Difference between revisions of "User:Nexii Malthus/GeometricLib"

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</lsl>
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Revision as of 11:43, 19 May 2008

Sandbox playground for Nexii Malthus for Geometric Library ideas and possible improvements.

Ideas.. 

What does a function do? Whats the point of it?
What can it do for me? What can I use for?
  • Restrictions?
    • Hmm, might require too much info
      • On a technical topic, is it better to give too much information or too little?
        • True true, it is quite a technical concept. But I'd rather have it up to the reader if they want it. Know how I can do collapsible points of information? I believe there was some sort of trick that I have seen been done before so that a button could be pressed to show/hide paragraphs of information.
  • Abilities?
  • Examples?
    • Example usage would be good
  • Explanations?

How could I condense it precisely and clearly what each function does?

Template structure?:

  • Function Name
    • Explanation
    • LSL Code
    • Input
    • Output
    • Example?
Heading A Heading B Heading C
Row A Value A Row A Value B Row A Value C
Row B Value A Row B Value B Row B Value C
Row C Value A Row C Value B Row C Value C
Row D Value A Row D Value B Row D Value C
Row E Value A Row E Value B Row E Value C


Line Functions

Line Nearest Point

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
  • returns origin of closest point on Line to Point

Line Nearest Point, Distance

Calculates distance of this vector, but faster on it's own <lsl> float gLXdZ(vector O,vector D,vector A){ 

   return llSqrt(CP((A-O),D)*CP((A-O),D));}

</lsl>

Input

Output


Line and Line, Vector

Shortest vector of two lines <lsl> vector gLLdV(vector O1,vector D1,vector O2,vector D2){ 

   return Project3D( (O2-O1), CP(D1,D2) );}

</lsl>

Input

Output


Line and Line, Distance

Returns the distance between two lines <lsl> float gLLdZ(vector O1,vector D1,vector O2,vector D2){ 

   vector A = CP(D1,D2);float B = llVecMag(A);A = <A.x/B,A.y/B,A.z/B>;
   return (O2-O1) * A;}

</lsl>

Input

Output

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

Output

Line and Line, two nearest points along both lines

Two closest points of two lines <lsl> vector X1;vector X2;vector V1;float Z1; 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 + CP(nD1,nD2);}

</lsl>

Input

Output

Line and Line, two nearest points with vector and distance

Computes two closest points of two lines, vector and distance <lsl> 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 = CP(nD1,nD2);
   Z1 = llVecMag(V1);}

</lsl>

Input

Output

Geometric Library Code

This is the script in its entirety.

<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){ 

   // Turns three vector points in space into a plane
   pN = llVecNorm( CP((p2-p1),(p3-p1)) );
   pD = -p1*pN;}

integer gTXcC(vector p1,vector p2,vector p3,vector x){ 

   // Can be used to check weather a point is inside a triangle
   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>

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