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

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== Line Functions ==
== Line Functions ==


{|{{Prettytable}}|
=== Line Nearest Point ===
=== Line Nearest Point ===
Calculates the vector from a point to the closest point on a line
Calculates the vector from a point to the closest point on a line
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| return vector gLXdV
| return vector gLXdV
| Returns origin of closest point on Line to Point
| Returns origin of closest point on Line to Point
|}
|}
|}


{|{{Prettytable}}|
=== Line Nearest Point, Distance ===
=== Line Nearest Point, Distance ===
{|{{Prettytable}}|
Calculates distance of this vector, but faster on it's own
Calculates distance of this vector, but faster on it's own
<lsl>
<lsl>
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|}
|}


{|{{Prettytable}}|
=== Line and Line, Vector ===
=== Line and Line, Vector ===
{|{{Prettytable}}|
Shortest vector of two lines
Shortest vector of two lines
<lsl>
<lsl>
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|}
|}


{|{{Prettytable}}|
=== Line and Line, Distance ===
=== Line and Line, Distance ===
Returns the distance between two lines
Returns the distance between two lines
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| return float gLLdZ
| return float gLLdZ
| Returns numerical distance between the two lines
| Returns numerical distance between the two lines
|}
|}
|}


{|{{Prettytable}}|
=== Line and Line, Nearest point ===
=== Line and Line, Nearest point ===
Closest point of two lines
Closest point of two lines
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| return vector gLLnX
| return vector gLLnX
| Returns closest point between the two lines
| Returns closest point between the two lines
|}
|}
|}


{|{{Prettytable}}|
=== Line and Line, two nearest points along both lines ===
=== Line and Line, two nearest points along both lines ===
Two closest points of two lines
Two closest points of two lines
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| vector X2
| vector X2
| Closest point on line 2 to line 1
| Closest point on line 2 to line 1
|}
|}
|}


{|{{Prettytable}}|
=== Line and Line, two nearest points with vector and distance ===
=== Line and Line, two nearest points with vector and distance ===
Computes two closest points of two lines, vector and distance
Computes two closest points of two lines, vector and distance
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| float Z1
| float Z1
| Numerical distance of line 1 to line 2
| Numerical distance of line 1 to line 2
|}
|}
|}


Revision as of 16:03, 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.
          • That's on my list of things to poke LL about. We really need collapsible sections and the citation extension.
  • 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
Test 1

Test 2

Test 3

Test 4

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
Output Description
return vector gLXdV 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 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

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 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

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 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

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

Line and Line, two nearest points along both lines

Two closest points of two lines <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 + CP(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

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 = CP(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

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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