add function find_image_atoms() used in StructureScene to draw images…

… of atoms

near opposite side of unit cell

with fractional tolerance for proximity to cell as option
also add unit test and fixtures for find_image_atoms()

src/lib/StructureScene.svelte

@@ -10,7 +10,7 @@
   import { pretty_num } from './labels'
   import { element_colors } from './stores'
   import type { PymatgenStructure, Site } from './structure'
-  import { atomic_radii, euclidean_dist } from './structure'
+  import { atomic_radii, euclidean_dist, find_image_atoms } from './structure'
 
   // output of pymatgen.core.Structure.as_dict()
   export let structure: PymatgenStructure | undefined = undefined
@@ -79,8 +79,8 @@
     {@const radius = (same_size_atoms ? 1 : atomic_radii[elem]) * atom_radius}
     <T.SphereGeometry args={[radius, 20, 20]} />
     <T.MeshStandardMaterial />
-    {#each structure.sites as site, idx}
-      {@const { xyz, species } = site}
+    {#each find_image_atoms(structure) as [site_idx, xyz], idx}
+      {@const { species } = structure.sites[site_idx]}
       <Instance
         position={xyz}
         color={$element_colors[species[0].element]}

src/lib/structure.ts

@@ -100,3 +100,53 @@ export function euclidean_dist(p1: Vector, p2: Vector): number {
   const dz = p1[2] - p2[2]
   return Math.sqrt(dx * dx + dy * dy + dz * dz)
 }
+
+function generate_permutations(length: number): number[][] {
+  const result: number[][] = []
+  for (let i = 0; i < Math.pow(2, length); i++) {
+    const binaryString = i.toString(2).padStart(length, `0`)
+    result.push(Array.from(binaryString).map(Number))
+  }
+  return result
+}
+
+export function find_image_atoms(
+  structure: PymatgenStructure,
+  { tolerance = 0.05 }: { tolerance?: number } = {}
+  // fractional tolerance for determining if a site is at the edge of the unit cell
+): Array<[number, Vector]> {
+  const edge_sites: Array<[number, Vector]> = []
+  const permutations = generate_permutations(3)
+
+  structure.sites.forEach((site, idx) => {
+    const abc = site.abc
+    const xyz = site.xyz
+
+    edge_sites.push([idx, xyz])
+
+    // Check if the site is at the edge and determine its image
+    const edges: number[] = [0, 1, 2].filter(
+      (i) => Math.abs(abc[i]) < tolerance || Math.abs(abc[i] - 1) < tolerance
+    )
+
+    const { a, b, c } = structure.lattice
+    if (edges.length > 0) {
+      for (const perm of permutations) {
+        const img_xyz: Vector = xyz.slice()
+        for (const [idx, edge] of edges.entries()) {
+          if (perm[idx] === 1) {
+            // Image atom at the opposite edge
+            if (Math.abs(abc[edge]) < tolerance) {
+              img_xyz[edge] += edge === 0 ? a : edge === 1 ? b : c
+            } else {
+              img_xyz[edge] -= edge === 0 ? a : edge === 1 ? b : c
+            }
+          }
+        }
+        edge_sites.push([idx, img_xyz])
+      }
+    }
+  })
+
+  return edge_sites
+}

tests/unit/fixtures/find_image_atoms/mp-1.json

@@ -0,0 +1,12 @@
+[
+  [0, [0, 0, 0]],
+  [0, [0, 0, 0]],
+  [0, [0, 0, 6.256930122878799]],
+  [0, [0, 6.256930122878799, 0]],
+  [0, [0, 6.256930122878799, 6.256930122878799]],
+  [0, [6.256930122878799, 0, 0]],
+  [0, [6.256930122878799, 0, 6.256930122878799]],
+  [0, [6.256930122878799, 6.256930122878799, 0]],
+  [0, [6.256930122878799, 6.256930122878799, 6.256930122878799]],
+  [1, [3.1284650614394, 3.1284650614393996, 3.1284650614394]]
+]

tests/unit/fixtures/find_image_atoms/mp-1234.json

@@ -0,0 +1,50 @@
+[
+  [0, [6.201186995551753e-16, 3.8561654465837516, 2.3612203355707076e-16]],
+  [0, [6.201186995551753e-16, 3.8561654465837516, 2.3612203355707076e-16]],
+  [0, [6.201186995551753e-16, 3.8561654465837516, 2.3612203355707076e-16]],
+  [0, [6.201186995551753e-16, 3.8561654465837516, 7.712330893167503]],
+  [0, [6.201186995551753e-16, 3.8561654465837516, 7.712330893167503]],
+  [0, [7.712330893167504, 3.8561654465837516, 2.3612203355707076e-16]],
+  [0, [7.712330893167504, 3.8561654465837516, 2.3612203355707076e-16]],
+  [0, [7.712330893167504, 3.8561654465837516, 7.712330893167503]],
+  [0, [7.712330893167504, 3.8561654465837516, 7.712330893167503]],
+  [1, [5.784248169875627, 1.9280827232918758, 1.9280827232918762]],
+  [2, [0, 0, 3.8561654465837516]],
+  [2, [0, 0, 3.8561654465837516]],
+  [2, [0, 0, 3.8561654465837516]],
+  [2, [0, 7.712330893167503, 3.8561654465837516]],
+  [2, [0, 7.712330893167503, 3.8561654465837516]],
+  [2, [7.712330893167503, 0, 3.8561654465837516]],
+  [2, [7.712330893167503, 0, 3.8561654465837516]],
+  [2, [7.712330893167503, 7.712330893167503, 3.8561654465837516]],
+  [2, [7.712330893167503, 7.712330893167503, 3.8561654465837516]],
+  [3, [5.784248169875628, 5.784248169875627, 5.784248169875628]],
+  [4, [3.856165446583752, 3.8561654465837516, 3.856165446583752]],
+  [5, [1.928082723291876, 1.9280827232918758, 5.784248169875628]],
+  [6, [3.8561654465837516, 0, 2.3612203355707076e-16]],
+  [6, [3.8561654465837516, 0, 2.3612203355707076e-16]],
+  [6, [3.8561654465837516, 0, 2.3612203355707076e-16]],
+  [6, [3.8561654465837516, 0, 7.712330893167503]],
+  [6, [3.8561654465837516, 0, 7.712330893167503]],
+  [6, [3.8561654465837516, 7.712330893167503, 2.3612203355707076e-16]],
+  [6, [3.8561654465837516, 7.712330893167503, 2.3612203355707076e-16]],
+  [6, [3.8561654465837516, 7.712330893167503, 7.712330893167503]],
+  [6, [3.8561654465837516, 7.712330893167503, 7.712330893167503]],
+  [7, [1.9280827232918767, 5.784248169875627, 1.9280827232918762]],
+  [8, [0.964041361645938, 0.9640413616459379, 0.964041361645938]],
+  [9, [4.82020680822969, 2.8921240849378136, 6.748289531521566]],
+  [10, [6.748289531521565, 0.9640413616459379, 6.748289531521566]],
+  [11, [2.892124084937814, 2.8921240849378136, 0.9640413616459382]],
+  [12, [0.9640413616459387, 4.820206808229689, 4.82020680822969]],
+  [13, [4.82020680822969, 6.748289531521565, 2.8921240849378145]],
+  [14, [6.748289531521566, 4.820206808229689, 2.8921240849378145]],
+  [15, [2.8921240849378145, 6.748289531521565, 4.82020680822969]],
+  [16, [4.820206808229689, 0.9640413616459379, 4.82020680822969]],
+  [17, [0.9640413616459383, 2.8921240849378136, 2.892124084937814]],
+  [18, [2.8921240849378136, 0.9640413616459379, 2.892124084937814]],
+  [19, [6.748289531521566, 2.8921240849378136, 4.82020680822969]],
+  [20, [4.82020680822969, 4.820206808229689, 0.9640413616459385]],
+  [21, [0.964041361645939, 6.748289531521565, 6.748289531521566]],
+  [22, [2.8921240849378145, 4.820206808229689, 6.748289531521566]],
+  [23, [6.748289531521566, 6.748289531521565, 0.9640413616459387]]
+]

tests/unit/fixtures/find_image_atoms/mp-2.json

@@ -0,0 +1,38 @@
+[
+  [0, [0, 0, 0]],
+  [0, [0, 0, 0]],
+  [0, [0, 0, 3.9173015749846063]],
+  [0, [0, 3.9173015749846063, 0]],
+  [0, [0, 3.9173015749846063, 3.9173015749846063]],
+  [0, [3.9173015749846063, 0, 0]],
+  [0, [3.9173015749846063, 0, 3.9173015749846063]],
+  [0, [3.9173015749846063, 3.9173015749846063, 0]],
+  [0, [3.9173015749846063, 3.9173015749846063, 3.9173015749846063]],
+  [1, [3.149750694173353e-16, 1.9586507874923031, 1.9586507874923034]],
+  [1, [3.149750694173353e-16, 1.9586507874923031, 1.9586507874923034]],
+  [1, [3.149750694173353e-16, 1.9586507874923031, 1.9586507874923034]],
+  [1, [3.149750694173353e-16, 1.9586507874923031, 1.9586507874923034]],
+  [1, [3.149750694173353e-16, 1.9586507874923031, 1.9586507874923034]],
+  [1, [3.9173015749846067, 1.9586507874923031, 1.9586507874923034]],
+  [1, [3.9173015749846067, 1.9586507874923031, 1.9586507874923034]],
+  [1, [3.9173015749846067, 1.9586507874923031, 1.9586507874923034]],
+  [1, [3.9173015749846067, 1.9586507874923031, 1.9586507874923034]],
+  [2, [1.9586507874923031, 0, 1.9586507874923034]],
+  [2, [1.9586507874923031, 0, 1.9586507874923034]],
+  [2, [1.9586507874923031, 0, 1.9586507874923034]],
+  [2, [1.9586507874923031, 0, 1.9586507874923034]],
+  [2, [1.9586507874923031, 0, 1.9586507874923034]],
+  [2, [1.9586507874923031, 3.9173015749846063, 1.9586507874923034]],
+  [2, [1.9586507874923031, 3.9173015749846063, 1.9586507874923034]],
+  [2, [1.9586507874923031, 3.9173015749846063, 1.9586507874923034]],
+  [2, [1.9586507874923031, 3.9173015749846063, 1.9586507874923034]],
+  [3, [1.9586507874923034, 1.9586507874923031, 2.3986554175498917e-16]],
+  [3, [1.9586507874923034, 1.9586507874923031, 2.3986554175498917e-16]],
+  [3, [1.9586507874923034, 1.9586507874923031, 2.3986554175498917e-16]],
+  [3, [1.9586507874923034, 1.9586507874923031, 2.3986554175498917e-16]],
+  [3, [1.9586507874923034, 1.9586507874923031, 2.3986554175498917e-16]],
+  [3, [1.9586507874923034, 1.9586507874923031, 3.9173015749846067]],
+  [3, [1.9586507874923034, 1.9586507874923031, 3.9173015749846067]],
+  [3, [1.9586507874923034, 1.9586507874923031, 3.9173015749846067]],
+  [3, [1.9586507874923034, 1.9586507874923031, 3.9173015749846067]]
+]