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authormaxim-yurchuk <maxim-yurchuk@yandex-team.com>2025-02-11 13:26:52 +0300
committermaxim-yurchuk <maxim-yurchuk@yandex-team.com>2025-02-11 13:57:59 +0300
commitf895bba65827952ed934b2b46f9a45e30a191fd2 (patch)
tree03260c906d9ec41cdc03e2a496b15d407459cec0 /contrib/python/matplotlib/py3/extern/agg24-svn/include/agg_math.h
parent5f7060466f7b9707818c2091e1a25c14f33c3474 (diff)
downloadydb-f895bba65827952ed934b2b46f9a45e30a191fd2.tar.gz
Remove deps on pandas
<https://github.com/ydb-platform/ydb/pull/14418> <https://github.com/ydb-platform/ydb/pull/14419> \-- аналогичные правки в gh Хочу залить в обход синка, чтобы посмотреть удалится ли pandas в нашей gh репе через piglet commit_hash:abca127aa37d4dbb94b07e1e18cdb8eb5b711860
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-//----------------------------------------------------------------------------
-// Anti-Grain Geometry - Version 2.4
-// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
-//
-// 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
-//----------------------------------------------------------------------------
-
-#ifndef AGG_MATH_INCLUDED
-#define AGG_MATH_INCLUDED
-
-#include <math.h>
-#include "agg_basics.h"
-
-namespace agg
-{
-
- //------------------------------------------------------vertex_dist_epsilon
- // Coinciding points maximal distance (Epsilon)
- const double vertex_dist_epsilon = 1e-14;
-
- //-----------------------------------------------------intersection_epsilon
- // See calc_intersection
- const double intersection_epsilon = 1.0e-30;
-
- //------------------------------------------------------------cross_product
- AGG_INLINE 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
- AGG_INLINE 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
- AGG_INLINE double calc_distance(double x1, double y1, double x2, double y2)
- {
- double dx = x2-x1;
- double dy = y2-y1;
- return sqrt(dx * dx + dy * dy);
- }
-
- //--------------------------------------------------------calc_sq_distance
- AGG_INLINE 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
- AGG_INLINE 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 = 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
- AGG_INLINE 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
- AGG_INLINE 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
- AGG_INLINE 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
- AGG_INLINE bool calc_intersection(double ax, double ay, double bx, double by,
- double cx, double cy, double dx, double dy,
- double* x, double* y)
- {
- double num = (ay-cy) * (dx-cx) - (ax-cx) * (dy-cy);
- double den = (bx-ax) * (dy-cy) - (by-ay) * (dx-cx);
- if(fabs(den) < intersection_epsilon) return false;
- double r = num / den;
- *x = ax + r * (bx-ax);
- *y = ay + r * (by-ay);
- return true;
- }
-
- //-----------------------------------------------------intersection_exists
- AGG_INLINE 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(fabs(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
- AGG_INLINE void calc_orthogonal(double thickness,
- double x1, double y1,
- double x2, double y2,
- double* x, double* y)
- {
- double dx = x2 - x1;
- double dy = y2 - y1;
- double d = sqrt(dx*dx + dy*dy);
- *x = thickness * dy / d;
- *y = -thickness * dx / d;
- }
-
- //--------------------------------------------------------dilate_triangle
- AGG_INLINE 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(fabs(loc) > intersection_epsilon)
- {
- if(cross_product(x1, y1, x2, y2, x3, y3) > 0.0)
- {
- 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);
- }
- *x++ = x1 + dx1; *y++ = y1 + dy1;
- *x++ = x2 + dx1; *y++ = y2 + dy1;
- *x++ = x2 + dx2; *y++ = y2 + dy2;
- *x++ = x3 + dx2; *y++ = y3 + dy2;
- *x++ = x3 + dx3; *y++ = y3 + dy3;
- *x++ = x1 + dx3; *y++ = y1 + dy3;
- }
-
- //------------------------------------------------------calc_triangle_area
- AGG_INLINE 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
- template<class Storage> double calc_polygon_area(const Storage& st)
- {
- unsigned 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.size(); i++)
- {
- const typename Storage::value_type& 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
- extern int16u g_sqrt_table[1024];
- extern int8 g_elder_bit_table[256];
-
-
- //---------------------------------------------------------------fast_sqrt
- //Fast integer Sqrt - really fast: no cycles, divisions or multiplications
- #if defined(_MSC_VER)
- #pragma warning(push)
- #pragma warning(disable : 4035) //Disable warning "no return value"
- #endif
- AGG_INLINE unsigned fast_sqrt(unsigned val)
- {
- #if defined(_M_IX86) && defined(_MSC_VER) && !defined(AGG_NO_ASM)
- //For Ix86 family processors this assembler code is used.
- //The key command here is bsr - determination the number of the most
- //significant bit of the value. For other processors
- //(and maybe compilers) the pure C "#else" section is used.
- __asm
- {
- mov ebx, val
- mov edx, 11
- bsr ecx, ebx
- sub ecx, 9
- jle less_than_9_bits
- shr ecx, 1
- adc ecx, 0
- sub edx, ecx
- shl ecx, 1
- shr ebx, cl
- less_than_9_bits:
- xor eax, eax
- mov ax, g_sqrt_table[ebx*2]
- mov ecx, edx
- shr eax, cl
- }
- #else
-
- //This code is actually pure C and portable to most
- //arcitectures including 64bit ones.
- unsigned t = val;
- int bit=0;
- unsigned 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
- //faster (sic!) then just one "bsr". On PIII and PIV the
- //bsr is optimized quite well.
- bit = t >> 24;
- if(bit)
- {
- bit = g_elder_bit_table[bit] + 24;
- }
- else
- {
- bit = (t >> 16) & 0xFF;
- if(bit)
- {
- bit = g_elder_bit_table[bit] + 16;
- }
- else
- {
- bit = (t >> 8) & 0xFF;
- if(bit)
- {
- 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 -= bit;
- val >>= (bit << 1);
- }
- return g_sqrt_table[val] >> shift;
- #endif
- }
- #if defined(_MSC_VER)
- #pragma warning(pop)
- #endif
-
-
-
-
- //--------------------------------------------------------------------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)
- //------------------------------------------------------------------------
- inline double besj(double x, int n)
- {
- if(n < 0)
- {
- return 0;
- }
- double d = 1E-6;
- double b = 0;
- if(fabs(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)fabs(x) + 6;
- if(fabs(x) > 5)
- {
- m1 = (int)(fabs(1.4 * x + 60 / x));
- }
- int m2 = (int)(n + 2 + fabs(x) / 4);
- if (m1 > m2)
- {
- m2 = m1;
- }
-
- // Apply recurrence down from curent 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 c6 = 2 * (m2 - i) * c2 / x - c3;
- c3 = c2;
- c2 = c6;
- if(m2 - i - 1 == n)
- {
- b = c6;
- }
- m8 = -1 * m8;
- if (m8 > 0)
- {
- c4 = c4 + 2 * c6;
- }
- }
- double c6 = 2 * c2 / x - c3;
- if(n == 0)
- {
- b = c6;
- }
- c4 += c6;
- b /= c4;
- if(fabs(b - b1) < d)
- {
- return b;
- }
- b1 = b;
- m2 += 3;
- }
- }
-
-}
-
-
-#endif