# Determine if point is within bounding box

How would you determine if a given point is within the bounding box?

My point is 48.847172 , 2.386597.

Boundingbox:

``````    "48.7998602295",
"48.8198640442",
"2.46138595581",
"2.48138619423"
``````

Do just as usual:

``````if( bb.ix <= p.x && p.x <= bb.ax && bb.iy <= p.y && p.y <= bb.ay ) {
// Point is in bounding box
}
``````

`bb` is the bounding box, `(ix,iy)` are its top-left coordinates, and `(ax,ay)` its bottom-right coordinates. `p` is the point and `(x,y)` its coordinates.

This solution also takes in consideration a case in which the UI sends a box which crosses longitude 180/-180 (maps views on low zoom level where you can see the whole world, allow infinite cyclic horizontal scrolling, so it is possible for example that a box's bottomLeft.lng=170 while topRight.lng=-170(=190) and by that including a range of 20 degrees.

``````def inBoundingBox(bl/*bottom left*/: Coordinates, tr/*top right*/: Coordinates, p: Coordinates): Boolean = {
// in case longitude 180 is inside the box
val isLongInRange =
if (tr.long < bl.long) {
p.long >= bl.long || p.long <= tr.long
} else
p.long >= bl.long && p.long <= tr.long

p.lat >= bl.lat  &&  p.lat <= tr.lat  &&  isLongInRange
}
``````

If you are using leaflet, you can create a new `LatLngBounds` and use its `contains()` operation:

``````var bounds = new L.LatLngBounds(
new L.LatLng(gc.bbox['_northEast'].lat, gc.bbox['_northEast'].lng),
new L.LatLng(gc.bbox['_southWest'].lat, gc.bbox['_southWest'].lng));

return bounds.contains(new L.LatLng(pos.latitude, pos.longitude))
``````

There are quite nice utility methods for CGRect and CGPoint (assuming you don't mind fact that they are using CGFloat for storing coordinates - and looking at your values, you don't :-) ).

You can do it like that:

``````// Create bounding box
CGRect area = CGRectMake(x, y, width, height);

// Define point
CGPoint point = CGPointMake(pX, pY);

/Check
BOOL isInside = CGRectContainsPoint(area, point);
``````

Use this function for c plus plus to check if a point exits inside a rectangle

``````struct Box{

Vec2 corner1;
Vec2 corner2;
Vec2 corner3;
Vec2 corner4;

};

bool boxContainsPoint(Vec2 point, Box box){

//Calculate distances from corner to corner
float abL = box.corner1.getDistance(box.corner2);////////////////////
float bcL = box.corner2.getDistance(box.corner3);////////////////////
float cdL = box.corner3.getDistance(box.corner4);////////////////////
float daL = box.corner4.getDistance(box.corner1);////////////////////

//Calculate corner touch distance//////////////////////////////////
float apL = box.corner1.getDistance(point);/////////////////////////
float bpL = box.corner2.getDistance(point);/////////////////////////
float cpL = box.corner3.getDistance(point);/////////////////////////
float dpL = box.corner4.getDistance(point);/////////////////////////

//Here we calculate the touch area
//Heron's Formula
///////////////////////////////////////////////////////////////////
float area1 = (abL + apL + bpL) / 2;///////////////////////////////
float area2 = (bcL + bpL + cpL) / 2;///////////////////////////////
float area3 = (cdL + cpL + dpL) / 2;///////////////////////////////
float area4 = (daL + dpL + apL) / 2;///////////////////////////////
float a1 = sqrtf(area1 * (area1 - abL)*(area1 - apL)*(area1 - bpL));
float a2 = sqrtf(area2 * (area2 - bcL)*(area2 - bpL)*(area2 - cpL));
float a3 = sqrtf(area3 * (area3 - cdL)*(area3 - cpL)*(area3 - dpL));
float a4 = sqrtf(area4 * (area4 - daL)*(area4 - dpL)*(area4 - apL));

//Calculate the rectangle area
float A = roundf(abL*bcL);

//Check to see if the point contains the polygon rect
if(A ==roundf(a1 + a2 + a3 + a4)) return true;
return false;

}
``````

This answer is identical to kumetix's answer above; however, for the life of me, I didn't understand what was happening in there since it was condensed quite a bit. Here is the same answer with detailed explanation. Also please note that the answer is in Kotlin as opposed to JavaScript as the original post requested but it is sufficiently readable so that converting to your language should be trivial.

First define Coordinate and BoundingBox classes:

``````data class Coordinate2D (val latitude: Double, val longitude: Double)

data class BoundingBox (val north: Double, val east: Double, val south: Double, val west: Double)
``````

Here is the function that determines whether

``````fun isPointInBoundingBox(point: Coordinate2D, boundingBox: BoundingBox): Boolean {
//initially assume the point is not in our bounding box of interest
var isPointEastOfWestLine = false
var isPointWestOfEastLine = false
var isPointSouthOfNorthLine = false
var isPointNorthOfSouthLine = false

if (boundingBox.east < boundingBox.west) {
//east longitude will always have a higher value if the bounding box is not
//crossing the dateline, i.e. longitude 180 is inside the box
//so we are crossing the dateline, let's see what's happening with the point
if (point.longitude >= boundingBox.west) {
//imagine a bounding box where westernmost longitude is +170 and easternmost longitude is -170
//if the point in question has a latitude of +171 as in the case expressed in the if
//statement, then we can conclude that point lies east of the west line
isPointEastOfWestLine = true

//we can also infer that the point must lie west of east line because the point's longitude is positive
//therefore, the point's position must be to the west of the easternmost longitude of the bounding box
isPointWestOfEastLine = true
}

if (point.longitude <= boundingBox.east) {
//imagine a bounding box where westernmost longitude is +170 and easternmost longitude is -170
//if the point in question has a latitude of -171 as in the case expressed in the if
//statement, then we can conclude that point lies west of the east line
isPointWestOfEastLine = true

//we can also infer that the point must lie east of the west line because the point's longitude is negative
//therefore, the point's position must be to the east of the westernmost longitude of the bounding box
isPointEastOfWestLine = true
}
} else {
//in the else case, bounding box does not cross the dateline, so comparisons are more straightforward
//longitudes range from -180 to +180; therefore, western side of a bounding box will always
//have lower value than eastern side
if (point.longitude >= boundingBox.west) {
//in this case, point's longitude has a higher value than the west side of the bounding box
//we can conclude that point lies to the east of the west line of the bounding box
isPointEastOfWestLine = true
}
if (point.longitude <= boundingBox.east) {
//in this case, point's longitude has a lower value than the east side of the bounding box
//we can conclude that point lies to the east of the west line of the bounding box
isPointWestOfEastLine = true
}
}

//comparing latitudes are little bit easier. latitude values range from -90 to +90 where
//-90 is the southern pole and +90 is the northern pole. The more north you go, higher the values.
if (point.latitude >= boundingBox.south) {
//point's latitude is higher, therefore, point must lie to the north of the south line
isPointNorthOfSouthLine = true
}

if (point.latitude <= boundingBox.north) {
//point's latitude is higher, therefore, point must lie to the north of the south line
isPointSouthOfNorthLine = true
}

return isPointEastOfWestLine &&
isPointWestOfEastLine &&
isPointNorthOfSouthLine &&
isPointSouthOfNorthLine
}
``````

This should be faster.

``````function doesPointCollide(p,box) {
return !(p.x < box.left || p.x > box.right || p.y > box.bottom || p.y < box.top)
}
``````

If the point is outside any of the dimensions we know that it's not in the bounding box, else it is in the bounding box, so we can ignore negated cases more quickly.