| #include <stdio.h> |
| /* |
| * (c) Copyright 1993, 1994, Silicon Graphics, Inc. |
| * ALL RIGHTS RESERVED |
| * Permission to use, copy, modify, and distribute this software for |
| * any purpose and without fee is hereby granted, provided that the above |
| * copyright notice appear in all copies and that both the copyright notice |
| * and this permission notice appear in supporting documentation, and that |
| * the name of Silicon Graphics, Inc. not be used in advertising |
| * or publicity pertaining to distribution of the software without specific, |
| * written prior permission. |
| * |
| * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS" |
| * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE, |
| * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR |
| * FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON |
| * GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT, |
| * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY |
| * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION, |
| * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF |
| * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN |
| * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON |
| * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE |
| * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE. |
| * |
| * US Government Users Restricted Rights |
| * Use, duplication, or disclosure by the Government is subject to |
| * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph |
| * (c)(1)(ii) of the Rights in Technical Data and Computer Software |
| * clause at DFARS 252.227-7013 and/or in similar or successor |
| * clauses in the FAR or the DOD or NASA FAR Supplement. |
| * Unpublished-- rights reserved under the copyright laws of the |
| * United States. Contractor/manufacturer is Silicon Graphics, |
| * Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311. |
| * |
| * OpenGL(TM) is a trademark of Silicon Graphics, Inc. |
| */ |
| /* |
| * 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 |
| */ |
| #if defined(_WIN32) |
| #pragma warning (disable:4244) /* disable bogus conversion warnings */ |
| #endif |
| #include <math.h> |
| #include "trackball.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 (0.8f) |
| |
| /* |
| * Local function prototypes (not defined in trackball.h) |
| */ |
| static float tb_project_to_sphere(float, float, float); |
| static void normalize_quat(float [4]); |
| |
| static void |
| vzero(float v[3]) |
| { |
| v[0] = 0.0; |
| v[1] = 0.0; |
| v[2] = 0.0; |
| } |
| |
| static void |
| vset(float v[3], float x, float y, float z) |
| { |
| v[0] = x; |
| v[1] = y; |
| v[2] = z; |
| } |
| |
| static void |
| vsub(const float src1[3], const float src2[3], float dst[3]) |
| { |
| dst[0] = src1[0] - src2[0]; |
| dst[1] = src1[1] - src2[1]; |
| dst[2] = src1[2] - src2[2]; |
| } |
| |
| static void |
| vcopy(const float v1[3], float v2[3]) |
| { |
| register int i; |
| for (i = 0 ; i < 3 ; i++) |
| v2[i] = v1[i]; |
| } |
| |
| static void |
| vcross(const float v1[3], const float v2[3], float cross[3]) |
| { |
| 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); |
| } |
| |
| static float |
| vlength(const float v[3]) |
| { |
| return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); |
| } |
| |
| static void |
| vscale(float v[3], float div) |
| { |
| v[0] *= div; |
| v[1] *= div; |
| v[2] *= div; |
| } |
| |
| static void |
| vnormal(float v[3]) |
| { |
| vscale(v,1.0/vlength(v)); |
| } |
| |
| static float |
| vdot(const float v1[3], const float v2[3]) |
| { |
| return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]; |
| } |
| |
| static void |
| vadd(const float src1[3], const float src2[3], float dst[3]) |
| { |
| 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(const float a[3], float phi, float q[4]) |
| { |
| vcopy(a,q); |
| vnormal(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(const float q1[4], const float q2[4], float dest[4]) |
| { |
| static int count=0; |
| float t1[4], t2[4], t3[4]; |
| float tf[4]; |
| |
| #if 0 |
| printf("q1 = %f %f %f %f\n", q1[0], q1[1], q1[2], q1[3]); |
| printf("q2 = %f %f %f %f\n", q2[0], q2[1], q2[2], q2[3]); |
| #endif |
| |
| 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); |
| |
| #if 0 |
| printf("tf = %f %f %f %f\n", tf[0], tf[1], tf[2], tf[3]); |
| #endif |
| |
| 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 = sqrt(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], const 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; |
| } |
| |