adding jarvis.jl file, to be linked to the main source file after merging the PR's and updating text.

Author: leios

chapters/computational_geometry/gift_wrapping/jarvis_march/code/jarvis.jl

@@ -0,0 +1,69 @@
+# Struct to hold an x, y position. A tuple would also be fine.
+struct Pos
+    x::Float64
+    y::Float64
+end
+
+# This returns a measure of how far "left" the vector is with a cross product
+function cross(point1::Pos, point2::Pos, point3::Pos)
+    vec1 = Pos(point2.x - point1.x, point2.y - point1.y)
+    vec2 = Pos(point3.x - point2.x, point3.y - point2.y)
+    ret_angle = vec1.x*vec2.y - vec1.y*vec2.x
+    return ret_angle*ret_angle
+end
+
+function jarvis_march(points::Vector{Pos})
+    hull = Vector{Pos}()
+
+    # sorting array based on leftmost point
+    sort!(points, by = item -> item.x)
+    push!(hull, points[1])
+
+    i = 1
+    curr_point = points[2]
+
+    # Find angle between points
+    curr_product = cross(Pos(0,0), hull[1], curr_point)
+
+    # We will hold a temp variable with the highest cross product as we iterate
+    # through all the points and move our hull vector forward.
+    while (curr_point != hull[1])
+        for point in points
+            product = 0.0
+
+            # Special case for the first element when there is no hull[i-1]
+            if (i == 1)
+                if (hull[i] != point)
+                    product = cross(Pos(0,0), hull[i], point)
+                end
+            else
+                if (hull[i] != point && hull[i-1] != point)
+                    product = cross(hull[i-1], hull[i], point)
+                end
+            end
+            if (product > curr_product)
+                curr_point = point
+                curr_product = product
+            end
+        end
+
+        # Pushing to hull, moving simulation forward and resetting the product
+        push!(hull, curr_point)
+        curr_product = 0
+        i += 1
+    end
+
+    return hull
+end
+
+function main()
+
+    # These points are chosen such that there is a clearly defined hull with
+    # several interior points. As a note, these will be generated either 
+    # randomly or via some mesh in practice.
+    points = [Pos(2,1.5), Pos(1, 1), Pos(2, 4), Pos(3, 1), Pos(2,2), Pos(2,0.5)]
+    hull = jarvis_march(points)
+    println(hull)
+end
+
+main()