PostgreSQL - Rotate geometric type giving unexpected results

问题

I'm using PostgresSQL 9.5 to generate a rectangle (geometric type BOX). That works fine

SELECT Box(Point(-50, -100), Point(50, 100)) ; -- this works

Then I try to rotate that box around the origin (its center point). The rotation function is both

*   Scaling/rotation    box '((0,0),(1,1))' * point '(2.0,0)'
/   Scaling/rotation    box '((0,0),(2,2))' / point '(2.0,0)'

where the x-point is the scaling factor (2.0 in this example) and the y-point is the rotation radians (0 in this example).

To check that the rotation is correct, I calculate the height, width and area of the box for each angle.

 SELECT
       xx.deg, -- angle in degrees
       xx.geom, -- geometry of box
       Area(xx.geom), 
       Center(xx.geom),
       Height(xx.geom),
       Width(xx.geom)
FROM   
      (SELECT deg,
               Box(Point(-5, -10), Point(5, 10)) / Point(1, Radians(deg)) -- scale box by factor 1 and rotate by radians(degrees)
               AS geom
        FROM   Generate_series(0, 360, 90) AS deg  -- generate list of degrees from 0 to 360 by 90
) xx;

The results, which don't change between using * or / functions,

deg;geom;area;center;height;width
0;"(5,10),(-5,-10)";200;"(0,0)";20;10
90;"(5.97218570021291,0.618912639168559),(-5.97218570021291,-0.618912639168559)";14.785044853294;"(0,0)";1.23782527833712;11.9443714004258
180;"(3.35025316397424,0.525130727607429),(-3.35025316397424,-0.525130727607429)";7.03728352666753;"(0,0)";1.05026145521486;6.70050632794848
270;"(2.24607945852279,0.584400089411209),(-2.24607945852279,-0.584400089411209)";5.25043614554159;"(0,0)";1.16880017882242;4.49215891704558
360;"(1.67575357650576,0.529070250354662),(-1.67575357650576,-0.529070250354662)";3.5463654570185;"(0,0)";1.05814050070932;3.35150715301153

show that the box is being rotated but also scaled - the height, width and area are all not constant. I read somewhere that a rotation needs to take into account scaling, but I don't understand what scaling factor should be used to compsenate for the rotation. The documentation doesn't give any examples, and most of the resources online are for PostGIS (i.e. ST_Rotate).

UPDATE

I have a working solution that is not the fastest but gives correct results. See here

https://stackoverflow.com/a/39680955/2327328

回答1:

TL/DR: You cannot rotate boxes

The two operators * and / can be confusing. The idea is that they treat the two dimensional points as complex numbers and perform multiply (or divide) them as complex numbers. So for example point '(2,3)' * point '(1,-1)' returns (5,1) because (2+3i)*(1-i)=5+i or point '(0,1)' * point '(0,1)' returns (-1,0) because i*i=-1.

So if you want to use * to rotate by an angle say φ, you have to multiply by the complex number exp(i*φ) which is equal to cos(φ)+i*sin(φ). For example:

SELECT point '(1,0)' * point(cos(radians(45)),sin(radians(45)));
=> (0.707106781186548,0.707106781186547)

rotates the point (1,0) by 45 degrees counter clockwise.

Unfortunately, this doesn't work very well with boxes. If you do

SELECT box '((0,0),(1,1))' * point(cos(radians(45)),sin(radians(45)));
=> (1.11022302462516e-16,1.41421356237309),(0,0)

which means that postgres rotated the two points as individual points and not the whole box. The problem is that a box is a rectangle with sides parallel to the x and y axes. By that definition, if you rotate a box by 45 degrees, what you get is not a box. So you cannot rotate boxes.

In theory, it should be possible to rotate polygons. Unfortunatelly, it seems that this has not been implemented (yet?) in postgresql:

$ SELECT polygon(box '((0,0),(1,1))') * point(1,0);
ERROR:  operator does not exist: polygon * point
LINE 1: SELECT polygon(box '((0,0),(1,1))') * point(1,0);

来源：https://stackoverflow.com/questions/39668459/postgresql-rotate-geometric-type-giving-unexpected-results

标签

postgresql

rotation

geometry