I hope someone can help me debug my code for performing rotations about three axiis using quaternions, and so avoiding gimbal-lock. I wrote the code after trawling the internet for information, but unfortunately the code I've written still suffers from the dreaded gimbal-lock! The information was mainly extracted from "www.gamasutra.com" and "www.flipcode.com/documents/matrfaq.html". I'm using the OpenGL API, and perform the rotation by calling glMultMatrixf(). The code is as follows: /*************************************************************************************************************** FILE NAME: rotate.h AUTHOR: Justin C. Nixon CREATED/UPDATED: 24/06/2000 24/06/2000 NOTES: ***************************************************************************************************************/ #ifndef ROTATE_H #define ROTATE_H typedef float RADIANS; typedef float DEGREES; #ifndef PI #define PI 3.14159265358979323846f #endif #define RADIANS_TO_DEGREES 360.0f/(2*PI) struct axis_angle { RADIANS x, y, z; }; struct quaternion { float w, x, y, z; }; struct attitude { DEGREES roll, pitch, heading; }; void normalise_quaternion(struct quaternion *); // Normalise a quaternion. void multiply_quaternion(struct quaternion *result_p, struct quaternion *a_p, struct quaternion *b_p); // Multiply two quaternions. void axis_angles_to_quaternion(struct quaternion *, struct axis_angle *); // Convert axis angles to a quaternion. void quaternion_to_matrix(struct quaternion *, float *); void quaternion_to_attitude(struct quaternion *, struct attitude *); // Convert a quaternion to familiar roll, pitch, and heading values. #endif void normalise_quaternion(struct quaternion *quaternion_p) { float magnitude; magnitude=(quaternion_p->w*quaternion_p->w)+(quaternion_p->x*quaternion_p->x)+(quaternion_p->y*quaternion_p->y)+(quaternion_p->z*quaternion_p->z); // Find the magnitude. // Divide by the magnitude to normalise. quaternion_p->w=quaternion_p->w/magnitude; quaternion_p->x=quaternion_p->x/magnitude; quaternion_p->y=quaternion_p->y/magnitude; quaternion_p->z=quaternion_p->z/magnitude; } void multiply_quaternion(struct quaternion *result_p, struct quaternion *quaternion1_p, struct quaternion *quaternion2_p) { float a, b, c, d, e, f, g, h; a=(quaternion1_p->w+quaternion1_p->x)*(quaternion2_p->w+quaternion2_p->x); b=(quaternion1_p->z-quaternion1_p->y)*(quaternion2_p->y-quaternion2_p->z); c=(quaternion1_p->x-quaternion1_p->w)*(quaternion2_p->y+quaternion2_p->z); d=(quaternion1_p->y+quaternion1_p->z)*(quaternion2_p->x-quaternion2_p->w); e=(quaternion1_p->x+quaternion1_p->z)*(quaternion2_p->x+quaternion2_p->y); f=(quaternion1_p->x-quaternion1_p->z)*(quaternion2_p->x-quaternion2_p->y); g=(quaternion1_p->w+quaternion1_p->y)*(quaternion2_p->w-quaternion2_p->z); h=(quaternion1_p->w-quaternion1_p->y)*(quaternion2_p->w+quaternion2_p->z); result_p->w=b+((-e-f+g+h)/2); result_p->x=a-((e+f+g+h)/2); result_p->y=-c+((e-f+g-h)/2); result_p->z=-d+((e-f-g+h)/2); normalise_quaternion(result_p); } void axis_angles_to_quaternion(struct quaternion *quaternion_p, struct axis_angle *axis_angle_p) { struct quaternion quaternion_wxy, quaternion_wx, quaternion_wy, quaternion_wz; quaternion_wx.w=(float)cos(axis_angle_p->x/2.0f); quaternion_wx.x=(float)sin(axis_angle_p->x/2.0f); quaternion_wx.y=0.0f; quaternion_wx.z=0.0f; normalise_quaternion(&quaternion_wx); quaternion_wy.w=(float)cos(axis_angle_p->y/2.0f); quaternion_wy.x=0.0f; quaternion_wy.y=(float)sin(axis_angle_p->y/2.0f); quaternion_wy.z=0.0f; normalise_quaternion(&quaternion_wy); quaternion_wz.w=(float)cos(axis_angle_p->z/2.0f); quaternion_wz.x=0.0f; quaternion_wz.y=0.0f; quaternion_wz.z=(float)sin(axis_angle_p->z/2.0f); normalise_quaternion(&quaternion_wz); multiply_quaternion(&quaternion_wxy, &quaternion_wx, &quaternion_wy); multiply_quaternion(quaternion_p, &quaternion_wxy, &quaternion_wz); } void quaternion_to_matrix(struct quaternion *quaternion_p, float *matrix_p) { float xx, xy, xz, xw, yy, yz, yw, zz, zw; xx=quaternion_p->x*quaternion_p->x; xy=quaternion_p->x*quaternion_p->y; xz=quaternion_p->x*quaternion_p->z; xw=quaternion_p->x*quaternion_p->w; yy=quaternion_p->y*quaternion_p->y; yz=quaternion_p->y*quaternion_p->z; yw=quaternion_p->y*quaternion_p->w; zz=quaternion_p->z*quaternion_p->z; zw=quaternion_p->z*quaternion_p->w; *matrix_p=1.0f-2.0f*(yy+zz); // Element 0 matrix_p++; *matrix_p=2.0f*(xy-zw); // Element 1 matrix_p++; *matrix_p=2.0f*(xz+yw); // Element 2 matrix_p++; *matrix_p=0.0f; // Element 3 matrix_p++; *matrix_p=2.0f*(xy+zw); // Element 4 matrix_p++; *matrix_p=1.0f-2.0f*(xx+zz); // Element 5 matrix_p++; *matrix_p=2.0f*(yz-xw); // Element 6 matrix_p++; *matrix_p=0.0f; // Element 7 matrix_p++; *matrix_p=2.0f*(xz-yw); // Element 8 matrix_p++; *matrix_p=2.0f*(yz+xw); // Element 9 matrix_p++; *matrix_p=1.0f-2.0f*(xx+yy); // Element 10 matrix_p++; *matrix_p=0.0f; // Element 11 matrix_p++; *matrix_p=0.0f; // Element 12 matrix_p++; *matrix_p=0.0f; // Element 13 matrix_p++; *matrix_p=0.0f; // Element 14 matrix_p++; *matrix_p=1.0f; // Element 15 } void quaternion_to_attitude(struct quaternion *quaternion_p, struct attitude *attitude_p) { float sine_angle, tx, ty, tz; attitude_p->roll=(float)acos(quaternion_p->w)*2*RADIANS_TO_DEGREES; // Calculate roll. sine_angle=(float)sqrt(1.0f-(quaternion_p->w*quaternion_p->w)); // Calculate sine angle. if(fabs(sine_angle)<0.0005f) sine_angle=1.0f; // Adjust sine angle if required. tx=quaternion_p->x/sine_angle; ty=quaternion_p->y/sine_angle; tz=quaternion_p->z/sine_angle; attitude_p->pitch=(float)-asin(ty)*RADIANS_TO_DEGREES; // Calculate pitch. if((tx*tx)+(tz*tz)<0.0005f) { attitude_p->heading=0.0f; // Set heading. } else { attitude_p->heading=(float)atan2(tx,tz)*RADIANS_TO_DEGREES; // Calculate heading. } if(attitude_p->heading<0.0f) attitude_p->heading+=360.0f; // Adjust heading if required. } Edited by - Justin Nixon on 7/2/00 12:06:33 PM

why do u ever use Open GL???
u can anyway use the D3DX library which has full support for Quaternions along with ur OpenGL code by just linking it along.

glMatrix mat;
D3DXMATRIX mat2 = (glMatrix)mat;


cast it in the above way.
hope this helps!
(i bet it didnt!!)



Raptor