#include "Quaternions.h" // Functions quaternion Quat_Mult(quaternion q1, quaternion q2) { quaternion QResult; float a, b, c, d, e, f, g, h; a = (q1.w + q1.x) * (q2.w + q2.x); b = (q1.z - q1.y) * (q2.y - q2.z); c = (q1.w - q1.x) * (q2.y + q2.z); d = (q1.y + q1.z) * (q2.w - q2.x); e = (q1.x + q1.z) * (q2.x + q2.y); f = (q1.x - q1.z) * (q2.x - q2.y); g = (q1.w + q1.y) * (q2.w - q2.z); h = (q1.w - q1.y) * (q2.w + q2.z); QResult.w = b + (-e - f + g + h) / 2; QResult.x = a - (e + f + g + h) / 2; QResult.y = c + (e - f + g - h) / 2; QResult.z = d + (e - f - g + h) / 2; return QResult; } XYZ XYZ::operator+(XYZ add){ XYZ ne; ne=add; ne.x+=x; ne.y+=y; ne.z+=z; return ne; } XYZ XYZ::operator-(XYZ add){ XYZ ne; ne=add; ne.x=x-ne.x; ne.y=y-ne.y; ne.z=z-ne.z; return ne; } XYZ XYZ::operator*(float add){ XYZ ne; ne.x=x*add; ne.y=y*add; ne.z=z*add; return ne; } XYZ XYZ::operator*(XYZ add){ XYZ ne; ne.x=x*add.x; ne.y=y*add.y; ne.z=z*add.z; return ne; } XYZ XYZ::operator/(float add){ XYZ ne; ne.x=x/add; ne.y=y/add; ne.z=z/add; return ne; } void XYZ::operator+=(XYZ add){ x+=add.x; y+=add.y; z+=add.z; } void XYZ::operator-=(XYZ add){ x=x-add.x; y=y-add.y; z=z-add.z; } void XYZ::operator*=(float add){ x=x*add; y=y*add; z=z*add; } void XYZ::operator*=(XYZ add){ x=x*add.x; y=y*add.y; z=z*add.z; } void XYZ::operator/=(float add){ x=x/add; y=y/add; z=z/add; } void XYZ::operator=(float add){ x=add; y=add; z=add; } void XYZ::vec(Vector add){ x=add.x; y=add.y; z=add.z; } bool XYZ::operator==(XYZ add){ if(x==add.x&&y==add.y&&z==add.z)return 1; return 0; } quaternion To_Quat(Matrix_t m) { // From Jason Shankel, (C) 2000. quaternion Quat; double Tr = m[0][0] + m[1][1] + m[2][2] + 1.0, fourD; double q[4]; int i,j,k; if (Tr >= 1.0) { fourD = 2.0 * sqrt(Tr); q[3] = fourD/4.0; q[0] = (m[2][1] - m[1][2]) / fourD; q[1] = (m[0][2] - m[2][0]) / fourD; q[2] = (m[1][0] - m[0][1]) / fourD; } else { if (m[0][0] > m[1][1]) { i = 0; } else { i = 1; } if (m[2][2] > m[i][i]) { i = 2; } j = (i+1)%3; k = (j+1)%3; fourD = 2.0 * sqrt(m[i][i] - m[j][j] - m[k][k] + 1.0); q[i] = fourD / 4.0; q[j] = (m[j][i] + m[i][j]) / fourD; q[k] = (m[k][i] + m[i][k]) / fourD; q[3] = (m[j][k] - m[k][j]) / fourD; } Quat.x = q[0]; Quat.y = q[1]; Quat.z = q[2]; Quat.w = q[3]; return Quat; } void Quat_2_Matrix(quaternion Quat, Matrix_t m) { // From the GLVelocity site (http://glvelocity.gamedev.net) float fW = Quat.w; float fX = Quat.x; float fY = Quat.y; float fZ = Quat.z; float fXX = fX * fX; float fYY = fY * fY; float fZZ = fZ * fZ; m[0][0] = 1.0f - 2.0f * (fYY + fZZ); m[1][0] = 2.0f * (fX * fY + fW * fZ); m[2][0] = 2.0f * (fX * fZ - fW * fY); m[3][0] = 0.0f; m[0][1] = 2.0f * (fX * fY - fW * fZ); m[1][1] = 1.0f - 2.0f * (fXX + fZZ); m[2][1] = 2.0f * (fY * fZ + fW * fX); m[3][1] = 0.0f; m[0][2] = 2.0f * (fX * fZ + fW * fY); m[1][2] = 2.0f * (fX * fZ - fW * fX); m[2][2] = 1.0f - 2.0f * (fXX + fYY); m[3][2] = 0.0f; m[0][3] = 0.0f; m[1][3] = 0.0f; m[2][3] = 0.0f; m[3][3] = 1.0f; } quaternion To_Quat(angle_axis Ang_Ax) { // From the Quaternion Powers article on gamedev.net quaternion Quat; Quat.x = Ang_Ax.x * sin(Ang_Ax.angle / 2); Quat.y = Ang_Ax.y * sin(Ang_Ax.angle / 2); Quat.z = Ang_Ax.z * sin(Ang_Ax.angle / 2); Quat.w = cos(Ang_Ax.angle / 2); return Quat; } angle_axis Quat_2_AA(quaternion Quat) { angle_axis Ang_Ax; float scale, tw; tw = (float)acos(Quat.w) * 2; scale = (float)sin(tw / 2.0); Ang_Ax.x = Quat.x / scale; Ang_Ax.y = Quat.y / scale; Ang_Ax.z = Quat.z / scale; Ang_Ax.angle = 2.0 * acos(Quat.w)/(float)PI*180; return Ang_Ax; } quaternion To_Quat(int In_Degrees, euler Euler) { // From the gamasutra quaternion article quaternion Quat; float cr, cp, cy, sr, sp, sy, cpcy, spsy; //If we are in Degree mode, convert to Radians if (In_Degrees) { Euler.x = Euler.x * (float)PI / 180; Euler.y = Euler.y * (float)PI / 180; Euler.z = Euler.z * (float)PI / 180; } //Calculate trig identities //Formerly roll, pitch, yaw cr = float(cos(Euler.x/2)); cp = float(cos(Euler.y/2)); cy = float(cos(Euler.z/2)); sr = float(sin(Euler.x/2)); sp = float(sin(Euler.y/2)); sy = float(sin(Euler.z/2)); cpcy = cp * cy; spsy = sp * sy; Quat.w = cr * cpcy + sr * spsy; Quat.x = sr * cpcy - cr * spsy; Quat.y = cr * sp * cy + sr * cp * sy; Quat.z = cr * cp * sy - sr * sp * cy; return Quat; } quaternion QNormalize(quaternion Quat) { float norm; norm = Quat.x * Quat.x + Quat.y * Quat.y + Quat.z * Quat.z + Quat.w * Quat.w; Quat.x = float(Quat.x / norm); Quat.y = float(Quat.y / norm); Quat.z = float(Quat.z / norm); Quat.w = float(Quat.w / norm); return Quat; } XYZ Quat2Vector(quaternion Quat) { QNormalize(Quat); float fW = Quat.w; float fX = Quat.x; float fY = Quat.y; float fZ = Quat.z; XYZ tempvec; tempvec.x = 2.0f*(fX*fZ-fW*fY); tempvec.y = 2.0f*(fY*fZ+fW*fX); tempvec.z = 1.0f-2.0f*(fX*fX+fY*fY); return tempvec; } void CrossProduct(XYZ P, XYZ Q, XYZ *V){ V->x = P.y * Q.z - P.z * Q.y; V->y = P.z * Q.x - P.x * Q.z; V->z = P.x * Q.y - P.y * Q.x; } void Normalise(XYZ *vectory) { float d = sqrt(vectory->x*vectory->x+vectory->y*vectory->y+vectory->z*vectory->z); if(d==0){return;} vectory->x /= d; vectory->y /= d; vectory->z /= d; } float normaldotproduct(XYZ point1, XYZ point2){ GLfloat returnvalue; Normalise(&point1); Normalise(&point2); returnvalue=(point1.x*point2.x+point1.y*point2.y+point1.z*point2.z); return returnvalue; } extern float u0, u1, u2; extern float v0, v1, v2; extern float a, b; extern int i, j; extern bool bInter; extern float pointv[3]; extern float p1v[3]; extern float p2v[3]; extern float p3v[3]; extern float normalv[3]; bool PointInTriangle(Vector *p, Vector normal, float p11, float p12, float p13, float p21, float p22, float p23, float p31, float p32, float p33) { bInter=0; pointv[0]=p->x; pointv[1]=p->y; pointv[2]=p->z; p1v[0]=p11; p1v[1]=p12; p1v[2]=p13; p2v[0]=p21; p2v[1]=p22; p2v[2]=p23; p3v[0]=p31; p3v[1]=p32; p3v[2]=p33; normalv[0]=normal.x; normalv[1]=normal.y; normalv[2]=normal.z; #define ABS(X) (((X)<0.f)?-(X):(X) ) #define MAX(A, B) (((A)<(B))?(B):(A)) float max = MAX(MAX(ABS(normalv[0]), ABS(normalv[1])), ABS(normalv[2])); #undef MAX if (max == ABS(normalv[0])) {i = 1; j = 2;} // y, z if (max == ABS(normalv[1])) {i = 0; j = 2;} // x, z if (max == ABS(normalv[2])) {i = 0; j = 1;} // x, y #undef ABS u0 = pointv[i] - p1v[i]; v0 = pointv[j] - p1v[j]; u1 = p2v[i] - p1v[i]; v1 = p2v[j] - p1v[j]; u2 = p3v[i] - p1v[i]; v2 = p3v[j] - p1v[j]; if (u1 > -1.0e-05f && u1 < 1.0e-05f)// == 0.0f) { b = u0 / u2; if (0.0f <= b && b <= 1.0f) { a = (v0 - b * v2) / v1; if ((a >= 0.0f) && (( a + b ) <= 1.0f)) bInter = 1; } } else { b = (v0 * u1 - u0 * v1) / (v2 * u1 - u2 * v1); if (0.0f <= b && b <= 1.0f) { a = (u0 - b * u2) / u1; if ((a >= 0.0f) && (( a + b ) <= 1.0f )) bInter = 1; } } return bInter; } bool LineFacet(Vector p1,Vector p2,Vector pa,Vector pb,Vector pc,Vector *p) { float d; float denom, mu; Vector n, pa1, pa2, pa3; //Calculate the parameters for the plane n.x = (pb.y - pa.y)*(pc.z - pa.z) - (pb.z - pa.z)*(pc.y - pa.y); n.y = (pb.z - pa.z)*(pc.x - pa.x) - (pb.x - pa.x)*(pc.z - pa.z); n.z = (pb.x - pa.x)*(pc.y - pa.y) - (pb.y - pa.y)*(pc.x - pa.x); n.Normalize(); d = - n.x * pa.x - n.y * pa.y - n.z * pa.z; //Calculate the position on the line that intersects the plane denom = n.x * (p2.x - p1.x) + n.y * (p2.y - p1.y) + n.z * (p2.z - p1.z); if (abs(denom) < 0.0000001) // Line and plane don't intersect return 0; mu = - (d + n.x * p1.x + n.y * p1.y + n.z * p1.z) / denom; p->x = p1.x + mu * (p2.x - p1.x); p->y = p1.y + mu * (p2.y - p1.y); p->z = p1.z + mu * (p2.z - p1.z); if (mu < 0 || mu > 1) // Intersection not along line segment return 0; if(!PointInTriangle( p, n, pa.x, pa.y, pa.z, pb.x, pb.y, pb.z, pc.x, pc.y, pc.z)){return 0;} return 1; } bool PointInTriangle(XYZ *p, XYZ normal, XYZ *p1, XYZ *p2, XYZ *p3) { bInter=0; pointv[0]=p->x; pointv[1]=p->y; pointv[2]=p->z; p1v[0]=p1->x; p1v[1]=p1->y; p1v[2]=p1->z; p2v[0]=p2->x; p2v[1]=p2->y; p2v[2]=p2->z; p3v[0]=p3->x; p3v[1]=p3->y; p3v[2]=p3->z; normalv[0]=normal.x; normalv[1]=normal.y; normalv[2]=normal.z; #define ABS(X) (((X)<0.f)?-(X):(X) ) #define MAX(A, B) (((A)<(B))?(B):(A)) float max = MAX(MAX(ABS(normalv[0]), ABS(normalv[1])), ABS(normalv[2])); #undef MAX if (max == ABS(normalv[0])) {i = 1; j = 2;} // y, z if (max == ABS(normalv[1])) {i = 0; j = 2;} // x, z if (max == ABS(normalv[2])) {i = 0; j = 1;} // x, y #undef ABS u0 = pointv[i] - p1v[i]; v0 = pointv[j] - p1v[j]; u1 = p2v[i] - p1v[i]; v1 = p2v[j] - p1v[j]; u2 = p3v[i] - p1v[i]; v2 = p3v[j] - p1v[j]; if (u1 > -1.0e-05f && u1 < 1.0e-05f)// == 0.0f) { b = u0 / u2; if (0.0f <= b && b <= 1.0f) { a = (v0 - b * v2) / v1; if ((a >= 0.0f) && (( a + b ) <= 1.0f)) bInter = 1; } } else { b = (v0 * u1 - u0 * v1) / (v2 * u1 - u2 * v1); if (0.0f <= b && b <= 1.0f) { a = (u0 - b * u2) / u1; if ((a >= 0.0f) && (( a + b ) <= 1.0f )) bInter = 1; } } return bInter; } bool LineFacet(XYZ p1,XYZ p2,XYZ pa,XYZ pb,XYZ pc,XYZ *p) { float d; float denom, mu; XYZ n; //Calculate the parameters for the plane n.x = (pb.y - pa.y)*(pc.z - pa.z) - (pb.z - pa.z)*(pc.y - pa.y); n.y = (pb.z - pa.z)*(pc.x - pa.x) - (pb.x - pa.x)*(pc.z - pa.z); n.z = (pb.x - pa.x)*(pc.y - pa.y) - (pb.y - pa.y)*(pc.x - pa.x); Normalise(&n); d = - n.x * pa.x - n.y * pa.y - n.z * pa.z; //Calculate the position on the line that intersects the plane denom = n.x * (p2.x - p1.x) + n.y * (p2.y - p1.y) + n.z * (p2.z - p1.z); if (abs(denom) < 0.0000001) // Line and plane don't intersect return 0; mu = - (d + n.x * p1.x + n.y * p1.y + n.z * p1.z) / denom; p->x = p1.x + mu * (p2.x - p1.x); p->y = p1.y + mu * (p2.y - p1.y); p->z = p1.z + mu * (p2.z - p1.z); if (mu < 0 || mu > 1) // Intersection not along line segment return 0; if(!PointInTriangle( p, n, &pa, &pb, &pc)){return 0;} return 1; } extern float d; extern float a1,a2,a3; extern float total,denom,mu; extern XYZ pa1,pa2,pa3,n; float LineFacetd(XYZ p1,XYZ p2,XYZ pa,XYZ pb,XYZ pc,XYZ *p) { //Calculate the parameters for the plane n.x = (pb.y - pa.y)*(pc.z - pa.z) - (pb.z - pa.z)*(pc.y - pa.y); n.y = (pb.z - pa.z)*(pc.x - pa.x) - (pb.x - pa.x)*(pc.z - pa.z); n.z = (pb.x - pa.x)*(pc.y - pa.y) - (pb.y - pa.y)*(pc.x - pa.x); Normalise(&n); d = - n.x * pa.x - n.y * pa.y - n.z * pa.z; //Calculate the position on the line that intersects the plane denom = n.x * (p2.x - p1.x) + n.y * (p2.y - p1.y) + n.z * (p2.z - p1.z); if (abs(denom) < 0.0000001) // Line and plane don't intersect return 0; mu = - (d + n.x * p1.x + n.y * p1.y + n.z * p1.z) / denom; p->x = p1.x + mu * (p2.x - p1.x); p->y = p1.y + mu * (p2.y - p1.y); p->z = p1.z + mu * (p2.z - p1.z); if (mu < 0 || mu > 1) // Intersection not along line segment return 0; if(!PointInTriangle( p, n, &pa, &pb, &pc)){return 0;} return 1; } float LineFacetd(XYZ p1,XYZ p2,XYZ pa,XYZ pb,XYZ pc, XYZ n, XYZ *p) { //Calculate the parameters for the plane d = - n.x * pa.x - n.y * pa.y - n.z * pa.z; //Calculate the position on the line that intersects the plane denom = n.x * (p2.x - p1.x) + n.y * (p2.y - p1.y) + n.z * (p2.z - p1.z); if (abs(denom) < 0.0000001) // Line and plane don't intersect return 0; mu = - (d + n.x * p1.x + n.y * p1.y + n.z * p1.z) / denom; p->x = p1.x + mu * (p2.x - p1.x); p->y = p1.y + mu * (p2.y - p1.y); p->z = p1.z + mu * (p2.z - p1.z); if (mu < 0 || mu > 1) // Intersection not along line segment return 0; if(!PointInTriangle( p, n, &pa, &pb, &pc)){return 0;} return 1; } float LineFacetd(XYZ *p1,XYZ *p2,XYZ *pa,XYZ *pb,XYZ *pc, XYZ *n, XYZ *p) { //Calculate the parameters for the plane d = - n->x * pa->x - n->y * pa->y - n->z * pa->z; //Calculate the position on the line that intersects the plane denom = n->x * (p2->x - p1->x) + n->y * (p2->y - p1->y) + n->z * (p2->z - p1->z); if (abs(denom) < 0.0000001) // Line and plane don't intersect return 0; mu = - (d + n->x * p1->x + n->y * p1->y + n->z * p1->z) / denom; p->x = p1->x + mu * (p2->x - p1->x); p->y = p1->y + mu * (p2->y - p1->y); p->z = p1->z + mu * (p2->z - p1->z); if (mu < 0 || mu > 1) // Intersection not along line segment return 0; if(!PointInTriangle( p, *n, pa, pb, pc)){return 0;} return 1; } void ReflectVector(XYZ *vel, XYZ *n) { XYZ vn; XYZ vt; float dotprod; dotprod=dotproduct(*n,*vel); vn.x=n->x*dotprod; vn.y=n->y*dotprod; vn.z=n->z*dotprod; vt.x=vel->x-vn.x; vt.y=vel->y-vn.y; vt.z=vel->z-vn.z; vel->x = vt.x - vn.x; vel->y = vt.y - vn.y; vel->z = vt.z - vn.z; } float dotproduct(XYZ point1, XYZ point2){ GLfloat returnvalue; returnvalue=(point1.x*point2.x+point1.y*point2.y+point1.z*point2.z); return returnvalue; } float findDistance(XYZ point1, XYZ point2){ return sqrt((point1.x-point2.x)*(point1.x-point2.x)+(point1.y-point2.y)*(point1.y-point2.y)+(point1.z-point2.z)*(point1.z-point2.z)); } float findLength(XYZ point1){ return sqrt((point1.x)*(point1.x)+(point1.y)*(point1.y)+(point1.z)*(point1.z)); } float findLengthfast(XYZ point1){ return((point1.x)*(point1.x)+(point1.y)*(point1.y)+(point1.z)*(point1.z)); } float findDistancefast(XYZ point1, XYZ point2){ return((point1.x-point2.x)*(point1.x-point2.x)+(point1.y-point2.y)*(point1.y-point2.y)+(point1.z-point2.z)*(point1.z-point2.z)); } XYZ DoRotation(XYZ thePoint, float xang, float yang, float zang){ XYZ newpoint; if(xang){ xang*=6.283185; xang/=360; } if(yang){ yang*=6.283185; yang/=360; } if(zang){ zang*=6.283185; zang/=360; } if(yang){ newpoint.z=thePoint.z*cos(yang)-thePoint.x*sin(yang); newpoint.x=thePoint.z*sin(yang)+thePoint.x*cos(yang); thePoint.z=newpoint.z; thePoint.x=newpoint.x; } if(zang){ newpoint.x=thePoint.x*cos(zang)-thePoint.y*sin(zang); newpoint.y=thePoint.y*cos(zang)+thePoint.x*sin(zang); thePoint.x=newpoint.x; thePoint.y=newpoint.y; } if(xang){ newpoint.y=thePoint.y*cos(xang)-thePoint.z*sin(xang); newpoint.z=thePoint.y*sin(xang)+thePoint.z*cos(xang); thePoint.z=newpoint.z; thePoint.y=newpoint.y; } return thePoint; } float square( float f ) { return (f*f) ;} bool sphere_line_intersection ( float x1, float y1 , float z1, float x2, float y2 , float z2, float x3, float y3 , float z3, float r ) { // x1,y1,z1 P1 coordinates (point of line) // x2,y2,z2 P2 coordinates (point of line) // x3,y3,z3, r P3 coordinates and radius (sphere) // x,y,z intersection coordinates // // This function returns a pointer array which first index indicates // the number of intersection point, followed by coordinate pairs. float a, b, c, i; if(x1>x3+r&&x2>x3+r)return(0); if(x1y3+r&&y2>y3+r)return(0); if(y1z3+r&&z2>z3+r)return(0); if(z1