feat(shader-ast-stdlib): add SDF polyhedra fns

packages/shader-ast-stdlib/src/sdf/polyhedra.ts

@@ -0,0 +1,118 @@
+import {
+    abs,
+    add,
+    defn,
+    div,
+    dot,
+    FLOAT0,
+    FLOAT1,
+    FloatTerm,
+    max,
+    PHI,
+    pow,
+    ret,
+    sub,
+    TaggedFn2,
+    TaggedFn3,
+    vec3,
+    Vec3Term,
+} from "@thi.ng/shader-ast";
+
+// could use @thi.ng/vectors, but avoiding dependency
+const normalize = ([x, y, z]: number[]) => {
+    const m = 1 / Math.hypot(x, y, z);
+    return [x * m, y * m, z * m];
+};
+
+const phi = PHI.val;
+
+const GDF = [
+    [1, 0, 0],
+    [0, 1, 0],
+    [0, 0, 1],
+    [1, 1, 1],
+    [-1, 1, 1],
+    [1, -1, 1],
+    [1, 1, -1],
+    [0, 1, phi + 1],
+    [0, -1, phi + 1],
+    [phi + 1, 0, 1],
+    [-phi - 1, 0, 1],
+    [1, phi + 1, 0],
+    [-1, phi + 1, 0],
+    [0, phi, 1],
+    [0, -phi, 1],
+    [1, 0, phi],
+    [-1, 0, phi],
+    [phi, 1, 0],
+    [-phi, 1, 0],
+].map((v) => vec3(...(<[]>normalize(v))));
+
+/**
+ * @remarks
+ * Based on: "Generalized Distance Functions" (E. Akleman, J. Chen)
+ * http://people.tamu.edu/~ergun/research/implicitmodeling/papers/sm99.pdf
+ *
+ * Also based on: HG_SDF (Mercury Demogroup)
+ *
+ * @param id
+ * @param vecs
+ */
+const defGDF = (
+    id: string,
+    vecs: Vec3Term[]
+): [
+    TaggedFn2<"vec3", "float", "float">,
+    TaggedFn3<"vec3", "float", "float", "float">
+] => [
+    defn("float", id, ["vec3", "float"], (p, r) => [
+        ret(
+            sub(
+                vecs.reduce(
+                    (acc: FloatTerm, v) => max(acc, abs(dot(p, v))),
+                    FLOAT0
+                ),
+                r
+            )
+        ),
+    ]),
+    defn("float", id + "Smooth", ["vec3", "float", "float"], (p, r, e) => [
+        ret(
+            sub(
+                pow(
+                    vecs.reduce(
+                        (acc: FloatTerm, v) => add(acc, pow(abs(dot(p, v)), e)),
+                        FLOAT0
+                    ),
+                    div(FLOAT1, e)
+                ),
+                r
+            )
+        ),
+    ]),
+];
+
+export const [sdfOctahedron, sdfOctahedronSmooth] = defGDF(
+    "sdfOctahedron",
+    GDF.slice(3, 7)
+);
+
+export const [sdfDodecahedron, sdfDodecahedronSmooth] = defGDF(
+    "sdfDodecahedron",
+    GDF.slice(13)
+);
+
+export const [sdfIcosahedron, sdfIcosahedronSmooth] = defGDF(
+    "sdfIcosahedron",
+    GDF.slice(3, 13)
+);
+
+export const [sdfTruncatedOctahedron, sdfTruncatedOctahedronSmooth] = defGDF(
+    "sdfTruncatedOctahedron",
+    GDF.slice(0, 7)
+);
+
+export const [sdfTruncatedIcosahedron, sdfTruncatedIcosahedronSmooth] = defGDF(
+    "sdfTruncatedIcosahedron",
+    GDF.slice(3)
+);