Check if a polygon overlaps with a rectangle
Check if a polygon overlaps with a rectangle
You are encouraged to solve this task according to the task description, using any language you may know.
You are encouraged to solve this task according to the task description, using any language you may know.
Self-explanatory: given a polygon (as an array/vector/list of its vertices) and a rectangle (in x, y, width, height format), check if they intersect.
Phix
with javascript_semantics function getAxes(sequence poly) integer l = length(poly) sequence axes = repeat(0,l) for i=1 to l do sequence p = poly[i], n = poly[iff(i=l?1:i+1)] axes[i] = {n[2]-p[2],p[1]-n[1]} end for return axes end function function projectOntoAxis(sequence poly,axis) atom {ax,ay} = axis, mn, mx for i,pi in poly do atom {px,py} = pi, p = ax*px+ay*py if i=1 then mn = p mx = p elsif p<mn then mn = p elsif p>mx then mx = p end if end for return {mn,mx} end function function projectionsOverlap(sequence proj1, proj2) return proj1[2] >= proj2[1] and proj2[2] >= proj1[1] end function function rectToPolygon(sequence r) atom {x,y,w,h} = r return {{x, y}, {x, y+h}, {x+w, y+h}, {x+w, y}} end function function polygonOverlapsRect(sequence poly1, rect) sequence poly2 = rectToPolygon(rect), axes1 = getAxes(poly1), axes2 = getAxes(poly2) for axes in {axes1, axes2} do for axis in axes do sequence proj1 = projectOntoAxis(poly1, axis), proj2 = projectOntoAxis(poly2, axis) if not projectionsOverlap(proj1, proj2) then return false end if end for end for return true end function constant poly = {{0, 0}, {0, 2}, {1, 4}, {2, 2}, {2, 0}}, rect1 = {4, 0, 2, 2}, rect2 = {1, 0, 8, 2}, fmt = """ poly = %v rect2 = %v => %v rect3 = %v => %v poly and rect1 overlap? %t poly and rect2 overlap? %t """ printf(1,fmt,{poly,rect1,rectToPolygon(rect1), rect2,rectToPolygon(rect2), polygonOverlapsRect(poly, rect1), polygonOverlapsRect(poly, rect2)})
- Output:
poly = {{0,0},{0,2},{1,4},{2,2},{2,0}} rect2 = {4,0,2,2} => {{4,0},{4,2},{6,2},{6,0}} rect3 = {1,0,8,2} => {{1,0},{1,2},{9,2},{9,0}} poly and rect1 overlap? false poly and rect2 overlap? true
Wren
This is just a special case of the Check if two polygons overlap task where one of the polygons is a rectangle though, for convenience, the common code is repeated here.
import "./vector" for Vector2
import "./dynamic" for Tuple
var Projection = Tuple.create("Projection", ["min", "max"])
var Rectangle = Tuple.create("Rectangle", ["x", "y", "w", "h"])
/* In the following a polygon is represented as a list of vertices
and a vertex by a pair of x, y coordinates in the plane. */
var getAxes = Fn.new { |poly|
var axes = List.filled(poly.count, null)
for (i in 0...poly.count) {
var vertex1 = poly[i]
var vertex2 = poly[(i+1 == poly.count) ? 0 : i+1]
var vector1 = Vector2.new(vertex1[0], vertex1[1])
var vector2 = Vector2.new(vertex2[0], vertex2[1])
var edge = vector1 - vector2
axes[i] = edge.perp
}
return axes
}
var projectOntoAxis = Fn.new { |poly, axis|
var vertex0 = poly[0]
var vector0 = Vector2.new(vertex0[0], vertex0[1])
var min = axis.dot(vector0)
var max = min
for (i in 1...poly.count) {
var vertex = poly[i]
var vector = Vector2.new(vertex[0], vertex[1])
var p = axis.dot(vector)
if (p < min) {
min = p
} else if (p > max) {
max = p
}
}
return Projection.new(min, max)
}
var projectionsOverlap = Fn.new { |proj1, proj2|
if (proj1.max < proj2.min) return false
if (proj2.max < proj1.min) return false
return true
}
var rectToPolygon = Fn.new { |r|
return [[r.x, r.y], [r.x, r.y + r.h], [r.x + r.w, r.y + r.h], [r.x + r.w, r.y]]
}
var polygonOverlapsRect = Fn.new { |poly1, rect|
// Convert 'rect' object into polygon form.
var poly2 = rectToPolygon.call(rect)
var axes1 = getAxes.call(poly1)
var axes2 = getAxes.call(poly2)
for (axes in [axes1, axes2]) {
for (axis in axes) {
var proj1 = projectOntoAxis.call(poly1, axis)
var proj2 = projectOntoAxis.call(poly2, axis)
if (!projectionsOverlap.call(proj1, proj2)) return false
}
}
return true
}
var poly = [[0, 0], [0, 2], [1, 4], [2, 2], [2, 0]]
var rect1 = Rectangle.new(4, 0, 2, 2)
var rect2 = Rectangle.new(1, 0, 8, 2)
System.print("poly = %(poly)")
System.print("rect1 = %(rect1) => %(rectToPolygon.call(rect1))")
System.print("rect2 = %(rect2) => %(rectToPolygon.call(rect2))")
System.print()
System.print("poly and rect1 overlap? %(polygonOverlapsRect.call(poly, rect1))")
System.print("poly and rect2 overlap? %(polygonOverlapsRect.call(poly, rect2))")
- Output:
poly = [[0, 0], [0, 2], [1, 4], [2, 2], [2, 0]] rect1 = (4, 0, 2, 2) => [[4, 0], [4, 2], [6, 2], [6, 0]] rect2 = (1, 0, 8, 2) => [[1, 0], [1, 2], [9, 2], [9, 0]] poly and rect1 overlap? false poly and rect2 overlap? true