Deform the assembly

This seems like a good starting point, even though the code is messy and
the deformation routine has some numerical quirks. Note that the translation
direction is mixed up: the keys are for x, but the velocity field is for z.

app-proto/src/assembly.rs

@@ -1,4 +1,4 @@
-use nalgebra::{DMatrix, DVector, Vector3};
+use nalgebra::{DMatrix, DVector, DVectorView, Vector3};
 use rustc_hash::FxHashMap;
 use slab::Slab;
 use std::{collections::BTreeSet, sync::atomic::{AtomicU64, Ordering}};
@@ -152,6 +152,13 @@ impl Assembly {
         let id = elt.id.clone();
         let key = self.elements.update(|elts| elts.insert(elt));
         self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, key));
+        
+        // realize to update the tangent space
+        /* KLUDGE */
+        // since the newly inserted element is unconstrained, we should be able
+        // to update the tangent space without recomputing the Hessian and its
+        // eigendecomposition
+        self.realize();
     }
     
     pub fn try_insert_element(&self, elt: Element) -> bool {
@@ -266,6 +273,7 @@ impl Assembly {
         ));
         console::log_2(&JsValue::from("Steps:"), &JsValue::from(history.scaled_loss.len() - 1));
         console::log_2(&JsValue::from("Loss:"), &JsValue::from(*history.scaled_loss.last().unwrap()));
+        console::log_2(&JsValue::from("Tangent dimension:"), &JsValue::from(tangent.dim()));
         
         if success {
             // read out the solution
@@ -279,4 +287,41 @@ impl Assembly {
             self.tangent.set_silent(tangent);
         }
     }
+    
+    // --- deformation ---
+    
+    pub fn deform(&self, element_motions: Vec<(ElementKey, DVectorView<f64>)>) {
+        /* KLUDGE */
+        // when the tangent space is zero, we currently need to avoid calling
+        // its `proj` method, because it will panic rather than returning zero.
+        // in the future, we'll want a more intentionally designed system for
+        // handling this case
+        if self.tangent.with(|tan| tan.dim() <= 0) {
+            console::log_1(&JsValue::from("The assembly is rigid"));
+            return;
+        }
+        
+        const ELEMENT_DIM: usize = 5;
+        let assembly_dim = self.elements.with(|elts| elts.len());
+        let mut motion_proj = DMatrix::zeros(ELEMENT_DIM, assembly_dim);
+        
+        // project the element motions onto the tangent space of the solution
+        // variety, and sum them to get a deformation of the whole assembly
+        for (elt_key, elt_motion) in element_motions {
+            let column_index = self.elements.with(|elts| elts[elt_key].column_index);
+            motion_proj += self.tangent.with(|tan| tan.proj(&elt_motion, column_index));
+        }
+        
+        // step the configuration linearly along the tangent space of the
+        // solution variety
+        for (_, elt) in self.elements.get_clone_untracked() {
+            elt.representation.update_silent(|rep| {
+                let rep_next = &*rep + motion_proj.column(elt.column_index);
+                rep.set_column(0, &rep_next);
+            });
+        }
+        
+        // bring the configuration back onto the solution variety
+        self.realize();
+    }
 }