element with a
|
||||
/// moved node, its corners as they were in `model` and as `relaxed` left them.
|
||||
pub fn field_cells(model: &Model, relaxed: &Relaxed) -> Vec<RelaxationCell> {
|
||||
let mut cells = Vec::new();
|
||||
for e in model.elements().values() {
|
||||
let Some(kind) = linear(e.kind) else { continue };
|
||||
if !e.nodes.iter().any(|n| relaxed.positions.contains_key(n)) {
|
||||
continue;
|
||||
}
|
||||
let corners: Vec<u32> = e.nodes.iter().take(kind.node_count()).copied().collect();
|
||||
let at: Vec<P> = corners.iter().filter_map(|n| model.node(*n).map(|x| x.xyz)).collect();
|
||||
if at.len() != corners.len() {
|
||||
continue;
|
||||
}
|
||||
let moved = corners.iter().zip(&at).map(|(n, a)| relaxed.positions.get(n).copied().unwrap_or(*a)).collect();
|
||||
cells.push(RelaxationCell { kind, at, moved });
|
||||
}
|
||||
cells
|
||||
}
|
||||
|
||||
/// Linear shape functions of a cell at parametric `xi`, and the domain's dimension.
|
||||
fn shape(kind: ElementKind, xi: P) -> (Vec<f64>, usize) {
|
||||
let [u, v, w] = xi;
|
||||
match kind {
|
||||
ElementKind::Tri3 => (vec![1.0 - u - v, u, v], 2),
|
||||
ElementKind::Quad4 => (vec![(1.0 - u) * (1.0 - v), u * (1.0 - v), u * v, (1.0 - u) * v], 2),
|
||||
ElementKind::Tet4 => (vec![1.0 - u - v - w, u, v, w], 3),
|
||||
ElementKind::Wedge6 => {
|
||||
let t = [1.0 - u - v, u, v];
|
||||
(t.iter().map(|a| a * (1.0 - w)).chain(t.iter().map(|a| a * w)).collect(), 3)
|
||||
}
|
||||
_ => {
|
||||
let b = [(1.0 - u) * (1.0 - v), u * (1.0 - v), u * v, (1.0 - u) * v];
|
||||
(b.iter().map(|a| a * (1.0 - w)).chain(b.iter().map(|a| a * w)).collect(), 3)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/// How far `xi` lies outside the cell's parametric domain (0 inside).
|
||||
fn outside(kind: ElementKind, xi: P) -> f64 {
|
||||
let [u, v, w] = xi;
|
||||
let box01 = |x: f64| (-x).max(x - 1.0).max(0.0);
|
||||
match kind {
|
||||
ElementKind::Tri3 => (-u).max(-v).max(u + v - 1.0).max(0.0),
|
||||
ElementKind::Tet4 => (-u).max(-v).max(-w).max(u + v + w - 1.0).max(0.0),
|
||||
ElementKind::Quad4 => box01(u).max(box01(v)),
|
||||
ElementKind::Wedge6 => (-u).max(-v).max(u + v - 1.0).max(0.0).max(box01(w)),
|
||||
_ => box01(u).max(box01(v)).max(box01(w)),
|
||||
}
|
||||
}
|
||||
|
||||
/// The nearest point of the parametric domain to `xi`.
|
||||
fn clamp_domain(kind: ElementKind, xi: P) -> P {
|
||||
let c = |x: f64| x.clamp(0.0, 1.0);
|
||||
let simplex = |u: f64, v: f64, w: f64| {
|
||||
let (u, v, w) = (u.max(0.0), v.max(0.0), w.max(0.0));
|
||||
let s = u + v + w;
|
||||
if s > 1.0 { (u / s, v / s, w / s) } else { (u, v, w) }
|
||||
};
|
||||
match kind {
|
||||
ElementKind::Tri3 => {
|
||||
let (u, v, _) = simplex(xi[0], xi[1], 0.0);
|
||||
[u, v, 0.0]
|
||||
}
|
||||
ElementKind::Tet4 => {
|
||||
let (u, v, w) = simplex(xi[0], xi[1], xi[2]);
|
||||
[u, v, w]
|
||||
}
|
||||
ElementKind::Wedge6 => {
|
||||
let (u, v, _) = simplex(xi[0], xi[1], 0.0);
|
||||
[u, v, c(xi[2])]
|
||||
}
|
||||
ElementKind::Quad4 => [c(xi[0]), c(xi[1]), 0.0],
|
||||
_ => [c(xi[0]), c(xi[1]), c(xi[2])],
|
||||
}
|
||||
}
|
||||
|
||||
fn combine(n: &[f64], x: &[P]) -> P {
|
||||
n.iter().zip(x).fold([0.0; 3], |s, (w, p)| add(s, scale(*p, *w)))
|
||||
}
|
||||
|
||||
/// The parametric coordinates of `x` in the cell (Gauss–Newton on the linear map; for a shell,
|
||||
/// of the nearest point of its surface), and the distance left.
|
||||
fn locate(c: &RelaxationCell, x: P) -> (P, f64) {
|
||||
let (_, dim) = shape(c.kind, [0.0; 3]);
|
||||
let mut xi = match c.kind {
|
||||
ElementKind::Tri3 | ElementKind::Tet4 => [0.25; 3],
|
||||
ElementKind::Wedge6 => [1.0 / 3.0, 1.0 / 3.0, 0.5],
|
||||
_ => [0.5; 3],
|
||||
};
|
||||
if dim == 2 {
|
||||
xi[2] = 0.0;
|
||||
}
|
||||
let map = |xi: P| combine(&shape(c.kind, xi).0, &c.at);
|
||||
for _ in 0..20 {
|
||||
let r = sub(x, map(xi));
|
||||
// The Jacobian's columns (the map is at most trilinear: a unit-step difference of the
|
||||
// two sides of `xi` is exact along each axis).
|
||||
let h = 1e-3;
|
||||
let mut j = [[0.0; 3]; 3];
|
||||
for (k, col) in j.iter_mut().enumerate().take(dim) {
|
||||
let (mut a, mut b) = (xi, xi);
|
||||
a[k] += h;
|
||||
b[k] -= h;
|
||||
*col = scale(sub(map(a), map(b)), 0.5 / h);
|
||||
}
|
||||
// Normal equations JᵀJ δ = Jᵀ r.
|
||||
let mut m = [[0.0; 3]; 3];
|
||||
let mut rhs = [0.0; 3];
|
||||
for a in 0..dim {
|
||||
rhs[a] = dot(j[a], r);
|
||||
for b in 0..dim {
|
||||
m[a][b] = dot(j[a], j[b]);
|
||||
}
|
||||
}
|
||||
if dim == 2 {
|
||||
m[2][2] = 1.0;
|
||||
}
|
||||
let det = m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1]) - m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0])
|
||||
+ m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
|
||||
if !(det.abs() > 1e-300) || !det.is_finite() {
|
||||
break;
|
||||
}
|
||||
let solve = |col: usize| {
|
||||
let mut t = m;
|
||||
for row in 0..3 {
|
||||
t[row][col] = rhs[row];
|
||||
}
|
||||
(t[0][0] * (t[1][1] * t[2][2] - t[1][2] * t[2][1]) - t[0][1] * (t[1][0] * t[2][2] - t[1][2] * t[2][0])
|
||||
+ t[0][2] * (t[1][0] * t[2][1] - t[1][1] * t[2][0]))
|
||||
/ det
|
||||
};
|
||||
let delta = [solve(0), solve(1), if dim == 3 { solve(2) } else { 0.0 }];
|
||||
xi = add(xi, delta);
|
||||
if !xi.iter().all(|v| v.is_finite()) || dot(delta, delta) < 1e-28 {
|
||||
break;
|
||||
}
|
||||
}
|
||||
(xi, dist(x, map(clamp_domain(c.kind, xi))))
|
||||
}
|
||||
|
||||
/// The cell's size: its longest corner-to-corner span.
|
||||
fn cell_size(c: &RelaxationCell) -> f64 {
|
||||
let mut s = 0.0f64;
|
||||
for a in &c.at {
|
||||
for b in &c.at {
|
||||
s = s.max(dist(*a, *b));
|
||||
}
|
||||
}
|
||||
s
|
||||
}
|
||||
|
||||
/// Parametric slack accepted around a cell (a node of a finer mesh on a curved face lies off the
|
||||
/// coarse cell's flat side by its chord error).
|
||||
const SLACK: f64 = 0.25;
|
||||
|
||||
/// The field's displacement at `x`: from the cell holding it (or the nearest within the slack),
|
||||
/// with that cell's shape functions; `None` outside the field.
|
||||
pub fn field_displacement(cells: &[RelaxationCell], x: P) -> Option<P> {
|
||||
let mut best: Option<(f64, &RelaxationCell, P)> = None;
|
||||
for c in cells {
|
||||
let size = cell_size(c);
|
||||
let lo = c.at.iter().fold([f64::INFINITY; 3], |m, p| [m[0].min(p[0]), m[1].min(p[1]), m[2].min(p[2])]);
|
||||
let hi = c.at.iter().fold([f64::NEG_INFINITY; 3], |m, p| [m[0].max(p[0]), m[1].max(p[1]), m[2].max(p[2])]);
|
||||
let pad = SLACK * size;
|
||||
if (0..3).any(|k| x[k] < lo[k] - pad || x[k] > hi[k] + pad) {
|
||||
continue;
|
||||
}
|
||||
let (xi, gap) = locate(c, x);
|
||||
let badness = outside(c.kind, xi).max(gap / size.max(f64::MIN_POSITIVE));
|
||||
if badness <= SLACK && best.is_none_or(|(b, _, _)| badness < b) {
|
||||
best = Some((badness, c, xi));
|
||||
}
|
||||
}
|
||||
let (_, c, xi) = best?;
|
||||
let n = shape(c.kind, clamp_domain(c.kind, xi)).0;
|
||||
let d: Vec<P> = c.moved.iter().zip(&c.at).map(|(m, a)| sub(*m, *a)).collect();
|
||||
Some(combine(&n, &d))
|
||||
}
|
||||
|
||||
/// Apply a relaxation field to the mesh: each node of `nodes` (default every node of a measured
|
||||
/// element) inside the field moves by the interpolated displacement as `geometry` allows (on its
|
||||
/// face or edge); a move that would make a valid element invalid is undone; then one guarded
|
||||
/// smoothing sweep (strength `polish`, 0 for none) evens out what the interpolation left. The
|
||||
/// model is not changed.
|
||||
pub fn apply_field(
|
||||
model: &Model,
|
||||
cells: &[RelaxationCell],
|
||||
nodes: Option<&BTreeSet<u32>>,
|
||||
geometry: &dyn Constraints,
|
||||
polish: f64,
|
||||
) -> Result<Relaxed> {
|
||||
let candidates: BTreeSet<u32> = match nodes {
|
||||
Some(n) => n.clone(),
|
||||
None => model.elements().values().filter(|e| quality::is_measured(e.kind)).flat_map(|e| e.nodes.iter().copied()).collect(),
|
||||
};
|
||||
if candidates.len() > fieldcraft_model::MAX_NODES {
|
||||
return Err(Error::Limit("too many nodes".into()));
|
||||
}
|
||||
let skin = skin_nodes(model, &candidates);
|
||||
let mut work = model.clone();
|
||||
let mut moved: BTreeMap<u32, P> = BTreeMap::new();
|
||||
for &n in &candidates {
|
||||
let Some(x) = model.node(n).map(|p| p.xyz) else { continue };
|
||||
let Some(d) = field_displacement(cells, x) else { continue };
|
||||
if !(dot(d, d) > 0.0) {
|
||||
continue;
|
||||
}
|
||||
let freedom = match geometry.freedom(n) {
|
||||
Some(f) => f,
|
||||
None if skin.contains(&n) => Freedom::Fixed,
|
||||
None => Freedom::Free,
|
||||
};
|
||||
let q = match freedom {
|
||||
Freedom::Fixed => None,
|
||||
Freedom::Free => Some(add(x, d)),
|
||||
Freedom::Face(f) => geometry.slide_face(f, x, d),
|
||||
Freedom::Curve(c) => geometry.slide_curve(c, x, d),
|
||||
};
|
||||
if let Some(q) = q.filter(|q| q.iter().all(|v| v.is_finite() && v.abs() <= fieldcraft_model::MAX_COORD)) {
|
||||
work.set_node(n, q)?;
|
||||
moved.insert(n, q);
|
||||
}
|
||||
}
|
||||
// Undo the moves around any element they would invalidate.
|
||||
let touched: Vec<(u32, ElementKind, Vec<u32>)> = model
|
||||
.elements()
|
||||
.iter()
|
||||
.filter(|(_, e)| quality::is_measured(e.kind) && e.nodes.iter().any(|n| moved.contains_key(n)))
|
||||
.map(|(l, e)| (*l, e.kind, e.nodes.clone()))
|
||||
.collect();
|
||||
let at = |m: &Model, nodes: &[u32]| -> Vec<P> { nodes.iter().map(|n| m.node(*n).map_or([0.0; 3], |p| p.xyz)).collect() };
|
||||
for _ in 0..10 {
|
||||
let mut reverted = false;
|
||||
for (label, kind, nodes) in &touched {
|
||||
let x0 = at(model, nodes);
|
||||
let e = Elem { label: *label, kind: *kind, nodes: nodes.clone(), normal: shell_normal(*kind, &x0) };
|
||||
if measure(&e, &x0).1 && !measure(&e, &at(&work, nodes)).1 {
|
||||
for n in nodes {
|
||||
if moved.remove(n).is_some()
|
||||
&& let Some(p) = model.node(*n)
|
||||
{
|
||||
work.set_node(*n, p.xyz)?;
|
||||
reverted = true;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
if !reverted {
|
||||
break;
|
||||
}
|
||||
}
|
||||
let mut out = Relaxed::default();
|
||||
let corners = corner_nodes(model);
|
||||
if polish > 0.0 {
|
||||
let weights = uniform_weights(&work, &moved.keys().copied().filter(|n| corners.contains(n)).collect(), polish.min(1.0))?;
|
||||
if !weights.is_empty() {
|
||||
let r = relax(&work, &weights, 1, geometry)?;
|
||||
for (n, p) in &r.positions {
|
||||
work.set_node(*n, *p)?;
|
||||
moved.insert(*n, *p);
|
||||
}
|
||||
out.after = r.after;
|
||||
}
|
||||
}
|
||||
for (n, p) in moved {
|
||||
let Some(o) = model.node(n) else { continue };
|
||||
let d = dist(o.xyz, p);
|
||||
if d > 0.0 {
|
||||
out.max_displacement = out.max_displacement.max(d);
|
||||
out.moved += usize::from(corners.contains(&n));
|
||||
out.positions.insert(n, p);
|
||||
}
|
||||
}
|
||||
out.iterations = 1;
|
||||
Ok(out)
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests;
|
||||
Reference in new issue
Block a user