TSQL (MS SQL) Polygon issues :)

dbo.BelongsToPolygon

CREATE function [dbo].[BelongsToPolygon](@id int, @X1 float, @Y1 float) returns int
as begin
	declare @result int
	declare @maxx float 
	
	if exists(select 1 from P where polygon_id=@id and x=@X1 and y=@Y1) return 1
	
	declare  @point  table(id int, x float, y float)
	insert into @point (id,x,y) select point_id, x, y from P
	where polygon_id = @id order by point_id asc
	
	if @@ROWCOUNT<3  set @result = 0
	else 
	  begin
	    select @maxx = MAX(x) from @point
		  select @res = case when sum(dbo.LineSegmentCollision(@x1,@y1,@maxx+1,@y1,p1.x,p1.y,p2.x,p2.y))%2=0 then 'No' else 'Yes' end from @point p1
		    left join @point p2 on p1.id+1 = p2.id or (p1.id = (select MAX(id) from @point) and p2.id = (select MIN(id) from @point))
	  end
		return @res
	end

dbo.CalcPerimetr

--CALCULATING PERIMETR OF POLYGON
CREATE function [dbo].[calcPerimetr](@id int) returns float
as begin
  declare @result float

	declare  @point  table(id int, x float, y float)
	insert into @point (id,x,y) select point_id, x, y from P
	where polygon_id = @id order by point_id asc

	if @@ROWCOUNT<3  set @result = 0
	else select @result = sum(sqrt(square(p2.x-p1.x)+SQUARE(p2.y-p1.y))) from @point p1
		left join @point p2 on p1.id+1 = p2.id or (p1.id = (select MAX(id) from @point) and p2.id = (select MIN(id) from @point))
	return @res
end

dbo.CalcSquare

--CALCULATING SQUARE OF POLYGON
CREATE function [dbo].[calcSquare](@id int) returns float
as begin
  declare @result float
  
	declare  @point  table(id int, x float, y float)
	insert into @point (id,x,y) select point_id, x, y from P
	where polygon_id = @id order by point_id asc

	if @@ROWCOUNT<3  set @result = 0
	else select @result = abs(IsNull(NullIf((sum(p1.x*p2.y)-SUM(p1.y*p2.x)),0),(sum(p1.x*p2.y)+SUM(p1.y*p2.x)))/2) from @point p1
		left join @point p2 on p1.id+1 = p2.id or (p1.id = (select MAX(id) from @point) and p2.id = (select MIN(id) from @point))
	return @result
end

dbo.LineSegmentCollision

--CHECKING THE CROSSING TWO SEGMENTS
--SEGMENT1 consists of two points A1(Ax1,Ay1) and B1(Bx1,By1)
--SEGMENT2 consists of two points A2(Ax2,Ay2) and B2(Bx2,By2)
CREATE function [dbo].[LineSegmentCollision](@AX1 float, @AY1 float, @AX2 float, @AY2 float, @BX1 float, @BY1 float, @BX2 float, @BY2 float) returns int
as begin
return case when (((@BX2-@BX1)*(@AY1-@BY1)-(@BY2-@BY1)*(@AX1-@BX1))*
  ((@BX2-@BX1)*(@AY2-@BY1)-(@BY2-@BY1)*(@AX2-@BX1)))<0 and
  (((@AX2-@AX1)*(@BY1-@AY1)-(@AY2-@AY1)*(@BX1-@AX1))*
  ((@AX2-@AX1)*(@BY2-@AY1)-(@AY2-@AY1)*(@BX2-@AX1)))<0 then 1 else 0 end
end

Formulation of the problem

Is a table containing identifiers and the vertex coordinates of figures.
P (Polygon_id int, point_id int, x float, y float)
Points are listed sequentially in a clockwise or counter- clockwise


1. It is necessary to write a function that returns the area of a selected polygon
2. It is necessary to write a function that returns the perimeter of the selected polygon
3. Check whether the point is on the specified coordinates inside the polygon