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/* |
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* math support |
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* most of the more complicated code is taken from mesa. |
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*/ |
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|
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#include <cstdio> // ugly |
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|
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#include <cmath> |
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|
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#include <blitz/tinymat.h> |
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|
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using namespace blitz; |
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|
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#include "util.h" |
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|
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#define DEG2RAD (M_PI / 180.) |
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|
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const vec3 normalize (const vec3 &v) |
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{ |
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GLfloat s = abs (v); |
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|
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if (!s) |
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return v; |
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|
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s = 1. / s; |
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return vec3 (v.x * s, v.y * s, v.z * s); |
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} |
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|
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const vec3 cross (const vec3 &a, const vec3 &b) |
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{ |
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return vec3 ( |
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a.y * b.z - a.z * b.y, |
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a.z * b.x - a.x * b.z, |
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a.x * b.y - a.y * b.x |
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); |
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} |
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|
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void gl_matrix::diagonal (GLfloat v) |
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{ |
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for (int i = 4; i--; ) |
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for (int j = 4; j--; ) |
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data[i][j] = i == j ? v : 0.; |
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} |
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|
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const gl_matrix operator *(const gl_matrix &a, const gl_matrix &b) |
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{ |
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gl_matrix r; |
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|
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// taken from mesa |
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for (int i = 0; i < 4; i++) |
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{ |
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const GLfloat ai0=a(i,0), ai1=a(i,1), ai2=a(i,2), ai3=a(i,3); |
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|
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r(i,0) = ai0 * b(0,0) + ai1 * b(1,0) + ai2 * b(2,0) + ai3 * b(3,0); |
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r(i,1) = ai0 * b(0,1) + ai1 * b(1,1) + ai2 * b(2,1) + ai3 * b(3,1); |
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r(i,2) = ai0 * b(0,2) + ai1 * b(1,2) + ai2 * b(2,2) + ai3 * b(3,2); |
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r(i,3) = ai0 * b(0,3) + ai1 * b(1,3) + ai2 * b(2,3) + ai3 * b(3,3); |
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} |
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|
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return r; |
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} |
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|
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void gl_matrix::rotate (GLfloat angle, const vec3 &axis) |
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{ |
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gl_matrix m; |
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GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c; |
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|
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s = (GLfloat) sinf (angle * DEG2RAD); |
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c = (GLfloat) cosf (angle * DEG2RAD); |
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|
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const GLfloat mag = abs (axis); |
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|
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if (mag <= 1.0e-4) |
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return; /* no rotation, leave mat as-is */ |
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|
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const vec3 n = axis * (1. / mag); |
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|
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/* |
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* Arbitrary axis rotation matrix. |
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* |
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* This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied |
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* like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation |
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* (which is about the X-axis), and the two composite transforms |
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* Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary |
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* from the arbitrary axis to the X-axis then back. They are |
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* all elementary rotations. |
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* |
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* Rz' is a rotation about the Z-axis, to bring the axis vector |
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* into the x-z plane. Then Ry' is applied, rotating about the |
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* Y-axis to bring the axis vector parallel with the X-axis. The |
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* rotation about the X-axis is then performed. Ry and Rz are |
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* simply the respective inverse transforms to bring the arbitrary |
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* axis back to it's original orientation. The first transforms |
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* Rz' and Ry' are considered inverses, since the data from the |
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* arbitrary axis gives you info on how to get to it, not how |
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* to get away from it, and an inverse must be applied. |
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* |
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* The basic calculation used is to recognize that the arbitrary |
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* axis vector (x, y, z), since it is of unit length, actually |
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* represents the sines and cosines of the angles to rotate the |
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* X-axis to the same orientation, with theta being the angle about |
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* Z and phi the angle about Y (in the order described above) |
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* as follows: |
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* |
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* cos ( theta ) = x / sqrt ( 1 - z^2 ) |
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* sin ( theta ) = y / sqrt ( 1 - z^2 ) |
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* |
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* cos ( phi ) = sqrt ( 1 - z^2 ) |
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* sin ( phi ) = z |
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* |
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* Note that cos ( phi ) can further be inserted to the above |
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* formulas: |
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* |
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* cos ( theta ) = x / cos ( phi ) |
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* sin ( theta ) = y / sin ( phi ) |
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* |
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* ...etc. Because of those relations and the standard trigonometric |
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* relations, it is pssible to reduce the transforms down to what |
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* is used below. It may be that any primary axis chosen will give the |
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* same results (modulo a sign convention) using this method. |
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* |
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* Particularly nice is to notice that all divisions that might |
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* have caused trouble when parallel to certain planes or |
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* axis go away with care paid to reducing the expressions. |
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* After checking, it does perform correctly under all cases, since |
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* in all the cases of division where the denominator would have |
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* been zero, the numerator would have been zero as well, giving |
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* the expected result. |
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*/ |
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|
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xx = n.x * n.x; |
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yy = n.y * n.y; |
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zz = n.z * n.z; |
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xy = n.x * n.y; |
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yz = n.y * n.z; |
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zx = n.z * n.x; |
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xs = n.x * s; |
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ys = n.y * s; |
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zs = n.z * s; |
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one_c = 1.0F - c; |
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|
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m(0,0) = (one_c * xx) + c; |
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m(0,1) = (one_c * xy) - zs; |
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m(0,2) = (one_c * zx) + ys; |
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m(0,3) = 0; |
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|
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m(1,0) = (one_c * xy) + zs; |
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m(1,1) = (one_c * yy) + c; |
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m(1,2) = (one_c * yz) - xs; |
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m(1,3) = 0; |
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|
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m(2,0) = (one_c * zx) - ys; |
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m(2,1) = (one_c * yz) + xs; |
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m(2,2) = (one_c * zz) + c; |
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m(2,3) = 0; |
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|
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m(3,0) = 0; |
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m(3,1) = 0; |
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m(3,2) = 0; |
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m(3,3) = 1; |
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|
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(*this) = (*this) * m; |
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} |
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|
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const vec3 operator *(const gl_matrix &a, const vec3 &v) |
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{ |
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return vec3 ( |
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a(0,0) * v.x + a(1,0) * v.y + a(2,0) * v.z + a(3,0), |
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a(0,1) * v.x + a(1,1) * v.y + a(2,1) * v.z + a(3,1), |
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a(0,2) * v.x + a(1,2) * v.y + a(2,2) * v.z + a(3,2) |
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); |
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} |
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|
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void gl_matrix::print () |
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{ |
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printf ("\n"); |
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printf ("[ %f, %f, %f, %f ]\n", data[0][0], data[1][0], data[2][0], data[3][0]); |
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printf ("[ %f, %f, %f, %f ]\n", data[0][1], data[1][1], data[2][1], data[3][1]); |
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printf ("[ %f, %f, %f, %f ]\n", data[0][2], data[1][2], data[2][2], data[3][2]); |
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printf ("[ %f, %f, %f, %f ]\n", data[0][3], data[1][3], data[2][3], data[3][3]); |
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} |
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|
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void gl_matrix::translate (const vec3 &v) |
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{ |
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gl_matrix m(1); |
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|
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m(3,0) = v.x; |
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m(3,1) = v.y; |
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m(3,2) = v.z; |
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m(3,3) = 1; |
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|
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(*this) = (*this) * m; |
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} |
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|
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void box::add (const box &o) |
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{ |
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a.x = min (a.x, o.a.x); |
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a.y = min (a.y, o.a.y); |
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a.z = min (a.z, o.a.z); |
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b.x = max (b.x, o.b.x); |
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b.y = max (b.y, o.b.y); |
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b.z = max (b.z, o.b.z); |
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} |
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|
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void box::add (const point &p) |
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{ |
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a.x = min (a.x, p.x); |
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a.y = min (a.y, p.y); |
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a.z = min (a.z, p.z); |
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b.x = max (b.x, p.x); |
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b.y = max (b.y, p.y); |
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b.z = max (b.z, p.z); |
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} |
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|
