//----------------------------------------------------------------------------
// Anti-Grain Geometry (AGG) - Version 2.5
// A high quality rendering engine for C++
// Copyright (C) 2002-2006 Maxim Shemanarev
// Contact: mcseem@antigrain.com
// mcseemagg@yahoo.com
// http://antigrain.com
//
// AGG is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 2
// of the License, or (at your option) any later version.
//
// AGG is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with AGG; if not, write to the Free Software
// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
// MA 02110-1301, USA.
//----------------------------------------------------------------------------
// 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
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