From 7ddb44a0eed82833f8da08dc0a32e9d0817f5c30 Mon Sep 17 00:00:00 2001
From: Daniel VandenHeuvel <95613936+DanielVandH@users.noreply.github.com>
Date: Fri, 11 Aug 2023 07:05:40 +1000
Subject: [PATCH] Clipping Voronoi tessellations to arbitrary bounding boxes
 (#76)

---
 Project.toml                              |   2 +-
 docs/src/tessellations/figs/unbounded.png | Bin 82217 -> 82490 bytes
 src/DelaunayTriangulation.jl              |   3 +
 src/data_structures/voronoi/voronoi.jl    | 164 ++-------------
 src/geometry_utils/intersections.jl       |  89 +++++++-
 src/geometry_utils/polygons.jl            |   3 +-
 src/geometry_utils/sutherland_hodgman.jl  |  89 ++++++++
 src/interfaces/points.jl                  |  24 ++-
 src/predicates/general.jl                 |  71 ++++++-
 src/voronoi/coordinates.jl                | 231 ++++++++++++++++++++
 src/voronoi/main.jl                       |  18 +-
 test/geo_utils.jl                         | 173 ++++++++++++++-
 test/interfaces/points.jl                 |   9 +-
 test/temp_makie.jl                        |   3 +-
 test/voronoi/voronoi.jl                   | 245 ++++++++++++++++++----
 15 files changed, 920 insertions(+), 204 deletions(-)
 create mode 100644 src/geometry_utils/sutherland_hodgman.jl
 create mode 100644 src/voronoi/coordinates.jl

diff --git a/Project.toml b/Project.toml
index 06acbb797..fa8aa1630 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "DelaunayTriangulation"
 uuid = "927a84f5-c5f4-47a5-9785-b46e178433df"
 authors = ["Daniel VandenHeuvel <danj.vandenheuvel@gmail.com>"]
-version = "0.8.3"
+version = "0.8.4"
 
 [deps]
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
diff --git a/docs/src/tessellations/figs/unbounded.png b/docs/src/tessellations/figs/unbounded.png
index faa337536686c6b041921541930ca1b0b3f08663..a8cfa47816f882de7201ff880c3d68f0e3e2dc8c 100644
GIT binary patch
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diff --git a/src/DelaunayTriangulation.jl b/src/DelaunayTriangulation.jl
index e7bb2878e..20eedc9f8 100644
--- a/src/DelaunayTriangulation.jl
+++ b/src/DelaunayTriangulation.jl
@@ -191,6 +191,7 @@ export convert_boundary_points_to_indices
 include("geometry_utils/polygons.jl")
 include("geometry_utils/polylabel.jl")
 include("geometry_utils/intersections.jl")
+include("geometry_utils/sutherland_hodgman.jl")
 
 const polylabel = pole_of_inaccessibility
 
@@ -205,8 +206,10 @@ include("voronoi/main.jl")
 include("voronoi/unbounded_construction.jl")
 include("voronoi/clipped_construction.jl")
 include("voronoi/lloyd.jl")
+include("voronoi/coordinates.jl")
 
 export voronoi
 export centroidal_smooth
+export get_polygon_coordinates
 
 end
\ No newline at end of file
diff --git a/src/data_structures/voronoi/voronoi.jl b/src/data_structures/voronoi/voronoi.jl
index c9e6a2f1f..cb8cd57e2 100644
--- a/src/data_structures/voronoi/voronoi.jl
+++ b/src/data_structures/voronoi/voronoi.jl
@@ -16,6 +16,9 @@ while the values are the coordinates; we need to use a `Dict` in case the triang
 
 The points defining the vertices of the polygons. The points are not guaranteed to be unique if a circumcenter 
 appears on the boundary and you are considering a clipped tessellation.
+
+See also [`get_polygon_coordinates`](@ref).
+
 - `polygons::Dict{I, Vector{I}}`
 
 A `Dict` mapping a polygon index (same as a generator index) to the vertices of the polygon. The polygons are given in counter-clockwise order,
@@ -150,136 +153,6 @@ function get_triangle_to_circumcenter(vor::VoronoiTessellation, T)
     end
 end
 
-"""
-    get_polygon_coordinates(vor::VoronoiTessellation, j, bbox=nothing)
-
-Gets the coordinates of the `j`th polygon of `vor`. If `bbox` is given, then the coordinates are clipped to the bounding box `bbox`, with 
-`bbox` a `Tuple` of the form `(xmin, xmax, ymin, ymax)` so that the bounding box is `[xmin, xmax] × [ymin, ymax]`.
-
-See also [`polygon_bounds`](@ref) for `bbox`.
-"""
-function get_polygon_coordinates(vorn::VoronoiTessellation, j, bbox=nothing)
-    C = get_polygon(vorn, j)
-    F = number_type(vorn)
-    coords = Vector{NTuple{2,F}}(undef, length(C) - 1)
-    unbounded_indices = (0, 0)
-    for i in firstindex(C):(lastindex(C)-1)
-        if !is_boundary_index(C[i])
-            coords[i] = get_polygon_point(vorn, C[i])
-        else
-            ghost_tri = get_circumcenter_to_triangle(vorn, C[i])
-            u, v, _ = indices(ghost_tri) # w is the ghost vertex
-            p, q = get_generator(vorn, u, v)
-            px, py = _getxy(p)
-            qx, qy = _getxy(q)
-            @assert bbox[1] ≤ px ≤ bbox[2] && bbox[1] ≤ qx ≤ bbox[2] && bbox[3] ≤ py ≤ bbox[4] && bbox[3] ≤ qy ≤ bbox[4] "The bounding box is not large enough to contain the circumcenter."
-            m = (px + qx) / 2, (py + qy) / 2
-            is_first = is_first_boundary_index(C, i)
-            if is_first
-                prev_index = previndex_circular(C, i)
-                r = get_polygon_point(vorn, C[prev_index])
-            else
-                next_index = nextindex_circular(C, i)
-                r = get_polygon_point(vorn, C[next_index])
-            end
-            if r == m # It's possible for the circumcenter to lie on the edge and exactly at the midpoint (e.g. [(0.0,1.0),(-1.0,2.0),(-2.0,-1.0)]). In this case, just rotate 
-                mx, my = _getxy(m)
-                dx, dy = qx - mx, qy - my
-                rotated_dx, rotated_dy = -dy, dx
-                r = mx + rotated_dx, my + rotated_dy
-                if is_right(point_position_relative_to_line(p, q, r))
-                    rotated_dx, rotated_dy = dy, -dx
-                    r = mx + rotated_dx, my + rotated_dy
-                end
-            end
-            r = _getxy(r)
-            if is_left(point_position_relative_to_line(p, q, r))
-                intersection = intersection_of_ray_with_bounding_box(m, r, bbox[1], bbox[2], bbox[3], bbox[4])
-            else
-                intersection = intersection_of_ray_with_bounding_box(r, m, bbox[1], bbox[2], bbox[3], bbox[4])
-            end
-            coords[i] = intersection
-            if is_first
-                unbounded_indices = (i, unbounded_indices[2])
-            else
-                unbounded_indices = (unbounded_indices[1], i)
-            end
-        end
-    end
-    if all(≠(0), unbounded_indices) # Need to check if we need to insert the corner point of the polygon 
-        xmin, xmax, ymin, ymax = bbox
-        c1 = coords[unbounded_indices[1]]
-        c2 = coords[unbounded_indices[2]]
-        side1 = identify_side(c1, xmin, xmax, ymin, ymax)
-        side2 = identify_side(c2, xmin, xmax, ymin, ymax)
-        if side1 ≠ side2 # There is a better way to do this if we treat sides as numbers 0, 1, 2, 3 rather than symbols, but it doesn't really matter.
-            if side1 == :bottom && side2 == :right 
-                corner = xmax, ymin
-                insert!(coords, unbounded_indices[1] + 1, corner)
-            elseif side1 == :bottom && side2 == :top 
-                corner1 = xmax, ymin 
-                corner2 = xmax, ymax 
-                insert!(coords, unbounded_indices[1] + 1, corner1)
-                insert!(coords, unbounded_indices[1] + 2, corner2)
-            elseif side1 == :bottom && side2 == :left
-                corner1 = xmax, ymin 
-                corner2 = xmax, ymax 
-                corner3 = xmin, ymax
-                insert!(coords, unbounded_indices[1] + 1, corner1)
-                insert!(coords, unbounded_indices[1] + 2, corner2)
-                insert!(coords, unbounded_indices[1] + 3, corner3)
-            elseif side1 == :right && side2 == :top
-                corner = xmax, ymax
-                insert!(coords, unbounded_indices[1] + 1, corner)
-            elseif side1 == :right && side2 == :left
-                corner1 = xmax, ymax
-                corner2 = xmin, ymax
-                insert!(coords, unbounded_indices[1] + 1, corner1)
-                insert!(coords, unbounded_indices[1] + 2, corner2)
-            elseif side1 == :right && side2 == :bottom
-                corner1 = xmax, ymax
-                corner2 = xmin, ymax
-                corner3 = xmin, ymin
-                insert!(coords, unbounded_indices[1] + 1, corner1)
-                insert!(coords, unbounded_indices[1] + 2, corner2)
-                insert!(coords, unbounded_indices[1] + 3, corner3)
-            elseif side1 == :top && side2 == :left
-                corner = xmin, ymax
-                insert!(coords, unbounded_indices[1] + 1, corner)
-            elseif side1 == :top && side2 == :bottom
-                corner1 = xmin, ymax
-                corner2 = xmin, ymin
-                insert!(coords, unbounded_indices[1] + 1, corner1)
-                insert!(coords, unbounded_indices[1] + 2, corner2)
-            elseif side1 == :top && side2 == :right
-                corner1 = xmin, ymax
-                corner2 = xmin, ymin
-                corner3 = xmax, ymin
-                insert!(coords, unbounded_indices[1] + 1, corner1)
-                insert!(coords, unbounded_indices[1] + 2, corner2)
-                insert!(coords, unbounded_indices[1] + 3, corner3)
-            elseif side1 == :left && side2 == :bottom
-                corner = xmin, ymin
-                insert!(coords, unbounded_indices[1] + 1, corner)
-            elseif side1 == :left && side2 == :right
-                corner1 = xmin, ymin
-                corner2 = xmax, ymin
-                insert!(coords, unbounded_indices[1] + 1, corner1)
-                insert!(coords, unbounded_indices[1] + 2, corner2)
-            elseif side1 == :left && side2 == :top
-                corner1 = xmin, ymin
-                corner2 = xmax, ymin
-                corner3 = xmax, ymax
-                insert!(coords, unbounded_indices[1] + 1, corner1)
-                insert!(coords, unbounded_indices[1] + 2, corner2)
-                insert!(coords, unbounded_indices[1] + 3, corner3)
-            end
-        end
-    end
-    push!(coords, coords[begin])
-    return coords
-end
-
 """
     get_neighbouring_boundary_edges(vor::VoronoiTessellation, e)
 
@@ -475,23 +348,28 @@ Gets the centroid of the polygon with index `i` in `vor`.
 get_centroid(vor::VoronoiTessellation, i) = polygon_features(vor, i)[2]
 
 """
-    polygon_bounds(vorn::VoronoiTessellation, unbounded_extension_factor=0.0)
+    polygon_bounds(vorn::VoronoiTessellation, unbounded_extension_factor=0.0; include_polygon_vertices=true)
 
 Gets the bounding box of the polygons in `vorn`. If `unbounded_extension_factor` is positive, the bounding box is extended by this factor in each direction,
 proportional to the width of each axis.
+
+If `include_polygon_vertices=true`, then the bounds both the generators and the polygons. Otherwise, only the generators 
+will be considered.
 """
-function polygon_bounds(vorn::VoronoiTessellation, unbounded_extension_factor=0.0)
+function polygon_bounds(vorn::VoronoiTessellation, unbounded_extension_factor=0.0; include_polygon_vertices=true)
     F = number_type(vorn)
     xmin = typemax(F)
     xmax = typemin(F)
     ymin = typemax(F)
     ymax = typemin(F)
-    for i in each_polygon_vertex(vorn)
-        x, y = _getxy(get_polygon_point(vorn, i))
-        xmin = min(xmin, x)
-        xmax = max(xmax, x)
-        ymin = min(ymin, y)
-        ymax = max(ymax, y)
+    if include_polygon_vertices
+        for i in each_polygon_vertex(vorn)
+            x, y = _getxy(get_polygon_point(vorn, i))
+            xmin = min(xmin, x)
+            xmax = max(xmax, x)
+            ymin = min(ymin, y)
+            ymax = max(ymax, y)
+        end
     end
     for i in each_generator(vorn)
         x, y = _getxy(get_generator(vorn, i))
@@ -500,11 +378,11 @@ function polygon_bounds(vorn::VoronoiTessellation, unbounded_extension_factor=0.
         ymin = min(ymin, y)
         ymax = max(ymax, y)
     end
-    xmin -= unbounded_extension_factor * (xmax - xmin)
-    xmax += unbounded_extension_factor * (xmax - xmin)
-    ymin -= unbounded_extension_factor * (ymax - ymin)
-    ymax += unbounded_extension_factor * (ymax - ymin)
-    return xmin, xmax, ymin, ymax
+    _xmin = xmin - unbounded_extension_factor * (xmax - xmin)
+    _xmax = xmax + unbounded_extension_factor * (xmax - xmin)
+    _ymin = ymin - unbounded_extension_factor * (ymax - ymin)
+    _ymax = ymax + unbounded_extension_factor * (ymax - ymin)
+    return _xmin, _xmax, _ymin, _ymax
 end
 
 """
diff --git a/src/geometry_utils/intersections.jl b/src/geometry_utils/intersections.jl
index 11849605e..efc2c4838 100644
--- a/src/geometry_utils/intersections.jl
+++ b/src/geometry_utils/intersections.jl
@@ -197,4 +197,91 @@ function classify_and_compute_segment_intersection(a, b, c, d)
         F = number_type(a)
         return cert, cert_c, cert_d, (F(NaN), F(NaN))
     end
-end
\ No newline at end of file
+end
+
+"""
+    intersection_of_ray_with_edge(p, q, a, b)
+
+Given a ray starting at `p` and in the direction of `q` out to 
+infinity, finds the intersection of the ray with the edge from `a` to `b`.
+If no such intersection exists, then the coordinates of the intersection are returned 
+as `(NaN, NaN)`.
+"""
+function intersection_of_ray_with_edge(p, q, a, b)
+    p1, p2 = _getxy(p)
+    q1, q2 = _getxy(q)
+    a1, a2 = _getxy(a)
+    b1, b2 = _getxy(b)
+    den = a2 * q1 - a2 * p1 - b1 * p2 + b2 * p1 + b1 * q2 - b2 * q1 + a1 * (p2 - q2)
+    t = -(a1 * b2 - a2 * b1 - a1 * p2 + a2 * p1 + b1 * p2 - b2 * p1) / den
+    u = (a2 * q1 - a2 * p1 + p1 * q2 - p2 * q1 + a1 * (p2 - q2)) / den
+    if t < 0 || u < 0 || u > 1
+        return (NaN, NaN)
+    else
+        return (p1 + t * (q1 - p1), p2 + t * (q2 - p2))
+    end
+end
+
+"""
+    liang_barsky(a, b, c, d, p, q)
+
+Applies the Liang-Barsky algorithm to find the intersection of the line segment from `p` to `q`
+with the rectangle from `[a, b] × [c, d]`. Returns `(u, v)`, where:
+
+- If there is an intersection, then `u` and `v` are the coordinates of the two intersections. 
+- If there is no intersection, then `u = v = (NaN, NaN)`.
+"""
+function liang_barsky(a, b, c, d, p, q)
+    t1 = 0.0
+    t2 = 1.0
+    px, py = _getxy(p)
+    qx, qy = _getxy(q)
+    Δx = qx - px
+    t1, t2, inside = liang_barsky_clipper(-Δx, px - a, t1, t2)
+    if inside
+        t1, t2, inside = liang_barsky_clipper(Δx, b - px, t1, t2)
+        if inside
+            Δy = qy - py
+            t1, t2, inside = liang_barsky_clipper(-Δy, py - c, t1, t2)
+            if inside
+                t1, t2, inside = liang_barsky_clipper(Δy, d - py, t1, t2)
+                if inside
+                    if t2 < 1
+                        qx = px + t2 * Δx
+                        qy = py + t2 * Δy
+                    end
+                    if t1 > 0
+                        px = px + t1 * Δx
+                        py = py + t1 * Δy
+                    end
+                end
+            end
+        end
+    end
+    if inside
+        return (px, py), (qx, qy)
+    else
+        return (NaN, NaN), (NaN, NaN)
+    end
+end
+function liang_barsky_clipper(p, q, t1, t2)
+    inside = true
+    if p < 0
+        r = q / p
+        if r > t2
+            inside = false
+        elseif r > t1
+            t1 = r
+        end
+    elseif p > 0
+        r = q / p
+        if r < t1
+            inside = false
+        elseif r < t2
+            t2 = r
+        end
+    elseif q < 0
+        inside = false
+    end
+    return t1, t2, inside
+end
diff --git a/src/geometry_utils/polygons.jl b/src/geometry_utils/polygons.jl
index 8b93bc9a6..c0c178f89 100644
--- a/src/geometry_utils/polygons.jl
+++ b/src/geometry_utils/polygons.jl
@@ -245,4 +245,5 @@ function sort_convex_polygon!(vertices, points)
     vert_to_angle = v -> (to_angle ∘ get_point)(points, v)
     sort!(vertices, by=vert_to_angle)
     return vertices
-end 
\ No newline at end of file
+end 
+
diff --git a/src/geometry_utils/sutherland_hodgman.jl b/src/geometry_utils/sutherland_hodgman.jl
new file mode 100644
index 000000000..5700903e1
--- /dev/null
+++ b/src/geometry_utils/sutherland_hodgman.jl
@@ -0,0 +1,89 @@
+struct Polygon{T,V,P} <: AbstractVector{T}
+    vertices::V
+    points::P
+    @inline function Polygon(vertices::V, points::P) where {V,P}
+        p = get_point(points, vertices[begin])
+        T = typeof(p)
+        if vertices[begin] ≠ vertices[end]
+            return new{T,V,P}(vertices, points)
+        else
+            _verts = @views vertices[begin:(end-1)]
+            return new{T,typeof(_verts),P}(_verts, points)
+        end
+    end
+end
+Base.size(P::Polygon) = (length(P.vertices),)
+Base.getindex(P::Polygon, i::Int) = get_point(P.points, P.vertices[i])
+Base.getindex(P::Polygon, i::Vararg{Int,N}) where {N} =
+    map(i) do j
+        P[j]
+    end
+
+"""
+    clip_polygon(vertices, points, clip_vertices, clip_points)
+
+Clips the counter-clockwise polygon defined by `(vertices, points)` against the clip 
+polygon `(clip_vertices, clip_points)`, assumed to be convex and counter-clockwise. The 
+Sutherland-Hodgman algorithm is used. It is assumed that 
+`vertices[begin] == vertices[end]` and `clip_vertices[begin] == clip_vertices[end]`.
+
+The returned result is another counter-clockwise polygon `P` that also satisfies `P[begin] == P[end]`.
+
+Note that this algorithm may potentially return overlapping edges, but this is fine for rendering.
+"""
+function clip_polygon(vertices, points, clip_vertices, clip_points)
+    return clip_polygon(Polygon(vertices, points), Polygon(clip_vertices, clip_points))
+end
+
+"""
+    clip_polygon_to_edge(input_list, q, p)
+
+Clips the input polygon `input_list` against the edge `qp`. This is the 
+intermediate step used in the Sutherland-Hodgman algorithm.
+"""
+function clip_polygon_to_edge(input_list, q, p)
+    output_list = eltype(input_list)[]
+    s = input_list[end]
+    for vertex in input_list
+        # By considering s = input_list[end], we can consider each edge of the 
+        # input polygon one at a time, with the initial edge being s-vertex. 
+        # The first step is to check if vertex is to the left or to the right of the 
+        # edge qp. If it's to the left, then it is outside of the original polygon  
+        # (note the assumption here that the poylgon is counter-clockwise).
+        if (is_left ∘ point_position_relative_to_line)(q, p, vertex)
+            # Now that we know that vertex is outside of the polygon, we need to know 
+            # if there is any intersection to consider. In particular, does s-vertex intersect 
+            # the edge qp? If s is also to the left of the line, then no there is no intersection 
+            # and we can safely ignore the intersection (note that this check makes the implicit 
+            # assumption that the clipping polygon is convex). If s is to the right of the line,
+            # then there is an intersection and we need to consider it.
+            flag = point_position_relative_to_line(q, p, s)
+            if !is_left(flag) # allow for is_on. If left, then the edge s-vertex is not inside the clipping polygon, so there is no intersection to consider
+                r = segment_intersection_coordinates(q, p, s, vertex)
+                push!(output_list, r)
+            end
+            # We still need to add back in the vertex to the output list regardless so that 
+            # we can keep going with the next edge of the clipping polygon easily.
+            push!(output_list, vertex)
+        elseif (is_left ∘ point_position_relative_to_line)(q, p, s)
+            # In this case, vertex is to the right of qp, but now s is outside. This means there 
+            # is an intersection of s-vertex with qp.
+            r = segment_intersection_coordinates(q, p, s, vertex)
+            push!(output_list, r)
+        end
+        s = vertex
+    end
+    return output_list
+end
+
+function clip_polygon(poly::Polygon, clip_poly::Polygon{T}) where {T}
+    output_list = poly
+    q = clip_poly[end]
+    for p in clip_poly
+        input_list = output_list 
+        output_list = clip_polygon_to_edge(input_list, q, p)
+        q = p
+    end
+    !isempty(output_list) && push!(output_list, output_list[begin])
+    return output_list::Vector{T}
+end
\ No newline at end of file
diff --git a/src/interfaces/points.jl b/src/interfaces/points.jl
index 10f03ffaa..53db5455d 100644
--- a/src/interfaces/points.jl
+++ b/src/interfaces/points.jl
@@ -52,7 +52,7 @@ Given a collection of points `pts`, returns a `Tuple`
 of the `x` and `y` coordinates of the `i`th point in 
 the collection. The methods currently defined are 
 
-    getpoint(pts::AbstractVector, i)
+    getpoint(pts::AbstractVecOrTuple, i)
     getpoint(pts::AbstractMatrix, i)
 
 You can extend this function as you need. 
@@ -66,7 +66,7 @@ function getpoint end
 function getpoint(::P, ::Integer) where {P}
     return error("The getpoint function has not been defined for the type $P.")
 end
-function getpoint(pts::AbstractVector, i::Integer)
+function getpoint(pts::Union{AbstractVector,Tuple}, i::Integer)
     pt = pts[i]
     x, y = getx(pt), gety(pt)
     return (x, y)
@@ -76,7 +76,7 @@ function getpoint(pts::AbstractMatrix, i::Integer)
     x, y = getx(pt), gety(pt)
     return (x, y)
 end
-getpoint(pts, p) = (getx(p), gety(p))
+getpoint(pts, p) = (getx(p), gety(p)) # so that we can mix points and vertices
 
 """
     get_point(pts::P, i...)
@@ -133,7 +133,7 @@ Given a collection of points `pts`, returns an iterator
 over the indices of the collection. The methods currently 
 defined are 
 
-    each_point_index(pts::AbstractVector)
+    each_point_index(pts::AbstractVecOrTuple)
     each_point_index(pts::AbstractMatrix) 
 
 with the first returning `eachindex(pts)` and the second 
@@ -144,7 +144,7 @@ function each_point_index end
 function each_point_index(::P) where {P}
     return error("The each_point_index function has not been defined for the type $P.")
 end
-each_point_index(pts::AbstractVector) = eachindex(pts)
+each_point_index(pts::Union{AbstractVector,Tuple}) = eachindex(pts)
 each_point_index(pts::AbstractMatrix) = axes(pts, 2)
 
 """
@@ -154,7 +154,7 @@ For a given collection of points `p`, returns an iterator that
 goes over each point in the collection. The methods currently 
 defined are 
 
-    each_point(pts::AbstractVector)
+    each_point(pts::AbstractVecOrTuple)
     each_point(pts::AbstractMatrix)
 
 with the first method simply returning `pts`, and the second returning 
@@ -164,19 +164,25 @@ function each_point end
 function each_point(::P) where {P}
     return error("The each_point function has not been defined for the type $P.")
 end
-each_point(pts::AbstractVector) = pts
+each_point(pts::Union{AbstractVector,Tuple}) = pts
 each_point(pts::AbstractMatrix) = eachcol(pts)
 
 """
     num_points(pts)
 
-Returns the number of points in `pts`.
+Returns the number of points in `pts`. The methods currently defined are 
+
+    num_points(pts::AbstractVecOrTuple)
+    num_points(pts::AbstractMatrix)
+
+with the first returning `length(pts)` and the second returning
+`size(pts, 2)`. You can extend this function as you need.
 """
 function num_points end
 function num_points(::P) where {P}
     return error("The num_points function has not been defined for the type $P.")
 end
-num_points(pts::AbstractVector) = length(pts)
+num_points(pts::Union{AbstractVector,Tuple}) = length(pts)
 num_points(pts::AbstractMatrix) = size(pts, 2)
 
 """
diff --git a/src/predicates/general.jl b/src/predicates/general.jl
index 1bc6b5acb..223f0fa14 100644
--- a/src/predicates/general.jl
+++ b/src/predicates/general.jl
@@ -489,4 +489,73 @@ function triangle_line_segment_intersection(p, q, r, a, b)
             return Cert.Multiple
         end
     end
-end
\ No newline at end of file
+end
+
+"""
+    point_position_relative_to_box(a, b, c, d, p)
+
+Tests if the point `p` is inside the box `[a, b] × [c, d]`. Returns:
+
+- `Cert.Inside`: Inside the box.
+- `Cert.On`: On the boundary of the box.
+- `Cert.Outside`: Outside the box.
+"""
+function point_position_relative_to_box(a, b, c, d, p)
+    x, y = _getxy(p)
+    if (x < a) || (x > b) || (y < c) || (y > d)
+        return Cert.Outside
+    elseif (x == a) || (x == b) || (y == c) || (y == d)
+        return Cert.On
+    else
+        return Cert.Inside
+    end
+end
+
+#= 
+THIS IS WRONG FOR [(0.0, 1.0), (-1.0, 2.0), (-2.0, -1.0)] and A, B, C, D = -1.0, 0.0, -1.0, 2.0
+"""
+    polygon_position_relative_to_box(a, b, c, d, vertices, points)
+
+Tests the position of the polygon defined by `(vertices, points)` relative to the box `[a, b] × [c, d]`. The 
+polygon is defined so that the indices in `vertices` correspond to points in `points`, and is defined so that 
+`vertex[begin] == vertex[end]`.
+
+- `Cert.Inside`: The polygon is contained entirely within the box.
+- `Cert.Outside`: The polygon is entirely outside the box.
+- `Cert.Touching`: The polygon is contained entirely within the box, but touches the boundary of the box. Note that if a polygon touches the boundary of the box but is entirely outside otherwise, `Cert.Outside` will be returned instead. 
+- `Cert.Multiple`: The polygon intersects the box in multiple places.
+
+Boundary indices are treated as being outside.
+"""
+function polygon_position_relative_to_box(a, b, c, d, vertices, points)
+    @assert vertices[begin] == vertices[end]
+    num_on = 0
+    num_in = 0
+    num_out = 0
+    nv = length(vertices) - 1
+    for i in @views vertices[begin:(end-1)]
+        if is_boundary_index(i)
+            num_out += 1 
+            continue
+        end
+        p = get_point(points, i)
+        cert = point_position_relative_to_box(a, b, c, d, p)
+        if is_on(cert)
+            num_on += 1
+        elseif is_inside(cert)
+            num_in += 1
+        else
+            num_out += 1
+        end
+    end
+    if (num_out == nv) || (num_on ≥ 1 && num_out ≥ 1)
+        return Cert.Outside
+    elseif (num_in == nv) && num_on == 0
+        return Cert.Inside
+    elseif (num_out == 0) && (num_on ≥ 1)
+        return Cert.Touching
+    else
+        return Cert.Multiple
+    end
+end
+=#
\ No newline at end of file
diff --git a/src/voronoi/coordinates.jl b/src/voronoi/coordinates.jl
new file mode 100644
index 000000000..a93d51c8e
--- /dev/null
+++ b/src/voronoi/coordinates.jl
@@ -0,0 +1,231 @@
+"""
+    get_polygon_coordinates(vorn::VoronoiTessellation, i, bounding_box = nothing)
+
+Returns a vector for the coordinates of the `i`th polygon in `vorn`. If `bounding_box` 
+is provided, the polygon will be clipped to the bounding box, assuming that it takes 
+the form `(xmin, xmax, ymin, ymax)`. Some specific cases:
+
+- If the polygon is unbounded but `bounding_box` is `nothing`, then an error will be thrown. 
+- If the polygon is bounded and `bounding_box` is `nothing`, then the polygon coordinates will be returned as if without any clipping.
+- If the polygon is outside of the bounding box entirely, then an empty vector will be returned.
+
+If you do need to consider clipping your polygon to an arbitrary polygon, see the 
+[`polygon_clip`](@ref) function; this function (`get_polygon_coordinates`) uses 
+`polygon_clip` for rectangular clipping when `bounding_box` is considered.
+
+See also [`polygon_bounds`](@ref) for a good default for `bounding_box`.
+"""
+function get_polygon_coordinates(vorn::VoronoiTessellation, i, bounding_box=nothing)
+    if !isnothing(bounding_box)
+        a, b, c, d = bounding_box
+        @assert a < b && c < d "The bounding box must be of the form (xmin, xmax, ymin, ymax) with xmin < xmax and ymin < ymax."
+    end
+    if i ∈ get_unbounded_polygons(vorn)
+        isnothing(bounding_box) && throw(ArgumentError("The polygon is unbounded, so a bounding box must be provided. See DelaunayTriangulation.polygon_bounds for a reasonable default."))
+        return get_unbounded_polygon_coordinates(vorn, i, bounding_box)
+    else
+        return get_bounded_polygon_coordinates(vorn, i, bounding_box)
+    end
+end
+
+#=
+"""
+    polygon_position_relative_to_box(vorn::VoronoiTessellation, bounding_box, i)
+
+Tests the position of the `i`th polygon of `vorn` relative to the bounding box`, ignoring 
+boundary indices. Returns:
+
+- `Cert.Inside`: The polygon is contained entirely within the box.
+- `Cert.Outside`: The polygon is entirely outside the box.
+- `Cert.Touching`: The polygon is contained entirely within the box, but touches the boundary of the box. Note that if a polygon touches the boundary of the box but is entirely outside otherwise, `Cert.Outside` will be returned instead. 
+- `Cert.Multiple`: The polygon intersects the box in multiple places.
+"""
+function polygon_position_relative_to_box(vorn::VoronoiTessellation, bounding_box, i)
+    a, b, c, d = bounding_box
+    vertices = get_polygon(vorn, i)
+    points = get_polygon_points(vorn)
+    flag = polygon_position_relative_to_box(a, b, c, d, vertices, points)
+    return flag
+end
+=#
+
+function get_clipping_poly_structs(vorn::VoronoiTessellation, i, bounding_box)
+    vertices = get_polygon(vorn, i)
+    points = get_polygon_points(vorn)
+    clip_vertices = (1, 2, 3, 4)
+    a, b, c, d = bounding_box
+    clip_points = ((a, c), (b, c), (b, d), (a, d))
+    return Polygon(vertices, points), Polygon(clip_vertices, clip_points)
+end
+
+"""
+    clip_bounded_polygon_to_bounding_box(vorn::VoronoiTessellation, i, bounding_box)
+
+Clips the `i`th polygon of `vorn` to the bounding box, assuming it is bounded.
+The Sutherland-Hodgman algorithm is used. 
+"""
+function clip_bounded_polygon_to_bounding_box(vorn::VoronoiTessellation, i, bounding_box)
+    poly, clip_poly = get_clipping_poly_structs(vorn, i, bounding_box)
+    return clip_polygon(poly, clip_poly)
+end
+
+"""
+    _get_ray(vorn, i, boundary_index)
+
+Extracts the ray from the `i`th polygon of `vorn` corresponding to the `boundary_index`, where `boundary_index` 
+here means that `get_polygon(vorn, i)[boundary_index]` is a boundary index.
+The returned points are given in the form `(p, q)`, defining the oriented line `pq` such that the line 
+is in the direction of infinity.
+"""
+function _get_ray(vorn, i, boundary_index)
+    C = get_polygon(vorn, i)
+    ghost_tri = get_circumcenter_to_triangle(vorn, C[boundary_index])
+    u, v, _ = indices(ghost_tri) # w is the ghost vertex
+    p, q = get_generator(vorn, u, v)
+    px, py = _getxy(p)
+    qx, qy = _getxy(q)
+    mx, my = (px + qx) / 2, (py + qy) / 2
+    m = (mx, my)
+    is_first = is_first_boundary_index(C, boundary_index)
+    if is_first
+        prev_index = previndex_circular(C, boundary_index)
+        r = get_polygon_point(vorn, C[prev_index])
+    else
+        next_index = nextindex_circular(C, boundary_index)
+        r = get_polygon_point(vorn, C[next_index])
+    end
+    if r == m # It's possible for the circumcenter to lie on the edge and exactly at the midpoint (e.g. [(0.0,1.0),(-1.0,2.0),(-2.0,-1.0)]). In this case, just rotate 
+        dx, dy = qx - mx, qy - my
+        if (is_right ∘ point_position_relative_to_line)(p, q, r)
+            rotated_dx, rotated_dy = dy, -dx
+            r = mx + rotated_dx, my + rotated_dy
+        else
+            rotated_dx, rotated_dy = -dy, dx
+            r = mx + rotated_dx, my + rotated_dy
+        end
+    end
+    if (is_right ∘ point_position_relative_to_line)(p, q, r) # in this case, the circumcenter is inside and so mr points inwards rather than outwards 
+        m, r = r, m
+    end
+    return m, r
+end
+
+"""
+    grow_polygon_outside_of_box(vorn::VoronoiTessellation, i, bounding_box)
+
+Truncates unbounded edges of the `i`th polygon of `vorn`, assumed to be unbounded,
+so that the line connecting the truncated unbounded edges is entirely outside 
+of the polygon. The method of growth is iterative, utilising the Liang-Barsky algorithm 
+at each stage while we translate the line. The returned polygon does not satisfy 
+`P[begin] == P[end]`.
+"""
+function grow_polygon_outside_of_box(vorn::VoronoiTessellation, i, bounding_box)
+    a, b, c, d = bounding_box
+    vertices = get_polygon(vorn, i)
+    new_vertices, new_points, boundary_indices = get_new_polygon_indices(vorn, vertices)
+    inside = true
+    t = 1.0 # don't do 0.5 so we get t = 1 later, else we get duplicated vertices for polygons completely outside of the box
+    u, v = boundary_indices
+    u_m, u_r = _get_ray(vorn, i, u)
+    v_m, v_r = _get_ray(vorn, i, v)
+    u_mx, u_my = _getxy(u_m)
+    u_rx, u_ry = _getxy(u_r)
+    v_mx, v_my = _getxy(v_m)
+    v_rx, v_ry = _getxy(v_r)
+    p = (0.0, 0.0)
+    q = (0.0, 0.0)
+    while inside
+        t *= 2.0
+        p = (u_mx + t * (u_rx - u_mx), u_my + t * (u_ry - u_my))
+        q = (v_mx + t * (v_rx - v_mx), v_my + t * (v_ry - v_my))
+        int1, int2 = liang_barsky(a, b, c, d, p, q)
+        outside = all(isnan, int1) && all(isnan, int2)
+        inside = !outside
+    end
+    new_points[u] = p
+    new_points[v] = q
+    new_vertices[u] = u
+    new_vertices[v] = v
+    return new_vertices, new_points
+end
+
+"""
+    get_new_polygon_indices(vorn, vertices)
+
+Given an unbounded Voronoi polygon from `vorn` with `vertices`, returns 
+`(new_vertices, new_points, boundary_indices)`, where `new_vertices` are vertices 
+mapping to the points in `new_points`, which is just a vector of all the polygon points, 
+and `boundary_indices` is a `Tuple` of the indices of the points in `new_points` that correspond 
+to points out at infinity.
+"""
+function get_new_polygon_indices(vorn, vertices)
+    new_points = NTuple{2,Float64}[]
+    sizehint!(new_points, length(vertices))
+    new_vertices = similar(vertices, length(vertices) - 1)
+    boundary_indices = (0, 0)
+    for i in firstindex(vertices):(lastindex(vertices)-1)
+        v = vertices[i]
+        if is_boundary_index(v)
+            is_first = is_first_boundary_index(vertices, i)
+            if is_first
+                boundary_indices = (i, boundary_indices[2])
+            else
+                boundary_indices = (boundary_indices[1], i)
+            end
+            push!(new_points, (NaN, NaN))
+            new_vertices[i] = v
+        else
+            push!(new_points, _getxy(get_polygon_point(vorn, v)))
+            new_vertices[i] = length(new_points)
+        end
+    end
+    return new_vertices, new_points, boundary_indices
+end
+
+"""
+    get_bounded_polygon_coordinates(vorn::VoronoiTessellation, i, bounding_box)
+
+Returns the coordinates of the `i`th polygon of `vorn`, assuming it is bounded. If 
+`bounding_box` is `nothing`, then the polygon coordinates will be returned as if without
+any clipping. If `bounding_box` is provided, the polygon will be clipped to the bounding box 
+using [`clip_to_bounding_box`](@ref).
+"""
+function get_bounded_polygon_coordinates(vorn::VoronoiTessellation, i, bounding_box)
+    if isnothing(bounding_box)
+        C = get_polygon(vorn, i)
+        F = number_type(vorn)
+        coords = Vector{NTuple{2,F}}(undef, length(C) - 1)
+        for j in firstindex(C):(lastindex(C)-1)
+            coords[j] = get_polygon_point(vorn, C[j])
+        end
+        return coords
+    else
+        return clip_bounded_polygon_to_bounding_box(vorn, i, bounding_box)
+    end
+end
+
+"""
+    get_unbounded_polygon_coordinates(vorn::VoronoiTessellation, i, bounding_box)
+
+Returns the coordinates of the `i`th polygon of `vorn`, assuming it is unbounded, clipping 
+the polygon to the bounding box.
+"""
+function get_unbounded_polygon_coordinates(vorn::VoronoiTessellation, i, bounding_box)
+    return clip_unbounded_polygon_to_bounding_box(vorn, i, bounding_box)
+end
+
+"""
+    clip_unbounded_polygon_to_bounding_box(vorn::VoronoiTessellation, i, bounding_box)
+
+Clips the `i`th polygon of `vorn` to the bounding box, assuming it is unbounded.
+The unbounded polygon is truncated so that the line connecting the unbounded edges 
+is outside of the bounded box, and then the Sutherland-Hodgman algorithm 
+is used to clip the resulting polygon to the bounding box.
+"""
+function clip_unbounded_polygon_to_bounding_box(vorn::VoronoiTessellation, i, bounding_box)
+    new_vertices, new_points = grow_polygon_outside_of_box(vorn, i, bounding_box)
+    clip_vertices = (1, 2, 3, 4)
+    a, b, c, d = bounding_box
+    clip_points = ((a, c), (b, c), (b, d), (a, d))
+    return clip_polygon(new_vertices, new_points, clip_vertices, clip_points)
+end
\ No newline at end of file
diff --git a/src/voronoi/main.jl b/src/voronoi/main.jl
index 6bc46e197..a99fd61ea 100644
--- a/src/voronoi/main.jl
+++ b/src/voronoi/main.jl
@@ -4,6 +4,18 @@
 Construct the Voronoi tessellation of the points in `tri`. If `clip` is `true` then the
 Voronoi tessellation will be clipped to the convex hull of the points in `tri`. 
 
+!!! note "Accessing polygon coordinates and rectangle clipping" 
+
+    If you are interested instead in clipping the tessellation to a rectangular bounding box, see 
+    [`get_polygon_coordinates`](@ref) which allows for a bounding box to be applied to an 
+    unclipped tessellation, returning a vector of the coordinates of polygons, clipping 
+    to the bounding box where applicable. [`polygon_bounds`](@ref) can be used to obtain good 
+    default bounding boxes. Note that if you are not worried about this clipping, 
+    and you know that your polygon is not unbounded (which would mean it is not in the 
+    `unbounded_polygons` field of the `VoronoiTessellation` output), then you should instead use 
+    `get_polygon(vorn, i)` to get the indices of the points in `vorn` that define the polygon, 
+    and then use `get_polygon_point` to get the coordinates. 
+
 !!! warning 
 
     Exact predicates are used only for classifying intersections, but no special methods 
@@ -11,11 +23,7 @@ Voronoi tessellation will be clipped to the convex hull of the points in `tri`.
 
 !!! warning 
 
-    Clipping is not yet guaranteed to work for constrained triangulations. Unfortunate,
-    because that's really what I actually care about. If you have any thoughts for that, 
-    or just any thoughts on the reference clipping paper (by Yan, Wang, Levy, and Liu: 
-    "Efficient Computation of Clipped Voronoi Diagram for Mesh Generation), please let me know via 
-    an issue. There is certainly a lot of room for improvement in the clipping code too.
+    Clipping is not yet guaranteed to work for constrained triangulations. 
 """
 function voronoi(tri::Triangulation, clip=has_boundary_nodes(tri))
     has_ghost = has_ghost_triangles(tri)
diff --git a/test/geo_utils.jl b/test/geo_utils.jl
index ee808e535..70cb9ea50 100644
--- a/test/geo_utils.jl
+++ b/test/geo_utils.jl
@@ -4,9 +4,14 @@ using LinearAlgebra
 using Random
 using CairoMakie
 
-
 include("./helper_functions.jl")
 
+throw_f = expr -> @static if VERSION < v"1.8"
+      ErrorException(expr)
+else
+      expr
+end
+
 @testset "Getting polygon features" begin
       tri, label_map, index_map = simple_geometry()
       pts = get_points(tri)
@@ -963,4 +968,168 @@ end
                   @test collect(r) ≈ collect(rtrue)
             end
       end
-end
\ No newline at end of file
+end
+
+@testset "point_position_relative_to_box" begin
+      p = (4.0, 5.0)
+      a, b, c, d = 3.0, 7.0, 1.0, 8.0
+      @test DT.is_inside(DT.point_position_relative_to_box(a, b, c, d, p))
+      p = (2.0, 4.0)
+      @test DT.is_outside(DT.point_position_relative_to_box(a, b, c, d, p))
+      p = (a, (c + d) / 2)
+      @test DT.is_on(DT.point_position_relative_to_box(a, b, c, d, p))
+      p = (b, (c + d) / 2)
+      @test DT.is_on(DT.point_position_relative_to_box(a, b, c, d, p))
+      p = ((a + b) / 2, c)
+      @test DT.is_on(DT.point_position_relative_to_box(a, b, c, d, p))
+end
+
+@testset "Polygon" begin
+      verts = [1, 11, 18, 26, 32, 72]
+      _verts = [verts; 1]
+      points = [rand(2) for _ in 1:maximum(verts)]
+      for verts in (verts, _verts)
+            poly = DT.Polygon(verts, points)
+            @test length(poly) == 6
+            @test size(poly) == (6,)
+            @test poly[1] == Tuple(points[1])
+            @test poly[2] == Tuple(points[11])
+            @test poly[3] == Tuple(points[18])
+            @test poly[4] == Tuple(points[26])
+            @test poly[5] == Tuple(points[32])
+            @test poly[6] == Tuple(points[72])
+            @test eachindex(poly) == 1:6
+            @test collect(poly) == Tuple.(getindex.(Ref(points), [1, 11, 18, 26, 32, 72]))
+            @test poly[begin:end] == [poly[i] for i in 1:6]
+            @inferred poly[1]
+            @inferred poly[5]
+      end
+end
+
+@testset "Sutherland-Hodgman algorithm" begin
+      # rectangular
+      verts = [1, 2, 3, 4, 5, 6, 7, 8, 9]
+      points = [(50.0, 150.0), (200.0, 50.0), (350.0, 150.0), (350.0, 300.0),
+            (250.0, 300.0), (200.0, 250.0), (150.0, 350.0), (100.0, 250.0), (100.0, 200.0)]
+      clip_verts = [1, 2, 3, 4]
+      clip_points = [(100.0, 100.0), (300.0, 100.0), (300.0, 300.0), (100.0, 300.0)]
+      spoly = DT.Polygon(verts, points)
+      cpoly = DT.Polygon(clip_verts, clip_points)
+      result = DT.clip_polygon(spoly, cpoly)
+      @inferred DT.clip_polygon(spoly, cpoly)
+      @test collect.(result) ≈ [
+            [100.0, 116 + 2 / 3],
+            [125, 100],
+            [275, 100],
+            [300, 116 + 2 / 3],
+            [300, 300],
+            [250, 300],
+            [200, 250],
+            [175, 300],
+            [125, 300],
+            [100, 250],
+            [100.0, 116 + 2 / 3]
+      ]
+      @test DT.clip_polygon(verts, points, clip_verts, clip_points) == result
+      @test DT.polygon_features(result, eachindex(result))[1] > 0
+
+      # bigger example 
+      function to_rand_point_verts(___points)
+            _points = [Tuple(rand(2)) for _ in 1:500]
+            _points = [_points; ___points]
+            shuffle!(_points)
+            vertices = identity.(indexin(___points, _points)) # identity to convert eltype from Union{Nothing, Int}
+            return _points, vertices
+      end
+      a = (-4.0, 4.0)
+      b = (-1.0, 6.0)
+      c = (3.0, 6.0)
+      d = (4.0, 4.0)
+      e = (4.0, -1.0)
+      f = (2.0, -3.0)
+      g = (-2.94, -1.32)
+      points = [g, f, e, d, c, b, a] # ccw
+      npoints, nvertices = to_rand_point_verts(deepcopy(points))
+      h = (-2.0, 7.0)
+      i = (-5.0, 6.0)
+      j = (-5.0, 2.0)
+      k = (-4.0, -2.0)
+      ℓ = (-1.0, -3.0)
+      m = (2.0, 2.0)
+      n = (1.0, 5.0)
+      clip_points = [h, i, j, k, ℓ, m, n]
+      nclip_points, nclip_vertices = to_rand_point_verts(deepcopy(clip_points))
+      result = DT.clip_polygon(nvertices, npoints, nclip_vertices, nclip_points)
+      @test DT.circular_equality(collect.(result), collect.([
+            g,
+            (-0.4915938130464, -2.1526563550773),
+            m,
+            n,
+            (-0.5, 6.0),
+            b,
+            a,
+            g
+      ]), ≈)
+end
+
+@testset "intersection_of_ray_with_edge" begin
+      p, q, a, b = (0.0, 0.0), (5.0, 5.0), (-2.0, 5.0), (0.0, 5.0)
+      r = DT.intersection_of_ray_with_edge(p, q, a, b)
+      @test all(isnan, r)
+      b = (2.0, -1.0)
+      r = DT.intersection_of_ray_with_edge(p, q, a, b)
+      @test collect(r) ≈ [0.8, 0.8]
+      b = (0.0, -1.0)
+      r = DT.intersection_of_ray_with_edge(p, q, a, b)
+      @test all(isnan, r)
+      a, b = (-2.0, -2.0), (-4.0, -4.0)
+      r = DT.intersection_of_ray_with_edge(p, q, a, b)
+      @test all(isnan, r)
+      a, b = (4.0, 2.0), (2.0, 2.0)
+      r = DT.intersection_of_ray_with_edge(p, q, a, b)
+      @test collect(r) ≈ [2.0, 2.0]
+      p, q, a, b = (0.0, 0.0), (0.0, 6.0), (4.0, 0.0), (2.0, -2.0)
+      r = DT.intersection_of_ray_with_edge(p, q, a, b)
+      @test all(isnan, r)
+      b = (-2.0, 0.0)
+      r = DT.intersection_of_ray_with_edge(p, q, a, b)
+      @test collect(r) ≈ [0.0, 0.0]
+end
+
+@testset "Liang-Barsky algorithm" begin
+      p, q = (-7.0, 5.0), (1.0, 8.0)
+      a, b, c, d = 0.0, 8.0, 0.0, 4.0
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test all(isnan, u) && all(isnan, v)
+      p, q = (-3.0, 1.0), (10.0, 5.0)
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test collect(u) ≈ [0, 1.9230769230769]
+      @test collect(v) ≈ [6.75, 4.0]
+      p, q = (0.0, -2.0), (0.0, 6.0)
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test collect(u) ≈ [0, 0]
+      @test collect(v) ≈ [0, 4]
+      p, q = (2.0, 6.0), (-2.0, 2.0)
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test u == v && (collect(u) ≈ [0, 4])
+      p, q = (10.0, 6.0), (-2.0, 6.0)
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test all(isnan, u) && all(isnan, v)
+      p, q = (4.0, 6.0), (4.0, -2.0)
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test collect(u) ≈ [4.0, 4.0]
+      @test collect(v) ≈ [4.0, 0.0]
+      p, q = (2.0, 6.0), (10.0, -2.0)
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test collect(u) ≈ [4.0, 4.0]
+      @test collect(v) ≈ [8.0, 0.0]
+      a, b, c, d = 4, 10, 2, 8
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test collect(u) ≈ [4.0, 4.0]
+      @test collect(v) ≈ [6.0, 2.0]
+      p, q = (2.0, 6.0), (14.0, 8.0)
+      u, v = DT.liang_barsky(a, b, c, d, p, q)
+      @test collect(u) ≈ [4, 6 + 1 / 3]
+      @test collect(v) ≈ [10, 7 + 1 / 3]
+end
+
diff --git a/test/interfaces/points.jl b/test/interfaces/points.jl
index 796385cb7..70b067195 100644
--- a/test/interfaces/points.jl
+++ b/test/interfaces/points.jl
@@ -39,11 +39,12 @@ end
 global pts1 = [[2.0, 3.5], [1.7, 23.3], [-1.0, 0.0]]
 global pts2 = [(2.0, 3.5), (1.7, 23.3), (-1.0, 0.0)]
 global pts3 = [2.0 1.7 -1.0; 3.5 23.3 0.0]
+global pts4 = ((2.0, 3.5), (1.7, 23.3), (-1.0, 0.0))
 
 @testset "Collection of points" begin
     @testset "Getting points" begin
         @test_throws  throw_f("The getpoint function has not been defined for the type DataType.") DT.getpoint(String, 5)
-        for pts in (pts1, pts2, pts3)
+        for pts in (pts1, pts2, pts3, pts4)
             @test DT.getpoint(pts, 1) == (2.0, 3.5)
             @test DT.getpoint(pts, 2) == (1.7, 23.3)
             @test DT.getpoint(pts, 3) == (-1.0, 0.0)
@@ -68,7 +69,7 @@ global pts3 = [2.0 1.7 -1.0; 3.5 23.3 0.0]
 
     @testset "Each point index" begin
         @test_throws throw_f("The each_point_index function has not been defined for the type DataType.") each_point_index(String)
-        for pts in (pts1, pts2, pts3)
+        for pts in (pts1, pts2, pts3, pts4)
             @test each_point_index(pts) == 1:3
             @inferred each_point_index(pts)
         end
@@ -79,12 +80,14 @@ global pts3 = [2.0 1.7 -1.0; 3.5 23.3 0.0]
         @test each_point(pts1) == pts1
         @test each_point(pts2) == pts2
         @test each_point(pts3) == eachcol(pts3)
+        @test each_point(pts4) == pts4
+        @inferred each_point(pts4)
         @inferred each_point(pts3)
     end
 
     @testset "Number of points" begin
         @test_throws throw_f("The num_points function has not been defined for the type DataType.") num_points(String)
-        for pts in (pts1, pts2, pts3)
+        for pts in (pts1, pts2, pts3, pts4)
             @test num_points(pts) == 3
             @inferred num_points(pts)
         end
diff --git a/test/temp_makie.jl b/test/temp_makie.jl
index 622c410b2..2ce1561b9 100644
--- a/test/temp_makie.jl
+++ b/test/temp_makie.jl
@@ -238,9 +238,10 @@ if NEEDS_PLOT_DEFS
                 if bnd === Makie.automatic
                     return DelTri.polygon_bounds(vorn, extent)
                 else
-                    return p.bounding_box
+                    return bnd
                 end
             end
+            @show bbox
             map(generators_2f, polygons, bbox) do gens, polys, box
                 return get_voronoi_tiles!(gens, polys, vorn, box)
             end
diff --git a/test/voronoi/voronoi.jl b/test/voronoi/voronoi.jl
index f32aac7fa..80ba10085 100644
--- a/test/voronoi/voronoi.jl
+++ b/test/voronoi/voronoi.jl
@@ -112,47 +112,61 @@ end
     c5 = DT.get_polygon_coordinates(vorn, 5, bbox)
     c6 = DT.get_polygon_coordinates(vorn, 6, bbox)
     c7 = DT.get_polygon_coordinates(vorn, 7, bbox)
-    @test DT.circular_equality(collect.(c1), collect.([(-1.5, 0.5)
-        (0.16666666666666666, -1.1666666666666665)
+    @test DT.circular_equality(collect.(c1), collect.([
+        (-1.5, 0.5)
+        (0.166666666666, -1.1666666666666665)
         (1.0, 0.5)
         (1.0, 3.0)
-        (-1.5, 0.5)]), ≈)
-    @test DT.circular_equality(collect.(c2), collect.([(3.5, 0.5)
+        (-1.5, 0.5)
+    ]), ≈)
+    @test DT.circular_equality(collect.(c2), collect.([
+        (0.5, -3.2)
+        (5.7, -3.2)
+        (5.7, -1.700000000000001)
+        (3.5, 0.5)
         (0.5, -2.5)
-        (0.5, -3.2000000001862645)
-        (xmax, ymin)
-        (5.769999999552965, -1.7699999995529652)
-        (3.5, 0.5)]), ≈)
-    @test DT.circular_equality(collect.(c3), collect.([(3.5, 0.5)
+        (0.5, -3.2)
+    ]), ≈)
+    @test DT.circular_equality(collect.(c3), collect.([
+        (3.5, 0.5)
         (1.0, 0.5)
         (0.16666666666666666, -1.1666666666666665)
         (0.5, -2.5)
-        (3.5, 0.5)]), ≈)
-    @test DT.circular_equality(collect.(c4), collect.([(1.5, 5.270000000484288)
-        (xmin, ymax)
-        (-2.6999999997206032, 0.8999999999068677)
+        (3.5, 0.5)
+    ]), ≈)
+    @test DT.circular_equality(collect.(c4), collect.([
+        (1.5, 5.2)
+        (-2.7, 5.2)
+        (-2.7, 0.9000000000000001)
         (-1.5, 0.5)
         (1.0, 3.0)
         (1.5, 4.5)
-        (1.5, 5.270000000484288)]), ≈)
-    @test DT.circular_equality(collect.(c5), collect.([(1.5, 4.5)
+        (1.5, 5.2)
+    ]), ≈)
+    @test DT.circular_equality(collect.(c5), collect.([
+        (1.5, 4.5)
         (3.5, 0.5)
-        (5.769999999552965, 2.769999999552965)
-        (xmax, ymax)
-        (1.5, 5.270000000484288)
-        (1.5, 4.5)]), ≈)
-    @test DT.circular_equality(collect.(c6), collect.([(-2.6999999997206032, 0.8999999999068677)
-        (xmin, ymin)
-        (0.5, -3.2000000001862645)
+        (5.7, 2.6999999999999997)
+        (5.7, 5.2)
+        (1.5, 5.2)
+        (1.5, 4.5)
+    ]), ≈)
+    @test DT.circular_equality(collect.(c6), collect.([
+        (-2.7, 0.9000000000000001)
+        (-2.7, -3.2)
+        (0.5, -3.2)
         (0.5, -2.5)
         (0.16666666666666666, -1.1666666666666665)
         (-1.5, 0.5)
-        (-2.6999999997206032, 0.8999999999068677)]), ≈)
-    @test DT.circular_equality(collect.(c7), collect.([(1.5, 4.5)
+        (-2.7, 0.9000000000000001)
+    ]), ≈)
+    @test DT.circular_equality(collect.(c7), collect.([
+        (1.5, 4.5)
         (1.0, 3.0)
         (1.0, 0.5)
         (3.5, 0.5)
-        (1.5, 4.5)]), ≈)
+        (1.5, 4.5)
+    ]), ≈)
 end
 
 @testset "delete/add_polygon_adjacencies" begin
@@ -899,12 +913,12 @@ end
     vorn = voronoi(tri)
     clip = DT.get_polygon_coordinates(vorn, 9, DT.polygon_bounds(vorn, 0.1))
     @test DT.circular_equality(collect.(clip), collect.([
-        [2.0316769079740804, 0.11847746641647516],
-        [2.0316769079740804, 1.107189193410733],
-        [0.8433942004507264, 1.107189193410733],
-        [0.7271857522962732, 0.8973620981454822],
-        [1.7423743304675243, 0.24505806539308744],
-        [2.0316769079740804, 0.11847746641647516]
+        (0.8374509236290323, 1.0964579554357115)
+        (0.7271857522962732, 0.8973620981454822)
+        (1.7423743304675243, 0.24505806539308744)
+        (2.0053766736553027, 0.1299847935961671)
+        (2.0053766736553027, 1.0964579554357115)
+        (0.8374509236290323, 1.0964579554357115)
     ]), ≈)
 end
 
@@ -915,13 +929,11 @@ end
     vorn = voronoi(tri)
     clip = DT.get_polygon_coordinates(vorn, 2, DT.polygon_bounds(vorn, 2.0))
     @test DT.circular_equality(collect.(clip), collect.([
-        (-2.7441549307938113, 4.348255778263596)
+        (-2.551580488601045, 4.122780970352073)
         (-0.3314903102646037, 1.5233996567840244)
-        (3.319011238223682, -2.375672313568049)
-        (8.112835861587623, -2.375672313568049)
-        (8.112835861587623, 9.321543597488171)
-        (-2.7441549307938113, 9.321543597488171)
-        (-2.7441549307938113, 4.348255778263596)
+        (3.2875066205292076, -2.3420224793856605)
+        (3.2875066205292076, 4.122780970352073)
+        (-2.551580488601045, 4.122780970352073)
     ]), ≈)
 end
 
@@ -982,4 +994,163 @@ end
     tri = triangulate(points)
     vorn = voronoi(tri)
     @test validate_tessellation(vorn)
+end
+
+@testset "Polygon bounds with generators only" begin
+    points = rand(2, 50)
+    tri = triangulate(points)
+    vorn = voronoi(tri)
+    xmin, xmax, ymin, ymax = DT.polygon_bounds(vorn, 0.1; include_polygon_vertices=false)
+    _xmin, _xmax = extrema(points[1, :])
+    _ymin, _ymax = extrema(points[2, :])
+    @test xmin == _xmin - 0.1(_xmax - _xmin)
+    @test xmax == _xmax + 0.1(_xmax - _xmin)
+    @test ymin == _ymin - 0.1(_ymax - _ymin)
+    @test ymax == _ymax + 0.1(_ymax - _ymin)
+end
+
+#=
+@testset "Position of Voronoi polygons relative to box" begin
+    a = (-3.0, 7.0)
+    b = (1.0, 6.0)
+    c = (-1.0, 3.0)
+    d = (-2.0, 4.0)
+    e = (3.0, -2.0)
+    f = (5.0, 5.0)
+    g = (-4.0, -3.0)
+    h = (3.0, 8.0)
+    points = [a, b, c, d, e, f, g, h]
+    tri = triangulate(points)
+    vorn = voronoi(tri)
+    a, b, c, d = -8.0, 6.0, -2.0, 10.0
+    bounding_box = (a, b, c, d)
+    results = Dict(
+        1 => DT.has_multiple_intersections,
+        2 => DT.is_inside,
+        3 => DT.is_inside,
+        4 => DT.has_multiple_intersections,
+        5 => DT.has_multiple_intersections,
+        6 => DT.has_multiple_intersections,
+        7 => DT.has_multiple_intersections,
+        8 => DT.has_multiple_intersections,
+    )
+    for (i, cert_f) in results
+        @test cert_f(DT.polygon_position_relative_to_box(vorn, bounding_box, i))
+    end
+end
+=#
+
+@testset "grow_polygon_outside_of_box" begin
+    A = (-3.0, 7.0)
+    B = (1.0, 6.0)
+    C = (-1.0, 3.0)
+    D = (-2.0, 4.0)
+    E = (3.0, -2.0)
+    F = (5.0, 5.0)
+    G = (-4.0, -3.0)
+    H = (3.0, 8.0)
+    points = [A, B, C, D, E, F, G, H]
+    tri = triangulate(points)
+    vorn = voronoi(tri)
+    a, b, c, d = -4.0, 6.0, -2.0, 4.0
+    bounding_box = (a, b, c, d)
+    new_vertices, new_points = DT.grow_polygon_outside_of_box(vorn, 1, bounding_box)
+    @test collect.(new_points) ≈ collect.([
+        (-1.1363636363636365, 5.954545454545455)
+        (-0.2999999999999998, 9.3)
+        (-0.5999999999999996, 11.100000000000001)
+        (-18.115384615384613, 3.4615384615384617)
+        (-10.807692307692307, 2.730769230769231)
+    ])
+    @test new_vertices == [1, 2, 3, 4, 5]
+    new_vertices, new_points = DT.grow_polygon_outside_of_box(vorn, 5, bounding_box)
+    @test collect.(new_points) ≈ collect.([
+        (2.710526315789474, 1.868421052631579)
+        (-0.7307692307692308, -0.8846153846153846)
+        (1.1153846153846159, -13.807692307692308)
+        (13.026315789473683, -1.0789473684210529)
+    ])
+    @test new_vertices == [1, 2, 3, 4]
+    new_vertices, new_points = DT.grow_polygon_outside_of_box(vorn, 6, bounding_box)
+    @test collect.(new_points) ≈ collect.([
+        (7.868421052631579, 0.39473684210526305)
+        (6.699999999999999, 8.299999999999999)
+        (3.1, 5.9)
+        (2.357142857142857, 2.9285714285714284)
+        (2.710526315789474, 1.868421052631579)
+    ])
+    @test new_vertices == [1, 2, 3, 4, 5]
+    new_vertices, new_points = DT.grow_polygon_outside_of_box(vorn, 7, bounding_box)
+    @test collect.(new_points) ≈ collect.([
+        (-0.7307692307692308, -0.8846153846153846)
+        (-4.166666666666666, 0.8333333333333335)
+        (-10.807692307692307, 2.730769230769231)
+        (-18.115384615384613, 3.4615384615384617)
+        (-0.26923076923076916, -4.115384615384615)
+    ])
+    @test new_vertices == [1, 2, 3, 4, 5]
+    new_vertices, new_points = DT.grow_polygon_outside_of_box(vorn, 8, bounding_box)
+    @test collect.(new_points) ≈ collect.([
+        (4.9, 7.1)
+        (-0.5999999999999996, 11.100000000000001)
+        (-0.2999999999999998, 9.3)
+        (3.1, 5.9)
+    ])
+    @test new_vertices == [1, 2, 3, 4]
+    @inferred DT.grow_polygon_outside_of_box(vorn, 8, bounding_box)
+end
+
+@testset "Clipping polygons to arbitrary bounding box" begin
+    A = (-3.0, 7.0)
+    B = (1.0, 6.0)
+    C = (-1.0, 3.0)
+    D = (-2.0, 4.0)
+    E = (3.0, -2.0)
+    F = (5.0, 5.0)
+    G = (-4.0, -3.0)
+    H = (3.0, 8.0)
+    points = [A, B, C, D, E, F, G, H]
+    tri = triangulate(points)
+    vorn = voronoi(tri)
+    a, b, c, d = -4.0, 6.0, -2.0, 4.0
+    bounding_box = (a, b, c, d)
+    _pa = get_polygon_coordinates(vorn, 1, bounding_box)
+    _pb = get_polygon_coordinates(vorn, 2, bounding_box)
+    _pc = get_polygon_coordinates(vorn, 3, bounding_box)
+    _pd = get_polygon_coordinates(vorn, 4, bounding_box)
+    _pe = get_polygon_coordinates(vorn, 5, bounding_box)
+    _pf = get_polygon_coordinates(vorn, 6, bounding_box)
+    _pg = get_polygon_coordinates(vorn, 7, bounding_box)
+    _ph = get_polygon_coordinates(vorn, 8, bounding_box)
+    pa = NTuple{2,Float64}[]
+    pb = [(0.75, 4.0), (2.357142857142857, 2.9285714285714284), (2.625, 4.0), (0.75, 4.0)]
+    pc = [(2.710526315789474, 1.868421052631579), (2.357142857142857, 2.9285714285714284), (0.75, 4.0), (-1.0, 4.0), (-4.0, 1.0), (-4.0, 0.75), (-0.7307692307692308, -0.8846153846153846), (2.710526315789474, 1.868421052631579)]
+    pd = [(-4.0, 4.0), (-4.0, 1.0), (-1.0, 4.0), (-4.0, 4.0)]
+    pe = [(6.0, 0.9285714285714279), (2.710526315789474, 1.868421052631579), (-0.7307692307692308, -0.8846153846153846), (-0.5714285714285712, -2.0), (6.0, -2.0), (6.0, 0.9285714285714279)]
+    pf = [(6.0, 0.9285714285714284), (6.0, 4.0), (2.625, 4.0), (2.357142857142857, 2.9285714285714284), (2.710526315789474, 1.868421052631579), (6.0, 0.9285714285714284)]
+    pg = [(-0.5714285714285721, -2.0), (-0.7307692307692308, -0.8846153846153846), (-4.0, 0.75), (-4.0, -2.0), (-0.5714285714285721, -2.0)]
+    ph = NTuple{2,Float64}[]
+    @test DT.circular_equality(collect.(pa), collect.(_pa), ≈)
+    @test DT.circular_equality(collect.(pb), collect.(_pb), ≈)
+    @test DT.circular_equality(collect.(pc), collect.(_pc), ≈)
+    @test DT.circular_equality(collect.(pd), collect.(_pd), ≈)
+    @test DT.circular_equality(collect.(pe), collect.(_pe), ≈)
+    @test DT.circular_equality(collect.(pf), collect.(_pf), ≈)
+    @test DT.circular_equality(collect.(pg), collect.(_pg), ≈)
+    @test DT.circular_equality(collect.(ph), collect.(_ph), ≈)
+
+    # test a small example 
+    points = [(0.0, 1.0), (-1.0, 2.0), (-2.0, -1.0)]
+    tri = triangulate(points)
+    vorn = voronoi(tri)
+    bb = (-1.0, 0.0, -1.0, 2.0)
+    coord1 = get_polygon_coordinates(vorn, 1, bb)
+    coord2 = get_polygon_coordinates(vorn, 2, bb)
+    coord3 = get_polygon_coordinates(vorn, 3, bb)
+    _coord1 = [(0.0, 2.0), (0.0, 2.0), (-1.0, 1.0), (-1.0, 0.0), (0.0, -1.0), (0.0, 2.0)]
+    _coord2 = [(-1.0, 2.0), (-1.0, 1.0), (0.0, 2.0), (-1.0, 2.0)]
+    _coord3 = [(-1.0, -1.0), (0.0, -1.0), (0.0, -1.0), (-1.0, 0.0), (-1.0, -1.0)]
+    @test DT.circular_equality(collect.(coord1), collect.(_coord1), ≈)
+    @test DT.circular_equality(collect.(coord2), collect.(_coord2), ≈)
+    @test DT.circular_equality(collect.(coord3), collect.(_coord3), ≈)
 end
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