1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
|
//----------------------------------------------------------------------------
// Anti-Grain Geometry - Version 2.3
// 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
//----------------------------------------------------------------------------
#ifndef AGG_MATH_INCLUDED
#define AGG_MATH_INCLUDED
#include <math.h>
#include "agg_basics.h"
namespace agg
{
const double intersection_epsilon = 1.0e-8;
//------------------------------------------------------calc_point_location
AGG_INLINE double calc_point_location(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 = calc_point_location(x1, y1, x2, y2, x, y) < 0.0;
bool cp2 = calc_point_location(x2, y2, x3, y3, x, y) < 0.0;
bool cp3 = calc_point_location(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_point_line_distance
AGG_INLINE double calc_point_line_distance(double x1, double y1,
double x2, double y2,
double x, double y)
{
double dx = x2-x1;
double dy = y2-y1;
return ((x - x2) * dy - (y - y2) * dx) / sqrt(dx * dx + dy * dy);
}
//-------------------------------------------------------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;
}
//--------------------------------------------------------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 = calc_point_location(x1, y1, x2, y2, x3, y3);
if(fabs(loc) > intersection_epsilon)
{
if(calc_point_location(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_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 is calculation sqrt itself.
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
}
#endif
|
