Geometric

Please vote for: https://jira.secondlife.com/browse/WEB-235 So that I can expand each function into deeper detail without the page starting to fail in readability. --Nexii Malthus 23:05, 24 October 2008 (UTC)

:Break it up so each major section has its own page... thats why hypertext was invented. -Overbrain Unplugged 13:36, 10 October 2010 (UTC)

Geometric Library

Line Functions

Line and Point, Vector
Calculates the vector from a point 'to' the closest point on a line <lsl> vector gLXdV(vector O,vector D,vector A){ return (O-A)-((O-A)*D)*D;} </lsl> Input Description vector O Origin of Line vector D Direction of Line vector A Origin of Point Output Description return vector gLXdV Returns origin of closest point on Line to Point 3D By Nexii Malthus

Line and Point, Distance

Calculates distance of line to point, same as measuring magnitude of Line and Point Vector, but faster on it's own <lsl> float gLXdZ(vector O,vector D,vector A){ vector k = ( A - O ) % D; return llSqrt( k * k );} </lsl> Input Description vector O Origin of Line vector D Direction of Line vector A Origin of Point Output Description return float gLXdZ Returns numerical distance from Line to Point 3D By Nexii Malthus

Line Nearest Point, Nearest Point
Returns nearest point on line to given point <lsl> vector gLXnX(vector O,vector D,vector A){ return gLXdV(O,D,A) + A;} </lsl> Input Description vector O Origin of Line vector D Direction of Line vector A Origin of Point Output Description return vector gLXnX Returns nearest point on line given point Requirement function vector gLXdV(vector O,vector D,vector A) 3D By Nexii Malthus

Line and Line, Vector

Shortest vector of two lines <lsl> vector gLLdV(vector O1,vector D1,vector O2,vector D2){ vector A = O2 - O1; vector B = D1 % D2; return B*( (A*B)/(B*B) );} </lsl> Input Description vector O1 Origin of Line 1 vector D1 Direction of Line 1 vector O2 Origin of Line 2 vector D2 Direction of Line 2 Output Description return vector gLLdV Returns shortest vector between the two lines 3D By Nexii Malthus

Line and Line, Distance

Returns the distance between two lines <lsl> float gLLdZ(vector O1,vector D1,vector O2,vector D2){ vector A = D1%D2;float B = llVecMag(A);A = <A.x/B,A.y/B,A.z/B>; return (O2-O1) * A;} </lsl> Input Description vector O1 Origin of Line 1 vector D1 Direction of Line 1 vector O2 Origin of Line 2 vector D2 Direction of Line 2 Output Description return float gLLdZ Returns numerical distance between the two lines 3D By Nexii Malthus

Line and Line, Nearest point

Closest point of two lines <lsl> vector gLLnX(vector O1,vector D1,vector O2,vector D2){ 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;} </lsl> Input Description vector O1 Origin of Line 1 vector D1 Direction of Line 1 vector O2 Origin of Line 2 vector D2 Direction of Line 2 Output Description return vector gLLnX Returns closest point between the two lines 2D By Nexii Malthus

Line and Line, intersection point

Computes intersection point of two lines, if there is any, else <-1,-1,-1> if none. <lsl> vector gLLxX( vector A, vector B, vector C, vector D ){ vector b = B-A; vector d = D-C; float dotperp = b.x*d.y - b.y*d.x; if (dotperp == 0) return <-1,-1,-1>; vector c = C-A; float t = (c.x*d.y - c.y*d.x) / dotperp; return <A.x + t*b.x, A.y + t*b.y, 0>;} </lsl> Input Description vector A Start of Line 1 vector B End of Line 1 vector C Start of Line 2 vector D End of Line 2 Output Description return vector gLLxX The intersection point of the two lines, else <-1,-1,-1> if none 2D By Nexii Malthus

Line and Line, two nearest points of lines

Two closest points of two lines on each line <lsl> vector X1;vector X2; gLLnnXX(vector O1,vector D1,vector O2,vector D2){ 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 + nD1%nD2;} </lsl> Input Description vector O1 Origin of Line 1 vector D1 Direction of Line 1 vector O2 Origin of Line 2 vector D2 Direction of Line 2 Output Description vector X1 Closest point on line 1 to line 2 vector X2 Closest point on line 2 to line 1 Requirement global vector X1 global vector X2 2D By Nexii Malthus

Line and Line, nearest line

Input two lines, the function will return a list containing two vectors responding to the line nearest between them. As well as two floats corresponding to the scalar value on the two line of where the line has an end located at. <lsl> list gLLnL( vector v0, vector v1, vector v2, vector v3 ) { float Eps = 0.000001; vector vx; vector vy; vector va; vector vb; vector vc; float x; float y; float d0; float d1; float d2; float d3; float d4; va = v0-v2; vb = v3-v2; if(llVecMag(vb)<Eps) return []; vc = v1-v0; if(llVecMag(vc)<Eps) return []; d0 = va*vb; d1 = vb*vc; d2 = va*vc; d3 = vb*vb; d4 = vc*vc; float den = d4*d3-d1*d1; if( llFabs(den) < Eps ) return []; float num = d0*d1-d2*d3; x = num/den; y = (d0+d1*x)/d3; vx = v0+vc*x; vy = v2+vb*y; return [vx,vy,x,y]; } </lsl> Input Description vector v0 Point on Line 1 vector v1 Point on Line 1 vector v2 Point on Line 2 vector v3 Point on Line 2 Output Description [vx] Nearest point on Line 1 to Line 2 [vy] Nearest point on Line 2 to Line 1 [x] Scalar value representing location of vx on line 1 (range [v0,v1]) [y] Scalar value representing location of vy on line 2 (range [v2,v3]) 3D By Nexii Malthus

Line and Line Segments, nearest line segment

Input two line segments, the function will return a list containing two vectors responding to the line segment nearest between them. As well as two floats corresponding to the scalar value on the two line segments of where the line segment has an end located at. <lsl> list gLSLSnLS( vector v0, vector v1, vector v2, vector v3 ) { float Eps = 0.000001; vector vx; vector vy; vector va; vector vb; vector vc; float x; float y; float d0; float d1; float d2; float d3; float d4; va = v0-v2; vb = v3-v2; if(llVecMag(vb)<Eps) return []; vc = v1-v0; if(llVecMag(vc)<Eps) return []; if( llFabs(vc.x + vc.y + vc.z) < Eps ) return []; d0 = va*vb; d1 = vb*vc; d2 = va*vc; d3 = vb*vb; d4 = vc*vc; float den = d4*d3-d1*d1; if( llFabs(den) < Eps ) return []; float num = d0*d1-d2*d3; x = num/den; y = (d0+d1*x)/d3; if(x<0)x=0; else if(x>1)x=1; if(y<0)y=0; else if(y>1)y=1; vx = v0+vc*x; vy = v2+vb*y; return [vx,vy,x,y]; } </lsl> Input Description vector v0 Start of Line Segment 1 vector v1 End of Line Segment 1 vector v2 Start of Line Segment 2 vector v3 End of Line Segment 2 Output Description [vx] Nearest point on Line Segment 1 to Line Segment 2 [vy] Nearest point on Line Segment 2 to Line Segment 1 [x] Scalar value representing location of vx on Line Segment 1 (range [v0,v1]) [y] Scalar value representing location of vy on Line Segment 2 (range [v2,v3]) 3D By Nexii Malthus

Line and Line, two nearest points with vector and distance

Computes two closest points of two lines, vector and distance <lsl> vector X1;vector X2;vector V1;float Z1; gLLnnXXVZ(vector O1,vector D1,vector O2,vector D2){ 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 = nD1%nD2; Z1 = llVecMag(V1);} </lsl> Input Description vector O1 Origin of Line 1 vector D1 Direction of Line 1 vector O2 Origin of Line 2 vector D2 Direction of Line 2 Output Description vector X1 Closest point on line 1 to line 2 vector X2 Closest point on line 2 to line 1 vector V1 Direction vector of line 1 to line 2 float Z1 Numerical distance of line 1 to line 2 Requirement global vector X1 global vector X2 global vector V1 global float Z1 2D By Nexii Malthus

Line and Point, Direction

Works out where point (X) is relative to the line of the segment (L0, L1). <lsl> float gLSPdir( vector L0, vector L1, vector X ){ return (L1.x - L0.x)*(X.y - L0.y) - (X.x - L0.x)*(L1.y - L0.y); } </lsl> Input Description vector L0, vector L1 Start and End of line segment vector X Origin of Point Output Description float isLeft( vector L0, vector L1, vector X ) Returns float, >0 is Left, 0 on Line, <0 is Right, according to line angle 2D Copyright 2001, softSurfer (www.softsurfer.com) (Must accept License #2), LSL-Port By Nexii Malthus

Plane Functions

Plane and Point, Distance
Finds distance of a point from a plane <lsl> float gPXdZ(vector Pn,float Pd,vector A){ return A * Pn + Pd;} </lsl> Input Description vector Pn Normal of Plane (unit vector) float Pd Distance of Plane vector A Origin of Point Output Description return float gPXdZ Returns Distance between plane and point 3D By Nexii Malthus

Plane and Point, Vector
Finds vector that points from point to nearest on plane <lsl> vector gPXdV(vector Pn,float Pd,vector A){ return -(Pn * A + Pd)*Pn;} </lsl> Input Description vector Pn Normal of Plane (unit vector) float Pd Distance of Plane vector A Origin of Point Output Description return vector gPXdV Returns vector from point to closest point on plane 3D By Nexii Malthus

Plane and Point, Nearest point
Finds closest point on plane given point <lsl> vector gPXnX(vector Pn,float Pd,vector A){ return A - (Pn * A + Pd) * Pn;} </lsl> Input Description vector Pn Normal of Plane (unit vector) float Pd Distance of Plane vector A Origin of Point Output Description return vector gPXnX Returns vector of a point from closest of point to plane 3D By Nexii Malthus

Plane and Ray, Intersection Distance
Finds distance to intersection of plane along ray <lsl> float gPRxZ(vector Pn,float Pd,vector O,vector D){ return -((Pn*O+Pd)/(Pn*D));} </lsl> Input Description vector Pn Normal of Plane (unit vector) float Pd Distance of Plane vector O Origin of Ray vector D Direction of Ray Output Description return float gPRxZ Returns float distance of intersection between ray and plane 3D By Nexii Malthus

Plane and Ray, Vector

Finds distance vector along a ray to a plane <lsl> vector gPRdV(vector Pn,float Pd,vector O,vector D){ return D * gPRxZ(Pn,Pd,O,D);} </lsl> Input Description vector Pn Normal of Plane (unit vector) float Pd Distance of Plane vector O Origin of Ray vector D Direction of Ray Output Description return vector gPRdV Returns vector along a ray to a plane Requirement function float gPRxZ(vector Pn,float Pd,vector O,vector D) 3D By Nexii Malthus

Plane and Ray, Intersection Point

Finds intersection point along a ray to a plane <lsl> vector gPRxX(vector Pn,float Pd,vector O,vector D){ return O + gPRdV(Pn,Pd,O,D);} </lsl> Input Description vector Pn Normal of Plane (unit vector) float Pd Distance of Plane vector O Origin of Ray vector D Direction of Ray Output Description return vector gPRxX Returns vector point of intersection between ray and plane Requirement function vector gPRdV(vector Pn,float Pd,vector O,vector D) 3D By Nexii Malthus

Plane and Line, Intersection Point

Finds interesection point of a line and a plane <lsl> vector gPLxX(vector Pn,float Pd,vector O,vector D){ return O + D*-( (Pn*O-Pd)/(Pn*D) );} </lsl> Input Description vector Pn Normal of Plane (unit vector) float Pd Distance of Plane vector O Origin of Line vector D Direction of Line Output Description return vector gPLxX Returns vector point of intersection between line and plane 3D By Nexii Malthus

Plane and Plane, Intersection Line

Finds line of intersection of two planes <lsl> vector oO;vector oD; gPPxL(vector Pn,float Pd,vector Qn,float Qd){ oD = (Pn%Qn)/llVecMag(Pn%Qn); vector Cross = (Pn%Qn)%Pn; vector Bleh = (-Pd*Pn); oO = Bleh - (Qn*Cross)/(Qn*Bleh+Qd)*Cross/llVecMag(Cross);} </lsl> Input Description vector Pn Normal of Plane 1 (unit vector) float Pd Distance of Plane 1 vector Qn Normal of Plane 2 (unit vector) float Qd Distance of Plane 2 Output Description vector oO Intersection Line's origin vector oD Intersection Line's direction Requirement global vector oO global vector oD 3D By Nexii Malthus

Plane and Ray, Projection

Projects a ray onto a plane <lsl> vector oO;vector oD; gPRpR(vector Pn,float Pd,vector O,vector D){ oO = O - (Pn * O + Pd) * Pn; vector t = llVecNorm( D - (Pn*((D*Pn)/(Pn*Pn))) );t = <1.0/t.x,1.0/t.y,1.0/t.z>; oD = Pn%t;} </lsl> Input Description vector Pn Normal of Plane (unit vector) float Pd Distance of Plane vector O Origin of Ray vector D Direction of Ray Output Description vector oO Projected Ray Origin vector oD Projected Ray Direction Requirement global vector oO global vector oD 3D By Nexii Malthus

Sphere Functions

Sphere and Ray, Intersection Point

Finds intersection point of sphere and ray <lsl> vector gSRxX(vector Sp, float Sr, vector Ro, vector Rd){ float t; Ro -= Sp; 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 Sp + Ro + (t * Rd); } </lsl> Input Description vector Sp Origin of Sphere float Sr Radius of Sphere vector Ro Origin of Ray vector Rd Direction of Ray Output Description vector gSRxX Returns intersection point of sphere and ray otherwise ZERO_VECTOR 3D By Nexii Malthus

Sphere and Ray, Intersection Boolean

Finds if there is a intersection of sphere and ray <lsl> 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; } </lsl> Input Description vector Sp Origin of Sphere float Sr Radius of Sphere vector Ro Origin of Ray vector Rd Direction of Ray Output Description integer gSRx Returns a boolean indicating if there is a valid intersection 3D By Nexii Malthus

Ray Functions

Ray and Point, projected distance
Finds projected distance of a point along a ray <lsl> float gRXpZ(vector O,vector D,vector A){ return (A-O)*D;} </lsl> Input Description vector O Origin of Ray vector D Direction of Ray vector A Origin of Point Output Description float gRXpZ Returns projected distance of a point along a ray 3D By Nexii Malthus

Box Functions

Box and Ray, Intersection Distance

Finds intersection of a Ray to a Box and returns intersection distance, otherwise -1 if there is no legal intersection. <lsl> float gBRxZ(vector Ro,vector Rd, vector Bo, vector Bs, rotation Br){ vector oB = (Ro-Bo)/Br; vector dB = Rd/Br; vector eB = 0.5*Bs; float mD = -1.0; float D; vector X; if(llFabs(dB.x) > 0.000001){ D = (-eB.x - oB.x ) / dB.x; if(D >= 0.0){ X = oB + D * dB; if(X.y >= -eB.y && X.y <= eB.y && X.z >= -eB.z && X.z <= eB.z) mD = D; } D = ( eB.x - oB.x ) / dB.x; if (D >= 0.0){ X = oB + D * dB; if(X.y >= -eB.y && X.y <= eB.y && X.z >= -eB.z && X.z <= eB.z) if (mD < 0.0 || mD > D) mD = D; } } if(llFabs(dB.y) > 0.000001){ D = (-eB.y - oB.y ) / dB.y; if(D >= 0.0){ X = oB + D * dB; if(X.x >= -eB.x && X.x <= eB.x && X.z >= -eB.z && X.z <= eB.z) if (mD < 0.0 || mD > D) mD = D; } D = ( eB.y - oB.y ) / dB.y; if (D >= 0.0){ X = oB + D * dB; if(X.x >= -eB.x && X.x <= eB.x && X.z >= -eB.z && X.z <= eB.z) if (mD < 0.0 || mD > D) mD = D; } } if(llFabs(dB.z) > 0.000001){ D = (-eB.z - oB.z ) / dB.z; if(D >= 0.0){ X = oB + D * dB; if(X.x >= -eB.x && X.x <= eB.x && X.y >= -eB.y && X.y <= eB.y) if (mD < 0.0 || mD > D) mD = D; } D = ( eB.z - oB.z ) / dB.z; if (D >= 0.0){ X = oB + D * dB; if(X.x >= -eB.x && X.x <= eB.x && X.y >= -eB.y && X.y <= eB.y) if (mD < 0.0 || mD > D) mD = D; } } return mD; } </lsl> Input Description vector Ro Origin of Ray vector Rd Direction of Ray vector Bo Origin of Box vector Bs Size of Box rotation Br Rotation of Box Output Description float gBRxZ Returns distance to intersection of a ray and a box 3D By Hewee Zetkin

Box and Ray, Intersection Point

Finds intersection of a Ray to a Box and returns intersection point, otherwise ZERO_VECTOR if there is no legal intersection. <lsl> vector gBRxX( vector Ro, vector Rd, vector Bo, vector Bs, rotation Br){ float k = gBRxZ(Ro,Rd,Bo,Bs,Br); if( k != -1.0 ) return Ro + Rd * k; else return ZERO_VECTOR;} </lsl> Input Description vector Ro Origin of Ray vector Rd Direction of Ray vector Bo Origin of Box vector Bs Size of Box rotation Br Rotation of Box Output Description vector gBRxX Returns point of intersection of a ray and a box Requirement float gBRxZ(vector Ro,vector Rd, vector Bo, vector Bs, rotation Br) 3D By Hewee Zetkin

Box and Point, Intersection Boolean

Finds if there is an intersection of a Point and a Box and returns boolean <lsl> integer gBXx(vector A, vector Bo, vector Bs, rotation Br){ vector eB = 0.5*Bs; vector rA = (A-Bo)/Br; return (rA.x<eB.x && rA.x>-eB.x && rA.y<eB.y && rA.y>-eB.y && rA.z<eB.z && rA.z>-eB.z); } </lsl> Input Description vector A Origin of Point vector Bo Origin of Box vector Bs Size of Box rotation Br Rotation of Box Output Description integer gBXx(vector A, vector Bo, vector Bs, rotation Br) Returns boolean check of intersection of a point and a box if there is one, otherwise FALSE 3D By Nexii Malthus

Box and Point, Nearest Point on Edge

Processes point on nearest edge of box to given point <lsl> vector gBXnEX(vector A, vector Bo, vector Bs, rotation Br){ vector eB = 0.5*<llFabs(Bs.x),llFabs(Bs.y),llFabs(Bs.z)>; vector rA = (A-Bo)/Br; float mD = 3.402823466E+38; vector X; list EdgesX = [< 0, eB.y, eB.z>, < 0,-eB.y, eB.z>, < 0,-eB.y,-eB.z>, < 0, eB.y,-eB.z>]; list EdgesY = [< eB.x, 0, eB.z>, <-eB.x, 0, eB.z>, <-eB.x, 0,-eB.z>, < eB.x, 0,-eB.z>]; list EdgesZ = [< eB.x, eB.y, 0>, <-eB.x, eB.y, 0>, <-eB.x,-eB.y, 0>, < eB.x,-eB.y, 0>]; integer x = (EdgesX != []); while( x-- ){ float y = gLXdZ( llList2Vector( EdgesX, x ), <1,0,0>, rA ); if( rA.x > eB.x ) y += rA.x - eB.x; else if( rA.x < -eB.x ) y -= rA.x - -eB.x; if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesX, x ), <1,0,0>, rA ); } } x = (EdgesY != []); while( x-- ){ float y = gLXdZ( llList2Vector( EdgesY, x ), <0,1,0>, rA ); if( rA.y > eB.y ) y += rA.y - eB.y; else if( rA.y < -eB.y ) y -= rA.y - -eB.y; if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesY, x ), <0,1,0>, rA ); } } x = (EdgesZ != []); while( x-- ){ float y = gLXdZ( llList2Vector( EdgesZ, x ), <0,0,1>, rA ); if( rA.z > eB.z ) y += rA.z - eB.z; else if( rA.z < -eB.z ) y -= rA.z - -eB.z; if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesZ, x ), <0,0,1>, rA ); } } if( mD < 0.000001 ) return <-1,-1,-1>; if( X.x > eB.x ) X.x = eB.x; else if( X.x < -eB.x ) X.x = -eB.x; if( X.y > eB.y ) X.y = eB.y; else if( X.y < -eB.y ) X.y = -eB.y; if( X.z > eB.z ) X.z = eB.z; else if( X.z < -eB.z ) X.z = -eB.z; return Bo + ( X * Br );} </lsl> Input Description vector A Origin of Point vector Bo Origin of Box vector Bs Size of Box rotation Br Rotation of Box Output Description vector gBXnEX(vector A, vector Bo, vector Bs, rotation Br) Returns nearest point on edge of box B closest to point A. Returns <-1,-1,-1> if already on closest point. Requirement float gLXdZ(vector O,vector D,vector A) vector gLXdV(vector O,vector D,vector A) vector gLXnX(vector O,vector D,vector A) 3D By Nexii Malthus

Cylinder

Cylinder and Point, Intersection Boolean

Finds if there is an intersection of a Point and a Cylinder and returns boolean <lsl> integer gCXx( vector A, vector O, rotation R, vector S ) { A = ( A - O ) / R;// Converts to local object frame return (llPow(A.x/S.x*2,2) + llPow(A.y/S.y*2,2)) <= 1. // Test radius && llFabs(A.z/S.z*2) <= 1.;// Test top/bottom } </lsl> Input Description vector A Origin of Point vector Bo Origin of Cylinder vector Bs Size of Cylinder rotation Br Rotation of Cylinder Output Description integer gCXx( vector A, vector O, rotation R, vector S ) Returns boolean check of intersection of a point and a cylinder if there is one, otherwise FALSE 3D By Nexii Malthus

Polygon

Polygon and Point, Intersection Boolean

Figures out if point is inside of polygon or otherwise. <lsl> integer gCPXx( list CP, vector X ) {//Copyright (c) 1970-2003, Wm. Randolph Franklin; 2008, Strife Onizuka integer i = ~(CP != []); integer c = 0; if(i < -2){ vector vi = llList2Vector(CP, -1); do { vector vj = vi; vi = llList2Vector(CP, i); if((vi.y > X.y) ^ (vj.y > X.y)){ if(vj.y != vi.y) c = c ^ (X.x < (((vj.x - vi.x) * (X.y - vi.y) / (vj.y - vi.y)) + vi.x)); else c = c ^ (0 < ((vj.x-vi.x) * (X.y-vi.y))); } } while (++i); } return c; } </lsl> Input Description list CP Vertices of Concave Polygon vector X Origin of Point Output Description integer gCPXx( list CP, vector X ) Returns TRUE if point (X) intersects concave polygon (CP), otherwise FALSE 2D Copyright (c) 1970-2003, Wm. Randolph Franklin (Must accept License #1), LSL-Port By Strife Onizuka

Polygon and Line Segment, Intersection Boolean

Figures out if line segment intersects with polygon. <lsl> integer gVPLSx( vector P0, vector P1, list VP ){ //Copyright 2001, softSurfer (www.softsurfer.com); 2008, Nexii Malthus if( P0 == P1 ) return gCPXx( VP, P0 ); float tE = 0; float tL = 1; float t; float N; float D; vector dS = P1 - P0; vector e; integer x; integer y = VP!=[]; @start; for( x = 0; x < y; ++x ){ e = llList2Vector( VP, x+1 ) - llList2Vector( VP, x ); N = Perp( e, P0 - llList2Vector( VP, x ) ); D = -Perp( e, dS ); if( llFabs(D) < 0.00000001 ) if( N < 0 ) return FALSE; else jump start; t = N / D; if( D < 0 ){ if( t > tE ){ tE = t; if( tE > tL ) return FALSE; } } else { if( t < tL ){ tL = t; if( tL < tE ) return FALSE; } } } // PointOfEntrance = P0 + tE * dS; // PointOfExit = P0 + tL * dS; return TRUE; } </lsl> Input Description list VP Vertices of Convex Polygon vector P0, vector P1 Start and End of Line Segment Output Description integer gVPLSx( vector P0, vector P1, list VP ) Returns TRUE if line segment (P0,P1) intersects convex polygon (VP), otherwise FALSE Requirement <lsl>float Perp( vector U, vector V ){ return U.x*V.y - U.y*V.x; }</lsl> Perpendicular dot product integer gCPXx( list CP, vector X ) Only needed for (P0 == P1) safety catch check, so optional 2D Copyright 2001, softSurfer (www.softsurfer.com) (Must accept License #2), LSL-Port By Nexii Malthus

Other Functions

3D Projection
Projects a vector A by vector B. <lsl> vector Project3D(vector A,vector B){ return B * ( ( A * B ) / ( B * B ) );} </lsl> Input Description vector A First Vector vector B Second Vector Output Description return Project3D(vector A, vector B) Returns result of projection 3D By Nexii Malthus

Reflection
Reflects Ray R with surface normal N <lsl> vector Reflect(vector R,vector N){ return R - 2 * N * ( R * N );} </lsl> Input Description vector R Ray Normal vector N Surface Normal Output Description return Reflect(vector R, vector N) Returns result of reflection 3D By Nexii Malthus

Glossary

For anyone curious to the shorthand used and who wish to use a lookup table can use this as a reference. Or anyone who wishes to add a new function to the library is welcome to but it would be recommended to keep consistency. I tried to minimize the script function names to be easily readable. All the geometric function names start with a g.

g (Shape1) (Shape2) (Process) (Return (Only needed if other than integer))

Here is the legend:

Shorthand	Name	Description
Geometric Types, all the shapes in the library
X	Point	vector defining a point in space
L	Line	A line has an origin and a direction and is infinitely long
LS	Line Segment	A line segment is a finite line and therefore consists of a start and end position
R	Ray	A ray is like a line, except it is more distinct as it defines wether it points forward or back
P	Plane	A 2D doubly ruled surface of infinite size
S	Sphere	A sphere is defined by origin and radius (No ellipsoid functions available yet)
B	Box	A box primitive is six sided and defined by origin, size as well as a rotation.
C	Cylinder	An elliptic cylinder primitive .
VP	Convex Polygon	Convex Polygon defined by list of vertices.
CP	Concave Polygon	Concave Polygon defined by list of vertices. Automatic backward compatibility with Convex Polygons.
The Process, What does it do?
d	distance	Calculate distance
n	nearest	Calculate nearest
p	project	Calculates projection
x	Intersection	Calculates intersection
dir	direction	Calculates direction
Return, What kind of data do I get out of it?
Z	Float	Represents that a float is returned
V	Vector	Represents that a vector is returned
O	Origin	Represents the Origin of the ray or line
D	Direction	Direction from the Origin
E	Edge	Edge of a shape, such as an edge on a box, suffix may mark special case return type

Licenses

#1

<lsl> //Copyright (c) 1970-2003, Wm. Randolph Franklin //Copyright (c) 2008, Strife Onizuka (porting to LSL) // //Permission is hereby granted, free of charge, to any person obtaining a copy //of this software and associated documentation files (the "Software"), to deal //in the Software without restriction, including without limitation the rights //to use, copy, modify, merge, publish, distribute, sublicense, and/or sell //copies of the Software, and to permit persons to whom the Software is //furnished to do so, subject to the following conditions: // // 1. Redistributions of source code must retain the above copyright notice, // this list of conditions and the following disclaimers. // 2. Redistributions in binary form must reproduce the above copyright // notice in the documentation and/or other materials provided with the // distribution. // 3. The name of W. Randolph Franklin may not be used to endorse or promote // products derived from this Software without specific prior written // permission.

//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR //IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, //FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE //AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER //LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, //OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE //SOFTWARE. </lsl>

#2

<lsl> // Copyright 2001, softSurfer (www.softsurfer.com); 2008, LSL-port by Nexii Malthus // This code may be freely used and modified for any purpose // providing that this copyright notice is included with it. // SoftSurfer makes no warranty for this code, and cannot be held // liable for any real or imagined damage resulting from its use. // Users of this code must verify correctness for their application. </lsl>