Add a face truncation method to Polyhedron class

[jplab]

Currently, it is possible to do a truncation of a polytope via the method ".edge_truncation()".

See http://en.wikipedia.org/wiki/Truncation_%28geometry%29

I currently need the notion of edge-truncation, which is achieve by cutting the polytope along a "well-chosen" hyperplane whose normal vector lies in the normal cone of the edge. This edge truncation uses only one edge. Not all edges at once.

Further, one can define a face truncation similarly with the same code. I am implementing a method called ".face_truncation(face, normal_coefficient, cut_frac)" taking a face of the polytope, and two optional parameters to vary the angle of the cut.

This new method makes the old method ill-named. It should be renamed simply "truncation" or "complete_vertex_truncation".

While at it, I corrected a few writing conventions in the file.

CC: @vbraun @sagetrac-mhampton @mo271

Component: geometry

Keywords: face truncation, polytope

Author: Jean-Philippe Labbé

Branch/Commit: 55f9cf6

Reviewer: Vincent Delecroix, Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/18128

[jplab]

Branch: u/jipilab/ge_truncation

[jplab]

New commits:

2182d7e	Initial commit: added a face truncation method
8bec9b2	Added deprecation warning

[jplab]

Commit: 8bec9b2

[jplab]

comment:4

All test passed on sage 6.6.b5. The tests do not take more than 0.1 sec more than before on my old laptop.

[jplab]

Author: Jean-Philippe Labbé

[vbraun]

comment:6

Conflicts, can you merge in the latest beta?

[jplab]

comment:7

Sure, will do.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

d26a570	Merge branch 'develop' into edge_truncation
b66b4ed	Merge branch sage6.7.beta3 into ticket18128

[sagetrac-git]

Changed commit from 8bec9b2 to b66b4ed

[jplab]

comment:9

I don't really know why there are two commits for the merge. Perhaps I typed something more by accident(!?)

[vbraun]

comment:10

You checked in a conflict marker (the thing starting with <<<<<<< HEAD).

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

0ba2629

Solved forgotten conflict

[sagetrac-git]

Changed commit from b66b4ed to 0ba2629

[sagetrac-git]

Changed commit from 0ba2629 to eef9e96

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

cf567e8	Merge branch 'sage-6.8.beta2' into edge_truncation
eef9e96	Made test pass on 6.8.beta2

[fchapoton]

comment:14

two failing doctests (should be easy to fix)

[sagetrac-git]

Changed commit from eef9e96 to 6a555a5

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

6a555a5

Merge branch 'u/jipilab/ge_truncation' of trac.sagemath.org:sage into ticket18128

[sagetrac-git]

Changed commit from 09f517c to ee4ac08

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

ee4ac08

Made tests pass

[jplab]

comment:34

I have difficulty decoding what is the test which fails on the bot.

[fchapoton]

comment:35

The patchbot librae currently misbehaves. Look at the other bots instead.

[jplab]

comment:36

Okay, so the other bots seems to give a green flag...

Needs proper review again then!

[fchapoton]

comment:37

does not apply..

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

ec17f2b

Merge branch 'u/jipilab/ge_truncation' of trac.sagemath.org:sage into 18128

[sagetrac-git]

Changed commit from ee4ac08 to ec17f2b

[jplab]

comment:39

This is a rebased version on 7.6.b2, solved the conflicts.

All test passed on the three modified files. Let's see what the bot says.

[fchapoton]

Changed reviewer from Vincent Delecroix to Vincent Delecroix, Frédéric Chapoton

[fchapoton]

comment:40

Salut,

two remarks, otherwise this is good to go:

1. in

+            normal_vector = sum([linear_coefficients[i]*normal_vectors[i] for i
+                                 in range(len(normal_vectors))])

there is no need for the [ ] just inside sum()

2. similarly in

+        linear_evaluation = set([-normal_vector * (v.vector()) for v in
+            self.vertices()])

inside set()

Once done and checked, you can set a positive review on my behalf.

[jplab]

comment:41

Salut!

Replying to @fchapoton:

Salut,

two remarks, otherwise this is good to go:

1. in

+            normal_vector = sum([linear_coefficients[i]*normal_vectors[i] for i
+                                 in range(len(normal_vectors))])

there is no need for the [ ] just inside sum()

2. similarly in

+        linear_evaluation = set([-normal_vector * (v.vector()) for v in
+            self.vertices()])

inside set()

Just for my information, where is this feature coming from? python3, sage?

Once done and checked, you can set a positive review on my behalf.

Great! Thanks a lot!

[sagetrac-git]

Changed commit from ec17f2b to 55f9cf6

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

55f9cf6

Removed brackets in sum and set

[fchapoton]

comment:44

Just for my information, where is this feature coming from? python3, sage?

This is just python. One can feed them an iterator, this avoids to build the list twice.

[jplab]

comment:46

This is just python. One can feed them an iterator, this avoids to build the list twice.

Good to know! Thanks!

[vbraun]

Changed branch from u/jipilab/ge_truncation to 55f9cf6