Algorithm – Calculation of the outer polygon

I need to compute an outer polygon from a self-intersecting polygon. I've found that Mathematica has recently implemented the following feature that could solve this problem. Does anyone know how it could be implemented?

https://reference.wolfram.com/language/ref/OuterPolygon.html

Any book or article dealing with this topic would also be helpful.

To illustrate my problem, I have a self-cutting polygon (blue) and want to get the outer polygon (red):

Auto-cutting polygon and outer polygon

If it helps, this polygon is created by "displacing" * a previous polygon that did not overlap itself:

Polygon-term development

Could there be a way to increase the polygon that considers self-overlapping?

Thanks a lot!

* not technically balancing, as only some parts of the polygon move in the normal direction.

Move the outer key inside in an association

I have a list that looks like this:

{15000001-><|"Loss" -> 2.85396*10^8, "Exposure" -> 6.61052*10^10|>,
 15000002 -> <|"Loss" -> 1.25297*10^8, "Exposure" -> 1.57863*10^11|>,
 15000003 -> <|"Loss" -> 2.05979*10^8, "Exposure" -> 6.88024*10^10|>}

I would like to come to the following conclusion:

{<|"Event"->15000001,"Loss" -> 2.85396*10^8, "Exposure" -> 6.61052*10^10|>,
 <|"Event"->15000002,"Loss" -> 1.25297*10^8, "Exposure" -> 1.57863*10^11|>,
 <|"Event"->15000003,"Loss" -> 2.05979*10^8, "Exposure" -> 6.88024*10^10|>}

I tried to make two lists, one with keys and one with values, and put them together, but I could not quite get that to work. I would be happy about suggestions.

linear algebra – The various products on $ k $ -altering forms and their relationship to the outer product

To let $ V $ be a vector space and $ k in mathbb {N} $, Describe $ Lambda ^ k V $ the outer $ k
$
-Power of $ V $,

To let $ f: Lambda ^ k V ^ * to ( Lambda ^ k V) ^ * $ if the card is such that a $ k $-Covector $ eta_1 wedge cdots wedge eta_k $ will be sent to the $ k $– alternating form (identified as a dual element of $ Lambda ^ k V $) $ (v_1, cdots, v_k) mapsto sum_ { sigma} epsilon ( sigma) eta_1 (v_ { sigma (1)}) cdots eta_k (v_ { sigma (k) }) $, (It seems that there is another convention with one factor $ frac {1} {k!} $ in this formula.)

There are two ways (see here) of defining natural products in between $ k $alternating forms. Let's call $ wedge_1 $ the product is based on the formula with the $ Old $ Operator (in the previous link) and $ wedge_2 $ the product is based on the formula with a sum via shuffle permutations (in the previous link).

Question: What is true and what is wrong in the following statements? To let $ omega in lambda ^ k V ^ * $ and $ omega in lambda ^ {k & # 39; v ^ * $,

1) $ f ( omega wedge omega & # 39;) = f ( omega) wedge_1 f ( omega & # 39;) $

1 & # 39;) As 1), but with the $ 1 / k! $ Factor in the definition of $ f $,

2) $ f ( omega wedge omega #) = f ( omega) wedge_2 f ( omega #) $

2 & # 39;) As 2), but with the $ 1 / k! $ Factor in the definition of $ f $,

postgresql – Lateral / Outer Apply Join speed

I have the following Postgres database & query. It takes some time items and multiply his hours by a role tariff if a matching value for a exists Employee& # 39; s roleotherwise it will multiply by a personal rate if there is a match.

Processing 300,000 lines takes about 7 minutes, and I wonder if I can do something to speed it up.

Delete table if data cascade exists;
Create the time_entries table (id int, staff_id integer, entry_date date, hours numeric).
insert in time_entries
values
(1, 1, to_date (& # 39; 15 -01-2019 & # 39 ;, & # 39; tt-mm-yyyy & # 39 ;, 1),
(2, 1, to_date (& # 39; 15 -02-2019 & # 39 ;, & # 39; d-mm-yyyy & # 39 ;, 2),
(3, 1, to_date (& # 39; 15 -03-2019 & # 39 ;, & # 39; d-mm-yyyy & # 39 ;, 3)),
(4, 2, to_date (& # 39; 15 -01-2019 & # 39 ;, & # 39; tt-mm-yyyy & # 39;) 4),
(5, 2, to_date (& # 39; 15 -02-2019 & # 39 ;, & # 39; tt-mm-yyyy & # 39;), 5),
(6, 2, to_date (& # 39; 15 -03-2019 & # 39 ;, & # 39; DD-MM-YYYY & # 39 ;, 6);

Create a table staff_rates (id int, staff_id integer, start_date date, rate numeric);
insert in staff_rates
values
(1, 1, to_date (# 01 -01-2019,, # t -t-mm-yyyy &), 1),
(2, 1, to_date (# 01 -02-2019,, # t -t-mm-yyyy &), 2),
(3, 1, to_date (& # 39; 01 -03-2019 & # 39 ;, & # 39; t-mm-yyyy & # 39 ;, 3),
(4, 2, to_date (# 01 -01-2019,, # t -t-mm-yyyy &), 4),
(5, 2, to_date (# 01 -02-2019,, # tt-mm-yyyy #), 5),
(6, 2, to_date (# 01 -03-2019,, TT DD-MM-YYYY)), 6);

Create the role_rates table (id int, role_id integer, start_date date, rate numeric).
insert in role_rates
values
(1, 2, to_date (# 01 -01-2019,, # t -t-mm-yyyy)), 7),
(2, 2, to_date (# 01 -02-2019,, # t -t-mm-yyyy &), 8),
(3, 2, to_date (& # 39; 01 -03-2019 & # 39 ;, & # 39; dd-MM-YYYY & # 39 ;, 9);

Create table staff (id int, role_id integer);
to insert in staff
values
(1, 1),
(2, 2);

CHOOSE
t.staff_id,
staff.role_id,
t.entry_date,
t.hours * (at rr.rate> 0 then rr.rate else sr.rate end) AS total_rate
FROM time_entries t, staff
LEFT JOIN LATERAL (
SELECT sr.rate
FROM staff_rates sr
WHERE sr.staff_id = t.staff_id
AND sr.start_date <= t.entry_date - "at or before this time entry"
ORDER BY sr.start_date DESC NULLS LAST
LIMIT 1
) sr ON true
LEFT JOIN LATERAL (
SELECT rr.rate
FROM role_rates rr, staff
WO rr.role_id = staff.role_id AND t.staff_id = staff.id
AND rr.start_date <= t.entry_date - "at or before this time entry"
ORDER BY rr.start_date DESC NULLS LAST
LIMIT 1
) rr ON true
WO t.staff_id = staff.id

Theming – Passing data from the outer pre-process to the inner template

I have two templates:
a child who prints each entry in a list;
– And a parent who calls it
There is also an inter-field template that is not involved.

The parent element has access in advance to node field data that each child element (node ‚Äč‚Äčteaser) must use. The child element prints elements in a multi-valued entity reference field.

How can the child get the data from the parent fields so that it can print the correct HTML?

real analysis – Hausdorff's outer measure is finite if $ sum_ {j = 1} ^ m | f (x_i) -f (x_ {i-1}) | ^ s le c $

To let $ f:[0,1] to mathbb {R}, G = graph (f) $,

If $ sum_ {j = 1} ^ m | f (x_i) -f (x_ {i-1}) | ^ s le c $ for all partitions $ 0 = x_0 < ldots <x_m = 1 $ then $ H ^ s (G) < infty $

With which technique can I prove this result?

Can it be reduced to the Thorem that there is a correctable curve $ Gamma $ Has $ H ^ 1 ( Gamma) < infty $?

SQL Server – Full Outer Join does not pull all the records from the right table

I'm trying to pull all the rows from the left table and the right table with the following example query. However, there is one row from the right table that is not included because it does not exist in the left table and I can not see why. What do I miss?

CHOOSE *
OF required i
full outside JOIN planned RI
ON I.yr = RI.yr
And I.num = RI.num
AND I.typ = RI.type

Forms – Why do radio buttons not fill the entire outer circle?

This is a nice article about the history of radio buttons: https://www.jitbit.com/alexblog/242-the-history-of-a-radio-button/

As stated in the article:

Radio buttons are named after the actual buttons used in old radios to switch between radio waves and sometimes preset frequencies. When a key was pressed, all the other keys jumped out.

So it was a skeuomorphic reason.

I believe that a completed radio button would confuse users based on the "system-real world" principle. It says that:

Interfaces that follow real conventions and display information in a natural and logical order show empathy and appreciation to users.

Users are used to option buttons in this format. So if you have a really good reason to change that, you should use the default.

Use FULL OUTER JOIN in SQL Server 2012

I have the following question:

SELECT A.USUARIO_ENE, A.SUCURSAL_ENE, A.ACTIVADAS_ENE, B.USUARIO_FEB, B.SUCURSAL_FEB, B.ACTIVADAS_FEB
FROM AR_ENERO A
FULL OUTER JOIN AR_FEBRERO B ON B.USUARIOS = A.USUARIO

My result is:

Enter the description of the picture here

The detail I have is that in January 12 cards 6 were activated in the store Terrazas and 6 in the branch Xilitla and in February only 6 in the branch Xilitla
but if I use the & # 39; FULL OUTER JOIN & # 39; I am duplicating the February registration