Add the geopoly_regular(X,Y,R,N) function to the geopoly extension.

FossilOrigin-Name: 4505bbae58357eacab262b642b2a56d6dd380de72faceb5bbfd042eb94a12c06

ext/rtree/geopoly.c

@@ -486,6 +486,64 @@ static void geopolyAreaFunc(
   }            
 }
 
+#define GEOPOLY_PI 3.1415926535897932385
+
+/* Fast approximation for cosine(X) for X between -0.5*pi and 2*pi
+*/
+static double geopolyCosine(double r){
+  assert( r>=-0.5*GEOPOLY_PI && r<=2.0*GEOPOLY_PI );
+  if( r>=1.5*GEOPOLY_PI ){
+    r -= 2.0*GEOPOLY_PI;
+  }
+  if( r>=0.5*GEOPOLY_PI ){
+    return -geopolyCosine(r-GEOPOLY_PI);
+  }else{
+    double r2 = r*r;
+    double r3 = r2*r;
+    double r5 = r3*r2;
+    return 0.9996949*r - 0.1656700*r3 + 0.0075134*r5;
+  }
+}
+
+/*
+** Function:   geopoly_regular(X,Y,R,N)
+**
+** Construct a simple, convex, regular polygon centered at X, Y
+** with circumradius R and with N sides.
+*/
+static void geopolyRegularFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  double x = sqlite3_value_double(argv[0]);
+  double y = sqlite3_value_double(argv[1]);
+  double r = sqlite3_value_double(argv[2]);
+  int n = sqlite3_value_int(argv[3]);
+  int i;
+  GeoPoly *p;
+
+  if( n<3 || r<=0.0 ) return;
+  if( n>1000 ) n = 1000;
+  p = sqlite3_malloc64( sizeof(*p) + (n-1)*2*sizeof(GeoCoord) );
+  if( p==0 ){
+    sqlite3_result_error_nomem(context);
+    return;
+  }
+  i = 1;
+  p->hdr[0] = *(unsigned char*)&i;
+  p->hdr[1] = 0;
+  p->hdr[2] = (n>>8)&0xff;
+  p->hdr[3] = n&0xff;
+  for(i=0; i<n; i++){
+    double rAngle = 2.0*GEOPOLY_PI*i/n;
+    p->a[i*2] = x - r*geopolyCosine(rAngle-0.5*GEOPOLY_PI);
+    p->a[i*2+1] = y + r*geopolyCosine(rAngle);
+  }
+  sqlite3_result_blob(context, p->hdr, 4+8*n, SQLITE_TRANSIENT);
+  sqlite3_free(p);
+}
+
 /*
 ** If pPoly is a polygon, compute its bounding box. Then:
 **
@@ -1654,6 +1712,7 @@ static int sqlite3_geopoly_init(sqlite3 *db){
      { geopolyDebugFunc,         1, 0,    "geopoly_debug"            },
      { geopolyBBoxFunc,          1, 1,    "geopoly_bbox"             },
      { geopolyXformFunc,         7, 1,    "geopoly_xform"            },
+     { geopolyRegularFunc,       4, 1,    "geopoly_regular"          },
   };
   static const struct {
     void (*xStep)(sqlite3_context*,int,sqlite3_value**);

ext/rtree/visual01.txt

@@ -586,4 +586,17 @@ SELECT geopoly_svg(poly,'style="fill:none;stroke:black;stroke-width:2"')
 ROLLBACK;
 .print '</svg>'
 
+.print '<h1>Regular Polygons</h1>'
+.print '<svg width="1000" height="200" style="border:1px solid black">'
+SELECT geopoly_svg(geopoly_regular(100,100,40,3),'style="fill:none;stroke:red;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(200,100,40,4),'style="fill:none;stroke:orange;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(300,100,40,5),'style="fill:none;stroke:green;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(400,100,40,6),'style="fill:none;stroke:blue;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(500,100,40,7),'style="fill:none;stroke:purple;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(600,100,40,8),'style="fill:none;stroke:red;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(700,100,40,10),'style="fill:none;stroke:orange;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(800,100,40,20),'style="fill:none;stroke:green;stroke-width:1"');
+SELECT geopoly_svg(geopoly_regular(900,100,40,30),'style="fill:none;stroke:blue;stroke-width:1"');
+.print '</svg>'
+
 .print '</html>'

manifest

@@ -1,5 +1,5 @@
-C Make\smost\sgeopoly\sfunctions\spure.
-D 2018-09-28T13:18:24.886
+C Add\sthe\sgeopoly_regular(X,Y,R,N)\sfunction\sto\sthe\sgeopoly\sextension.
+D 2018-09-28T14:01:17.539
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F Makefile.in 01e95208a78b57d056131382c493c963518f36da4c42b12a97eb324401b3a334
@@ -361,7 +361,7 @@ F ext/repair/test/checkfreelist01.test 3e8aa6aeb4007680c94a8d07b41c339aa635cc782
 F ext/repair/test/checkindex01.test 6945d0ffc0c1dc993b2ce88036b26e0f5d6fcc65da70fc9df27c2647bb358b0f
 F ext/repair/test/test.tcl 686d76d888dffd021f64260abf29a55c57b2cedfa7fc69150b42b1d6119aac3c
 F ext/rtree/README 6315c0d73ebf0ec40dedb5aa0e942bc8b54e3761
-F ext/rtree/geopoly.c c92eb2c5df436c0be3cffceb00769794ed8a28b38fe6e40cde2c68b026d20c8c
+F ext/rtree/geopoly.c cdf7972736f6c60e4309debad504de52ccd2dbe29e02bc8afc7912923ee68059
 F ext/rtree/rtree.c 6cc2e673cf1e9ea1619f13ab990f12389dfb951b131acbc2fbe164cee8992a20
 F ext/rtree/rtree.h 4a690463901cb5e6127cf05eb8e642f127012fd5003830dbc974eca5802d9412
 F ext/rtree/rtree1.test 309afc04d4287542b2cd74f933296832cc681c7b014d9405cb329b62053a5349
@@ -389,7 +389,7 @@ F ext/rtree/sqlite3rtree.h 9c5777af3d2921c7b4ae4954e8e5697502289d28
 F ext/rtree/tkt3363.test 142ab96eded44a3615ec79fba98c7bde7d0f96de
 F ext/rtree/util/randomshape.tcl 54ee03d0d4a1c621806f7f44d5b78d2db8fac26e0e8687c36c4bd0203b27dbff
 F ext/rtree/viewrtree.tcl eea6224b3553599ae665b239bd827e182b466024
-F ext/rtree/visual01.txt 17c3afefc208c375607aa82242e97fa79c316e539bcd0b7b3e59344c69445d05
+F ext/rtree/visual01.txt e9c2564083bcd30ec51b07f881bffbf0e12b50a3f6fced0c222c5c1d2f94ac66
 F ext/session/changeset.c 4ccbaa4531944c24584bf6a61ba3a39c62b6267a
 F ext/session/session1.test 4532116484f525110eb4cfff7030c59354c0cde9def4d109466b0df2b35ad5cc
 F ext/session/session2.test 284de45abae4cc1082bc52012ee81521d5ac58e0
@@ -1770,7 +1770,7 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
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-R fa3505d48ffa9af9252dfb9f6f5b940e
+P 944e167a98e995c5750c1fcd44df857d6b10c1cbb91731fad2849415c42b2cfc
+R 9e3d22ac82d673a7d5cc41392de57d72
 U drh
-Z 9e0a18a5e5cb49bc10f6b45134fb4708
+Z d2b850e1c73ac3950129550f18e00569

manifest.uuid

@@ -1 +1 @@
-944e167a98e995c5750c1fcd44df857d6b10c1cbb91731fad2849415c42b2cfc
+4505bbae58357eacab262b642b2a56d6dd380de72faceb5bbfd042eb94a12c06