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« Using DesignScript to visualize prime numbers in AutoCAD | Main | Last chance to sign up for the APPHACK! »

November 12, 2012

Finding primes in AutoCAD using .NET

After introducing the work down by Carlos Paris on using AutoCAD to hunt prime numbers, we then looked at some DesignScript code that essentially recreates the core geometry Carlos used to visualize prime numbers.

In this post, we’ll create some .NET code that iterates through the visualization, gathering primes and tagging them with rays to make them easily locatable. Now use AutoCAD as a graphical hash-table in this way is not the way you’re going to discover a billion-digit prime number, but the approach is interesting because it adds useful information to the primes visualization and also shows some potentially helpful techniques around geometry selection.

Here’s the C# code:

using Autodesk.AutoCAD.ApplicationServices;

using Autodesk.AutoCAD.DatabaseServices;

using Autodesk.AutoCAD.EditorInput;

using Autodesk.AutoCAD.Geometry;

using Autodesk.AutoCAD.Runtime;

using System.Collections.Generic;

 

namespace PrimeHunting

{

  public class Commands

  {

    [CommandMethod("TAGPRIMES")]

    static public void TagPrimes()

    {

      var doc =

        Application.DocumentManager.MdiActiveDocument;

      var ed = doc.Editor;

      var db = doc.Database;

 

      // A flag to know when we've finished and the number to check

 

      bool done = false;

      long i=1;

 

      // We'll store a list of the primes we find

 

      var primes = new List<long>();

 

      // Get the initial view, so we can reset at the end

 

      var vtr = ed.GetCurrentView();

 

      // As we're adding rays to the drawing we need a transaction

 

      var tr =

        db.TransactionManager.StartTransaction();

      using (tr)

      {

        // We'll create rays in the current space

 

        var btr =

          (BlockTableRecord)tr.GetObject(

            db.CurrentSpaceId,

            OpenMode.ForWrite

          );

 

        // When we select using a crossing window at a particular

        // x-value, we'll use a padding value to make sure we

        // have a valid window

 

        const double pad = 0.3;

 

        // We'll zoom to a range of numbers, to save some time

        // (the selection method we're using is dependent on

        // the display list, so zooming is necessary)

 

        const int rangeSize = 50;

 

        // Zoom to the initial range of numbers

 

        long zoomedTo = i + rangeSize;

        ZoomRange(ed, i, zoomedTo);

 

        while (!done)

        {

          i++;

 

          // Re-zoom, if needed

 

          if (i > zoomedTo)

          {

            ZoomRange(ed, zoomedTo, zoomedTo + rangeSize);

            zoomedTo += rangeSize;

          }

 

          // Create our selection extents

 

          var pt = new Point3d(i, 0, 0);

          var pt1 = new Point3d(i - pad, -pad, 0);

          var pt2 = new Point3d(i + pad, pad, 0);

 

          // Select via a crossing window

 

          var psr = ed.SelectCrossingWindow(pt1, pt2);

 

          // If selection failed or we got no results, it's over

 

          done =

            (psr.Status != PromptStatus.OK || psr.Value.Count == 0);

 

          // If we have exactly four objects (two of them for unit

          // circles, two for the number itself) then it's a prime

 

          if (!done && psr.Value.Count == 4)

          {

            // Add the number to the list

 

            primes.Add(i);

 

            // Create a ray to mark the location

 

            var ray = new Ray();

            ray.BasePoint = pt;

            ray.SecondPoint = pt + new Vector3d(0, 1, 0);

            btr.AppendEntity(ray);

            tr.AddNewlyCreatedDBObject(ray, true);

          }

        }

        tr.Commit();

      }

 

      ed.WriteMessage(

        "\nTagged {0} primes: stopped at {1}.\nList of primes: ",

        primes.Count, i

      );

      foreach (long prime in primes)

      {

        ed.WriteMessage("{0} ", prime);

      }

 

      // Set the original view back

 

      ed.SetCurrentView(vtr);

    }

 

    private static void ZoomRange(

      Editor ed, long min, long max

    )

    {

      const int pad = 1;

      var pt1 = new Point2d(min - pad, -pad);

      var pt2 = new Point2d(max + pad, pad);

      ZoomWin(ed, pt1, pt2);

    }

 

    // Zoom using a view object

 

    private static void ZoomWin(

      Editor ed, Point2d min, Point2d max

    )

    {

      var view = new ViewTableRecord();

      view.CenterPoint = min + ((max - min) / 2.0);

      view.Height = max.Y - min.Y;

      view.Width = max.X - min.X;

 

      ed.SetCurrentView(view);

    }

  }

}

I originally zoomed in to each integer index on the X-axis to determine whether the number of circles intersecting there – as selection via crossing window is dependent on the display list – but I then switched to the approach of zooming to a range of 50 units at a time.

To see the code in action, I ran the DesignScript code from the previous post (I adjusted the call to create_circles() to pass in 5000 instead of both 500 and 1000) and then executed the TAGPRIMES command defined by the above code.

The selection code stops as soon as it hits a hole in the geometry – i.e. it doesn’t find any entities at a particular integer location along the X-axis – which means that it stops fairly quickly after it runs out of unit circles (which go up to 5000). This is as designed: we could adjust the code to be more tolerant of geometry holes, but I haven’t spent time thinking through the implications and the requisite adjustments.

Here’s the overall graphical view of the primes found:

Tagged primes

And here’s a zoomed-in view of a portion of the geometry:

Zoomed in view of some tagged primes

And here’s what we see at the command-line, as the code reports the primes found up to 5000:

Tagged 669 primes: stopped at 5003.

List of primes: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999

I checked the primes up to 1000 – as these are listed on Wikipedia – and the technique was accurate at least to that point.

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