Add more in paper related to the DT comparison

paper/paper.md

@@ -67,13 +67,32 @@ More format are possible through the use of other Python libraries, there are a
 
 # Comparison with a few alternatives
 
-The table below shows the time it takes to construct the 2D DT, in a batch operation, for different datasets.
-The details of the (openly available) datasets are available on the [GitHub repository of startinpy](https://github.com/hugoledoux/startinpy/tree/joss/dt_comparisons), and the Python code to replicate the experiments is available.
+The tables below compare a few Python packages to startinpy.
 
-The [Delaunator package](https://github.com/HakanSeven12/Delaunator-Python): pure Python port of a proven fast triangulator [written original in JavaScript](https://github.com/mapbox/delaunator). 
+The [Delaunator package](https://github.com/HakanSeven12/Delaunator-Python) is pure Python port of a proven fast triangulator [written original in JavaScript](https://github.com/mapbox/delaunator). 
 [SciPy](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Delaunay.html)  is `scipy.spatial.Delaunay`, and SciPy-inc is the variation where an incremental algorithm is used.
 [Triangle](https://pypi.org/project/triangle/) is the Python bindings of the C code. 
 
+|                        | Delaunator | SciPy | SciPy-inc | Triangle | startinpy |
+|------------------------|------------|-------|-----------|----------|-----------|
+| constrained DT         |    ❌      | ❌   |     ❌    |   ✅     |   ❌     |
+| data structure exposed |    ✅      | ❌   |     ❌    |   ❌     |   ✅     |
+| efficient searches     |    ✅      | ✅   |     ✅    |   ❌     |   ✅     |
+| elevation/2.5D         |    ❌      | ❌   |     ❌    |   ❌     |   ✅     |
+| extra attributes       |    ❌      | ❌   |     ❌    |   ❌     |   ✅     |
+| fast                   |    ❌      | ❌   |     ❌    |   🚀     |   ✅     |
+| incremental insertion  |    ❌      | ❌   |     ✅    |   ❌     |   ✅     |
+| remove vertices        |    ❌      | ❌   |     ❌    |   ❌     |   ✅     |
+| xy-duplicate handling  |    ❌      | ❌   |     ❌    |   ❌     |   ✅     |
+
+
+Notice that startinpy is the only offering to store z-values and extra attributes, the others are pure 2D Delaunay triangulator.
+The parameter 'efficient searches' is if a point location function is available, to find the closest triangles to a given point.
+The parameter 'xy-duplicate handling' refers to the fact that startinpy allows to merge vertices that are close to each others (in the xy-plane, and it can be setup), and that if there are xy-duplicates then the z-value can be determined (lowest or highest, depending on the application).
+
+
+The table below shows the time it takes to construct the 2D DT, in a batch operation, for different datasets.
+The details of the (openly available) datasets are available on the [GitHub repository of startinpy](https://github.com/hugoledoux/startinpy/tree/joss/dt_comparisons), and the Python code to replicate the experiments is available.
 The datasets `random_X` are randomly generated points in unit square, the first one has 10,000 points and the other 50,000 points.
 The datasets `LAZ_X` are real-world lidar datasets obtained from the Netherlands, the `2M` contains exactly 2,144,049 points, and the `33M` 33,107,889 points. 
 The dataset `dem.tiff` is the GeoTIFF file in `/data/` and the centre of each grid cell is inserted by reading the rows and columns, the total is 277,750 points.
@@ -92,19 +111,6 @@ Notice that while startinpy is somewhat slower than Triangle, it is expected sin
 It is also faster and more stable (no crash or wrong results) than the SciPy.
 
 
-|                        | Delaunator | SciPy | SciPy-inc | Triangle | startinpy |
-|------------------------|------------|-------|-----------|----------|-----------|
-| constrained DT         |    ❌      | ❌   |     ❌    |   ✅     |   ❌     |
-| data structure exposed |    ✅      | ✅   |     ✅    |   ✅     |   ✅     |
-| efficient searches     |    ✅      | ✅   |     ✅    |   ✅     |   ✅     |
-| elevation/2.5D         |    ❌      | ❌   |     ❌    |   ❌     |   ✅     |
-| extra attributes       |    ❌      | ❌   |     ❌    |   ❌     |   ✅     |
-| incremental insertion  |    ❌      | ❌   |     ✅    |   ❌     |   ✅     |
-| removal                |    ❌      | ❌   |     ❌    |   ❌     |   ✅     |
-| xy-duplicate handling  |    ❌      | ❌   |     ❌    |   ✅     |   ✅     |
-
-
-
 # Acknowledgements
 
 I acknowledge the help of the students following the course *Digital terrain modelling (GEO1015)* at TUDelft over the last few years, their feedback, questions, and frustrations on preliminary versions of startinpy helped me greatly.