STContains - 多边形内的点测试失败

Question

第一，SQL版本：

我声明了一个封闭多边形（使用左手法则正确定向），根据 SQL 是有效的：

DECLARE @g geography;
SET @g = geography::STPolyFromText('POLYGON((-141.251221 60.177476, -134.351807 52.952478, -124.859620 48.440718, -123.623658 48.163009, -123.132020 48.232578, -122.906113 48.998367, -95.169068 48.966372, -94.980927 49.021337, -94.627991 48.700606, -93.907013 48.594450, -93.845215 48.495351, -93.510132 48.517642, -93.197022 48.583549, -92.743836 48.507408, -92.422486 48.211991, -91.573792 48.021520, -90.973664 48.095065, -90.146256 48.021693, -89.428711 47.911409, -88.442688 48.232120, -84.935303 46.850463, -84.819947 46.614678, -84.531556 46.397991, -84.200593 46.493917, -84.117508 46.124608, -83.620034 45.782175, -82.591267 45.290317, -82.166749 43.592965, -82.661133 42.606311, -82.886353 42.391659, -83.097840 42.332805, -83.187104 42.071357, -83.135605 41.842088, -82.865410 41.657411, -82.463379 41.587347, -81.068116 42.119252, -80.049134 42.334835, -78.887330 42.783953, -78.868104 42.953046, -78.995820 43.161758, -79.090577 43.433616, -78.664856 43.557148, -76.766968 43.541223, -76.398926 44.064539, -74.852601 44.971250, -71.471558 44.957647, -70.846711 45.205884, -70.589219 45.379779, -70.207787 45.900179, -69.238587 47.291005, -68.891488 47.116066, -68.297196 47.291936, -67.850361 47.016678, -67.864953 45.667941, -65.966034 43.191802, -49.229737 45.124550, -59.425049 68.026407, -75.421143 74.789051, -73.663331 78.324047, -57.315674 82.569900, -71.378174 83.545629, -112.335206 79.852216, -141.163331 70.394745, -141.251221 60.177476 ))', 4326);
SELECT @g.IsValidDetailed() AS 'IsValidDetailed', @g.STIsClosed() AS 'STIsClosed', @g.EnvelopeAngle() AS 'EnvelopeAngle';

执行上述查询时，SQL 响应：

IsValidDetailed STIsClosed  EnvelopeAngle
24400: Valid    True        33.0780372828377

为了视觉验证，我绘制了多边形（通过 Google 地图），还包括多边形内部的 3 个点以及多边形外部的 3 个点。下面是多边形的屏幕快照和缩放级别的点，显示了完整的多边形（红色区域表示包围多边形的 "bounds"）：

放大地图，您可以开始看到各个点，即：

进一步放大，可以看到其中两个点非常靠近多边形的边缘，一个在里面（绿色），一个在外面（红色）：

以下查询用于测试多边形内部的点：

SELECT lat, lon, 
       @g.STContains( geography::Point( lat, lon, 4326 ) ) AS STContains,
       geography::Point( lat, lon, 4326 ).STWithin( @g ) AS STWithin
 FROM ( VALUES ( 49.119404, -102.988586 ),
               ( 49.004776, -102.996875 ),
               ( 48.975416, -103.005152 )
       ) points( lat, lon )

SQL 响应：

lat         lon         STContains  STWithin
49.119404   -102.988586 False       False
49.004776   -102.996875 False       False
48.975416   -103.005152 False       False

-- 对于多边形内的点，期望 STContains 和 STwithin 到 return "True"？？？

以下查询用于测试多边形外部的点：

SELECT lat, lon, 
       @g.STContains( geography::Point( lat, lon, 4326 ) ) AS STContains,
       geography::Point( lat, lon, 4326 ).STWithin( @g ) AS STWithin
 FROM ( VALUES ( 48.975409, -103.005151 ),
               ( 48.974153, -103.005144 ),
               ( 48.951739, -103.005627 )
       ) points( lat, lon )

SQL 响应：

lat         lon         STContains  STWithin
48.975409   -103.005151 False       False
48.974153   -103.005144 False       False
48.951739   -103.005627 False       False

-- 所有点都在多边形外部的预期结果。

问题:

为什么 STContains / STWithin 对于位于多边形内部的点失败？

我必须假设我做错了什么，但我遵循了构建多边形的规则（左手），SQL 表示多边形是 "valid"。

如有任何建议，我们将不胜感激。

Answer 1

因为在球面几何中，纬线不是直线。大圆弧是。多边形的最近边缘是 -122.906113 48.998367, -95.169068 48.966372，它位于经度 -103 的第 49 平行线以北。

select geography::STLineFromText('LINESTRING(-122.906113 48.998367, -95.169068 48.966372)', 4326);

是

STContains - 多边形内的点测试失败

STContains - tests failing for points INSIDE polygon

sql-server

sqlgeography