Shaker/Veldrid/Agg/agg/agg_math.cs

// <auto-generated>
// Hack to disable analyzers and their warnings - too many issues to address
// </auto-generated>
//----------------------------------------------------------------------------
// Anti-Grain Geometry - Version 2.4
// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
//
// C# port by: Lars Brubaker
//                  larsbrubaker@gmail.com
// Copyright (C) 2007
//
// 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
//----------------------------------------------------------------------------
using System;

namespace MatterHackers.Agg
{
	public static class agg_math
	{
		//------------------------------------------------------vertex_dist_epsilon
		// Coinciding points maximal distance (Epsilon)
		public const double vertex_dist_epsilon = 1e-14;

		//-----------------------------------------------------intersection_epsilon
		// See calc_intersection
		public const double intersection_epsilon = 1.0e-30;

		//------------------------------------------------------------cross_product
		public static double cross_product(double x1, double y1,
										double x2, double y2,
										double x, double y)
		{
			return (x - x2) * (y2 - y1) - (y - y2) * (x2 - x1);
		}

		//--------------------------------------------------------point_in_triangle
		public static bool point_in_triangle(double x1, double y1,
										  double x2, double y2,
										  double x3, double y3,
										  double x, double y)
		{
			bool cp1 = cross_product(x1, y1, x2, y2, x, y) < 0.0;
			bool cp2 = cross_product(x2, y2, x3, y3, x, y) < 0.0;
			bool cp3 = cross_product(x3, y3, x1, y1, x, y) < 0.0;
			return cp1 == cp2 && cp2 == cp3 && cp3 == cp1;
		}

		//-----------------------------------------------------------calc_distance
		public static double calc_distance(double x1, double y1, double x2, double y2)
		{
			double dx = x2 - x1;
			double dy = y2 - y1;
			return Math.Sqrt(dx * dx + dy * dy);
		}

		//--------------------------------------------------------calc_sq_distance
		public static double calc_sq_distance(double x1, double y1, double x2, double y2)
		{
			double dx = x2 - x1;
			double dy = y2 - y1;
			return dx * dx + dy * dy;
		}

		//------------------------------------------------calc_line_point_distance
		public static double calc_line_point_distance(double x1, double y1,
												   double x2, double y2,
												   double x, double y)
		{
			double dx = x2 - x1;
			double dy = y2 - y1;
			double d = Math.Sqrt(dx * dx + dy * dy);
			if (d < vertex_dist_epsilon)
			{
				return calc_distance(x1, y1, x, y);
			}
			return ((x - x2) * dy - (y - y2) * dx) / d;
		}

		//-------------------------------------------------------calc_line_point_u
		public static double calc_segment_point_u(double x1, double y1,
											   double x2, double y2,
											   double x, double y)
		{
			double dx = x2 - x1;
			double dy = y2 - y1;

			if (dx == 0 && dy == 0)
			{
				return 0;
			}

			double pdx = x - x1;
			double pdy = y - y1;

			return (pdx * dx + pdy * dy) / (dx * dx + dy * dy);
		}

		//---------------------------------------------calc_line_point_sq_distance
		public static double calc_segment_point_sq_distance(double x1, double y1,
														 double x2, double y2,
														 double x, double y,
														 double u)
		{
			if (u <= 0)
			{
				return calc_sq_distance(x, y, x1, y1);
			}
			else
				if (u >= 1)
				{
					return calc_sq_distance(x, y, x2, y2);
				}
			return calc_sq_distance(x, y, x1 + u * (x2 - x1), y1 + u * (y2 - y1));
		}

		//---------------------------------------------calc_line_point_sq_distance
		public static double calc_segment_point_sq_distance(double x1, double y1,
														 double x2, double y2,
														 double x, double y)
		{
			return
				calc_segment_point_sq_distance(
					x1, y1, x2, y2, x, y,
					calc_segment_point_u(x1, y1, x2, y2, x, y));
		}

		//-------------------------------------------------------calc_intersection
		public static bool calc_intersection(double aX1, double aY1, double aX2, double aY2,
										  double bX1, double bY1, double bX2, double bY2,
										  out double x, out double y)
		{
			double num = (aY1 - bY1) * (bX2 - bX1) - (aX1 - bX1) * (bY2 - bY1);
			double den = (aX2 - aX1) * (bY2 - bY1) - (aY2 - aY1) * (bX2 - bX1);
			if (Math.Abs(den) < intersection_epsilon)
			{
				x = 0;
				y = 0;
				return false;
			}
			double r = num / den;
			x = aX1 + r * (aX2 - aX1);
			y = aY1 + r * (aY2 - aY1);
			return true;
		}

		//-----------------------------------------------------intersection_exists
		public static bool intersection_exists(double x1, double y1, double x2, double y2,
											double x3, double y3, double x4, double y4)
		{
			// It's less expensive but you can't control the
			// boundary conditions: Less or LessEqual
			double dx1 = x2 - x1;
			double dy1 = y2 - y1;
			double dx2 = x4 - x3;
			double dy2 = y4 - y3;
			return ((x3 - x2) * dy1 - (y3 - y2) * dx1 < 0.0) !=
				   ((x4 - x2) * dy1 - (y4 - y2) * dx1 < 0.0) &&
				   ((x1 - x4) * dy2 - (y1 - y4) * dx2 < 0.0) !=
				   ((x2 - x4) * dy2 - (y2 - y4) * dx2 < 0.0);

			// It's is more expensive but more flexible
			// in terms of boundary conditions.
			//--------------------
			//double den  = (x2-x1) * (y4-y3) - (y2-y1) * (x4-x3);
			//if(Math.Abs(den) < intersection_epsilon) return false;
			//double nom1 = (x4-x3) * (y1-y3) - (y4-y3) * (x1-x3);
			//double nom2 = (x2-x1) * (y1-y3) - (y2-y1) * (x1-x3);
			//double ua = nom1 / den;
			//double ub = nom2 / den;
			//return ua >= 0.0 && ua <= 1.0 && ub >= 0.0 && ub <= 1.0;
		}

		//--------------------------------------------------------calc_orthogonal
		public static void calc_orthogonal(double thickness,
										double x1, double y1,
										double x2, double y2,
										out double x, out double y)
		{
			double dx = x2 - x1;
			double dy = y2 - y1;
			double d = Math.Sqrt(dx * dx + dy * dy);
			x = thickness * dy / d;
			y = -thickness * dx / d;
		}

		//--------------------------------------------------------dilate_triangle
		public static void dilate_triangle(double x1, double y1,
										double x2, double y2,
										double x3, double y3,
										double[] x, double[] y,
										double d)
		{
			double dx1 = 0.0;
			double dy1 = 0.0;
			double dx2 = 0.0;
			double dy2 = 0.0;
			double dx3 = 0.0;
			double dy3 = 0.0;
			double loc = cross_product(x1, y1, x2, y2, x3, y3);
			if (Math.Abs(loc) > intersection_epsilon)
			{
				if (cross_product(x1, y1, x2, y2, x3, y3) > 0.0)
				{
					d = -d;
				}
				calc_orthogonal(d, x1, y1, x2, y2, out dx1, out dy1);
				calc_orthogonal(d, x2, y2, x3, y3, out dx2, out dy2);
				calc_orthogonal(d, x3, y3, x1, y1, out dx3, out dy3);
			}
			x[0] = x1 + dx1; y[0] = y1 + dy1;
			x[1] = x2 + dx1; y[1] = y2 + dy1;
			x[2] = x2 + dx2; y[2] = y2 + dy2;
			x[3] = x3 + dx2; y[3] = y3 + dy2;
			x[4] = x3 + dx3; y[4] = y3 + dy3;
			x[5] = x1 + dx3; y[5] = y1 + dy3;
		}

		//------------------------------------------------------calc_triangle_area
		public static double calc_triangle_area(double x1, double y1,
											 double x2, double y2,
											 double x3, double y3)
		{
			return (x1 * y2 - x2 * y1 + x2 * y3 - x3 * y2 + x3 * y1 - x1 * y3) * 0.5;
		}

		//-------------------------------------------------------calc_polygon_area
		public static double calc_polygon_area(VertexSequence st)
		{
			int i;
			double sum = 0.0;
			double x = st[0].x;
			double y = st[0].y;
			double xs = x;
			double ys = y;

			for (i = 1; i < st.Count; i++)
			{
				VertexDistance v = st[i];
				sum += x * v.y - y * v.x;
				x = v.x;
				y = v.y;
			}
			return (sum + x * ys - y * xs) * 0.5;
		}

		//------------------------------------------------------------------------
		// Tables for fast sqrt
		public static ushort[] g_sqrt_table =                       //----------g_sqrt_table
        {
            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
        };

		public static byte[] g_elder_bit_table = //---------g_elder_bit_table
        {
            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
        };

		//---------------------------------------------------------------fast_sqrt
		//Fast integer Sqrt - really fast: no cycles, divisions or multiplications
		public static int fast_sqrt(int val)
		{
			//This code is actually pure C and portable to most
			//architectures including 64bit ones.
			int t = val;
			int bit = 0;
			int shift = 11;

			//The following piece of code is just an emulation of the
			//Ix86 assembler command "bsr" (see above). However on old
			//Intels (like Intel MMX 233MHz) this code is about twice
			//as fast as just one "bsr". On PIII and PIV the
			//bsr is optimized quite well.
			bit = (int)t >> 24;
			if (bit != 0)
			{
				bit = g_elder_bit_table[bit] + 24;
			}
			else
			{
				bit = ((int)t >> 16) & 0xFF;
				if (bit != 0)
				{
					bit = g_elder_bit_table[bit] + 16;
				}
				else
				{
					bit = ((int)t >> 8) & 0xFF;
					if (bit != 0)
					{
						bit = g_elder_bit_table[bit] + 8;
					}
					else
					{
						bit = g_elder_bit_table[t];
					}
				}
			}

			//This code calculates the sqrt.
			bit -= 9;
			if (bit > 0)
			{
				bit = (bit >> 1) + (bit & 1);
				shift -= (int)bit;
				val >>= (bit << 1);
			}
			return (int)((int)g_sqrt_table[val] >> (int)shift);
		}

		//--------------------------------------------------------------------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
		// Converted from equivalent FORTRAN library
		// Converted 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)
		//------------------------------------------------------------------------
		public static double besj(double x, int n)
		{
			if (n < 0)
			{
				return 0;
			}
			double d = 1E-6;
			double b = 0;
			if (Math.Abs(x) <= d)
			{
				if (n != 0) return 0;
				return 1;
			}
			double b1 = 0; // b1 is the value from the previous iteration
			// Set up a starting order for recurrence
			int m1 = (int)Math.Abs(x) + 6;
			if (Math.Abs(x) > 5)
			{
				m1 = (int)(Math.Abs(1.4 * x + 60 / x));
			}
			int m2 = (int)(n + 2 + Math.Abs(x) / 4);
			if (m1 > m2)
			{
				m2 = m1;
			}

			// Apply recurrence down from current max order
			for (; ; )
			{
				double c3 = 0;
				double c2 = 1E-30;
				double c4 = 0;
				int m8 = 1;
				if (m2 / 2 * 2 == m2)
				{
					m8 = -1;
				}
				int imax = m2 - 2;
				for (int i = 1; i <= imax; i++)
				{
					double c6t = 2 * (m2 - i) * c2 / x - c3;
					c3 = c2;
					c2 = c6t;
					if (m2 - i - 1 == n)
					{
						b = c6t;
					}
					m8 = -1 * m8;
					if (m8 > 0)
					{
						c4 = c4 + 2 * c6t;
					}
				}
				double c6 = 2 * c2 / x - c3;
				if (n == 0)
				{
					b = c6;
				}
				c4 += c6;
				b /= c4;
				if (Math.Abs(b - b1) < d)
				{
					return b;
				}
				b1 = b;
				m2 += 3;
			}
		}
	}
}