/* * Trackball code: * * Implementation of a virtual trackball. * Implemented by Gavin Bell, lots of ideas from Thant Tessman and * the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129. * * Vector manip code: * * Original code from: * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli * * Much mucking with by: * Gavin Bell */ #include #include "trackbal.h" /* * This size should really be based on the distance from the center of * rotation to the point on the object underneath the mouse. That * point would then track the mouse as closely as possible. This is a * simple example, though, so that is left as an Exercise for the * Programmer. */ #define TRACKBALLSIZE (0.8) /* * Local function prototypes (not defined in trackball.h) */ static float tb_project_to_sphere(float, float, float); static void normalize_quat(float [4]); void vzero(float *v) { v[0] = 0.0; v[1] = 0.0; v[2] = 0.0; } void vset(float *v, float x, float y, float z) { v[0] = x; v[1] = y; v[2] = z; } void vsub(const float *src1, const float *src2, float *dst) { dst[0] = src1[0] - src2[0]; dst[1] = src1[1] - src2[1]; dst[2] = src1[2] - src2[2]; } void vcopy(const float *v1, float *v2) { register int i; for (i = 0 ; i < 3 ; i++) v2[i] = v1[i]; } void vcross(const float *v1, const float *v2, float *cross) { float temp[3]; temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]); temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]); temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]); vcopy(temp, cross); } float vlength(const float *v) { return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); } void vscale(float *v, float div) { v[0] *= div; v[1] *= div; v[2] *= div; } void vnormal(float *v) { vscale(v,1.0/vlength(v)); } float vdot(const float *v1, const float *v2) { return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]; } void vadd(const float *src1, const float *src2, float *dst) { dst[0] = src1[0] + src2[0]; dst[1] = src1[1] + src2[1]; dst[2] = src1[2] + src2[2]; } /* * Ok, simulate a track-ball. Project the points onto the virtual * trackball, then figure out the axis of rotation, which is the cross * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0) * Note: This is a deformed trackball-- is a trackball in the center, * but is deformed into a hyperbolic sheet of rotation away from the * center. This particular function was chosen after trying out * several variations. * * It is assumed that the arguments to this routine are in the range * (-1.0 ... 1.0) */ void trackball(float q[4], float p1x, float p1y, float p2x, float p2y) { float a[3]; /* Axis of rotation */ float phi; /* how much to rotate about axis */ float p1[3], p2[3], d[3]; float t; if (p1x == p2x && p1y == p2y) { /* Zero rotation */ vzero(q); q[3] = 1.0; return; } /* * First, figure out z-coordinates for projection of P1 and P2 to * deformed sphere */ vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y)); vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y)); /* * Now, we want the cross product of P1 and P2 */ vcross(p2,p1,a); /* * Figure out how much to rotate around that axis. */ vsub(p1,p2,d); t = vlength(d) / (2.0*TRACKBALLSIZE); /* * Avoid problems with out-of-control values... */ if (t > 1.0) t = 1.0; if (t < -1.0) t = -1.0; phi = 2.0 * asin(t); axis_to_quat(a,phi,q); } /* * Given an axis and angle, compute quaternion. */ void axis_to_quat(float a[3], float phi, float q[4]) { vnormal(a); vcopy(a,q); vscale(q,sin(phi/2.0)); q[3] = cos(phi/2.0); } /* * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet * if we are away from the center of the sphere. */ static float tb_project_to_sphere(float r, float x, float y) { float d, t, z; d = sqrt(x*x + y*y); if (d < r * 0.70710678118654752440) { /* Inside sphere */ z = sqrt(r*r - d*d); } else { /* On hyperbola */ t = r / 1.41421356237309504880; z = t*t / d; } return z; } /* * Given two rotations, e1 and e2, expressed as quaternion rotations, * figure out the equivalent single rotation and stuff it into dest. * * This routine also normalizes the result every RENORMCOUNT times it is * called, to keep error from creeping in. * * NOTE: This routine is written so that q1 or q2 may be the same * as dest (or each other). */ #define RENORMCOUNT 97 void add_quats(float q1[4], float q2[4], float dest[4]) { static int count=0; int i; float t1[4], t2[4], t3[4]; float tf[4]; vcopy(q1,t1); vscale(t1,q2[3]); vcopy(q2,t2); vscale(t2,q1[3]); vcross(q2,q1,t3); vadd(t1,t2,tf); vadd(t3,tf,tf); tf[3] = q1[3] * q2[3] - vdot(q1,q2); dest[0] = tf[0]; dest[1] = tf[1]; dest[2] = tf[2]; dest[3] = tf[3]; if (++count > RENORMCOUNT) { count = 0; normalize_quat(dest); } } /* * Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0 * If they don't add up to 1.0, dividing by their magnitued will * renormalize them. * * Note: See the following for more information on quaternions: * * - Shoemake, K., Animating rotation with quaternion curves, Computer * Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985. * - Pletinckx, D., Quaternion calculus as a basic tool in computer * graphics, The Visual Computer 5, 2-13, 1989. */ static void normalize_quat(float q[4]) { int i; float mag; mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]); for (i = 0; i < 4; i++) q[i] /= mag; } /* * Build a rotation matrix, given a quaternion rotation. * */ void build_rotmatrix(float m[4][4], float q[4]) { m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]); m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]); m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]); m[0][3] = 0.0; m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]); m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]); m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]); m[1][3] = 0.0; m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]); m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]); m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]); m[2][3] = 0.0; m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0; }