CODEWITHSUNDEEP
javageolocationgeometry
Braveness
Braveness

Reputation: 49

Calculating center of rectangle with coordinate, length, width and angle

I want to determine the center of a rotated rectangle. This rectangle has to be calculated first (see figure). For this the distance in all four directions from the existing coordinate p(x1, y1) is known (bow, port, star, stern). The orientation of the square is also given in degrees.

enter image description here

The easiest solution for me was to calculate a rectangle around the blue axes and then determine the center of this rectangle. Unfortunately I already have a problem with determining the vertices of the square considering the rotation.

Does anyone know how to calculate the coordinates of the vertices with these inputs (preferred in Java)? If someone knows another simpler approach, I would be very grateful. Thanks a lot!

Upvotes: 0

Views: 1731

Answers (2)

Braveness
Braveness

Reputation: 49

Alternative formula (source: https://www.researchgate.net/publication/238090180_A_Study_on_the_efficiency_enhancement_of_automatic_radar_tracking_and_analyses_of_marine_traffic_in_Tokyo_Bay):

c_cog = Math.toRadians(course);
double xc = pos_x + (bow - stern) * Math.sin(course) / 2 + (star-port) * Math.sin(course+90) / 2;
double yc = pos_y + (bow - stern) * Math.cos(course)/2 + (star-port) * Math.cos(course+90) / 2;

Upvotes: 0

MBo
MBo

Reputation: 80107

If star axis has rotation phi relative to OX axis, then direction vector for it is

sx, sy = cos(phi), sin(phi)   //don't forget about radians and degrees

perpendicular (bow direction) vector is

bx, by = -sy, sx

So the topmost vertex at the picture has coordinates

tx = px + star * sx + bow * bx
ty = py + star * sy + bow * by

Bottom vertex:

ux = px - port * sx - stern * bx
uy = py - port * sy - stern * by

Rectangle center is middle of these vertices

cx = px + sx * (star - port) / 2 + bx * (bow - stern) / 2
cy = py + sy * (star - port) / 2 + by * (bow - stern) / 2

And reverting b* variables to sx, sy:
and accounting for desired angle direction:

cx = px + sx * (star - port) / 2 + sy * (bow - stern) / 2
cy = py - sy * (star - port) / 2 + sx * (bow - stern) / 2

Upvotes: 1

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