Differential geometry – Gram-Schmidt map as partial isometry

We equip $ Gl (n, mathbb {R}) $ and $ O (n) $ with their left-invariant metrics, whose constraints on the corresponding neutral elements are the default inner product $ tr (AB ^ {tr}) $ from $ M_n ( mathbb {R}) $,

To let $ f: Gl (n, mathbb {R}) to O (n) $ be the Gram-Schmidt card.

is $ f $ a partial isometry with respect to these Riemann structures? If the answer is negative, we can change the Riemannian metrics of these spaces (not necessarily invariant in terms of group operations) $ f $ as a partial isometry?

java – map >> to save data – help to improve this code

Here I have –

Map >> newObjectsCreated and Map m_newObjects = new HashMap ();

  1. Get the list of keys from newObjectsCreated and compare them to DataType (Integer).

  2. If the key matches, iterates through the list to see if there is a match value and if break has been found.

  3. Otherwise, you will want to go through all the values ​​for all keys to see if there is a match in the list of values ​​for any key
  4. Add this map with DataType as a key to a new list newObjectsC. and finally add this to newObjectsCreated.

  5. If not found, create the object and add it to newObjectsCreated.

The code I wrote is as follows. I'm not sure this is the way to do what I want to do and I wanted to know how to do it in a clean and efficient way. Many Thanks

map     m_newObjects = new HashMap();

Map <integer, list <Map>> newObjectsCreated = new HashMap ();

List <Map> listOfObjects = new ArrayList ();
List <Map> listOfObjects1 = new ArrayList ();
boolean found = false;
Integer data type = 1234;

for (entry newObjectentry: m_newObjects.entrySet ()) {
Object ObjectToCreate = (Object) newObjectentry.getValue ();
Object ObjectToCopy = ObjectToCreate.clone ();
// if DataType matches the key
if (newObjectsCreated.containsKey (DataType) &&! found) {
List <Map> keyslist = newObjectsCreated.get (data type);

for (card map: key list) {
for (entry Entry: map.entrySet ()) {
if (entry.getKey (). equals (ObjectToCopy)) {

found = true;

} else {

// check if the object to be created has already been created (available in the list)
for (entry <integer, list <map>> newObjectCreatedEntry: newObjectsCreated
.entrySet ()) {

List <Map> keyslist = newObjectCreatedEntry.getValue ();

for (card map: key list) {
for (entry Entry: map.entrySet ()) {
if (entry.getKey (). equals (ObjectToCopy) &&! found) {

found = true;

map temp = new HashMap ();
temp.put (ObjectToCopy,
newObjectentry.getKey ());
listOfObjects1.add (Temp);
newObjectsC.put (data type, listOfObjects1);





if found) {

// create the new object
Object o1 = addnewObject (newObjectentry.getKey (), ObjectToCreate);

if (o1! = null) {
// Save the object in the newObjectsCreated list so we will not recreate it
map temp = new HashMap ();
temp.put (ObjectToCopy, o1);
listOfObjects.add (Temp);
newObjectsCreated.put (DataType, listOfObjects);



if (newObjectsC! = null)
newObjectsCreated.putAll (newObjectsC);


Google Map API Version 3 does not work on the SharePoint 2013 Publishing Site

  • Use a Google Maps API in the SharePoint site to display a map on the SharePoint page. The map works perfectly in SharePoint 2013 Team Site. Does not work in the SharePoint 2013 Publishing site. I'm using the Google Map API content editor web part. When code is being reviewed there is no error on the console screen in Chrome and Internet Explorer. I get an error message in the Mozilla Firefox browser.
    If you are not in the list "If you wish, you would see the list item" "in this list" If the label was found, not among the ones available in the list "https://maps.googleapis.com/ maps / api / js / AuthenticationService.Authenticate "http://en.rpdf.de/maps.googleapis.com/maps/AuthenticationService.Authenticate" ".

GUI design – track size on interactive map

I design ship tracks on an interactive map (openstreetmaps) (see example picture). There is a distinction in size and color to indicate what kind of track and how big the track is. But now I'm thinking about how I could define the minimum size of a track and the maximum size of a track.

It's important to be able to pick a song quickly and accurately, but it's also possible that there are a few hundred titles in the immediate vicinity, so I can not make it too big.

Does anyone have any suggestions for me on how to have a reason for choosing the size?

Really appreciate!

Many Thanks.


Example tracks

App Windows – AllMapSoft Offline Map Maker 8.00 | NulledTeam UnderGround

File size: 12.3 MB

Offline Map Maker is a tool that lets you get offline tiling from Google Maps, Yahoo maps, Bing maps, and Openstreetmap. All downloaded offline images are saved to your hard drive. You can view downloaded offline maps with the offline map viewer. You can make the offline map smaller or smaller or output the offline map as a .BMP file with a world xxx.bpw file and output an xxx.map file for OziExplorer. If you want to create an offline map of your city yourself, this is very useful for you.

Updates: Official site does not contain any information about changes in this version.

How can I map a processual cylinder network with a UV card? (Unit)

I have a script that generates a procedural cylinder.
Each side is a quad that consists of two triangles.
Since the two triangles have vertices, a page with two triangles is defined by 4 points.

The net produces a good result, as you see here:

Enter the image description here

However, I can not correctly assign the UV card.
My current progress has brought me here:

Enter the image description here

With a different texture you can see how it extends at certain points.
If the first quad is the "front" of the cylinder, these dots appear on each side.

Enter the image description here

I thought it would work to use the vertex data directly as UV points, but I can not make it work.

Here is the script.

private void _CreateSegmentSides ()
if (m_Sides> 2) {

float angleStep = 360.0f / (float) m_Sides;
Branch segment seg = new branch segment (m_NextID ++);
Quaternion rotation = quaternion.Euler (0.0f, angle step, 0.0f);
Float height = m_SegmentStartLength;
int max = m_sides - 1;
int index_tr = 0, index_tl = 3, index_br = 2, index_bl = 1;
Slip angle = 0f;

// Create first triangles.
seg.vertexes.Add (rotation * (new Vector3 (m_Radius, height, 0f))); // top right
seg.vertexes.Add (rotation * (new Vector3 (m_Radius, 0f, 0f))); // bottom left
seg.vertexes.Add (rotation * seg.vertexes[seg.vertexes.Count - 1]); // bottom right
seg.vertexes.Add (rotation * seg.vertexes[seg.vertexes.Count - 3]); // top left

// add triangle indices.
seg.triangles.add (index_tr); // 0
seg.triangles.add (index_bl); // 1
seg.triangles.add (index_br); // 2
seg.triangles.add (index_tr); // 0
seg.triangles.add (index_br); // 2
seg.triangles.Add (index_tl); // 3

// UV.
seg.uv.Add (rotation * seg.vertexes[seg.vertexes.Count - 4]);
seg.uv.Add (rotation * seg.vertexes[seg.vertexes.Count - 3]);
seg.uv.Add (rotation * seg.vertexes[seg.vertexes.Count - 2]);
seg.uv.Add (rotation * seg.vertexes[seg.vertexes.Count - 1]);

for (int i = 0; i <max; i ++)
Debug.Log ("add side (" + (i + 1) .ToString () + "/" + "max.ToString () +") Angle: "+ angle.ToString ());

// First triangle.
seg.vertexes.Add (rotation * seg.vertexes[seg.vertexes.Count - 2]);

seg.triangles.Add (seg.vertexes.Count - 1); // new vertex
seg.triangles.Add (seg.vertexes.Count - 2); // divided
seg.triangles.Add (seg.vertexes.Count - 3); // divided

seg.uv.Add (rotation * seg.vertexes[seg.vertexes.Count - 1]);

// Second triangle.
seg.vertexes.Add (rotation * seg.vertexes[seg.vertexes.Count - 2]);

seg.triangles.Add (seg.vertexes.Count - 3); // divided
seg.triangles.Add (seg.vertexes.Count - 2); // divided
seg.triangles.Add (seg.vertexes.Count - 1); // new vertex

seg.uv.Add (rotation * seg.vertexes[seg.vertexes.Count - 1]);

Angle + = angle step;
m_Segments.Add (seg);

I've been there all day, what's going wrong here?

Python – How do I calculate the gradient of a height map?

I'm trying to implement a contribution to hydraulic erosion based on this post in Python. I have to calculate that for the first step Slope of the terrain height to determine where water and sediment will move.

"I use the altitude gradient as downhill direction, "

Problem 1: Any code I could find that calculates the slope of a terrain elevation is different.

  • Some use the neighborhood of Moore, others prefer Von Neumann's neighborhood. (The author of the above-linked post uses only right and lower neighbors.)
  • The calculations for these neighbors are different: difference between left and right neighbors vs Average of 4 neighbors vs Point product of selected neighbors …

Issue 2: Topics and articles on this topic do not seem to have the same idea of ​​gradient.

  • Some say a gradient is the output of a Sobel (ex1, ex2, …)
  • others that it is similar aspect Calculation (aspect identifies the downward direction)
  • In any case, their formulas are very different

After some research, I quickly implemented the Aspect algorithm based on this article on the ArcGIS website and this document (Horn, B.K.P., 1981). Hill shading and reflection map).

Enter the image description here

What I see:

  • Color the height map (see original image here) based on the dzdx and dzdy Variables are very similar to normal mapping. (it seems, however, that the formula for calculating normals is different)

  • the aspect seems to correlate inversely to this "normal map"

  • The size-based coloring looks like the output of a Sobel operator

Enter the image description here


  • Which of these issues should be considered as a slope of the elevation map?
  • Which of these services do I need to determine where water and sediment will go?

Location Map: Show all locations based on search OR go through the search area?

We're trying to create a site search for the company so customers can find it in maps on the company's site.
How it works is:
1. The user enters the name of the city in the search for which he wants to display places
2. Zooms to this city and lists all available locations within the visible area

Since cities / suburbs are available in all shapes and sizes, we can not scale down to the limit, so there is a predefined zoom level that we must agree to.

As you can see in the diagram, some positions are out of sight. My argument is, for example, if the user enters London in the results list, we should list those that are out of the visible range, even if we do not zoom out to accommodate all positions in the view. However, they refuse and say that this is a location search for "MAP" so that the user must move the map for it to appear in the results list.

My considerations are:
1. The search is respected, the place IS in London we have to list
2. If the user searches on a slow 3G phone, he has no time to zoom out to increase the visible area. Just let him choose the location on the list to display the phone number or hours worked.

What do you think?

Enter the image description here

ag.algebraic geometry – When does a homotopy of topological spaces correspond to an algebraic map?

My question is simple, but I do not expect that there will be simple answers.

To let $ X $ and $ Y $ be a pair of schemes and leave $ X ( mathbb {C}) $ and $ Y ( mathbb {C}) $ designate their respective spaces with complex points. Suppose we get spaces $ X simeq X ( mathbb {C}) $ and $ Y simeq Y ( mathbb {C}) $, from where $ simeq $ denotes a weak equivalence of spaces.

What is known about necessary or sufficient conditions for a card? $ f & # 39 ;: X & # 39; to Y # $ To be homotopy, which corresponds to a map that comes from a morphism $ f: X to Y $ of schemes?

I am particularly interested in showing that there is a particular map of spaces Not Homotopy corresponds to a map that derives from a morphism of schemata.

ag.algebraic geometry – injection map on spectra

I know that when we have a surprise $ f: B rightarrow A $This induces an injection into the spectra $ f ^ * Spec A hookrightarrow Spec B. $

What about the opposite? Does an injection of affine systems into the spectra lead to a surjection in rings?

I would assume that I would have found such a property somewhere online, if it is such a beautiful property. So can you give me a counterexample? There is also a natural set of conditions when $ f ^ * $ satisfy them, then we can close that $ f $ It is a surprise?