Don't Panic if you see Crazy Cost Percentage in SQL Execution Plan.

I've had situations when very complicated execution plans showed billions of percents for single operations within a query plan. Unfortunately I did not capture these extreme situations and have only pretty modest percentage example. Just up to several million percents:

That is documented bug and very well described by Aaron Bertrand on StackExchange:

http://dba.stackexchange.com/questions/40274/how-does-sql-server-generate-a-query-execution-plan-that-adds-up-to-6-000

In the theory, SUM of all tasks in Execution plan must not exceed 100%, but as you see it is not always the truth.
In this post I try to reproduce that bug in test environment, learn it's dependencies and workaround.

At first will create a test table and fill it wit 4K dummy records.

USE Tempdb
GO
CREATE TABLE tbl_Test
(
Demo_ID INT PRIMARY KEY IDENTITY(1,1) NOT NULL,
Demo_Number INT NOT NULL,
Demo_Type CHAR(1) NOT NULL,
Demo_Text NVARCHAR(450) NOT NULL
);
GO
;WITH SampleData_1 AS (SELECT CAST(0 AS TINYINT) AS SampleData UNION ALL SELECT 0 UNION ALL SELECT 0 UNION ALL SELECT 0)
    , SampleData_2 AS (SELECT sd1.SampleData FROM SampleData_1 AS sd1, SampleData_1 AS sd2)
    , SampleData_3 AS (SELECT sd1.SampleData FROM SampleData_2 AS sd1, SampleData_2 AS sd2, SampleData_2)
INSERT INTO tbl_Test(Demo_Number, Demo_Type, Demo_Text)
SELECT ROW_NUMBER() OVER(ORDER BY SampleData) rn, 'T', REPLICATE(N'A',447) FROM SampleData_3;

Then copy-paste following code in SSMS, highlight it, but do not execute. Just click "Display Estimated Execution Plan" or press "Ctrl+L"

IF EXISTS (SELECT * FROM tbl_Test WHERE Demo_Number % 33 = 0)
DELETE FROM tbl_Test WHERE Demo_Number % 33 = 0;

You will get thousands of percents in the bottom line.

Will look why did it happened.
First look at Estimated Cost:
Estimated Subtree Cost for the whole query is 0.0063008.
Estimated Cost for "Clustered Index Delete" is 0.108937, which is exactly 1728.939%  from the cost of whole query.

That means that percentage was calculated correctly, but Estimated Subtree Cost for the whole query was not.

It is obvious why that was happened. As you can see, the query contains two sub queries, but total Subtree Cost is calculated only for the first sub-query, without including costs for the second sub-query.

Now, when we know WHY and HOW the problem happens, will take a look at what is contributing to the additional percentage.

First, will double amount of records by using second part of the first query:

;WITH SampleData_1 AS (SELECT CAST(0 AS TINYINT) AS SampleData UNION ALL SELECT 0 UNION ALL SELECT 0 UNION ALL SELECT 0)
    , SampleData_2 AS (SELECT sd1.SampleData FROM SampleData_1 AS sd1, SampleData_1 AS sd2)
    , SampleData_3 AS (SELECT sd1.SampleData FROM SampleData_2 AS sd1, SampleData_2 AS sd2, SampleData_2)
INSERT INTO tbl_Test(Demo_Number, Demo_Type, Demo_Text)
SELECT ROW_NUMBER() OVER(ORDER BY SampleData) rn, 'T', REPLICATE(N'A',447) FROM SampleData_3;

Look at estimated execution plan again:

Percentages are also almost doubled.

That is easy to explain. In order to delete, SQL Server has to deal with higher volume of data, that results in higher Estimated Costs.

Now will try to add bunch of indexes to our table:

CREATE INDEX IX_tbl_Test1 ON tbl_Test(Demo_Number);
CREATE INDEX IX_tbl_Test2 ON tbl_Test(Demo_Type);
CREATE INDEX IX_tbl_Test3 ON tbl_Test(Demo_Text);
CREATE INDEX IX_tbl_Test4 ON tbl_Test(Demo_Text, Demo_Type);
CREATE INDEX IX_tbl_Test5 ON tbl_Test(Demo_Type, Demo_Text);
CREATE INDEX IX_tbl_Test6 ON tbl_Test(Demo_Type, Demo_Text, Demo_Number);
CREATE INDEX IX_tbl_Test7 ON tbl_Test(Demo_Number, Demo_Type, Demo_Text);
CREATE INDEX IX_tbl_Test8 ON tbl_Test(Demo_Type, Demo_Number, Demo_Text);

I'd expect percentages also to rise:

And they increased dramatically!


As the conclusion I'd say:
In case you see crazy percentage values in your Execution query plan:

Everything is OK, that is just SSMS does not show you correct percentages.

Draw American flag in SSMS using Spatial methods. Step by Step.

Yep. That is possible using SQL Server Spatial functionality.
In my few prior posts I already uncovered some Spatial drawing abilities, but now I want to draw real picture.

Let's STARt from drawing stars!

1. Draw a star.

1.1. Start in the center of a star.

   - Center will be coordinates x=0, y=0
   - Circle radius = 10

1.2. Figure out ending point of one bottom ray:

   - Angle between rays is 360 / 5 = 72 degrees.
   - To calc coordinates we need a half: 36 degrees.
   - Define coordinates of ending point of the ray as
     X = radius x SIN(36)
     Y = radius x COS(36)
   - To use SIN & COS have to use "RADIANS" function.
   - RADIANS function does not accept integer!
   "SELECT X = 100 * SIN(RADIANS(36.)), Y = - 100 * COS(RADIANS(36.))"
  
   - Middle ray angle is 90 - 72 = 18 Degrees
     X = radius x COS(18)
     Y = radius x SIN(18)

   - Top ray just has coordinates
     X = 0
     Y = radius
Here is what we get:

SELECT CAST('LINESTRING(0 0, 0 10)' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, 10 * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, -10 * COS(RADIANS(36.))) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, -10 * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, -10 * COS(RADIANS(36.))) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, 10 * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, 10 * SIN(RADIANS(18.))) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, -10 * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, 10 * SIN(RADIANS(18.))) + ')' as geometry);

And here is a result:

Not a star yet, just a skeleton.

1.3. Will connect the rays:

SELECT CAST('LINESTRING(0 10, '
+ CONVERT(VARCHAR, 10 * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, -10 * COS(RADIANS(36.))) + ','
+ CONVERT(VARCHAR, -10 * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, 10 * SIN(RADIANS(18.))) + ','
+ CONVERT(VARCHAR, 10 * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, 10 * SIN(RADIANS(18.))) + ','
+ CONVERT(VARCHAR, -10 * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, -10 * COS(RADIANS(36.))) + ','
+ '0 10)' as geometry);

That is more like a star:

1.4. Pretty, but we do not need internal lines.

Lets calculate middle Ray's bottom points:
    X = radius * SIN(18) * TAN(36)
    Y = radius * SIN(18)
Here are coordinartes of lover Ray's bottom points:
    X = radius * SIN(18) * TAN(36)
    Y = radius * SIN(18)

Also, to simplify our select, replace formulas by variables:

DECLARE @r FLOAT = 10;
DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

SELECT CAST('LINESTRING(0 0, 0 10)' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, @r * @SIN36) + ' ' + CONVERT(VARCHAR, -@r * @COS36) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, -@r * @SIN36) + ' ' + CONVERT(VARCHAR, -@r * @COS36) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, @r * @COS18) + ' ' + CONVERT(VARCHAR, @r * @SIN18) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, -@r * @COS18) + ' ' + CONVERT(VARCHAR, @r * @SIN18) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @r * @SIN18 ) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, -@r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @r * @SIN18 ) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, -@r * @SIN18 * @SIN18 / @COS36 ) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0,' + CONVERT(VARCHAR, -@r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, -@r * @SIN18 * @SIN18 / @COS36 ) + ')' as geometry)
UNION ALL
SELECT CAST('LINESTRING(0 0, 0 ' + CONVERT(VARCHAR, -@r * @SIN18 / @COS36 ) + ')' as geometry);

Again bunch of rays:

1.5. Will connect rays ones again:

DECLARE @r FLOAT = 10;
DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

SELECT CAST('LINESTRING(0 10, '
+ CONVERT(VARCHAR, @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @r * @SIN18 ) + ','
+ CONVERT(VARCHAR, @r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @r * SIN(RADIANS(18.))) + ','
+ CONVERT(VARCHAR, @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, -@r * @SIN18 * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, -@r * COS(RADIANS(36.))) + ','
+ '0 ' + CONVERT(VARCHAR, -@r * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, -@r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, -@r * COS(RADIANS(36.))) + ','
+ CONVERT(VARCHAR, -@r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, -@r * @SIN18 * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, -@r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @r * SIN(RADIANS(18.))) + ','
+ CONVERT(VARCHAR, -@r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @r * @SIN18 ) + ','
+ '0 10)' as geometry);

Now we get a real star:

1.6. Very nice star and we will learn how to move the star on our field:

Will add extra coordinates X and Y
Now we can place our star wherever we want:

DECLARE @r FLOAT = 10;
DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

DECLARE @x FLOAT = 50;
DECLARE @y FLOAT = 50;

SELECT CAST('LINESTRING('
+ CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r) + ','
+ CONVERT(VARCHAR, @x + @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
+ CONVERT(VARCHAR, @x + @r * COS(RADIANS(18.)) ) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
+ CONVERT(VARCHAR, @x + @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, @x + @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
+ CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, @x - @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
+ CONVERT(VARCHAR, @x - @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, @x - @r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
+ CONVERT(VARCHAR, @x - @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
+ CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r)
+ ')' AS GEOMETRY);

1.7. To color our star we have to build a Polygon   

MOST IMPORTANT: Polygon line must end at the same point where it started.

DECLARE @r FLOAT = 10;
DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

DECLARE @x FLOAT = 50;
DECLARE @y FLOAT = 50;

SELECT CAST('POLYGON(('
+ CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r) + ','
+ CONVERT(VARCHAR, @x + @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
+ CONVERT(VARCHAR, @x + @r * COS(RADIANS(18.)) ) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
+ CONVERT(VARCHAR, @x + @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, @x + @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
+ CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, @x - @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
+ CONVERT(VARCHAR, @x - @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
+ CONVERT(VARCHAR, @x - @r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
+ CONVERT(VARCHAR, @x - @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
+ CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r)
+ '))' AS GEOMETRY);

Now star is colored:

1.8. And now we will make all 50 stars at once:

DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

DECLARE @x FLOAT;
DECLARE @y FLOAT;

DECLARE @r FLOAT = 6.16/2; -- Star Radius
DECLARE @hd FLOAT = 6.3; -- Horisontal distance between stars
DECLARE @vd FLOAT = 5.4; -- Vertical distance between stars

DECLARE @h TINYINT = 0, @v TINYINT = 0; -- Horisontal & Vertical Star counters

DECLARE @Stars TABLE(Star GEOMETRY);

WHILE @h < 11
BEGIN
SET @h += 1;
WHILE @v < 9
BEGIN
    SET @v += 2;
    SELECT
        @x = @hd * (@h + (@v + 1) % 2),
        @y = @vd * (@v + (@h + 1) % 2) * (-1);
    INSERT INTO @Stars(Star)
    SELECT CAST('POLYGON(('
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x + @r * COS(RADIANS(18.)) ) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x + @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r)
    + '))' AS GEOMETRY);

    IF @v = 8 and @h % 2 = 0 SET @v = 9;
END
SET @v = 0;
END

SELECT * FROM @Stars;

Here are our 50 stars:

1.9. Let's make all 50 stars as one POLYGON:

DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

DECLARE @x FLOAT;
DECLARE @y FLOAT;

DECLARE @r FLOAT = 6.16/2; -- Star Radius
DECLARE @hd FLOAT = 6.3; -- Horisontal distance between stars
DECLARE @vd FLOAT = 5.4; -- Vertical distance between stars

DECLARE @h TINYINT = 0, @v TINYINT = 0; -- Horisontal & Vertical Star counters

DECLARE @StarPolygon VARCHAR(MAX) = '';

WHILE @h < 11
BEGIN
SET @h += 1;
WHILE @v < 9
BEGIN
    SET @v += 2;
    SELECT
        @x = @hd * (@h - 1 + (@v + 1) % 2),
        @y = @vd * (@v - 1 + (@h + 1) % 2) * (-1);

    SET @StarPolygon += ',('
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x + @r * COS(RADIANS(18.)) ) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x + @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r)
    + ')';

    IF @v = 8 and @h % 2 = 0 SET @v = 9;
END
SET @v = 0;
END

SELECT CAST('POLYGON(' + SUBSTRING(@StarPolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

Here are all stars as one POLYGON:

1.10. Final step with stars is putting them in a box:

DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

DECLARE @x FLOAT;
DECLARE @y FLOAT;

DECLARE @r FLOAT = 6.16/2; -- Star Radius
DECLARE @hd FLOAT = 6.3; -- Horisontal distance between stars
DECLARE @vd FLOAT = 5.4; -- Vertical distance between stars

DECLARE @h TINYINT = 0, @v TINYINT = 0; -- Horisontal & Vertical Star counters

DECLARE @StarPolygon VARCHAR(MAX) = '';
-- DECLARE @Stars TABLE(Star GEOMETRY);

WHILE @h < 11
BEGIN
SET @h += 1;
WHILE @v < 9
BEGIN
    SET @v += 2;
    SELECT
        @x = @hd * (@h - 1 + (@v + 1) % 2),
        @y = @vd * (@v - 1 + (@h + 1) % 2) * (-1);

    SET @StarPolygon += ',('
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x + @r * COS(RADIANS(18.)) ) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x + @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r)
    + ')';

    IF @v = 8 and @h % 2 = 0 SET @v = 9;
END
SET @v = 0;
END

SELECT CAST('POLYGON('
+ '(0 0,0 ' + CONVERT(VARCHAR, @vd * -10)
+ ',' + CONVERT(VARCHAR, @hd * 12) + ' ' + CONVERT(VARCHAR, @vd * -10)
+ ',' + CONVERT(VARCHAR, @hd * 12) + ' 0,0 0),'
+ SUBSTRING(@StarPolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

We are done with most difficult part of the American Flag:

2. Stripes.

2.1. Stripes are pretty easy:

DECLARE @A FLOAT = 100; -- Flag Width
DECLARE @B FLOAT = 190; -- Flag Length
DECLARE @UA FLOAT = @A * 7 / 13; -- UNION Length
DECLARE @UB FLOAT = 76; -- UNION Length
DECLARE @s TINYINT = 1; -- Stripe Count
DECLARE @StripePolygon VARCHAR(MAX) = '';

WHILE @s <= 13
BEGIN
SELECT @StripePolygon += ',('
+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ','

+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, @s * @A / -13) + ','

+ CONVERT(VARCHAR, @B) + ' '
+ CONVERT(VARCHAR, @s * @A / -13) + ','

+ CONVERT(VARCHAR, @B) + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ','

+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ')', @s += 2;
END

SELECT CAST('POLYGON(' + SUBSTRING(@StripePolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

Here they are.Remind me flag of Greece.

2.2. Will finish with stripes by framing them:

DECLARE @A FLOAT = 100; -- Flag Width
DECLARE @B FLOAT = 190; -- Flag Length
DECLARE @UA FLOAT = @A * 7 / 13; -- UNION Length
DECLARE @UB FLOAT = 76; -- UNION Length
DECLARE @s TINYINT = 1; -- Stripe Count
DECLARE @StripePolygon VARCHAR(MAX) = '';

WHILE @s <= 13
BEGIN
SELECT @StripePolygon += ',('
+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ','

+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, @s * @A / -13) + ','

+ CONVERT(VARCHAR, @B) + ' '
+ CONVERT(VARCHAR, @s * @A / -13) + ','

+ CONVERT(VARCHAR, @B) + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ','

+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ')', @s += 2;
END

SELECT CAST('POLYGON((0 0, 0 '
+ CONVERT(VARCHAR, -@A) + ', '
+ CONVERT(VARCHAR, @B) + ' ' + CONVERT(VARCHAR, -@A) + ', '
+ CONVERT(VARCHAR, @B) + ' 0,0 0),'
+ '(0.1 -0.1,0.1 '
+ CONVERT(VARCHAR, 0.1 - @A ) + ', '
+ CONVERT(VARCHAR, @B - 0.1) + ' ' + CONVERT(VARCHAR, 0.1 - @A) + ', '
+ CONVERT(VARCHAR, @B - 0.1) + ' -0.1,0.1 -0.1)'
+ ')' AS GEOMETRY)
UNION ALL
SELECT CAST('POLYGON(' + SUBSTRING(@StripePolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

Here how they look in frame:

3. Now will combine Stars and Stripes:

DECLARE @A FLOAT = 100; -- Flag Width
DECLARE @B FLOAT = 190; -- Flag Length
DECLARE @UA FLOAT = @A * 7 / 13; -- UNION Length
DECLARE @UB FLOAT = 76; -- UNION Length
DECLARE @s TINYINT = 1; -- Stripe Count

DECLARE @StripePolygon VARCHAR(MAX) = '';
DECLARE @r FLOAT = 6.16/2; -- Star Radius
DECLARE @hd FLOAT = @UB/12; -- Horisontal distance between stars
DECLARE @vd FLOAT = 5.4; -- Vertical distance between stars

DECLARE @h TINYINT = 0, @v TINYINT = 0; -- Horisontal & Vertical Star counters
DECLARE @x FLOAT;
DECLARE @y FLOAT;

DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

DECLARE @StarPolygon VARCHAR(MAX) = '';

DECLARE @Flag TABLE(Polygon GEOMETRY, ID INT IDENTITY(1,1))

WHILE @h < 11
BEGIN
SET @h += 1;
WHILE @v < 9
BEGIN
    SET @v += 2;
    SELECT
        @x = @hd * (@h - 1 + (@v + 1) % 2),
        @y = @vd * (@v - 1 + (@h + 1) % 2) * (-1);

    SET @StarPolygon += ',('
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x + @r * COS(RADIANS(18.)) ) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x + @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r)
    + ')';

    IF @v = 8 and @h % 2 = 0 SET @v = 9;
END
SET @v = 0;
END

INSERT INTO @Flag(Polygon)
SELECT CAST('POLYGON('
+ '(0 0,0 ' + CONVERT(VARCHAR, @vd * -10)
+ ',' + CONVERT(VARCHAR, @hd * 12) + ' ' + CONVERT(VARCHAR, @vd * -10)
+ ',' + CONVERT(VARCHAR, @hd * 12) + ' 0,0 0),'
+ SUBSTRING(@StarPolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

WHILE @s <= 13
BEGIN
SELECT @StripePolygon += ',('
+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ','

+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, @s * @A / -13) + ','

+ CONVERT(VARCHAR, @B) + ' '
+ CONVERT(VARCHAR, @s * @A / -13) + ','

+ CONVERT(VARCHAR, @B) + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ','

+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' '
+ CONVERT(VARCHAR, (@s - 1) * @A / -13) + ')', @s += 2;
END

INSERT INTO @Flag(Polygon)
SELECT CAST('POLYGON((0 0, 0 '
+ CONVERT(VARCHAR, -@A) + ', '
+ CONVERT(VARCHAR, @B) + ' ' + CONVERT(VARCHAR, -@A) + ', '
+ CONVERT(VARCHAR, @B) + ' 0,0 0),'
+ '(0.1 -0.1,0.1 '
+ CONVERT(VARCHAR, 0.1 - @A ) + ', '
+ CONVERT(VARCHAR, @B - 0.1) + ' ' + CONVERT(VARCHAR, 0.1 - @A) + ', '
+ CONVERT(VARCHAR, @B - 0.1) + ' -0.1,0.1 -0.1)'
+ ')' AS GEOMETRY)

INSERT INTO @Flag(Polygon)
SELECT CAST('POLYGON(' + SUBSTRING(@StripePolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

SELECT * FROM @Flag;

Picture is good, but colors are ugly:

4. Coloring. Very important step.

As you noticed, on all prior pics all colors are random. That is because we CAN'T control them!
However, even though they are random, but they are random in the certain order and we can use that order for our needs.

Let's Look at colors we  can use:

DECLARE @SSMSColourPalette table (id INT IDENTITY(1,1), geom geometry)

DECLARE @x INT = 0, @y INT = 0;
WHILE @y < 100
BEGIN
WHILE @x < 20
BEGIN
INSERT INTO @SSMSColourPalette VALUES(
'POLYGON((' + CAST(@x AS VARCHAR(32)) + ' ' + CAST(@y AS VARCHAR(32)) + ','
+ CAST(@x + 1 AS VARCHAR(32)) + ' ' + CAST(@y AS VARCHAR(32)) + ','
+ CAST(@x + 1 AS VARCHAR(32)) + ' ' + CAST(@y + 1 AS VARCHAR(32)) + ','
+ CAST(@x AS VARCHAR(32)) + ' ' + CAST(@y + 1 AS VARCHAR(32)) + ','
+ CAST(@x AS VARCHAR(32)) + ' ' + CAST(@y AS VARCHAR(32)) + '))'
)
SET @x = @x + 1;
END
SET @x = 0;
SET @y = @y + 1;
END

SELECT * FROM @SSMSColourPalette
ORDER BY id;

Here are the firs couple of hundred colors fro selected 2000:

In order to get necessary color we have to do draw some empty objects, which will hold colors we want to skip using following script:

SELECT TOP 140
CAST('POLYGON((0 0, 0 0.0000001, 0.0000001 0.0000001, 0 0))' AS GEOMETRY)  
FROM sys.messages;

5. And Now our Final Step and the Final script of drawing the Flag:

GO

DECLARE @A FLOAT = 100; -- Flag Width
DECLARE @B FLOAT = 190; -- Flag Length
DECLARE @UA FLOAT = @A * 7 / 13; -- UNION Length
DECLARE @UB FLOAT = 76; -- UNION Length
DECLARE @s TINYINT = 1; -- Stripe Count

DECLARE @StripePolygon VARCHAR(MAX) = '';
DECLARE @r FLOAT = 6.16/2; -- Star Radius
DECLARE @hd FLOAT = @UB/12; -- Horisontal distance between stars
DECLARE @vd FLOAT = 5.4; -- Vertical distance between stars

DECLARE @h TINYINT = 0, @v TINYINT = 0; -- Horisontal & Vertical Star counters
DECLARE @x FLOAT;
DECLARE @y FLOAT;

DECLARE @rad18 FLOAT = RADIANS(18.);
DECLARE @rad36 FLOAT = RADIANS(36.);
DECLARE @SIN18 FLOAT = SIN(@rad18);
DECLARE @COS18 FLOAT = COS(@rad18);
DECLARE @SIN36 FLOAT = SIN(@rad36);
DECLARE @COS36 FLOAT = COS(@rad36);
DECLARE @TAN36 FLOAT = TAN(@rad36);

DECLARE @StarPolygon VARCHAR(MAX) = '';

DECLARE @Flag TABLE(Polygon GEOMETRY, ID INT IDENTITY(1,1))

-- Building SET of 50 stars
WHILE @h < 11
BEGIN
SET @h += 1;
WHILE @v < 9
BEGIN
    SET @v += 2;
    SELECT
        @x = @hd * (@h - 1 + (@v + 1) % 2),
        @y = @vd * (@v - 1 + (@h + 1) % 2) * (-1);

    -- Building Individual star
    SET @StarPolygon += ',('
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x + @r * COS(RADIANS(18.)) ) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x + @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x + @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * SIN(RADIANS(36.))) + ' ' + CONVERT(VARCHAR, @y - @r * COS(RADIANS(36.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @COS18 / @COS36 ) + ' ' + CONVERT(VARCHAR, @y - @r * @SIN18 * @SIN18 / @COS36 ) + ','
    + CONVERT(VARCHAR, @x - @r * COS(RADIANS(18.))) + ' ' + CONVERT(VARCHAR, @y + @r * SIN(RADIANS(18.))) + ','
    + CONVERT(VARCHAR, @x - @r * @SIN18 * @TAN36 ) + ' ' + CONVERT(VARCHAR, @y + @r * @SIN18 ) + ','
    + CONVERT(VARCHAR, @x) + ' ' + CONVERT(VARCHAR, @y + @r)
    + ')';

    IF @v = 8 and @h % 2 = 0 SET @v = 9;
END
SET @v = 0;
END

-- Building SET of 13 stripes
WHILE @s <= 13
BEGIN
-- Building Individual stripe
SELECT @StripePolygon += ',('
+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' ' + CONVERT(VARCHAR, (@s - 1) * @A / -13) + ','
+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' ' + CONVERT(VARCHAR, @s * @A / -13) + ','
+ CONVERT(VARCHAR, @B) + ' ' + CONVERT(VARCHAR, @s * @A / -13) + ','
+ CONVERT(VARCHAR, @B) + ' ' + CONVERT(VARCHAR, (@s - 1) * @A / -13) + ','
+ CASE WHEN @s < 9 THEN CONVERT(VARCHAR, @UB) ELSE '0' END + ' ' + CONVERT(VARCHAR, (@s - 1) * @A / -13) + ')'
, @s += 2;
END

---------------------------------------------------------------------------------------------------------------

-- Adjust Frame Color
INSERT INTO @Flag(Polygon)
SELECT TOP 149 CAST('POLYGON((0 0, 0 0.0000001, 0.0000001 0.0000001, 0 0))' AS GEOMETRY) FROM sys.messages

-- Adding Frame
INSERT INTO @Flag(Polygon)
SELECT CAST('POLYGON((0 0, 0 '
+ CONVERT(VARCHAR, -@A) + ', '
+ CONVERT(VARCHAR, @B) + ' ' + CONVERT(VARCHAR, -@A) + ', '
+ CONVERT(VARCHAR, @B) + ' 0,0 0),'
+ '(0.1 -0.1,0.1 '
+ CONVERT(VARCHAR, 0.1 - @A ) + ', '
+ CONVERT(VARCHAR, @B - 0.1) + ' ' + CONVERT(VARCHAR, 0.1 - @A) + ', '
+ CONVERT(VARCHAR, @B - 0.1) + ' -0.1,0.1 -0.1)'
+ ')' AS GEOMETRY)

-- Adjust UNION Color
INSERT INTO @Flag(Polygon)
SELECT TOP 140 CAST('POLYGON((0 0, 0 0.0000001, 0.0000001 0.0000001, 0 0))' AS GEOMETRY) FROM sys.messages

-- Adding UNION
INSERT INTO @Flag(Polygon)
SELECT CAST('POLYGON('
+ '(0 0,0 ' + CONVERT(VARCHAR, @vd * -10)
+ ',' + CONVERT(VARCHAR, @hd * 12) + ' ' + CONVERT(VARCHAR, @vd * -10)
+ ',' + CONVERT(VARCHAR, @hd * 12) + ' 0,0 0),'
+ SUBSTRING(@StarPolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

-- Adjust Stripe's Color
INSERT INTO @Flag(Polygon)
SELECT TOP 4 CAST('POLYGON((0 0, 0 0.0000001, 0.0000001 0.0000001, 0 0))' AS GEOMETRY) FROM sys.messages

-- Adding Strips
INSERT INTO @Flag(Polygon)
SELECT CAST('POLYGON(' + SUBSTRING(@StripePolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

-- Adjust Stars' Color
INSERT INTO @Flag(Polygon)
SELECT TOP 28 CAST('POLYGON((0 0, 0 0.0000001, 0.0000001 0.0000001, 0 0))' AS GEOMETRY) FROM sys.messages

-- Adding Stars
INSERT INTO @Flag(Polygon)
SELECT CAST('POLYGON(' + SUBSTRING(@StarPolygon, 2, @@TEXTSIZE) + ')' AS GEOMETRY);

SELECT * FROM @Flag;

And here is the beautiful result:

Actually, American flag is easy to draw. I wonder if somebody woud draw Mexican Flag.