void rot_axis (gleDouble omega, /* input */ gleDouble axis[3]) /* input */ { gleDouble m[4][4]; urot_axis (m, omega, axis); MULTMATRIX (m); }
void urot_about_axis (gleDouble m[4][4], /* returned */ gleDouble angle, /* input */ gleDouble axis[3]) /* input */ { gleDouble len, ax[3]; angle *= M_PI/180.0; /* convert to radians */ /* renormalize axis vector, if needed */ len = axis[0]*axis[0] + axis[1]*axis[1] + axis[2]*axis[2]; /* we can save some machine instructions by normalizing only * if needed. The compiler should be able to schedule in the * if test "for free". */ if (len != 1.0) { len = (gleDouble) (1.0 / sqrt ((double) len)); ax[0] = axis[0] * len; ax[1] = axis[1] * len; ax[2] = axis[2] * len; urot_axis (m, angle, ax); } else { urot_axis (m, angle, axis); } }
void urot_omega (gleDouble m[4][4], /* returned */ gleDouble axis[3]) /* input */ { gleDouble len, ax[3]; /* normalize axis vector */ len = axis[0]*axis[0] + axis[1]*axis[1] + axis[2]*axis[2]; len = (gleDouble) (1.0 / sqrt ((double) len)); ax[0] = axis[0] * len; ax[1] = axis[1] * len; ax[2] = axis[2] * len; /* the amount of rotation is equal to the length, in radians */ urot_axis (m, len, ax); }
/* * The uview_dire subroutine computes and returns a 4x4 rotation * matrix that puts the negative z axis along the direction v21 and * puts the y axis along the up vector. * * It computes exactly the same matrix as the code above * (uview_direction), but with an entirely different (and slower) * algorithm. * * Note that the code below is slightly less robust than that above -- * it may croak if the supplied vectors are of zero length, or are * parallel to each other ... */ void uview_dire (float m[4][4], /* returned */ float v21[3], /* input */ float up[3]) /* input */ { gleDouble theta; float v_hat_21 [3]; float z_hat [3]; float v_cross_z [3]; float u[3]; float y_hat [3]; float u_cross_y [3]; gleDouble cosine; float zmat [4][4]; float upmat[4][4]; float dot; /* perform rotation to z-axis only if not already * pointing down z */ if ((v21[0] != 0.0 ) || (v21[1] != 0.0)) { /* find the unit vector that points in the v21 direction */ VEC_COPY (v_hat_21, v21); VEC_NORMALIZE (v_hat_21); /* cosine theta equals v_hat dot z_hat */ cosine = - v_hat_21 [2]; theta = - acos (cosine); /* Take cros product with z -- we need this, because we will rotate * about this axis */ z_hat[0] = 0.0; z_hat[1] = 0.0; z_hat[2] = -1.0; VEC_CROSS_PRODUCT (v_cross_z, v_hat_21, z_hat); VEC_NORMALIZE (v_cross_z); /* compute rotation matrix that takes -z axis to the v21 axis */ urot_axis (zmat, (float) theta, v_cross_z); } else { IDENTIFY_MATRIX_4X4 (zmat); if (v21[2] > 0.0) { /* if its pointing down the positive z-axis, flip it, so that * we point down negative z-axis. We flip x so that the partiy * isn't destroyed (looks like a rotation) */ zmat[0][0] = -1.0; zmat[2][2] = -1.0; } } /* --------------------- */ /* OK, now compute the part that takes the y-axis to the up vector */ VEC_COPY (u, up); /* the rotation blows up, if the up vector is not perpendicular to * the v21 vector. Let us make sure that this is so. */ VEC_PERP (u, u, v_hat_21); /* need to run the y axis through above x-form, to see where it went */ y_hat[0] = zmat [1][0]; y_hat[1] = zmat [1][1]; y_hat[2] = zmat [1][2]; /* perform rotation to up-axis only if not already * pointing along y axis */ VEC_DOT_PRODUCT (dot, y_hat, u); if ((-1.0 < dot) && (dot < 1.0)) { /* make sure that up really is a unit vector */ VEC_NORMALIZE (u); /* cosine phi equals y_hat dot up_vec */ VEC_DOT_PRODUCT (cosine, u, y_hat); theta = - acos (cosine); /* Take cross product with y */ VEC_CROSS_PRODUCT (u_cross_y, u, y_hat); VEC_NORMALIZE (u_cross_y); /* As a matter of fact, u_cross_y points either in the v21 direction, * or in the minus v21 direction. In either case, we needed to compute * it, because the the arccosine function returns values only for * 0 to 180 degree, not 0 to 360, which is what we need. The * cross-product helps us make up for this. */ /* rotate about the NEW z axis (i.e. v21) by the cosine */ urot_axis (upmat, (float) theta, u_cross_y); } else { IDENTIFY_MATRIX_4X4 (upmat); if (dot == -1.0) { /* if its pointing along the negative y-axis, flip it, so that * we point along the positive y-axis. We flip x so that the partiy * isn't destroyed (looks like a rotation) */ upmat[0][0] = -1.0; upmat[1][1] = -1.0; } } MATRIX_PRODUCT_4X4 (m, zmat, upmat); }
void draw_round_style_cap_callback (int ncp, double cap[][3], gleColor face_color, gleDouble cut[3], gleDouble bi[3], double norms[][3], int frontwards) { double axis[3]; double xycut[3]; double theta; double *last_contour, *next_contour; double *last_norm, *next_norm; double *cap_z; double *tmp; char *malloced_area; int i, j, k; double m[4][4]; if (face_color != NULL) C3F (face_color); /* ------------ start setting up rotation matrix ------------- */ /* if the cut vector is NULL (this should only occur in * a degenerate case), then we can't draw anything. return. */ if (cut == NULL) return; /* make sure that the cut vector points inwards */ if (cut[2] > 0.0) { VEC_SCALE (cut, -1.0, cut); } /* make sure that the bi vector points outwards */ if (bi[2] < 0.0) { VEC_SCALE (bi, -1.0, bi); } /* determine the axis we are to rotate about to get bi-contour. * Note that the axis will always lie in the x-y plane */ VEC_CROSS_PRODUCT (axis, cut, bi); /* reverse the cut vector for the back cap -- * need to do this to get angle right */ if (!frontwards) { VEC_SCALE (cut, -1.0, cut); } /* get angle to rotate by -- arccos of dot product of cut with cut * projected into the x-y plane */ xycut [0] = 0.0; xycut [1] = 0.0; xycut [2] = 1.0; VEC_PERP (xycut, cut, xycut); VEC_NORMALIZE (xycut); VEC_DOT_PRODUCT (theta, xycut, cut); theta = acos (theta); /* we'll tesselate round joins into a number of teeny pieces */ theta /= (double) __ROUND_TESS_PIECES; /* get the matrix */ urot_axis (m, theta, axis); /* ------------ done setting up rotation matrix ------------- */ /* This malloc is a fancy version of: * last_contour = (double *) malloc (3*ncp*sizeof(double); * next_contour = (double *) malloc (3*ncp*sizeof(double); */ malloced_area = malloc ((4*3+1) *ncp*sizeof (double)); last_contour = (double *) malloced_area; next_contour = last_contour + 3*ncp; cap_z = next_contour + 3*ncp; last_norm = cap_z + ncp; next_norm = last_norm + 3*ncp; /* make first copy of contour */ if (frontwards) { for (j=0; j<ncp; j++) { last_contour[3*j] = cap[j][0]; last_contour[3*j+1] = cap[j][1]; last_contour[3*j+2] = cap_z[j] = cap[j][2]; } if (norms != NULL) { for (j=0; j<ncp; j++) { VEC_COPY ((&last_norm[3*j]), norms[j]); } } } else { /* in order for backfacing polygon removal to work correctly, have * to have the sense in which the joins are drawn to be reversed * for the back cap. This can be done by reversing the order of * the contour points. Normals are a bit trickier, since the * reversal is off-by-one for facet normals as compared to edge * normals. */ for (j=0; j<ncp; j++) { k = ncp - j - 1; last_contour[3*k] = cap[j][0]; last_contour[3*k+1] = cap[j][1]; last_contour[3*k+2] = cap_z[k] = cap[j][2]; } if (norms != NULL) { if (__TUBE_DRAW_FACET_NORMALS) { for (j=0; j<ncp-1; j++) { k = ncp - j - 2; VEC_COPY ((&last_norm[3*k]), norms[j]); } } else { for (j=0; j<ncp; j++) { k = ncp - j - 1; VEC_COPY ((&last_norm[3*k]), norms[j]); } } } } /* &&&&&&&&&&&&&& start drawing cap &&&&&&&&&&&&& */ for (i=0; i<__ROUND_TESS_PIECES; i++) { for (j=0; j<ncp; j++) { next_contour [3*j+2] -= cap_z[j]; last_contour [3*j+2] -= cap_z[j]; MAT_DOT_VEC_3X3 ( (&next_contour[3*j]), m, (&last_contour[3*j])); next_contour [3*j+2] += cap_z[j]; last_contour [3*j+2] += cap_z[j]; } if (norms != NULL) { for (j=0; j<ncp; j++) { MAT_DOT_VEC_3X3 ( (&next_norm[3*j]), m, (&last_norm[3*j])); } } /* OK, now render it all */ if (norms == NULL) { draw_segment_plain (ncp, (gleVector *) next_contour, (gleVector *) last_contour, 0, 0.0); } else if (__TUBE_DRAW_FACET_NORMALS) { draw_binorm_segment_facet_n (ncp, (gleVector *) next_contour, (gleVector *) last_contour, (gleVector *) next_norm, (gleVector *) last_norm, 0, 0.0); } else { draw_binorm_segment_edge_n (ncp, (gleVector *) next_contour, (gleVector *) last_contour, (gleVector *) next_norm, (gleVector *) last_norm, 0, 0.0); } /* swap contours */ tmp = next_contour; next_contour = last_contour; last_contour = tmp; tmp = next_norm; next_norm = last_norm; last_norm = tmp; } /* &&&&&&&&&&&&&& end drawing cap &&&&&&&&&&&&& */ /* Thou shalt not leak memory */ free (malloced_area); }