diff --git a/.gitignore b/.gitignore
index 52ff58a..b81df1f 100644
--- a/.gitignore
+++ b/.gitignore
@@ -16,3 +16,5 @@ pom.xml.asc
 resources/isle_of_man.svg
 
 resources/small_hill.svg
+
+s.edn
diff --git a/src/walkmap/edge.clj b/src/walkmap/edge.clj
index a91df9c..6ddf3e2 100644
--- a/src/walkmap/edge.clj
+++ b/src/walkmap/edge.clj
@@ -3,7 +3,6 @@
   An edge is a line segment having just a start and an end, with no intervening
   nodes."
   (:require [clojure.math.numeric-tower :as m]
-            [walkmap.polygon :refer [polygon?]]
             [walkmap.vertex :refer [ensure2d ensure3d vertex vertex= vertex?]]))
 
 (defn edge
diff --git a/src/walkmap/polygon.clj b/src/walkmap/polygon.clj
index b68db2d..e3c42b9 100644
--- a/src/walkmap/polygon.clj
+++ b/src/walkmap/polygon.clj
@@ -1,6 +1,7 @@
 (ns walkmap.polygon
   "Essentially the specification for things we shall consider to be polygons."
   (:require [clojure.string :as s]
+            [walkmap.edge :as e]
             [walkmap.utils :refer [kind-type]]
             [walkmap.vertex :refer [vertex?]]))
 
@@ -18,6 +19,12 @@
       (:walkmap.id/id o)
       (or (nil? (:kind o)) (= (:kind o) :polygon)))))
 
+(defn triangle?
+  [o]
+  (and
+    (coll? o)
+    (= (count (:vertices o)) 3)))
+
 (defn polygon
   [vertices]
   (when-not (every? vertex? vertices)
@@ -26,3 +33,15 @@
                "Each item on path must be a vertex: "
                (s/join " " (map kind-type (remove vertex? vertices)))))))
   {:vertices vertices :walkmap.id/id (keyword (gensym "poly")) :kind :polygon})
+
+(defn gradient
+  "Return a unit vector representing the gradient across `triangle`."
+  [triangle]
+  (when-not (triangle? triangle)
+    (throw (IllegalArgumentException.
+             (s/join " " ["Must be a triangle:" (kind-type triangle)]))))
+  (let [order (sort #(max (:z %1) (:z %2)) (:vertices triangle))
+        highest (first order)
+        lowest (last order)]
+     (e/unit-vector (e/edge lowest highest))))
+
diff --git a/src/walkmap/vertex.clj b/src/walkmap/vertex.clj
index da0d1fa..679608e 100644
--- a/src/walkmap/vertex.clj
+++ b/src/walkmap/vertex.clj
@@ -5,6 +5,7 @@
   two vertices, create an edge from them and use `walkmap.edge/length`."
   (:require [clojure.math.numeric-tower :as m]
             [clojure.string :as s]
+            [taoensso.timbre :as l]
             [walkmap.geometry :refer [=ish]]
             [walkmap.utils :refer [truncate]]))
 
@@ -55,6 +56,25 @@
     #(=ish (% v1) (% v2))
     [:x :y :z]))
 
+(defn vertex*
+  "Return a vertex like `v1`, but with each of its coordinates multiplied
+  by the equivalent vertex in `v2`."
+  [v1 v2]
+  (if
+    (and (vertex? v1) (vertex? v2))
+    (let [f (fn [v1 v2 coord]
+              (* (or (coord v1) 0)
+                 ;; one here is deliberate!
+                 (or (coord v2) 1)))]
+      (assoc v1 :x (f v1 v2 :x)
+        :y (f v1 v2 :y)
+        :z (f v1 v2 :z)))
+    (do (l/warn
+          (s/join
+            " "
+            ["in `vertex-multiply`, both must be vectors. v1:" v1 "v2:" v2]))
+      v1)))
+
 (defn vertex
   "Make a vertex with this `x`, `y` and (if provided) `z` values. Returns a map
   with those values, plus a unique `:walkmap.id/id` value, and `:kind` set to `:vertex`.