Geometric
<lsl> //===================================================// // Geometric Library 1.0 // // "May 4 2008", "2:24:30" // // Copyright (C) 2008, Nexii Malthus (cc-by) // // http://creativecommons.org/licenses/by/3.0/ // //===================================================//
vector CP(vector A,vector B){
return A % B;}
vector Project3D(vector A,vector B){
vector proj; proj.x = ( (A*B) / (B.x*B.x + B.y*B.y + B.z*B.z) ) * B.x; proj.y = ( (A*B) / (B.x*B.x + B.y*B.y + B.z*B.z) ) * B.y; proj.z = ( (A*B) / (B.x*B.x + B.y*B.y + B.z*B.z) ) * B.z; return proj;}
// POINT float gXXdZ(vector A,vector B){
// Distance P2P. return llVecDist(A,B);}
vector gXXdV(vector A,vector B){
// Vector to move from P2P. return A-B;}
// LINE vector gLXdV(vector O,vector D,vector A){
// Calculates the vector from a point to the closest point on a line return (O-A)-((O-A)*D)*D;}
float gLXdZ(vector O,vector D,vector A){
// Calculates distance of this vector, but faster on it's own return llSqrt(CP((A-O),D)*CP((A-O),D));}
vector gLLdV(vector O1,vector D1,vector O2,vector D2){
// Shortest vector of two lines return Project3D( (O2-O1), CP(D1,D2) );}
float gLLdZ(vector O1,vector D1,vector O2,vector D2){
// Returns the distance between two lines vector A = CP(D1,D2);float B = llVecMag(A);A = <A.x/B,A.y/B,A.z/B>; return (O2-O1) * A;}
vector gLLnX(vector O1,vector D1,vector O2,vector D2){
// Closest point of two lines vector nO1 = < O1*D1, O1*D2, 0>; vector nO2 = < O2*D1, O2*D2, 0>; vector nD1 = < D1*D1, O1*D2, 0>; vector nD2 = < O2*D1, O2*D2, 0>; float t = ( nD2.x*nD1.y - nD1.x*nD2.y ); t = ( nD2.y*(nO1.x-nO2.x) - nD2.x*(nO1.y-nO2.y) ) / t; return O1 + D1*t;}
vector X1;vector X2;vector V1;float Z1;
gLLnnXX(vector O1,vector D1,vector O2,vector D2){
// Two closest points of two lines vector nO1 = < O1*D1, O1*D2, 0>; vector nO2 = < O2*D1, O2*D2, 0>; vector nD1 = < D1*D1, O1*D2, 0>; vector nD2 = < O2*D1, O2*D2, 0>; float t = ( nD2.x*nD1.y - nD1.x*nD2.y ); t = ( nD2.y*(nO1.x-nO2.x) - nD2.x*(nO1.y-nO2.y) ) / t; X1 = O1 + D1*t; X2 = X1 + CP(nD1,nD2);}
gLLnnXXVZ(vector O1,vector D1,vector O2,vector D2){
// Computes two closest points of two lines, vector and distance vector nO1 = < O1*D1, O1*D2, 0>; vector nO2 = < O2*D1, O2*D2, 0>; vector nD1 = < D1*D1, O1*D2, 0>; vector nD2 = < O2*D1, O2*D2, 0>; float t = ( nD2.x*nD1.y - nD1.x*nD2.y ); t = ( nD2.y*(nO1.x-nO2.x) - nD2.x*(nO1.y-nO2.y) ) / t; X1 = O1 + D1*t; X2 = X1 + CP(nD1,nD2); V1 = CP(nD1,nD2); Z1 = llVecMag(V1);}
// PLANE float gPXdZ(vector Pn,float Pd,vector A){
// Finds distance of a point from a plane return A * Pn + Pd;}
vector gPXdV(vector Pn,float Pd,vector A){
// Finds vector that points from point to nearest on plane return -(Pn * A + Pd)*Pn;}
vector gPXnX(vector Pn,float Pd,vector A){
// Finds closest point on plane given point return A - (Pn * A + Pd) * Pn;}
float gPRxZ(vector Pn,float Pd,vector O,vector D){
// Finds distance to intersection of plane along ray return -( ( (Pn*D)+(Pn*O) ) / (Pn*D) );} //return -( (Pn*D)/(Pn*O+Pd) );}
vector gPRdV(vector Pn,float Pd,vector O,vector D){
// Finds distance vector along a ray to a plane return D * gPRxZ(Pn,Pd,O,D);} //return -( (Pn*D)/(Pn*O+Pd) )*D;}
vector gPRxX(vector Pn,float Pd,vector O,vector D){
// Finds intersection point along a ray to a plane return O + gPRdV(Pn,Pd,O,D);}
vector gPLxX(vector Pn,float Pd,vector O,vector D){
// Finds interesection point of a line and a plane return O -( (Pn*D)/(Pn*O+Pd) )*D;}
vector oO;vector oD;
gPPxL(vector Pn,float Pd,vector Qn,float Qd){
// Finds line of intersection of two planes oD = CP(Pn,Qn)/llVecMag(CP(Pn,Qn)); vector Cross = CP(CP(Pn,Qn),Pn); vector Bleh = (-Pd*Pn); oO = Bleh - (Qn*Cross)/(Qn*Bleh+Qd)*Cross/llVecMag(Cross);}
float gRXpZ(vector O,vector D,vector A){
// Finds projected distance of a point along a ray return (A-O)*D;}
gPRpR(vector Pn,float Pd,vector O,vector D){
// Projects a ray onto a plane oO = O - (Pn * O + Pd) * Pn; vector t = llVecNorm( D - Project3D(D,Pn) );t = <1.0/t.x,1.0/t.y,1.0/t.z>; oD = CP(Pn,t);}
// SPHERE vector gSRxX(vector Sp, float Sr, vector Ro, vector Rd){
float t;Ro = Ro - Sp;
//vector RayOrg = llDetectedPos(x) - llGetPos();
if(Rd == ZERO_VECTOR) return ZERO_VECTOR;
float a = Rd * Rd;
float b = 2 * Rd * Ro;
float c = (Ro * Ro) - (Sr * Sr);
float disc = b * b - 4 * a * c;
if(disc < 0) return ZERO_VECTOR;
float distSqrt = llSqrt(disc);
float q;
if(b < 0)
q = (-b - distSqrt)/2.0;
else
q = (-b + distSqrt)/2.0;
float t0 = q / a;
float t1 = c / q;
if(t0 > t1){
float temp = t0;
t0 = t1;
t1 = temp;
}
if(t1 < 0) return ZERO_VECTOR;
if(t0 < 0)
t = t1;
else
t = t0;
return Ro + (t * Rd);
}
integer gSRx(vector Sp, float Sr, vector Ro, vector Rd){
float t;Ro = Ro - Sp; //vector RayOrg = llDetectedPos(x) - llGetPos(); if(Rd == ZERO_VECTOR) return FALSE; float a = Rd * Rd; float b = 2 * Rd * Ro; float c = (Ro * Ro) - (Sr * Sr); float disc = b * b - 4 * a * c; if(disc < 0) return FALSE; return TRUE;
}
// Other vector pN;float pD; gTiP(vector p1,vector p2,vector p3){
pN = llVecNorm( CP((p2-p1),(p3-p1)) ); pD = -p1*pN;}
integer gTXcC(vector p1,vector p2,vector p3,vector x){
gTiP(p1,p2,p3);
vector Vn;vector En;
Vn = p1 - x;
En = CP((p2-p1),pN);
if( ((p1-x)*CP(p2-p1,pN) >= 0)&&((p2-x)*CP(p3-p2,pN) >= 0)&&((p3-x)*CP(p1-p3,pN) >= 0) ) return TRUE;
return FALSE;}
integer gTVXcC(vector p1,vector p2,vector p3,vector v,vector x){
if( ((p1-x)*CP(p2-p1,v) >= 0)&&((p2-x)*CP(p3-p2,v) >= 0)&&((p3-x)*CP(p1-p3,v) >= 0) ) return TRUE; return FALSE;}
integer gTRcC(vector p1,vector p2,vector p3,vector O,vector D){
return gTVXcC(p1,p2,p3,O,D);}
vector gRZiX(vector O,vector D,float z){
return O+z*D;}
default{state_entry(){}}
</lsl>