HTM Indexing

Design Document for HTM Indexing in KStars


A spatial index was introduced to drastically speed up both the drawing of objects on the screen and searching for objects based upon a position such as finding the object nearest to the cursor or finding out which constellation a point is in. Drawing to the screen is sped up because the calculation to determine if an object is on screen is very expensive. Without the index we have to perform this calculation for every object which is time consuming. The index speeds things up because it can give us a list of all the objects on screen (plus a few extras that are off screen).

We are currently using a Hierarchical Triangular Mesh (HTM) spatial indexing library written by A. Szalay, John Doug Reynolds, Jim Gray, and Peter Z. Kunszt. An HTM divides the surface of a sphere into a bunch of little triangles just like a geodesic dome. Each triangle is called a trixel (triangular pixel) and each trixel has a unique integer ID.

We index point objects (i.e. stars) by creating a data structure that can quickly give us a list of all the stars that are located inside any trixel. To draw the stars, we get a list of all trixels that are possibly visible on the current screen. The worst case is when the screen is zoomed out so all trixel on the visible half the celestial sphere need to be used. When the screen is zoomed in, the number of visible trixels is reduced by roughly the area of the celestial sphere that is visible. To draw the stars, we use the HTM to find all of the trixels that are possibly visible and for each such trixel we draw the list of stars that are in that trixel.

Extended objects, such as constellation lines are a bit more tricky. If we indexed them with a single pointer in a single trixel then parts of the object could be on screen and not drawn. So for extended objects we create a data structure similar to that used for the stars which allows us to quickly get the list of all objects in any trixel but since more than one trixel may be needed to cover an object, there can be more than one pointer to an object in the index. If we use the point object algorithm and simply draw every object in the list of every visible trixel than the same object can be drawn repeatedly if it is covered by more than one trixel and if more than one of its covering trixels is visible. This is not a rare event. It is a very common occurence and if left unchecked, it would destroy much of the efficiency we gained by implementing the index in the first place.

Fortunately, there is an easy solution to prevent any given object from being drawn more than once in any given draw cycle (a draw cycle is when we draw all the objects on the screen. If the zoom scale or the center point of the screen change, or if the celestial sphere appears to rotate due to the rotation of the earth then we need to initiate a new draw cycle to update the screen). We use a global integer value that gets incremented at the start of each draw cycle which we call the global drawID. Every indexed extended object has its own internal integer drawID. When we go through the lists of pointers to visible object we compare the drawID of each object with the global drawID. If they are the same, we don't draw the object. If they are different we draw the object and set the object's drawID to the value of the global drawID which ensures that the object won't get drawn again in the same draw cycle. Since the global drawID is incremented at the beginning of every draw cycle, setting an object's drawID to the current global drawID will not prevent the object from being drawn in future draw cycles.


HTM Library Interface

The HTMesh class is an addition to the HTM library that provides a simple interface to that library by exposing only those parts that we need and hiding the rest. In addition, it contains some simple error checking for indexing polygons and it also contains a routine for indexing line segments (by creating a very narrow triangle that covers the line segment).

The SkyMesh class is a subclass of HTMesh. It mingles the HTM with QT objects and KStars objects. It has two purposes. The first is to provide a more convenient, higher level interface to the HTM library. For example to find the trixel containing a SkyPoint *p we can call:

skyMesh->index( p )

instead of:

HTMesh->index( p->ra()->Degrees(), p->dec()->Degrees() );

SkyMesh also has some real code in it that is used to find all of the trixels that cover a polygon with an arbitrary number of vertices and to find all of the trixels that cover a connected series of line segments (such as those that make up the outline of the Milky Way or the lines that make up a constellation). These routines work by calling the more primitive indexing routines and then or'ing together the resulting lists of indices. The or'ing is needed so that a pointer to a given object will show up at most once in the list of objects for a given pixel. The drawID would prevent these extra entries from causing the same object from being drawn more than once but the extra entries would still be a waste of both time and space.

The or'ing is done with a QHash that uses the trixel ID's as keys. When the keys of the QHash are read out, each unique trixel ID will only be read out once even if that ID was inserted multiple times. Since that QHash was needed to create a unique list of keys, it is also used as the output container of the indexing routines from which the caller reads the ID's. In the current implementation there is only one QHash and the line/poly indexing routines are always returning the address of the same QHash over and over. It might have looked better if we had copied the keys from the QHash into a QList or a QVector but that extra copying would have been wasteful.

Top Level

Most/all of the instances that use the HTM index are created from within the SkyMapComposite class. The SkyMesh parameter is currently explicit so you can quickly see which classes/instances use the index by looking that the list of constructors inside the SkyMapComposite constructor. SkyMapComposite is also where (for our purposes) the draw() calls get initiated. At the top of SkyMapComposite::draw() there is the code:

float radius = ks->map()->fov();
if ( radius > 90.0 ) radius = 90.0;

SkyPoint* focus = ks->map()->focus();
skyMesh->aperture(focus, radius + 1.0);

This code determines what objects will end up in the draw loops of the classes that use the index. This information is stored in the skyMesh object that was created at the top of the SkyMapComposite constructor. All classes that use the index have a pointer to this object which the use to construct an iterator which will iterate over all of the trixels that cover the circular area in the aperture call above.

For debugging, it's useful to change "radius + 1.0" to "radius / 2.0" which means that only trixels needed to cover a circle surrounding the central quarter of the screen will be returned by the iterators. Therefore objects that have been indexed properly will disappear as you pan the screen and objects that have not been indexed will always stay visible (as long as they are on screen).

You can also change the amount of debugging information that is printed when indexing near the top of the SkyMapComposite constructor:

skyMesh->debug( 1 );

0 (zero) means no printout, 1 (one) prints out one line per index and 10 (ten) causes the number of trixels of every indexed object to be printed. This can give you a sense of the speed of the index and is also useful for spotting bugs that cause an abnormal number of trixels to be added to the index. If you want to debug just one section you can pass similar debug numbers to the indexLines() and indexPolygons() calls in the LineListIndex end use subclasses.

Data and Drawing

In order to make the most efficient use of the HTM index, we need to break the composite/component model and in same cases even break the strict OOP model that insists that code and data go together. The approach used here is separate the code and the data. In much of the new code the data is held in very small lightweight classes that are little more than structs. The drawing code is in classes that hold lists of the lightweight data elements. This is not a new idea, in fact it is a traditional approach to boosting OOP performance.

Drawing Stars

For the sake of efficiency, the stars were already all being drawn from the single draw() routine in the StarComponent class which made adding the HTM index almost trivial. Two new data members were added:

  • SkyMesh* skyMesh;
  • QVector< StarList* > starIndex;

where StarList is a typedef for QVector<StarObject*>. The starIndex is populated when we read in the star data from the *.hip files:

  • int starID = skyMesh->index( (SkyPoint*) o );
  • starIndex[starID]->append( o );

For drawing, the biggest change is in the loop over stars inside the draw() routine. A simple loop over all of the star objects is replaced with a double loop, first iterating over all the visible trixels and then for each visible trixel we iterate over all of the stars that are in that trixel:

  • foreach ( SkyObject o, objectList() ) {
  • StarObject *curStar = (StarObject)o;
  • region = skyMesh->iterator();
  • while ( region->hasNext()) {
  • StarList* starList = starIndex[ region->next() ];
  • for (int i=0; i < starList->size(); ++i) {
  • StarObject curStar = (StarObject) starList->at( i );

The double loop looks more messy but this is where we get the performance boost because the list of stars we finally iterate over is at worst case slightly larger than half the original list and at best case (when the screen is greatly zoomed in) we can gain a factor of 10 or 100 in speed because the number of stars we iterate over is reduced by that factor.

The index was also used to drastically speed up the objectNearest() routine in StarComponent but we leave the explanation of how that works as an exercise for the reader. Hint: it works just like the change to the draw loop.


Adding the index to the drawing of DSO's was almost as trivial as the changes in StarComponent. There were two differences. First, the DSO's are being stored (and drawn) separately by catalog so we needed a separate index for each catalog. The other change that these indexes were implemented as:

typedef QVector< DeepSkyObject*> DeepSkyList; QHash<int, DeepSkyList> dsIndex;

This was done in order to save some space. The stars use a QVector because it is smaller and faster than a QHash if all of (or most of) the indices are being used as is the case with the stars. For indexes of sparse objects (where most of the trixel are empty), we save some space by using a QHash since the empty trixels take up no room at all. Adding point objects to a hash based index is only slightly more complicated than adding objects to a vector based index:

if ( ! dsIndex->contains( trixel ) ) {
    dsIndex->insert(trixel, new DeepSkyList() );
dsIndex->value( trixel )->append( o );

Adding extended objects to a hash based index is the most complicated case. You can see two examples of the code for that in the routines indexLines() and indexPolygons() both found in the LineListIndex class.

Drawing Lines and Polygons

Using the HTM index to help draw lines and polygons is a little bit more complicated than using it to index and draw points as was done with the stars and the DSO. The indexing is a little more complicated because if any part of an object may be visible then we want to draw the entire object. Also, we want to be able to clip objects that are on the celestial horizon. Since there are several different kinds of objects we want to draw which all require slightly different data structures, we have several different classes to handle them.

Class Structure:

Index Classes

Data Container Classes

The three abstract index classes and their associated data containers:

LineListIndex SkipListIndex PolyListIndex || || || LineList SkipHashList PolyList

NoPrecessIndex and LabeledListIndex uses the plain LineList data container. NoPrecessIndex does not precess the data in the containers and LabeledListIndex additionally allows a single label to be added to a curved line (equator, ecliptic). The LabeledListIndex code could easily be combined into NoPrecessIndex but I think it is more clear as a separate subclass at the expense of almost repeated code.

The LineList/LineListIndex (which we will call LineList[Index] for brevity) provide the base for all the other classes. They can be used for indexing and drawing either a series of line segments or a series of filled polygons but not both. If you want to draw both lines and filled polygons you need to use the SkipHashList[Index] combo that adds the ability to skip some of the lines that are drawn. If you don't want to skip any lines and want to draw filled polygons and the complete outline of the filled polygons then you can use the standard LineList[Index] combo.

Both the LineList[Index] and the SkipHashList[Index] store their data in QVector<SkyPoint*>'s. There is one such data structure in each LineList and each SkipHashList. The PolyList stores the data in a QPolygonF instead. This was needed to implement the code that uses the QPolygonF to find out which constellation a point is in. At present you can not directly draw the data stored in a PolyList's combo although it would not be difficult to add code to do the drawing if/when the need arises.

The LineListIndex class

The bulk of the code is in LineListLindex as can be seem by these relative sizes:

$ wc *index.cpp

572 2088 19073 linelistindex.cpp 60 200 2138 noprecessindex.cpp 143 489 4594 polylistindex.cpp 43 137 1623 skiplistindex.cpp

LineListIndex contains code to index both filled polygons and lines. There are two versions of each draw routine, one for integer drawing and the other for anti-aliased (float) drawing for a total of four in all. There are two indexing routines, one for filled polygons and another for lines.

In order to avoid code repetition there are three virtual "callback" methods that subclasses can override in order to customize the behavior. Most end use classes (such as ConstellationLines or CoordinateGrid) will want to override the preDraw() method in order to set the QPen (and QBrush or whatever) before their data is drawn. This routine is called right before the lines/polygons are drawn. The default is to set the QPen to a solid thin white line. The end use classes can also override the draw() method and set the QPen in their own draw method but in most cases this is slightly more complicated than overriding preDraw() because they will then have to call LineListIndex::draw() from inside their own draw() routine which you don't have to do if you use preDraw().

The other two virtual callback methods are overridden by the "abstract" SkipListIndex subclass. The method getIndexHash() is used to modify the line indexing routine. getIndexHash() is overridden by SkipListIndex so line segments that should be skipped from drawing are also skipped from the indexing.

Finally, skipAt() is overridden by SkipListIndex in order to not draw lines segments that should be skipped. It returns a boolean value and the default behavior is to always return false which means that by default all the line segments are drawn. There might be a small performance hit for having this callback since it is called for every single point, not just every LineList but the speed hit may not even be noticeable/measurable and it allows us to get by with just 4 almost identical draw routines. Without it, we would need 8 draw routines which would make the code matainance even more of a headache.

The iterator in the four draw*() routines is similar to the iterator in DeepSkyComponent but has the addition of the drawID to prevent objects from being drawn more than once in any given draw cycle:

DrawID drawID = skyMesh()->drawID();
MeshIterator region( skyMesh() );
while ( region.hasNext() ) {

    LineListList *lineListList = lineIndex()->value( region.next() );
    if ( lineListList == 0 ) continue;

    for (int i = 0; i < lineListList->size(); i++) {
        LineList* lineList = lineListList->at( i );

        if ( lineList->drawID == drawID ) continue;
        lineList->drawID = drawID;

Data Container Classes

The data container classes: LineList, SkipHashList, and PolyList are simple data containers with no non-trivial code. All of them just have header files and no .cpp files.

End Use Classes

There are currently seven different end use classes:

- CoordinateGrid
- ConstellationLines
- ConsellationBoundary
- MilkWay
- ConstellationBoundaryPoly
- Ecliptic
- Equator

These classes are typically small and simple, with just an init() routine to populate and append a bunch of LineList's (or their descendents) and a preDraw() routine to set the QPen. It is the responsibility of the end use classes to make sure the data containers they use match the *ListIndex file they subclass.

ConstellationBoundaryPoly class

Originally this was a subclass of LineListIndex but everthing is different about it so now it (and PolyListIndex) is in a class by themselves. Same with PolyList which used to be a subclass of LineList. Here are the differences:

o The data is stored on QPolygonF's instead of lists of SkyPoints.

o It is instantiated and initialized inside of ConstellationBoundary and not SkyMapComposite.

o The index is stored in a QVector instead of a QHash because the constellations are covered by every trixel on the sphere.

o There is no drawing done but there are routines for returning which constellation a SkyPoint is in.

o PolyLists have a name which LineLists don't have.

The only real code duplication is the indexPolygons() routine that was lifted directly from LineListIndex. But since both the input and output data structures were differt (QPolygonF vs. List of SkyPoints and QVector instead of QHash) it made the most sense to give ConstellationBoundaryPoly its own indexing routine. There is now duplication in the summary() debugging routine too.

Just-in-Time Updating

Just-in-time updating was recently added to all indexed objects. Instead of updating all the objects in a separate update() routine, the updates now take place inside the draw routine. Before SkyMapComposite::update() (which is still needed for objects that are not yet indexed) is called, an updateID is incremented in KStarsData. If the update call sends a non-zero KSNumbers then updateNumID is incremented also.

Every indexed object has its own updateID and updateNumID. Inside the draw routine if an object's updateID does not match the global updateID then the object is updated. In addition if the objects updateNumID does not match the global updateNumID then a more expensive update is performed. This should greatly speed up updates especially if the screen is zoomed in on a small section of the sky. This simple mechanism ensures that only objects that are (nearly) on the screen get updated as needed.

Error Detection and Prevention

The HTM library we use does not have any built-in error detection or prevention. We have to provide all of that ourselves. There are two types of failure modes in the library. The first failure mode has to do with passing it coordinates out of range. For example, if we pass it NaN as one of the coordinates, it will return bad results. The second type of failure is triggered when we send it two consecutive identical points to one of the polygon intersection routines. Since the library automatically wraps the last point back to the first point when intersecting polygons, if the last point is identical to the first we will also get a failure.

The identical point failures don't return incorrect results, instead, they cause library to hang, crash, or consume RAM relentlessly. Therefore these failures must all be detected and prevented before unleashing our code on the public even if it causes the program to run more slowly. Fortunately the polygon intersection routines are only used in indexing, not in drawing so error prevention has no effect on the drawing time. Even more fortunately, it has a minimal impact on the indexing time.

Repeated point failures in all the polygon intersection routines are detected and prevented in the HTMesh class which we use as an interface to the HTM library. It contains a somewhat arbitrary parameter called eps which is currently set to 1.0E-6. We consider two point identical if their Manhattan distance (in degrees) is less than eps:

fabs(ra1 - ra2) + fabs(dec1 - dec2) < eps

Since we typically use a level 5 or less mesh and average edge of a trixel at level 5 is about 3 degrees, an eps as large as 0.1 or so would probably suffice since the two points are very likely to be in the same trixel. The eps we use is 5 orders of magnitude smaller and yet still seems to prevent duplicate point errors in the library.

For the four-point polygon we check for four different consecutive points: p1:p2, p2:p3, p3:p4, and p4:p1. As soon as any one of these tests detects a duplicate, we drop one of the dupes and send the remaining three points to the three-point polygon intersection routine. If there are any dupes in the remaining three points, they will be resolved in the three-point intersection. We play the same trick with the three-point intersection, we do three tests and send two points to the two-point (line segment) intersection routine if we found a dupe. Finally if a dupe is found in the two-point intersection routine, we do a circular intersection around one of the points, using the distance between the two points as the radius.

Unlike the other polygon routines which use eps as the length scale, the two-point (line segment) routine uses the average edge size divided by 10 to trigger dropping down to the circular intersection. We might want to fine tune this later. The downside of the current method is that very rarely a few unneeded trixels may be added to the set of that covers a very short line segment. The performance impact (size and speed) of this slight imperfection may be too small to measure.

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