问题描述
我使用PostgresSQL 9.5生成一个矩形（ BOX）。
工作正常
SELECT BOX（点（-50，-100），点（50,100）） ; - 这个工程
然后我尝试围绕原点（它的中心点）旋转那个盒子。 既是
*缩放/旋转框'（（0,0），（1,1））'* point'（2.0,0）'
/（缩放/旋转框）'（（0,0），（2,2））'/ point'（2.0,0）'
其中x点是比例因子（本例中为2.0），y点是旋转弧度（本例中为0）。
$ b $为了检查旋转是否正确，我计算了每个角度的高度，宽度和框的面积。
选择
xx.deg， - 以度为单位的角度
xx.geom， - 框的几何形状
区域（xx.geom），
中心（xx.geom），
Height（xx.geom），
Width（xx.geom）
FROM
（SELECT deg，
Box（Point（-5，-10），Point （5，10））/ Point（1，Radians（deg）） - 按比例1放大比例框并旋转弧度（度）
AS geom
FROM Generate_series（0,360,90）AS deg - 根据90
）xx生成从0到360的度数列表;
结果在使用 * / 函数，
deg; geom; area; （5,10），（ - 5，-10）; 200;（0,0）; 20; 10
90;（5.97218570021291， （ - 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
表明该框正在旋转，但也被缩放 - 高度，宽度和面积都不是恒定的。我在某处看到轮换需要考虑缩放比例，但我不明白缩放因子应该用于轮换。该文档没有提供任何示例，并且大多数在线资源都是针对PostGIS（即ST_Rotate）。
更新
我有一个不是最快的工作解决方案，但可以给出正确的结果。看到这里
两个运算符 * 和 / 可能会造成混淆。这个想法是，他们将二维点视为复数，并将它们乘以（或划分）为复数。因此，例如点'（2,3）'*点'（1，-1）'返回（5,1）（2 + 3i）*（1-i）= 5 + i 或点'（0,1）'* （0,1）'返回（ - 1,0）因为 i * i = -1
所以如果你想用 * 来旋转一个角度，比如φ，您必须乘以复数 exp（i *φ），这等于 cos（φ ）+ I * SIN（φ）。例如：
SELECT point'（1,0）'* point（cos（radians（45）），sin（radians （45）））;
=> （0.707106781186548,0.707106781186547）
旋转点（1,0） code>逆时针45度。
不幸的是，这对盒子来说效果不佳。 （（0,0），（1,1））'*点（cos（弧度） （45）），SIN（弧度（45）））;
=> （1.11022302462516e-16,1.41421356237309），（0,0）
这意味着postgres将两个指向个别点而不是整个框。问题是一个盒子是一个矩形，其边与x和y轴平行。按照这个定义，如果你将盒子旋转45度，你得到的不是盒子。所以你不能旋转框。
理论上，应该可以旋转多边形。不幸的是，这似乎还没有在postgresql中实现（还没有？）：
$ SELECT多边形（box'（（0 ，0），（1,1））'）* point（1,0）;
ERROR：运算符不存在：polygon * point
LINE 1：SELECT polygon（box'（（0,0），（1,1））'）* point（1,0）;
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
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);
这篇关于PostgreSQL - 旋转几何类型给出意想不到的结果的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！