# Calculating the top left corner in a 2d field [closed]

Given I have a field with several rectangles like shown in the picture. A point with its x and y coordinates are given. The height(h) and the width(w) are also given. How can I calculate the top left corner with x, y h and w?

## closed as off-topic by m_goldberg, MarcoB, user9660, Öskå, kjoMay 28 '16 at 17:45

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• pos + size/2 ? – Kuba May 27 '16 at 13:35
• hm doesn't work for my example – Kris May 27 '16 at 13:40
• So your origin is the upper left hand corner? – gwr May 27 '16 at 13:44
• Correct. The purpose is a 2d Game where the user clicks somewhere into the field and the program needs to put a thing to the top left corner of a square in a field of squares – Kris May 27 '16 at 13:47
• I'm voting to close this question as off-topic because this question is about middle-school level math; nothing to do with Mathematica. – kjo May 28 '16 at 17:45

## 1 Answer

The solution is to work in grid positions, e.g. gridX × height and gridY × width to come up with screen coordinates that have to be corrected by an offset to line up the grid-origin one is using with its true screen coordinates.

The position in the grid can be obtained by using Quotient thus returning the grid coordinates as integers.

In the given example the width of a box (assuming the red point is in the middle) is 200 and the height is 120 so the x-Axis confusingly here is the ordinate and the x-Axis the abscissa:

Clear[ leftCorner ];
leftCorner[ x_, y_, w_, h_ ] := With[
{
offset = {50, 80} (* needed to correct for true screen position *)
},

{ Quotient[ x, h ], Quotient[  y, w ] } × {h, w} + offset

]

leftCorner[ 230, 180, (* w = *) 2 (180 - 80), (* h= *) 2 (230-170)  ]


{170,80}

leftCorner[ 100, 100, 200, 120]


{50,80}

So the origin of our implicit grid for calculations would be the left corner of the box above the marked one in the OP.

• I have now changed w and h to match the OP exactly where the axis are confusingly given with x-Axis as ordinate and y-Axis as abscissa. This all of course had to be deduced from a somewhat sloppy graph... – gwr May 28 '16 at 8:14