libgender/util.C

/*
 * math support
 * most of the more complicated code is taken from mesa.
 */

#include <cstdio> // ugly
#include <cmath>

#include <sys/time.h>
#include <time.h>

#include "util.h"

#define DEG2RAD (M_PI / 180.)

void renormalize (sector &s, point &p)
{
  float i;

  p.x = modff (p.x, &i); s.x += (int)i;
  p.y = modff (p.y, &i); s.y += (int)i;
  p.z = modff (p.z, &i); s.z += (int)i;
}

/////////////////////////////////////////////////////////////////////////////

const vec3 normalize (const vec3 &v)
{
  GLfloat s = abs (v);

  if (!s)
    return v;

  s = 1. / s;
  return vec3 (v.x * s, v.y * s, v.z * s);
}

const vec3 cross (const vec3 &a, const vec3 &b)
{
  return vec3 (
     a.y * b.z - a.z * b.y,
     a.z * b.x - a.x * b.z,
     a.x * b.y - a.y * b.x
  );
}

/////////////////////////////////////////////////////////////////////////////

void gl_matrix::diagonal (GLfloat v)
{
  for (int i = 4; i--; )
    for (int j = 4; j--; )
      data[i][j] = i == j ? v : 0.;
}

const gl_matrix operator *(const gl_matrix &a, const gl_matrix &b)
{
  gl_matrix r;

  // taken from mesa
  for (int i = 0; i < 4; i++)
    {
      const GLfloat ai0=a(i,0), ai1=a(i,1), ai2=a(i,2), ai3=a(i,3);

      r(i,0) = ai0 * b(0,0) + ai1 * b(1,0) + ai2 * b(2,0) + ai3 * b(3,0);
      r(i,1) = ai0 * b(0,1) + ai1 * b(1,1) + ai2 * b(2,1) + ai3 * b(3,1);
      r(i,2) = ai0 * b(0,2) + ai1 * b(1,2) + ai2 * b(2,2) + ai3 * b(3,2);
      r(i,3) = ai0 * b(0,3) + ai1 * b(1,3) + ai2 * b(2,3) + ai3 * b(3,3);
    }

  return r;
}

const gl_matrix gl_matrix::rotation (GLfloat angle, const vec3 &axis)
{
  GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;

  s = (GLfloat) sinf (angle * DEG2RAD);
  c = (GLfloat) cosf (angle * DEG2RAD);

  const GLfloat mag = abs (axis);

  if (mag <= 1.0e-4)
    return gl_matrix (1);

  gl_matrix m;
  const vec3 n = axis * (1. / mag);

  /*
   *     Arbitrary axis rotation matrix.
   *
   *  This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
   *  like so:  Rz * Ry * T * Ry' * Rz'.  T is the final rotation
   *  (which is about the X-axis), and the two composite transforms
   *  Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
   *  from the arbitrary axis to the X-axis then back.  They are
   *  all elementary rotations.
   *
   *  Rz' is a rotation about the Z-axis, to bring the axis vector
   *  into the x-z plane.  Then Ry' is applied, rotating about the
   *  Y-axis to bring the axis vector parallel with the X-axis.  The
   *  rotation about the X-axis is then performed.  Ry and Rz are
   *  simply the respective inverse transforms to bring the arbitrary
   *  axis back to it's original orientation.  The first transforms
   *  Rz' and Ry' are considered inverses, since the data from the
   *  arbitrary axis gives you info on how to get to it, not how
   *  to get away from it, and an inverse must be applied.
   *
   *  The basic calculation used is to recognize that the arbitrary
   *  axis vector (x, y, z), since it is of unit length, actually
   *  represents the sines and cosines of the angles to rotate the
   *  X-axis to the same orientation, with theta being the angle about
   *  Z and phi the angle about Y (in the order described above)
   *  as follows:
   *
   *  cos ( theta ) = x / sqrt ( 1 - z^2 )
   *  sin ( theta ) = y / sqrt ( 1 - z^2 )
   *
   *  cos ( phi ) = sqrt ( 1 - z^2 )
   *  sin ( phi ) = z
   *
   *  Note that cos ( phi ) can further be inserted to the above
   *  formulas:
   *
   *  cos ( theta ) = x / cos ( phi )
   *  sin ( theta ) = y / sin ( phi )
   *
   *  ...etc.  Because of those relations and the standard trigonometric
   *  relations, it is pssible to reduce the transforms down to what
   *  is used below.  It may be that any primary axis chosen will give the
   *  same results (modulo a sign convention) using this method.
   *
   *  Particularly nice is to notice that all divisions that might
   *  have caused trouble when parallel to certain planes or
   *  axis go away with care paid to reducing the expressions.
   *  After checking, it does perform correctly under all cases, since
   *  in all the cases of division where the denominator would have
   *  been zero, the numerator would have been zero as well, giving
   *  the expected result.
   */

  xx = n.x * n.x;
  yy = n.y * n.y;
  zz = n.z * n.z;
  xy = n.x * n.y;
  yz = n.y * n.z;
  zx = n.z * n.x;
  xs = n.x * s;
  ys = n.y * s;
  zs = n.z * s;
  one_c = 1.0F - c;

  m(0,0) = (one_c * xx) + c;
  m(0,1) = (one_c * xy) - zs;
  m(0,2) = (one_c * zx) + ys;
  m(0,3) = 0;
  
  m(1,0) = (one_c * xy) + zs;
  m(1,1) = (one_c * yy) + c;
  m(1,2) = (one_c * yz) - xs;
  m(1,3) = 0;
  
  m(2,0) = (one_c * zx) - ys;
  m(2,1) = (one_c * yz) + xs;
  m(2,2) = (one_c * zz) + c;
  m(2,3) = 0;
  
  m(3,0) = 0;
  m(3,1) = 0;
  m(3,2) = 0;
  m(3,3) = 1;

  return m;
}

const vec3 operator *(const gl_matrix &a, const vec3 &v)
{
  return vec3 (
    a(0,0) * v.x + a(0,1) * v.y + a(0,2) * v.z + a(0,3),
    a(1,0) * v.x + a(1,1) * v.y + a(1,2) * v.z + a(1,3),
    a(2,0) * v.x + a(2,1) * v.y + a(2,2) * v.z + a(2,3)
  );
}

void gl_matrix::print ()
{
  printf ("\n");
  printf ("[ %f, %f, %f, %f ]\n", data[0][0], data[1][0], data[2][0], data[3][0]);
  printf ("[ %f, %f, %f, %f ]\n", data[0][1], data[1][1], data[2][1], data[3][1]);
  printf ("[ %f, %f, %f, %f ]\n", data[0][2], data[1][2], data[2][2], data[3][2]);
  printf ("[ %f, %f, %f, %f ]\n", data[0][3], data[1][3], data[2][3], data[3][3]);
}

const gl_matrix gl_matrix::translation (const vec3 &v)
{
  gl_matrix m(1);

  m(0,3) = v.x;
  m(1,3) = v.y;
  m(2,3) = v.z;

  return m;
}

/////////////////////////////////////////////////////////////////////////////

plane::plane (GLfloat a, GLfloat b, GLfloat c, GLfloat d)
: n (vec3 (a,b,c))
{
  GLfloat s = 1. / abs (n);

  n = n * s;
  this->d = d * s;
}

/////////////////////////////////////////////////////////////////////////////

void box::add (const box &o)
{
  a.x = min (a.x, o.a.x);
  a.y = min (a.y, o.a.y);
  a.z = min (a.z, o.a.z);
  b.x = max (b.x, o.b.x);
  b.y = max (b.y, o.b.y);
  b.z = max (b.z, o.b.z);
}

void box::add (const sector &p)
{
  a.x = min (a.x, p.x);
  a.y = min (a.y, p.y);
  a.z = min (a.z, p.z);
  b.x = max (b.x, p.x);
  b.y = max (b.y, p.y);
  b.z = max (b.z, p.z);
}

void box::add (const point &p)
{
  a.x = min (a.x, (soffs)floorf (p.x));
  a.y = min (a.y, (soffs)floorf (p.y));
  a.z = min (a.z, (soffs)floorf (p.z));
  b.x = max (b.x, (soffs)ceilf  (p.x));
  b.y = max (b.y, (soffs)ceilf  (p.y));
  b.z = max (b.z, (soffs)ceilf  (p.z));
}

/////////////////////////////////////////////////////////////////////////////

struct timer timer;
static double base;
double timer::now = 0.;
double timer::diff;

void timer::frame ()
{
  struct timeval tv;
  gettimeofday (&tv, 0);

  double next = tv.tv_sec - base + tv.tv_usec / 1.e6;

  diff = next - now;
  now = next;
}

timer::timer ()
{
  struct timeval tv;
  gettimeofday (&tv, 0);
  base = tv.tv_sec + tv.tv_usec / 1.e6;
}

//skedjuhlar main_scheduler;
Revision:	1.10
Committed:	Tue Oct 5 01:18:57 2004 UTC (19 years, 8 months ago) by root
Content type:	text/plain
Branch:	MAIN
Changes since 1.9:	+1 -1 lines
Log Message:	* empty log message *
#	User	Rev	Content
1	root	1.3	/*
2			* math support
3			* most of the more complicated code is taken from mesa.
4			*/
5
6	root	1.2	#include <cstdio> // ugly
7	root	1.1	#include <cmath>
8
9	root	1.4	#include <sys/time.h>
10			#include <time.h>
11	root	1.2
12	root	1.1	#include "util.h"
13
14	root	1.3	#define DEG2RAD (M_PI / 180.)
15
16	root	1.6	void renormalize (sector &s, point &p)
17			{
18			float i;
19
20			p.x = modff (p.x, &i); s.x += (int)i;
21			p.y = modff (p.y, &i); s.y += (int)i;
22			p.z = modff (p.z, &i); s.z += (int)i;
23			}
24
25	root	1.7	/////////////////////////////////////////////////////////////////////////////
26
27	root	1.1	const vec3 normalize (const vec3 &v)
28			{
29	root	1.3	GLfloat s = abs (v);
30
31			if (!s)
32			return v;
33	root	1.1
34	root	1.3	s = 1. / s;
35	root	1.1	return vec3 (v.x * s, v.y * s, v.z * s);
36			}
37
38			const vec3 cross (const vec3 &a, const vec3 &b)
39			{
40			return vec3 (
41	root	1.3	a.y * b.z - a.z * b.y,
42			a.z * b.x - a.x * b.z,
43			a.x * b.y - a.y * b.x
44			);
45	root	1.2	}
46
47	root	1.7	/////////////////////////////////////////////////////////////////////////////
48
49	root	1.2	void gl_matrix::diagonal (GLfloat v)
50			{
51			for (int i = 4; i--; )
52			for (int j = 4; j--; )
53			data[i][j] = i == j ? v : 0.;
54			}
55
56			const gl_matrix operator *(const gl_matrix &a, const gl_matrix &b)
57			{
58			gl_matrix r;
59
60	root	1.3	// taken from mesa
61			for (int i = 0; i < 4; i++)
62			{
63			const GLfloat ai0=a(i,0), ai1=a(i,1), ai2=a(i,2), ai3=a(i,3);
64
65			r(i,0) = ai0 * b(0,0) + ai1 * b(1,0) + ai2 * b(2,0) + ai3 * b(3,0);
66			r(i,1) = ai0 * b(0,1) + ai1 * b(1,1) + ai2 * b(2,1) + ai3 * b(3,1);
67			r(i,2) = ai0 * b(0,2) + ai1 * b(1,2) + ai2 * b(2,2) + ai3 * b(3,2);
68			r(i,3) = ai0 * b(0,3) + ai1 * b(1,3) + ai2 * b(2,3) + ai3 * b(3,3);
69			}
70	root	1.2
71	root	1.3	return r;
72			}
73	root	1.2
74	root	1.9	const gl_matrix gl_matrix::rotation (GLfloat angle, const vec3 &axis)
75	root	1.3	{
76			GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
77	root	1.2
78	root	1.3	s = (GLfloat) sinf (angle * DEG2RAD);
79			c = (GLfloat) cosf (angle * DEG2RAD);
80
81			const GLfloat mag = abs (axis);
82
83			if (mag <= 1.0e-4)
84	root	1.9	return gl_matrix (1);
85	root	1.3
86	root	1.9	gl_matrix m;
87	root	1.3	const vec3 n = axis * (1. / mag);
88
89			/*
90			* Arbitrary axis rotation matrix.
91			*
92			* This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
93			* like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
94			* (which is about the X-axis), and the two composite transforms
95			* Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
96			* from the arbitrary axis to the X-axis then back. They are
97			* all elementary rotations.
98			*
99			* Rz' is a rotation about the Z-axis, to bring the axis vector
100			* into the x-z plane. Then Ry' is applied, rotating about the
101			* Y-axis to bring the axis vector parallel with the X-axis. The
102			* rotation about the X-axis is then performed. Ry and Rz are
103			* simply the respective inverse transforms to bring the arbitrary
104			* axis back to it's original orientation. The first transforms
105			* Rz' and Ry' are considered inverses, since the data from the
106			* arbitrary axis gives you info on how to get to it, not how
107			* to get away from it, and an inverse must be applied.
108			*
109			* The basic calculation used is to recognize that the arbitrary
110			* axis vector (x, y, z), since it is of unit length, actually
111			* represents the sines and cosines of the angles to rotate the
112			* X-axis to the same orientation, with theta being the angle about
113			* Z and phi the angle about Y (in the order described above)
114			* as follows:
115			*
116			* cos ( theta ) = x / sqrt ( 1 - z^2 )
117			* sin ( theta ) = y / sqrt ( 1 - z^2 )
118			*
119			* cos ( phi ) = sqrt ( 1 - z^2 )
120			* sin ( phi ) = z
121			*
122			* Note that cos ( phi ) can further be inserted to the above
123			* formulas:
124			*
125			* cos ( theta ) = x / cos ( phi )
126			* sin ( theta ) = y / sin ( phi )
127			*
128			* ...etc. Because of those relations and the standard trigonometric
129			* relations, it is pssible to reduce the transforms down to what
130			* is used below. It may be that any primary axis chosen will give the
131			* same results (modulo a sign convention) using this method.
132			*
133			* Particularly nice is to notice that all divisions that might
134			* have caused trouble when parallel to certain planes or
135			* axis go away with care paid to reducing the expressions.
136			* After checking, it does perform correctly under all cases, since
137			* in all the cases of division where the denominator would have
138			* been zero, the numerator would have been zero as well, giving
139			* the expected result.
140			*/
141
142			xx = n.x * n.x;
143			yy = n.y * n.y;
144			zz = n.z * n.z;
145			xy = n.x * n.y;
146			yz = n.y * n.z;
147			zx = n.z * n.x;
148			xs = n.x * s;
149			ys = n.y * s;
150			zs = n.z * s;
151			one_c = 1.0F - c;
152
153			m(0,0) = (one_c * xx) + c;
154			m(0,1) = (one_c * xy) - zs;
155			m(0,2) = (one_c * zx) + ys;
156			m(0,3) = 0;
157
158			m(1,0) = (one_c * xy) + zs;
159			m(1,1) = (one_c * yy) + c;
160			m(1,2) = (one_c * yz) - xs;
161			m(1,3) = 0;
162
163			m(2,0) = (one_c * zx) - ys;
164			m(2,1) = (one_c * yz) + xs;
165			m(2,2) = (one_c * zz) + c;
166			m(2,3) = 0;
167
168			m(3,0) = 0;
169			m(3,1) = 0;
170			m(3,2) = 0;
171			m(3,3) = 1;
172
173	root	1.9	return m;
174	root	1.3	}
175
176			const vec3 operator *(const gl_matrix &a, const vec3 &v)
177			{
178			return vec3 (
179	root	1.9	a(0,0) * v.x + a(0,1) * v.y + a(0,2) * v.z + a(0,3),
180			a(1,0) * v.x + a(1,1) * v.y + a(1,2) * v.z + a(1,3),
181			a(2,0) * v.x + a(2,1) * v.y + a(2,2) * v.z + a(2,3)
182	root	1.3	);
183	root	1.2	}
184
185			void gl_matrix::print ()
186			{
187			printf ("\n");
188			printf ("[ %f, %f, %f, %f ]\n", data[0][0], data[1][0], data[2][0], data[3][0]);
189			printf ("[ %f, %f, %f, %f ]\n", data[0][1], data[1][1], data[2][1], data[3][1]);
190			printf ("[ %f, %f, %f, %f ]\n", data[0][2], data[1][2], data[2][2], data[3][2]);
191			printf ("[ %f, %f, %f, %f ]\n", data[0][3], data[1][3], data[2][3], data[3][3]);
192			}
193
194	root	1.9	const gl_matrix gl_matrix::translation (const vec3 &v)
195	root	1.2	{
196			gl_matrix m(1);
197
198	root	1.9	m(0,3) = v.x;
199			m(1,3) = v.y;
200			m(2,3) = v.z;
201	root	1.2
202	root	1.9	return m;
203	root	1.1	}
204
205	root	1.7	/////////////////////////////////////////////////////////////////////////////
206
207			plane::plane (GLfloat a, GLfloat b, GLfloat c, GLfloat d)
208	root	1.9	: n (vec3 (a,b,c))
209	root	1.7	{
210			GLfloat s = 1. / abs (n);
211
212			n = n * s;
213	root	1.9	this->d = d * s;
214	root	1.7	}
215
216			/////////////////////////////////////////////////////////////////////////////
217
218	root	1.1	void box::add (const box &o)
219			{
220			a.x = min (a.x, o.a.x);
221			a.y = min (a.y, o.a.y);
222			a.z = min (a.z, o.a.z);
223			b.x = max (b.x, o.b.x);
224			b.y = max (b.y, o.b.y);
225			b.z = max (b.z, o.b.z);
226			}
227
228	root	1.5	void box::add (const sector &p)
229	root	1.1	{
230			a.x = min (a.x, p.x);
231			a.y = min (a.y, p.y);
232			a.z = min (a.z, p.z);
233			b.x = max (b.x, p.x);
234			b.y = max (b.y, p.y);
235			b.z = max (b.z, p.z);
236	root	1.5	}
237
238			void box::add (const point &p)
239			{
240			a.x = min (a.x, (soffs)floorf (p.x));
241			a.y = min (a.y, (soffs)floorf (p.y));
242			a.z = min (a.z, (soffs)floorf (p.z));
243	root	1.6	b.x = max (b.x, (soffs)ceilf (p.x));
244			b.y = max (b.y, (soffs)ceilf (p.y));
245			b.z = max (b.z, (soffs)ceilf (p.z));
246	root	1.1	}
247	root	1.7
248			/////////////////////////////////////////////////////////////////////////////
249	root	1.4
250			struct timer timer;
251			static double base;
252			double timer::now = 0.;
253			double timer::diff;
254
255			void timer::frame ()
256			{
257			struct timeval tv;
258			gettimeofday (&tv, 0);
259
260			double next = tv.tv_sec - base + tv.tv_usec / 1.e6;
261
262			diff = next - now;
263			now = next;
264			}
265
266			timer::timer ()
267			{
268			struct timeval tv;
269			gettimeofday (&tv, 0);
270			base = tv.tv_sec + tv.tv_usec / 1.e6;
271			}
272
273	root	1.10	//skedjuhlar main_scheduler;