summaryrefslogtreecommitdiff
path: root/src/corelib/render/software/agg_math.pas
diff options
context:
space:
mode:
Diffstat (limited to 'src/corelib/render/software/agg_math.pas')
-rw-r--r--src/corelib/render/software/agg_math.pas1186
1 files changed, 593 insertions, 593 deletions
diff --git a/src/corelib/render/software/agg_math.pas b/src/corelib/render/software/agg_math.pas
index 4f3734ac..8d1efa0f 100644
--- a/src/corelib/render/software/agg_math.pas
+++ b/src/corelib/render/software/agg_math.pas
@@ -1,593 +1,593 @@
-//----------------------------------------------------------------------------
-// Anti-Grain Geometry - Version 2.4 (Public License)
-// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
-//
-// Anti-Grain Geometry - Version 2.4 Release Milano 3 (AggPas 2.4 RM3)
-// Pascal Port By: Milan Marusinec alias Milano
-// milan@marusinec.sk
-// http://www.aggpas.org
-// Copyright (c) 2005-2006
-//
-// Permission to copy, use, modify, sell and distribute this software
-// is granted provided this copyright notice appears in all copies.
-// This software is provided "as is" without express or implied
-// warranty, and with no claim as to its suitability for any purpose.
-//
-//----------------------------------------------------------------------------
-// Contact: mcseem@antigrain.com
-// mcseemagg@yahoo.com
-// http://www.antigrain.com
-//
-//----------------------------------------------------------------------------
-// Bessel function (besj) was adapted for use in AGG library by Andy Wilk
-// Contact: castor.vulgaris@gmail.com
-//
-// [Pascal Port History] -----------------------------------------------------
-//
-// 23.06.2006-Milano: ptrcomp adjustments
-// 18.12.2005-Milano: Unit port establishment
-//
-{ agg_math.pas }
-unit
- agg_math ;
-
-INTERFACE
-
-{$I agg_mode.inc }
-{$Q- }
-{$R- }
-uses
- Math ,
- agg_basics ,
- agg_vertex_sequence ;
-
-{ GLOBAL VARIABLES & CONSTANTS }
-type
- double_xy_ptr = ^double_xy;
- double_xy = record
- x ,y : double;
-
- end;
-
- poly_xy_ptr = ^poly_xy;
- poly_xy = array[0..0 ] of double_xy;
-
- storage_xy_ptr = ^storage_xy;
- storage_xy = record
- poly : poly_xy_ptr;
- size : unsigned;
-
- end;
-
-const
- intersection_epsilon : double = 1.0e-30;
-
-// Tables for fast sqrt
-const
- g_sqrt_table : array[0..1023 ] of int16u = (0 ,
- 2048,2896,3547,4096,4579,5017,5418,5793,6144,6476,6792,7094,7384,7663,7932,8192,8444,
- 8689,8927,9159,9385,9606,9822,10033,10240,10443,10642,10837,11029,11217,11403,11585,
- 11765,11942,12116,12288,12457,12625,12790,12953,13114,13273,13430,13585,13738,13890,
- 14040,14189,14336,14482,14626,14768,14910,15050,15188,15326,15462,15597,15731,15864,
- 15995,16126,16255,16384,16512,16638,16764,16888,17012,17135,17257,17378,17498,17618,
- 17736,17854,17971,18087,18203,18318,18432,18545,18658,18770,18882,18992,19102,19212,
- 19321,19429,19537,19644,19750,19856,19961,20066,20170,20274,20377,20480,20582,20684,
- 20785,20886,20986,21085,21185,21283,21382,21480,21577,21674,21771,21867,21962,22058,
- 22153,22247,22341,22435,22528,22621,22713,22806,22897,22989,23080,23170,23261,23351,
- 23440,23530,23619,23707,23796,23884,23971,24059,24146,24232,24319,24405,24491,24576,
- 24661,24746,24831,24915,24999,25083,25166,25249,25332,25415,25497,25580,25661,25743,
- 25824,25905,25986,26067,26147,26227,26307,26387,26466,26545,26624,26703,26781,26859,
- 26937,27015,27092,27170,27247,27324,27400,27477,27553,27629,27705,27780,27856,27931,
- 28006,28081,28155,28230,28304,28378,28452,28525,28599,28672,28745,28818,28891,28963,
- 29035,29108,29180,29251,29323,29394,29466,29537,29608,29678,29749,29819,29890,29960,
- 30030,30099,30169,30238,30308,30377,30446,30515,30583,30652,30720,30788,30856,30924,
- 30992,31059,31127,31194,31261,31328,31395,31462,31529,31595,31661,31727,31794,31859,
- 31925,31991,32056,32122,32187,32252,32317,32382,32446,32511,32575,32640,32704,32768,
- 32832,32896,32959,33023,33086,33150,33213,33276,33339,33402,33465,33527,33590,33652,
- 33714,33776,33839,33900,33962,34024,34086,34147,34208,34270,34331,34392,34453,34514,
- 34574,34635,34695,34756,34816,34876,34936,34996,35056,35116,35176,35235,35295,35354,
- 35413,35472,35531,35590,35649,35708,35767,35825,35884,35942,36001,36059,36117,36175,
- 36233,36291,36348,36406,36464,36521,36578,36636,36693,36750,36807,36864,36921,36978,
- 37034,37091,37147,37204,37260,37316,37372,37429,37485,37540,37596,37652,37708,37763,
- 37819,37874,37929,37985,38040,38095,38150,38205,38260,38315,38369,38424,38478,38533,
- 38587,38642,38696,38750,38804,38858,38912,38966,39020,39073,39127,39181,39234,39287,
- 39341,39394,39447,39500,39553,39606,39659,39712,39765,39818,39870,39923,39975,40028,
- 40080,40132,40185,40237,40289,40341,40393,40445,40497,40548,40600,40652,40703,40755,
- 40806,40857,40909,40960,41011,41062,41113,41164,41215,41266,41317,41368,41418,41469,
- 41519,41570,41620,41671,41721,41771,41821,41871,41922,41972,42021,42071,42121,42171,
- 42221,42270,42320,42369,42419,42468,42518,42567,42616,42665,42714,42763,42813,42861,
- 42910,42959,43008,43057,43105,43154,43203,43251,43300,43348,43396,43445,43493,43541,
- 43589,43637,43685,43733,43781,43829,43877,43925,43972,44020,44068,44115,44163,44210,
- 44258,44305,44352,44400,44447,44494,44541,44588,44635,44682,44729,44776,44823,44869,
- 44916,44963,45009,45056,45103,45149,45195,45242,45288,45334,45381,45427,45473,45519,
- 45565,45611,45657,45703,45749,45795,45840,45886,45932,45977,46023,46069,46114,46160,
- 46205,46250,46296,46341,46386,46431,46477,46522,46567,46612,46657,46702,46746,46791,
- 46836,46881,46926,46970,47015,47059,47104,47149,47193,47237,47282,47326,47370,47415,
- 47459,47503,47547,47591,47635,47679,47723,47767,47811,47855,47899,47942,47986,48030,
- 48074,48117,48161,48204,48248,48291,48335,48378,48421,48465,48508,48551,48594,48637,
- 48680,48723,48766,48809,48852,48895,48938,48981,49024,49067,49109,49152,49195,49237,
- 49280,49322,49365,49407,49450,49492,49535,49577,49619,49661,49704,49746,49788,49830,
- 49872,49914,49956,49998,50040,50082,50124,50166,50207,50249,50291,50332,50374,50416,
- 50457,50499,50540,50582,50623,50665,50706,50747,50789,50830,50871,50912,50954,50995,
- 51036,51077,51118,51159,51200,51241,51282,51323,51364,51404,51445,51486,51527,51567,
- 51608,51649,51689,51730,51770,51811,51851,51892,51932,51972,52013,52053,52093,52134,
- 52174,52214,52254,52294,52334,52374,52414,52454,52494,52534,52574,52614,52654,52694,
- 52734,52773,52813,52853,52892,52932,52972,53011,53051,53090,53130,53169,53209,53248,
- 53287,53327,53366,53405,53445,53484,53523,53562,53601,53640,53679,53719,53758,53797,
- 53836,53874,53913,53952,53991,54030,54069,54108,54146,54185,54224,54262,54301,54340,
- 54378,54417,54455,54494,54532,54571,54609,54647,54686,54724,54762,54801,54839,54877,
- 54915,54954,54992,55030,55068,55106,55144,55182,55220,55258,55296,55334,55372,55410,
- 55447,55485,55523,55561,55599,55636,55674,55712,55749,55787,55824,55862,55900,55937,
- 55975,56012,56049,56087,56124,56162,56199,56236,56273,56311,56348,56385,56422,56459,
- 56497,56534,56571,56608,56645,56682,56719,56756,56793,56830,56867,56903,56940,56977,
- 57014,57051,57087,57124,57161,57198,57234,57271,57307,57344,57381,57417,57454,57490,
- 57527,57563,57599,57636,57672,57709,57745,57781,57817,57854,57890,57926,57962,57999,
- 58035,58071,58107,58143,58179,58215,58251,58287,58323,58359,58395,58431,58467,58503,
- 58538,58574,58610,58646,58682,58717,58753,58789,58824,58860,58896,58931,58967,59002,
- 59038,59073,59109,59144,59180,59215,59251,59286,59321,59357,59392,59427,59463,59498,
- 59533,59568,59603,59639,59674,59709,59744,59779,59814,59849,59884,59919,59954,59989,
- 60024,60059,60094,60129,60164,60199,60233,60268,60303,60338,60373,60407,60442,60477,
- 60511,60546,60581,60615,60650,60684,60719,60753,60788,60822,60857,60891,60926,60960,
- 60995,61029,61063,61098,61132,61166,61201,61235,61269,61303,61338,61372,61406,61440,
- 61474,61508,61542,61576,61610,61644,61678,61712,61746,61780,61814,61848,61882,61916,
- 61950,61984,62018,62051,62085,62119,62153,62186,62220,62254,62287,62321,62355,62388,
- 62422,62456,62489,62523,62556,62590,62623,62657,62690,62724,62757,62790,62824,62857,
- 62891,62924,62957,62991,63024,63057,63090,63124,63157,63190,63223,63256,63289,63323,
- 63356,63389,63422,63455,63488,63521,63554,63587,63620,63653,63686,63719,63752,63785,
- 63817,63850,63883,63916,63949,63982,64014,64047,64080,64113,64145,64178,64211,64243,
- 64276,64309,64341,64374,64406,64439,64471,64504,64536,64569,64601,64634,64666,64699,
- 64731,64763,64796,64828,64861,64893,64925,64957,64990,65022,65054,65086,65119,65151,
- 65183,65215,65247,65279,65312,65344,65376,65408,65440,65472,65504 );
-
- g_elder_bit_table : array[0..255 ] of int8 = (
- 0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
- 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
- 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
- 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
- 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
- 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
- 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
- 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7 );
-
-{ GLOBAL PROCEDURES }
- function calc_point_location(x1 ,y1 ,x2 ,y2 ,x ,y : double ) : double;
-
- function point_in_triangle(x1 ,y1 ,x2 ,y2 ,x3 ,y3 ,x ,y : double ) : boolean;
-
- function calc_distance(x1 ,y1 ,x2 ,y2 : double ) : double;
-
- function calc_line_point_distance(x1 ,y1 ,x2 ,y2 ,x ,y : double ) : double;
-
- function calc_intersection(ax ,ay ,bx ,by ,cx ,cy ,dx ,dy : double; x ,y : double_ptr ) : boolean;
-
- function intersection_exists(x1 ,y1 ,x2 ,y2 ,x3 ,y3 ,x4 ,y4 : double ) : boolean;
-
- procedure calc_orthogonal(thickness ,x1 ,y1 ,x2 ,y2 : double; x ,y : double_ptr );
-
- procedure dilate_triangle(x1 ,y1 ,x2 ,y2 ,x3 ,y3 : double; x ,y : double_ptr; d : double );
-
- function calc_triangle_area(x1 ,y1 ,x2 ,y2 ,x3 ,y3 : double ) : double;
-
- function calc_polygon_area(st : storage_xy_ptr ) : double;
-
- function calc_polygon_area_vs(st : vertex_sequence_ptr ) : double;
-
- function fast_sqrt(val : unsigned ) : unsigned;
-
- function besj(x : double; n : int ) : double;
-
- function cross_product(x1 ,y1 ,x2 ,y2 ,x ,y : double ) : double;
-
-
-IMPLEMENTATION
-{ LOCAL VARIABLES & CONSTANTS }
-{ UNIT IMPLEMENTATION }
-{ calc_point_location }
-function calc_point_location;
-begin
- result:=(x - x2 ) * (y2 - y1 ) - (y - y2 ) * (x2 - x1 );
-
-end;
-
-{ point_in_triangle }
-function point_in_triangle;
-var
- cp1 ,cp2 ,cp3 : boolean;
-
-begin
- cp1:=calc_point_location(x1 ,y1 ,x2 ,y2 ,x ,y ) < 0.0;
- cp2:=calc_point_location(x2 ,y2 ,x3 ,y3 ,x ,y ) < 0.0;
- cp3:=calc_point_location(x3 ,y3 ,x1 ,y1 ,x ,y ) < 0.0;
-
- result:=(cp1 = cp2 ) and (cp2 = cp3 ) and (cp3 = cp1 );
-
-end;
-
-{ calc_distance }
-function calc_distance;
-var
- dx ,dy : double;
-
-begin
- dx:=x2 - x1;
- dy:=y2 - y1;
-
- result:=sqrt(dx * dx + dy * dy );
-
-end;
-
-{ calc_line_point_distance }
-function calc_line_point_distance;
-var
- d ,
- dx ,
- dy : double;
-
-begin
- dx:=x2 - x1;
- dy:=y2 - y1;
- d :=sqrt(dx * dx + dy * dy );
-
- if d < intersection_epsilon then
- result:=calc_distance(x1 ,y1 ,x ,y )
- else
- result:=((x - x2 ) * dy - (y - y2 ) * dx) / d;
-
-end;
-
-{ calc_intersection }
-function calc_intersection;
-var
- r ,
-
- num ,
- den : double;
-
-begin
- num:=(ay - cy ) * (dx - cx ) - (ax - cx ) * (dy - cy );
- den:=(bx - ax ) * (dy - cy ) - (by - ay ) * (dx - cx );
-
- if Abs(den ) < intersection_epsilon then
- result:=false
-
- else
- begin
- r :=num / den;
- x^:=ax + r * (bx - ax );
- y^:=ay + r * (by - ay );
-
- result:=true;
-
- end;
-
-end;
-
-{ intersection_exists }
-function intersection_exists;
-var
- dx1 ,dy1 ,
- dx2 ,dy2 : double;
-
-begin
- dx1:=x2 - x1;
- dy1:=y2 - y1;
- dx2:=x4 - x3;
- dy2:=y4 - y3;
-
- result:=
- (((x3 - x2 ) * dy1 - (y3 - y2 ) * dx1 < 0.0 ) <>
- ((x4 - x2 ) * dy1 - (y4 - y2 ) * dx1 < 0.0 ) ) and
- (((x1 - x4 ) * dy2 - (y1 - y4 ) * dx2 < 0.0 ) <>
- ((x2 - x4 ) * dy2 - (y2 - y4 ) * dx2 < 0.0 ) );
-
-end;
-
-{ calc_orthogonal }
-procedure calc_orthogonal;
-var
- d ,dx ,dy : double;
-
-begin
- dx:=x2 - x1;
- dy:=y2 - y1;
- d :=sqrt(dx * dx + dy * dy );
- x^:=thickness * dy / d;
- y^:=thickness * dx / d;
-
-end;
-
-{ dilate_triangle }
-procedure dilate_triangle;
-var
- loc ,
- dx1 ,dy1 ,
- dx2 ,dy2 ,
- dx3 ,dy3 : double;
-
-begin
- dx1:=0.0;
- dy1:=0.0;
- dx2:=0.0;
- dy2:=0.0;
- dx3:=0.0;
- dy3:=0.0;
- loc:=calc_point_location(x1 ,y1 ,x2 ,y2 ,x3 ,y3 );
-
- if Abs(loc ) > intersection_epsilon then
- begin
- if calc_point_location(x1 ,y1 ,x2 ,y2 ,x3 ,y3 ) > 0.0 then
- d:=-d;
-
- calc_orthogonal(d ,x1 ,y1 ,x2 ,y2 ,@dx1 ,@dy1 );
- calc_orthogonal(d ,x2 ,y2 ,x3 ,y3 ,@dx2 ,@dy2 );
- calc_orthogonal(d ,x3 ,y3 ,x1 ,y1 ,@dx3 ,@dy3 );
-
- end;
-
- x^:=x1 + dx1; inc(ptrcomp(x ) ,sizeof(double ) );
- y^:=y1 - dy1; inc(ptrcomp(y ) ,sizeof(double ) );
- x^:=x2 + dx1; inc(ptrcomp(x ) ,sizeof(double ) );
- y^:=y2 - dy1; inc(ptrcomp(y ) ,sizeof(double ) );
- x^:=x2 + dx2; inc(ptrcomp(x ) ,sizeof(double ) );
- y^:=y2 - dy2; inc(ptrcomp(y ) ,sizeof(double ) );
- x^:=x3 + dx2; inc(ptrcomp(x ) ,sizeof(double ) );
- y^:=y3 - dy2; inc(ptrcomp(y ) ,sizeof(double ) );
- x^:=x3 + dx3; inc(ptrcomp(x ) ,sizeof(double ) );
- y^:=y3 - dy3; inc(ptrcomp(y ) ,sizeof(double ) );
- x^:=x1 + dx3; inc(ptrcomp(x ) ,sizeof(double ) );
- y^:=y1 - dy3; inc(ptrcomp(y ) ,sizeof(double ) );
-
-end;
-
-{ calc_triangle_area }
-function calc_triangle_area;
-begin
- result:=(x1 * y2 - x2 * y1 + x2 * y3 - x3 * y2 + x3 * y1 - x1 * y3 ) * 0.5;
-
-end;
-
-{ calc_polygon_area }
-function calc_polygon_area;
-var
- i : unsigned;
- v : double_xy_ptr;
-
- x ,y ,sum ,xs ,ys : double;
-
-begin
- sum:=0.0;
- x :=st.poly[0 ].x;
- y :=st.poly[0 ].y;
- xs :=x;
- ys :=y;
-
- if st.size > 0 then
- for i:=1 to st.size - 1 do
- begin
- v:=@st.poly[i ];
-
- sum:=sum + (x * v.y - y * v.x );
-
- x:=v.x;
- y:=v.y;
-
- end;
-
- result:=(sum + x * ys - y * xs ) * 0.5;
-
-end;
-
-{ calc_polygon_area_vs }
-function calc_polygon_area_vs;
-var
- i : unsigned;
- v : vertex_dist_ptr;
-
- x ,y ,sum ,xs ,ys : double;
-
-begin
- sum:=0.0;
- x :=vertex_dist_ptr(st.array_operator(0 ) ).x;
- y :=vertex_dist_ptr(st.array_operator(0 ) ).y;
- xs :=x;
- ys :=y;
-
- if st.size > 0 then
- for i:=1 to st.size - 1 do
- begin
- v:=st.array_operator(i );
-
- sum:=sum + (x * v.y - y * v.x );
-
- x:=v.x;
- y:=v.y;
-
- end;
-
- result:=(sum + x * ys - y * xs ) * 0.5;
-
-end;
-
-{ fast_sqrt }
-function fast_sqrt;
-var
- bit : int;
-
- t ,shift : unsigned;
-
-begin
- t :=val;
- bit:=0;
-
- shift:=11;
-
-//The following piece of code is just an emulation of the
-//Ix86 assembler command "bsr" (see below). However on old
-//Intels (like Intel MMX 233MHz) this code is about twice
-//faster (sic!) then just one "bsr". On PIII and PIV the
-//bsr is optimized quite well.
- bit:=t shr 24;
-
- if bit <> 0 then
- bit:=g_elder_bit_table[bit ] + 24
-
- else
- begin
- bit:=(t shr 16 ) and $FF;
-
- if bit <> 0 then
- bit:=g_elder_bit_table[bit ] + 16
- else
- begin
- bit:=(t shr 8 ) and $FF;
-
- if bit <> 0 then
- bit:=g_elder_bit_table[bit ] + 8
- else
- bit:=g_elder_bit_table[t ];
-
- end;
-
- end;
-
-// This is calculation sqrt itself.
- bit:=bit - 9;
-
- if bit > 0 then
- begin
- bit :=(shr_int32(bit ,1 ) ) + (bit and 1 );
- shift:=shift - bit;
- val :=val shr (bit shl 1 );
-
- end;
-
- result:=g_sqrt_table[val ] shr shift;
-
-end;
-
-//--------------------------------------------------------------------besj
-// Function BESJ calculates Bessel function of first kind of order n
-// Arguments:
-// n - an integer (>=0), the order
-// x - value at which the Bessel function is required
-//--------------------
-// C++ Mathematical Library
-// Convereted from equivalent FORTRAN library
-// Converetd by Gareth Walker for use by course 392 computational project
-// All functions tested and yield the same results as the corresponding
-// FORTRAN versions.
-//
-// If you have any problems using these functions please report them to
-// M.Muldoon@UMIST.ac.uk
-//
-// Documentation available on the web
-// http://www.ma.umist.ac.uk/mrm/Teaching/392/libs/392.html
-// Version 1.0 8/98
-// 29 October, 1999
-//--------------------
-// Adapted for use in AGG library by Andy Wilk (castor.vulgaris@gmail.com)
-//------------------------------------------------------------------------
-{ besj }
-function besj;
-var
- i ,m1 ,m2 ,m8 ,imax : int;
-
- d ,b ,b1 ,c2 ,c3 ,c4 ,c6 : double;
-
-begin
- if n < 0 then
- begin
- result:=0;
-
- exit;
-
- end;
-
- d:=1E-6;
- b:=0;
-
- if Abs(x ) <= d then
- begin
- if n <> 0 then
- result:=0
- else
- result:=1;
-
- exit;
-
- end;
-
- b1:=0; // b1 is the value from the previous iteration
-
-// Set up a starting order for recurrence
- m1:=trunc(Abs(x ) + 6 );
-
- if Abs(x ) > 5 then
- m1:=trunc(Abs(1.4 * x + 60 / x ) );
-
- m2:=trunc(n + 2 + Abs(x ) / 4 );
-
- if m1 > m2 then
- m2:=m1;
-
-// Apply recurrence down from curent max order
- repeat
- c3:=0;
- c2:=1E-30;
- c4:=0;
- m8:=1;
-
- if m2 div 2 * 2 = m2 then
- m8:=-1;
-
- imax:=m2 - 2;
-
- for i:=1 to imax do
- begin
- c6:=2 * (m2 - i ) * c2 / x - c3;
- c3:=c2;
- c2:=c6;
-
- if m2 - i - 1 = n then
- b:=c6;
-
- m8:=-1 * m8;
-
- if m8 > 0 then
- c4:=c4 + 2 * c6;
-
- end;
-
- c6:=2 * c2 / x - c3;
-
- if n = 0 then
- b:=c6;
-
- c4:=c4 + c6;
- b :=b / c4;
-
- if Abs(b - b1 ) < d then
- begin
- result:=b;
-
- exit;
-
- end;
-
- b1:=b;
-
- inc(m2 ,3 );
-
- until false;
-
-end;
-
-{ CROSS_PRODUCT }
-function cross_product(x1 ,y1 ,x2 ,y2 ,x ,y : double ) : double;
-begin
- result:=(x - x2 ) * (y2 - y1 ) - (y - y2 ) * (x2 - x1 );
-
-end;
-
-END.
-
+//----------------------------------------------------------------------------
+// Anti-Grain Geometry - Version 2.4 (Public License)
+// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
+//
+// Anti-Grain Geometry - Version 2.4 Release Milano 3 (AggPas 2.4 RM3)
+// Pascal Port By: Milan Marusinec alias Milano
+// milan@marusinec.sk
+// http://www.aggpas.org
+// Copyright (c) 2005-2006
+//
+// Permission to copy, use, modify, sell and distribute this software
+// is granted provided this copyright notice appears in all copies.
+// This software is provided "as is" without express or implied
+// warranty, and with no claim as to its suitability for any purpose.
+//
+//----------------------------------------------------------------------------
+// Contact: mcseem@antigrain.com
+// mcseemagg@yahoo.com
+// http://www.antigrain.com
+//
+//----------------------------------------------------------------------------
+// Bessel function (besj) was adapted for use in AGG library by Andy Wilk
+// Contact: castor.vulgaris@gmail.com
+//
+// [Pascal Port History] -----------------------------------------------------
+//
+// 23.06.2006-Milano: ptrcomp adjustments
+// 18.12.2005-Milano: Unit port establishment
+//
+{ agg_math.pas }
+unit
+ agg_math ;
+
+INTERFACE
+
+{$I agg_mode.inc }
+{$Q- }
+{$R- }
+uses
+ Math ,
+ agg_basics ,
+ agg_vertex_sequence ;
+
+{ GLOBAL VARIABLES & CONSTANTS }
+type
+ double_xy_ptr = ^double_xy;
+ double_xy = record
+ x ,y : double;
+
+ end;
+
+ poly_xy_ptr = ^poly_xy;
+ poly_xy = array[0..0 ] of double_xy;
+
+ storage_xy_ptr = ^storage_xy;
+ storage_xy = record
+ poly : poly_xy_ptr;
+ size : unsigned;
+
+ end;
+
+const
+ intersection_epsilon : double = 1.0e-30;
+
+// Tables for fast sqrt
+const
+ g_sqrt_table : array[0..1023 ] of int16u = (0 ,
+ 2048,2896,3547,4096,4579,5017,5418,5793,6144,6476,6792,7094,7384,7663,7932,8192,8444,
+ 8689,8927,9159,9385,9606,9822,10033,10240,10443,10642,10837,11029,11217,11403,11585,
+ 11765,11942,12116,12288,12457,12625,12790,12953,13114,13273,13430,13585,13738,13890,
+ 14040,14189,14336,14482,14626,14768,14910,15050,15188,15326,15462,15597,15731,15864,
+ 15995,16126,16255,16384,16512,16638,16764,16888,17012,17135,17257,17378,17498,17618,
+ 17736,17854,17971,18087,18203,18318,18432,18545,18658,18770,18882,18992,19102,19212,
+ 19321,19429,19537,19644,19750,19856,19961,20066,20170,20274,20377,20480,20582,20684,
+ 20785,20886,20986,21085,21185,21283,21382,21480,21577,21674,21771,21867,21962,22058,
+ 22153,22247,22341,22435,22528,22621,22713,22806,22897,22989,23080,23170,23261,23351,
+ 23440,23530,23619,23707,23796,23884,23971,24059,24146,24232,24319,24405,24491,24576,
+ 24661,24746,24831,24915,24999,25083,25166,25249,25332,25415,25497,25580,25661,25743,
+ 25824,25905,25986,26067,26147,26227,26307,26387,26466,26545,26624,26703,26781,26859,
+ 26937,27015,27092,27170,27247,27324,27400,27477,27553,27629,27705,27780,27856,27931,
+ 28006,28081,28155,28230,28304,28378,28452,28525,28599,28672,28745,28818,28891,28963,
+ 29035,29108,29180,29251,29323,29394,29466,29537,29608,29678,29749,29819,29890,29960,
+ 30030,30099,30169,30238,30308,30377,30446,30515,30583,30652,30720,30788,30856,30924,
+ 30992,31059,31127,31194,31261,31328,31395,31462,31529,31595,31661,31727,31794,31859,
+ 31925,31991,32056,32122,32187,32252,32317,32382,32446,32511,32575,32640,32704,32768,
+ 32832,32896,32959,33023,33086,33150,33213,33276,33339,33402,33465,33527,33590,33652,
+ 33714,33776,33839,33900,33962,34024,34086,34147,34208,34270,34331,34392,34453,34514,
+ 34574,34635,34695,34756,34816,34876,34936,34996,35056,35116,35176,35235,35295,35354,
+ 35413,35472,35531,35590,35649,35708,35767,35825,35884,35942,36001,36059,36117,36175,
+ 36233,36291,36348,36406,36464,36521,36578,36636,36693,36750,36807,36864,36921,36978,
+ 37034,37091,37147,37204,37260,37316,37372,37429,37485,37540,37596,37652,37708,37763,
+ 37819,37874,37929,37985,38040,38095,38150,38205,38260,38315,38369,38424,38478,38533,
+ 38587,38642,38696,38750,38804,38858,38912,38966,39020,39073,39127,39181,39234,39287,
+ 39341,39394,39447,39500,39553,39606,39659,39712,39765,39818,39870,39923,39975,40028,
+ 40080,40132,40185,40237,40289,40341,40393,40445,40497,40548,40600,40652,40703,40755,
+ 40806,40857,40909,40960,41011,41062,41113,41164,41215,41266,41317,41368,41418,41469,
+ 41519,41570,41620,41671,41721,41771,41821,41871,41922,41972,42021,42071,42121,42171,
+ 42221,42270,42320,42369,42419,42468,42518,42567,42616,42665,42714,42763,42813,42861,
+ 42910,42959,43008,43057,43105,43154,43203,43251,43300,43348,43396,43445,43493,43541,
+ 43589,43637,43685,43733,43781,43829,43877,43925,43972,44020,44068,44115,44163,44210,
+ 44258,44305,44352,44400,44447,44494,44541,44588,44635,44682,44729,44776,44823,44869,
+ 44916,44963,45009,45056,45103,45149,45195,45242,45288,45334,45381,45427,45473,45519,
+ 45565,45611,45657,45703,45749,45795,45840,45886,45932,45977,46023,46069,46114,46160,
+ 46205,46250,46296,46341,46386,46431,46477,46522,46567,46612,46657,46702,46746,46791,
+ 46836,46881,46926,46970,47015,47059,47104,47149,47193,47237,47282,47326,47370,47415,
+ 47459,47503,47547,47591,47635,47679,47723,47767,47811,47855,47899,47942,47986,48030,
+ 48074,48117,48161,48204,48248,48291,48335,48378,48421,48465,48508,48551,48594,48637,
+ 48680,48723,48766,48809,48852,48895,48938,48981,49024,49067,49109,49152,49195,49237,
+ 49280,49322,49365,49407,49450,49492,49535,49577,49619,49661,49704,49746,49788,49830,
+ 49872,49914,49956,49998,50040,50082,50124,50166,50207,50249,50291,50332,50374,50416,
+ 50457,50499,50540,50582,50623,50665,50706,50747,50789,50830,50871,50912,50954,50995,
+ 51036,51077,51118,51159,51200,51241,51282,51323,51364,51404,51445,51486,51527,51567,
+ 51608,51649,51689,51730,51770,51811,51851,51892,51932,51972,52013,52053,52093,52134,
+ 52174,52214,52254,52294,52334,52374,52414,52454,52494,52534,52574,52614,52654,52694,
+ 52734,52773,52813,52853,52892,52932,52972,53011,53051,53090,53130,53169,53209,53248,
+ 53287,53327,53366,53405,53445,53484,53523,53562,53601,53640,53679,53719,53758,53797,
+ 53836,53874,53913,53952,53991,54030,54069,54108,54146,54185,54224,54262,54301,54340,
+ 54378,54417,54455,54494,54532,54571,54609,54647,54686,54724,54762,54801,54839,54877,
+ 54915,54954,54992,55030,55068,55106,55144,55182,55220,55258,55296,55334,55372,55410,
+ 55447,55485,55523,55561,55599,55636,55674,55712,55749,55787,55824,55862,55900,55937,
+ 55975,56012,56049,56087,56124,56162,56199,56236,56273,56311,56348,56385,56422,56459,
+ 56497,56534,56571,56608,56645,56682,56719,56756,56793,56830,56867,56903,56940,56977,
+ 57014,57051,57087,57124,57161,57198,57234,57271,57307,57344,57381,57417,57454,57490,
+ 57527,57563,57599,57636,57672,57709,57745,57781,57817,57854,57890,57926,57962,57999,
+ 58035,58071,58107,58143,58179,58215,58251,58287,58323,58359,58395,58431,58467,58503,
+ 58538,58574,58610,58646,58682,58717,58753,58789,58824,58860,58896,58931,58967,59002,
+ 59038,59073,59109,59144,59180,59215,59251,59286,59321,59357,59392,59427,59463,59498,
+ 59533,59568,59603,59639,59674,59709,59744,59779,59814,59849,59884,59919,59954,59989,
+ 60024,60059,60094,60129,60164,60199,60233,60268,60303,60338,60373,60407,60442,60477,
+ 60511,60546,60581,60615,60650,60684,60719,60753,60788,60822,60857,60891,60926,60960,
+ 60995,61029,61063,61098,61132,61166,61201,61235,61269,61303,61338,61372,61406,61440,
+ 61474,61508,61542,61576,61610,61644,61678,61712,61746,61780,61814,61848,61882,61916,
+ 61950,61984,62018,62051,62085,62119,62153,62186,62220,62254,62287,62321,62355,62388,
+ 62422,62456,62489,62523,62556,62590,62623,62657,62690,62724,62757,62790,62824,62857,
+ 62891,62924,62957,62991,63024,63057,63090,63124,63157,63190,63223,63256,63289,63323,
+ 63356,63389,63422,63455,63488,63521,63554,63587,63620,63653,63686,63719,63752,63785,
+ 63817,63850,63883,63916,63949,63982,64014,64047,64080,64113,64145,64178,64211,64243,
+ 64276,64309,64341,64374,64406,64439,64471,64504,64536,64569,64601,64634,64666,64699,
+ 64731,64763,64796,64828,64861,64893,64925,64957,64990,65022,65054,65086,65119,65151,
+ 65183,65215,65247,65279,65312,65344,65376,65408,65440,65472,65504 );
+
+ g_elder_bit_table : array[0..255 ] of int8 = (
+ 0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
+ 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
+ 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
+ 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
+ 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
+ 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
+ 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
+ 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7 );
+
+{ GLOBAL PROCEDURES }
+ function calc_point_location(x1 ,y1 ,x2 ,y2 ,x ,y : double ) : double;
+
+ function point_in_triangle(x1 ,y1 ,x2 ,y2 ,x3 ,y3 ,x ,y : double ) : boolean;
+
+ function calc_distance(x1 ,y1 ,x2 ,y2 : double ) : double;
+
+ function calc_line_point_distance(x1 ,y1 ,x2 ,y2 ,x ,y : double ) : double;
+
+ function calc_intersection(ax ,ay ,bx ,by ,cx ,cy ,dx ,dy : double; x ,y : double_ptr ) : boolean;
+
+ function intersection_exists(x1 ,y1 ,x2 ,y2 ,x3 ,y3 ,x4 ,y4 : double ) : boolean;
+
+ procedure calc_orthogonal(thickness ,x1 ,y1 ,x2 ,y2 : double; x ,y : double_ptr );
+
+ procedure dilate_triangle(x1 ,y1 ,x2 ,y2 ,x3 ,y3 : double; x ,y : double_ptr; d : double );
+
+ function calc_triangle_area(x1 ,y1 ,x2 ,y2 ,x3 ,y3 : double ) : double;
+
+ function calc_polygon_area(st : storage_xy_ptr ) : double;
+
+ function calc_polygon_area_vs(st : vertex_sequence_ptr ) : double;
+
+ function fast_sqrt(val : unsigned ) : unsigned;
+
+ function besj(x : double; n : int ) : double;
+
+ function cross_product(x1 ,y1 ,x2 ,y2 ,x ,y : double ) : double;
+
+
+IMPLEMENTATION
+{ LOCAL VARIABLES & CONSTANTS }
+{ UNIT IMPLEMENTATION }
+{ calc_point_location }
+function calc_point_location;
+begin
+ result:=(x - x2 ) * (y2 - y1 ) - (y - y2 ) * (x2 - x1 );
+
+end;
+
+{ point_in_triangle }
+function point_in_triangle;
+var
+ cp1 ,cp2 ,cp3 : boolean;
+
+begin
+ cp1:=calc_point_location(x1 ,y1 ,x2 ,y2 ,x ,y ) < 0.0;
+ cp2:=calc_point_location(x2 ,y2 ,x3 ,y3 ,x ,y ) < 0.0;
+ cp3:=calc_point_location(x3 ,y3 ,x1 ,y1 ,x ,y ) < 0.0;
+
+ result:=(cp1 = cp2 ) and (cp2 = cp3 ) and (cp3 = cp1 );
+
+end;
+
+{ calc_distance }
+function calc_distance;
+var
+ dx ,dy : double;
+
+begin
+ dx:=x2 - x1;
+ dy:=y2 - y1;
+
+ result:=sqrt(dx * dx + dy * dy );
+
+end;
+
+{ calc_line_point_distance }
+function calc_line_point_distance;
+var
+ d ,
+ dx ,
+ dy : double;
+
+begin
+ dx:=x2 - x1;
+ dy:=y2 - y1;
+ d :=sqrt(dx * dx + dy * dy );
+
+ if d < intersection_epsilon then
+ result:=calc_distance(x1 ,y1 ,x ,y )
+ else
+ result:=((x - x2 ) * dy - (y - y2 ) * dx) / d;
+
+end;
+
+{ calc_intersection }
+function calc_intersection;
+var
+ r ,
+
+ num ,
+ den : double;
+
+begin
+ num:=(ay - cy ) * (dx - cx ) - (ax - cx ) * (dy - cy );
+ den:=(bx - ax ) * (dy - cy ) - (by - ay ) * (dx - cx );
+
+ if Abs(den ) < intersection_epsilon then
+ result:=false
+
+ else
+ begin
+ r :=num / den;
+ x^:=ax + r * (bx - ax );
+ y^:=ay + r * (by - ay );
+
+ result:=true;
+
+ end;
+
+end;
+
+{ intersection_exists }
+function intersection_exists;
+var
+ dx1 ,dy1 ,
+ dx2 ,dy2 : double;
+
+begin
+ dx1:=x2 - x1;
+ dy1:=y2 - y1;
+ dx2:=x4 - x3;
+ dy2:=y4 - y3;
+
+ result:=
+ (((x3 - x2 ) * dy1 - (y3 - y2 ) * dx1 < 0.0 ) <>
+ ((x4 - x2 ) * dy1 - (y4 - y2 ) * dx1 < 0.0 ) ) and
+ (((x1 - x4 ) * dy2 - (y1 - y4 ) * dx2 < 0.0 ) <>
+ ((x2 - x4 ) * dy2 - (y2 - y4 ) * dx2 < 0.0 ) );
+
+end;
+
+{ calc_orthogonal }
+procedure calc_orthogonal;
+var
+ d ,dx ,dy : double;
+
+begin
+ dx:=x2 - x1;
+ dy:=y2 - y1;
+ d :=sqrt(dx * dx + dy * dy );
+ x^:=thickness * dy / d;
+ y^:=thickness * dx / d;
+
+end;
+
+{ dilate_triangle }
+procedure dilate_triangle;
+var
+ loc ,
+ dx1 ,dy1 ,
+ dx2 ,dy2 ,
+ dx3 ,dy3 : double;
+
+begin
+ dx1:=0.0;
+ dy1:=0.0;
+ dx2:=0.0;
+ dy2:=0.0;
+ dx3:=0.0;
+ dy3:=0.0;
+ loc:=calc_point_location(x1 ,y1 ,x2 ,y2 ,x3 ,y3 );
+
+ if Abs(loc ) > intersection_epsilon then
+ begin
+ if calc_point_location(x1 ,y1 ,x2 ,y2 ,x3 ,y3 ) > 0.0 then
+ d:=-d;
+
+ calc_orthogonal(d ,x1 ,y1 ,x2 ,y2 ,@dx1 ,@dy1 );
+ calc_orthogonal(d ,x2 ,y2 ,x3 ,y3 ,@dx2 ,@dy2 );
+ calc_orthogonal(d ,x3 ,y3 ,x1 ,y1 ,@dx3 ,@dy3 );
+
+ end;
+
+ x^:=x1 + dx1; inc(ptrcomp(x ) ,sizeof(double ) );
+ y^:=y1 - dy1; inc(ptrcomp(y ) ,sizeof(double ) );
+ x^:=x2 + dx1; inc(ptrcomp(x ) ,sizeof(double ) );
+ y^:=y2 - dy1; inc(ptrcomp(y ) ,sizeof(double ) );
+ x^:=x2 + dx2; inc(ptrcomp(x ) ,sizeof(double ) );
+ y^:=y2 - dy2; inc(ptrcomp(y ) ,sizeof(double ) );
+ x^:=x3 + dx2; inc(ptrcomp(x ) ,sizeof(double ) );
+ y^:=y3 - dy2; inc(ptrcomp(y ) ,sizeof(double ) );
+ x^:=x3 + dx3; inc(ptrcomp(x ) ,sizeof(double ) );
+ y^:=y3 - dy3; inc(ptrcomp(y ) ,sizeof(double ) );
+ x^:=x1 + dx3; inc(ptrcomp(x ) ,sizeof(double ) );
+ y^:=y1 - dy3; inc(ptrcomp(y ) ,sizeof(double ) );
+
+end;
+
+{ calc_triangle_area }
+function calc_triangle_area;
+begin
+ result:=(x1 * y2 - x2 * y1 + x2 * y3 - x3 * y2 + x3 * y1 - x1 * y3 ) * 0.5;
+
+end;
+
+{ calc_polygon_area }
+function calc_polygon_area;
+var
+ i : unsigned;
+ v : double_xy_ptr;
+
+ x ,y ,sum ,xs ,ys : double;
+
+begin
+ sum:=0.0;
+ x :=st.poly[0 ].x;
+ y :=st.poly[0 ].y;
+ xs :=x;
+ ys :=y;
+
+ if st.size > 0 then
+ for i:=1 to st.size - 1 do
+ begin
+ v:=@st.poly[i ];
+
+ sum:=sum + (x * v.y - y * v.x );
+
+ x:=v.x;
+ y:=v.y;
+
+ end;
+
+ result:=(sum + x * ys - y * xs ) * 0.5;
+
+end;
+
+{ calc_polygon_area_vs }
+function calc_polygon_area_vs;
+var
+ i : unsigned;
+ v : vertex_dist_ptr;
+
+ x ,y ,sum ,xs ,ys : double;
+
+begin
+ sum:=0.0;
+ x :=vertex_dist_ptr(st.array_operator(0 ) ).x;
+ y :=vertex_dist_ptr(st.array_operator(0 ) ).y;
+ xs :=x;
+ ys :=y;
+
+ if st.size > 0 then
+ for i:=1 to st.size - 1 do
+ begin
+ v:=st.array_operator(i );
+
+ sum:=sum + (x * v.y - y * v.x );
+
+ x:=v.x;
+ y:=v.y;
+
+ end;
+
+ result:=(sum + x * ys - y * xs ) * 0.5;
+
+end;
+
+{ fast_sqrt }
+function fast_sqrt;
+var
+ bit : int;
+
+ t ,shift : unsigned;
+
+begin
+ t :=val;
+ bit:=0;
+
+ shift:=11;
+
+//The following piece of code is just an emulation of the
+//Ix86 assembler command "bsr" (see below). However on old
+//Intels (like Intel MMX 233MHz) this code is about twice
+//faster (sic!) then just one "bsr". On PIII and PIV the
+//bsr is optimized quite well.
+ bit:=t shr 24;
+
+ if bit <> 0 then
+ bit:=g_elder_bit_table[bit ] + 24
+
+ else
+ begin
+ bit:=(t shr 16 ) and $FF;
+
+ if bit <> 0 then
+ bit:=g_elder_bit_table[bit ] + 16
+ else
+ begin
+ bit:=(t shr 8 ) and $FF;
+
+ if bit <> 0 then
+ bit:=g_elder_bit_table[bit ] + 8
+ else
+ bit:=g_elder_bit_table[t ];
+
+ end;
+
+ end;
+
+// This is calculation sqrt itself.
+ bit:=bit - 9;
+
+ if bit > 0 then
+ begin
+ bit :=(shr_int32(bit ,1 ) ) + (bit and 1 );
+ shift:=shift - bit;
+ val :=val shr (bit shl 1 );
+
+ end;
+
+ result:=g_sqrt_table[val ] shr shift;
+
+end;
+
+//--------------------------------------------------------------------besj
+// Function BESJ calculates Bessel function of first kind of order n
+// Arguments:
+// n - an integer (>=0), the order
+// x - value at which the Bessel function is required
+//--------------------
+// C++ Mathematical Library
+// Convereted from equivalent FORTRAN library
+// Converetd by Gareth Walker for use by course 392 computational project
+// All functions tested and yield the same results as the corresponding
+// FORTRAN versions.
+//
+// If you have any problems using these functions please report them to
+// M.Muldoon@UMIST.ac.uk
+//
+// Documentation available on the web
+// http://www.ma.umist.ac.uk/mrm/Teaching/392/libs/392.html
+// Version 1.0 8/98
+// 29 October, 1999
+//--------------------
+// Adapted for use in AGG library by Andy Wilk (castor.vulgaris@gmail.com)
+//------------------------------------------------------------------------
+{ besj }
+function besj;
+var
+ i ,m1 ,m2 ,m8 ,imax : int;
+
+ d ,b ,b1 ,c2 ,c3 ,c4 ,c6 : double;
+
+begin
+ if n < 0 then
+ begin
+ result:=0;
+
+ exit;
+
+ end;
+
+ d:=1E-6;
+ b:=0;
+
+ if Abs(x ) <= d then
+ begin
+ if n <> 0 then
+ result:=0
+ else
+ result:=1;
+
+ exit;
+
+ end;
+
+ b1:=0; // b1 is the value from the previous iteration
+
+// Set up a starting order for recurrence
+ m1:=trunc(Abs(x ) + 6 );
+
+ if Abs(x ) > 5 then
+ m1:=trunc(Abs(1.4 * x + 60 / x ) );
+
+ m2:=trunc(n + 2 + Abs(x ) / 4 );
+
+ if m1 > m2 then
+ m2:=m1;
+
+// Apply recurrence down from curent max order
+ repeat
+ c3:=0;
+ c2:=1E-30;
+ c4:=0;
+ m8:=1;
+
+ if m2 div 2 * 2 = m2 then
+ m8:=-1;
+
+ imax:=m2 - 2;
+
+ for i:=1 to imax do
+ begin
+ c6:=2 * (m2 - i ) * c2 / x - c3;
+ c3:=c2;
+ c2:=c6;
+
+ if m2 - i - 1 = n then
+ b:=c6;
+
+ m8:=-1 * m8;
+
+ if m8 > 0 then
+ c4:=c4 + 2 * c6;
+
+ end;
+
+ c6:=2 * c2 / x - c3;
+
+ if n = 0 then
+ b:=c6;
+
+ c4:=c4 + c6;
+ b :=b / c4;
+
+ if Abs(b - b1 ) < d then
+ begin
+ result:=b;
+
+ exit;
+
+ end;
+
+ b1:=b;
+
+ inc(m2 ,3 );
+
+ until false;
+
+end;
+
+{ CROSS_PRODUCT }
+function cross_product(x1 ,y1 ,x2 ,y2 ,x ,y : double ) : double;
+begin
+ result:=(x - x2 ) * (y2 - y1 ) - (y - y2 ) * (x2 - x1 );
+
+end;
+
+END.
+
generated by cgit v1.2.3-70-g09d2 (git 2.47.0) at 2024-10-17 10:24:49 +0000